http://2014.igem.org/wiki/index.php?title=Special:Contributions/Jpico&feed=atom&limit=50&target=Jpico&year=&month=2014.igem.org - User contributions [en]2024-03-28T14:55:50ZFrom 2014.igem.orgMediaWiki 1.16.5http://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T22:58:58Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple. For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. </p><br/><br />
<br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div> <br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case. The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''. Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity''. Thus, $\vec{v}$<br />
would be the velocity of the air flow in or case.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
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<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
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<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. <br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations as finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the particles diffusing.<br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method, for it is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known, the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps:<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and backward differences are applied to the vector differential operator $\nabla$ (in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
</ol><br />
</div><br />
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<br />
<div id="tab3" class="tab"><br />
<br/><br />
<br />
<p align="left"><strong>The idea</strong></p><br/><br />
<br />
<br />
<p>When one observes moths behavior, they apparently move with erratic flight paths. This is possibly to avoid predators. This random flight is modified by the presence of sex pheromones. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> enters into a conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the female following a zigzag way. The male approaches the female, and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In <span class="red-bold">Sexy Plant</span> we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector depends on the change in the pheromone concentration level between points separated by a differential stretch in space. More precisely, the gradient points in the direction of the greatest rate of increase of the function, and its magnitude is the slope of the graph in that direction. The random vector is constrained in this ‘moth response’ model by a fixed angle upper bound, assuming that the turning movement is relatively continuous. For example, one can asume that the moth cannot turn 180 degrees from one time instant to the next.</p><br/><br />
<br />
<p>Our synthetic plants are supposed to release enough sexual pheromone so as to be able to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<br />
<p>The three clases of male moth behavior we consider for the characterization of males moth behavior are described in Table 1.</p><br/><br />
<br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>This ensemble of behaviors can be translated into a sum of vectors in which the random vector has constant module and changing direction within a range, whereas the module of the gradient vector is a function of the gradient in the field.<br />
The question now is how do we include the saturation effect in the resulting moth shift vector. With this in mind, and focusing on the implementation process, our approach consists on the following:</p><br />
<br />
<p>To model chemoattraction, the gradient vector will be always have fixed unit magnitude, and its direction is that of the greatest rate of increase of the pheromone concentration. </p><br/><br />
<br />
<p>To model the random flight, instead of using a random direction vector with constant module, we consider a random turning angle starting from the gradient vector direction.</p><br/><br />
<br />
<p>Thus, how do we include the saturation effect in the resulting moth shift vector? This is key to achieve sexual confusion. Our answer: the behaviour dependence on the moth saturation level --in turn related to the pheromone concentration in the field-- will be included in the random turning angle. </p><br/><br />
<br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the mean is zero (no angle detour from the gradient vector direction) and the standard-deviation will be inversely proportional to the intensity of the gradient of sex pheromone concentration in the field. This approach leads to ‘sexual confusion’ of the insect as the field homogeneity increases. This is because the direction of displacement of the moth will equal the gradient direction with certain probability which depends on how saturated it is.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. J. Ethol, 4, 1986</li> <br />
</ol><br />
</div><br />
<br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we simulate the approximate moth population behavior when the pheromone diffusion process take place.</p><br/><br />
<br />
<p> The <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be found in its website at Northwestern University. To download the source file of our <span class="red-bold">Sexy plant</span> simulation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a></p><br/><br />
<br />
<p align="left"><strong>Setup</strong></p><br/><br />
<br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexy plants</span>.</li><br />
<li>We have two kinds of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an open crop field where <span class="red-bold">sexy plants</span> are intercropped, and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, move following erratic random flight paths. After mating, females do not emit pheromones for a period of 2 hours.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">Sexy plants</span> act as continuously- emitting sources, and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> The pheromone diffusion process, it is simulated in Netlogo by implementing the Euler explicit method. </p><br/><br />
<br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<p align="left"><strong>Runs</strong></p><br/><br />
<br />
<p>When <span class="red-bold">sexy plants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>. In that case they follow them. </p><br />
<p>When <span class="red-bold">sexy plants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, <span class="red-bold">sexy plants</span> have the effect of acting as pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexy plants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexy plants are switched on and a male moth go towards the static source as it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a bigger detour from the faced gradient vector direction is higher. This means that it is less able to follow pheromone concentration gradients, so sexual confusion is induced.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<p align="left"><strong>Parameters</strong></p><br/><br />
<br />
<p>The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task. In the literature it is difficult to find a number experimentally obtained. So we decided to take an inverse engineering approach. Doing a model parameters swept, we simulated many possible scenarios, and then we came up with values of parameters corresponding to our desired goal: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. The parameters we found are: </p> <br/><br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (Sexy Plant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the chemicals above a certain emission rate will catch fewer males. The optimum release rate or dispenser load for trap catch varies greatly among species [4]. This emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distance]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distance]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!! we did not rely on this figure)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<p align="left"><strong>Simulation time step (ticks)</strong></p><br/><br />
<p>We consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<br/><br />
<p align="left"><strong>Patches</strong></p><br/><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li> <br />
</ol><br />
</div> <br />
<br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T22:13:22Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple. For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. </p><br/><br />
<br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
</html> <br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case. The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''. Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity''. Thus, $\vec{v}$<br />
would be the velocity of the air flow in or case.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. <br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations as finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the particles diffusing.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method, for it is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known, the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps:<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and backward differences are applied to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
<html><br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
</ol><br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:59:31Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple. For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. </p><br/><br />
<br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
</html> <br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case. The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''. Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity''. Thus, $\vec{v}$<br />
would be the velocity of the air flow in or case.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. <br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations as finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the particles diffusing.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method, for it is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known, the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps:<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and backward differences are applied to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
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<br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
</ol><br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
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</div><br />
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<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:55:59Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
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<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple. For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. </p><br/><br />
<br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
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</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
</html> <br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case. The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''. Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity''. Thus, $\vec{v}$<br />
would be the velocity of the air flow in or case.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
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<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. <br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations as finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the particles diffusing.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method, for it is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known, the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps:<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and backward differences are applied to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
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<br />
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<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
<br />
<br />
</ol><br />
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</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
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[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:45:36Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple. For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. </p><br/><br />
<br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
</html> <br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case. The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''. Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity''. Thus, $\vec{v}$<br />
would be the velocity of the air flow in or case.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. <br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations as finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the particles diffusing.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method, for it is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known, the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps:<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and backward differences are applied to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
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<br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:28:49Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (e.g. consider the potential final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation.</p><br/><br/><br />
<br />
<p align="left"><strong>Approximation</strong></p><br/><br />
<br />
<br />
</html> <br />
<br />
The diffusion equation is a partial differential equation that describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t, and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write the pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in the air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift, and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
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<br />
In order to determine a numeric solution for this partial differential equation, the so-called finite difference methods are used. The technic consists of<br />
approximating the differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in a system of algebraic equations. This is solved at each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable, so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in a given node in terms of initial values at that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now, applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method, the<br />
expression that gives the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, central differences is applied to the Laplace operator $\Delta$, and the backward differences are applied to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an open space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
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<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
<br />
<br />
</ol><br />
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<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:04:35Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [1].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles [2].</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br/><br />
<br />
</html> <br />
<br />
The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
<br />
<br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, chap. 9, SIAM, 1973</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T19:00:55Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve [1]. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [2].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles.</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br/><br />
<br />
</html> <br />
<br />
The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
<br />
<br />
<br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9</li><br />
<li> J. Philibert. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2,1.1-1.10, 2005.</li><br />
<br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T18:42:02Z<p>Jpico: </p>
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<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
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[[File:UPV_CEQA.jpg|500px|right]] <br />
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<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
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<br/><br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
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<h3><b>Interviews</b></h3><br />
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[[Image:VUPV_Coque.jpg|400px|left]] <br />
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<h3><i>“Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
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[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
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<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
<br />
<br/><br/><br />
<br />
<p>Our team also talked with Professor Sam Tothill, Professor of Biosensors in Health at Cranfield University, United Kingdom. Her current research mainly focuses in biosensors for microbial contaminants and pathogen's (bacteria, viruses, fungi) and their toxins. We really appreciated her feedback as part of her research consist in the detection of contaminants such as pesticides in food. We discussed about safety issues and how could our project be implemented in agriculture. She really liked the about the <span class="red-bold">Sexy Plant</span> project and wished our team succeeded at iGEM. </p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T18:40:56Z<p>Jpico: </p>
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<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
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[[File:UPV_CEQA.jpg|500px|right]] <br />
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<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
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<br/><br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
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<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
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<h3><b>Interviews</b></h3><br />
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<h3><i>“Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
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[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
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<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
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<p>Our team talked with Professor Sam Tothill, Professor of Biosensors in Health at Cranfield University, United Kingdom. Her current research mainly focuses in biosensors for microbial contaminants and pathogen's (bacteria, viruses, fungi) and their toxins. We really appreciated her feedback as part of her research consist in the detection of contaminants such as pesticides in food. We discussed about safety issues and how could our project be implemented in agriculture. She really liked the about the <span class="red-bold">Sexy Plant</span> project and wished our team succeeded at iGEM. </p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T18:14:40Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
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<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
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<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
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<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
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<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
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</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
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<br />
</ol><br />
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<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve [1]. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [2].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either using a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles.</p><br/><br />
<br />
<p>In our case, we decided to model our diffusion process using the <span class="black-bold">Fick's laws</span>. Thus, it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult. Even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
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<h3>Approximation</h3><br/><br/><br />
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The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
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<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
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<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
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<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
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[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
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[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
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<div id="tab4" class="tab"><br />
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<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
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[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
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[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
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<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T18:10:30Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
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<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. </p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="https://ccl.northwestern.edu/netlogo/">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve [1]. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [2].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles.</p><br/><br />
<br />
<p>In our case, we decided to hold our diffusion process by the <span class="black-bold">Fick's laws</span>. So it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult, even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br/><br />
<br />
</html> <br />
<br />
The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
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<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
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</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T18:07:37Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
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<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source [1]. Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <a class="normal-link-page" href="#">See more about heat equation and mathematical expressions for Euler method.</a></p><br/><br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis [2]. Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation [3]. <a class="normal-link-page" href="#"> See more about the modeling of moth flight paths.</a></p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="#">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of <span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9</li><br />
<li> J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop, Phil. Trans. R. Soc. Lond. B 10 May 1984 vol. 306 no. 1125 19-48</li><br />
<li>W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues, Annual Review of Entomology<br />
Vol. 22: 377-405, 1977</li><br />
<br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve [1]. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [2].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles.</p><br/><br />
<br />
<p>In our case, we decided to hold our diffusion process by the <span class="black-bold">Fick's laws</span>. So it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult, even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br/><br />
<br />
</html> <br />
<br />
The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
<html><br/><br />
<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
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<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
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<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
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[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
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<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/diffusionTeam:Valencia UPV/Modeling/diffusion2014-10-17T17:57:40Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/diffusion">Pheromone Diffusion</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>D</roja>iffusion <br/><br/> and <roja>M</roja>oths <roja>R</roja>esponse</span> </div><br />
</br></br><br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">Diffusion Equation</a></li><br />
<li><a href="#tab3">Moth Response</a></li><br />
<li><a href="#tab4">Simulation</a></li><br />
<li><a href="#tab5">Results</a></li><br />
</ul><br />
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<div class="tab-content"><br />
<div id="tab1" class="tab active"><br />
<p>Sexual communication among moths is accomplished chemically by the release of an "odor" into the air. This "odor" consists of <span class="black-bold">sexual pheromones</span>.</p><br/><br />
<br />
<div align="center"><img width="540px" src="https://static.igem.org/mediawiki/2014/9/9d/VUPVIntro_sexpheromone.png" alt="female_sex_pheromones" title="Female and Male Moths"></img></div><br/><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Female moth releasing sex pheromones, and male moth.</p></div><br/><br />
<br />
<br />
<br />
<p>Pheromones are molecules that easily diffuse in the air. During the diffusion process, the random movement of gas molecules transport the chemical away from its source (Sol I. Rubinow, Mathematical Problems in the Biological Sciences, Lecture 9). Diffusion processes are complex ones, and modeling them analytically and with accuracy is difficult. Even more when the geometry is not simple.</p><br/><br />
<br />
<p>For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the heat diffusion equation. Then, the equation is solved using the Euler numeric approximation in order to obtain the spatial and temporal distribution of pheromone concentration. <a class="normal-link-page" href="#">See more about heat equation and mathematical expressions for Euler method.</a></p><br/><br />
<br />
<p> Moths seem to respond to gradients of pheromone concentration to be attracted towards the source. Yet, there are other factors that lead moths to sexual pheromone sources, such as optomotor anemotaxis (J. N. Perry and C. Wall , A Mathematical Model for the Flight of Pea Moth to Pheromone Traps Through a Crop). Moreover, increasing the pheromone concentration to unnaturally high levels may disrupt male orientation (W. L. Roelofs and R. T. Carde, Responses of Lepidoptera to synthetic sex pheromone chemicals and their analogues). <a class="normal-link-page" href="#"> See more about the modeling of moth flight paths.</a></p><br/><br />
<br />
<p>Using a modeling environment called <a class="normal-link-page" href="#">Netlogo</a>, we simulated the approximate moths behavior during the pheromone dispersion process. So, this will help us to predict moth response when they are also in presence of ><span class="red-bold">Sexy Plant</span>.</p><br/><br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br />
<p>Since pheromones are chemicals released into the air, we have to consider both the motion of the fluid and the one of the particles suspended in the fluid.</p><br/><br />
<br />
<p>The motion of fluids can be described by the <span class="black-bold">Navier–Stokes equations</span>. But the typical nonlinearity of these equations when there may exist turbulences in the air flow, makes most problems difficult or impossible to solve [1]. Thus, attending to the particles suspended in the fluid, a simpler effective option for pheromone dispersion modeling consists in the assumption of pheromones diffusive-like behavior.<br />
That is, pheromones are molecules that can undergo a diffusion process in which the random movement of gas molecules transport the chemical away from its source [2].</p><br/><br />
<br />
<p>There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with <span class="black-bold"> Fick's laws of diffusion</span> and their mathematical consequences, or a physical and atomistic one, by considering the <span class="black-bold"> random walk</span> of the diffusing particles.</p><br/><br />
<br />
<p>In our case, we decided to hold our diffusion process by the <span class="black-bold">Fick's laws</span>. So it is postulated that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient. However, diffusion processes are complex, and modelling them analytically and with accuracy is difficult, even more when the geometry is not simple (final distribution of our plants in the crop field). For this reason, we decided to consider a simplified model in which pheromone chemicals obey to the <span class="black-bold"> heat diffusion equation</span>.</p><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br/><br />
<br />
</html> <br />
<br />
The '''diffusion equation''' is a partial differential equation which describes density dynamics<br />
in a material undergoing diffusion. It is also used to describe processes exhibiting<br />
diffusive-like behavior, like in our case.<br />
<br />
The equation is usually written as:<br />
<br />
$$\frac{\partial \phi (r,t) }{\partial t} = \nabla · [D(\phi,r) \nabla \phi(r,t)]$$<br />
<br />
where $\phi(r, t)$ is the density of the diffusing material at location r and time t and<br />
$D(\phi, r)$ is the collective diffusion coefficient for density $\phi$ at location $r$; and<br />
$\nabla$ represents the vector differential operator.<br />
<br />
If the diffusion coefficient does not depend on the density then the equation is linear and<br />
$D$ is constant. Thus, the equation reduces to the following linear differential equation:<br />
$$\frac{\partial \phi (r,t) }{\partial t} = D \nabla^2 \phi(r,t)$$<br />
<br />
also called the '''heat equation'''.<br />
<br />
Making use of this equation we can write pheromones chemicals diffusion equation with no<br />
wind effect consideration as:<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 C = D \Delta c$$<br />
<br />
where c is the pheromone concentration, $\Delta$ is the Laplacian operator, and $D$ is<br />
the pheromone diffusion constant in air.<br/><br/><br />
<br />
If we consider the wind, we face a diffusion system with drift and an advection term is<br />
added to the equation above.<br />
<br />
$$\frac{\partial c }{\partial t} = D \nabla^2 c - \nabla \cdot (\vec{v} c )$$<br />
<br />
where $\vec{v}$ is the average ''velocity'' that the quantity is moving. Thus, $\vec{v}$<br />
would be the velocity of the air flow.<br/><br />
<br />
For simplicity, we are not going to consider the third dimension. In $2D$ the equation<br />
would be:<br />
<br />
<br />
$$\frac{\partial c }{\partial t} = D \left(\frac{\partial^2 c }{\partial^2 x} + \frac{\partial^2 c }{\partial^2 y}\right) – \left(v_{x} \cdot \frac{\partial c }{\partial x} + v_{y} \cdot \frac{\partial c }{\partial y} \right) = D \left( c_{xx} + c_{yy}\right) - \left(v_{x} \cdot c_{x} + v_{y} \cdot c_{y}\right) $$<br />
<br />
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<div align="center"><img width="650px" src="https://static.igem.org/mediawiki/2014/1/11/VUPVDiffusion_purple.png" alt="modeling_equations_solving" title="Netlogo Screen"></img></div><br/><br/><br />
</html><br />
<br />
For determining a numeric solution for this partial differential equation are<br />
used the so-called finite difference methods. The technic consists in<br />
approximating differential ratios as $h$ is closer to zero, so they are useful to<br />
approximate differential equations.<br />
<br />
With finite difference methods, partial differential equations are replaced by<br />
its approximations in finite differences, resulting in an algebraic equations<br />
system. The algebraic equations system is solved in each node<br />
$(x_i,y_j,t_k)$. These discrete values describe the temporal and spatial<br />
distribution of the unknown function.<br/><br/><br />
<br />
Although implicit methods are unconditionally stable so time steps could be larger and<br />
make the calculus process faster, the tool we have used to solve our heat equation is the<br />
Euler explicit method.<br />
<br />
Euler explicit method is the simplest option to approximate spatial derivatives, in which all<br />
values are assumed at the beginning of Time.<br/><br/><br />
<br />
The equation gives the new value of the pheromone level in terms of initial values in that<br />
node and its immediate neighbors. Since all these values are known the process is called<br />
explicit.<br />
<br />
$$c(t_{k+1}) = c(t_k) + dt \cdot c'(t_k),$$<br />
<br />
Now applying this method for the first case (with no wind consideration) we followed the<br />
next steps.<br />
<br />
1. Split time $t$ into $n$ slices of equal length <i>dt</i>:<br />
$$ \left\{ \begin{array}{c} t_0 &=& 0 \\ t_k &=& k \cdot dt \\ t_n &=& t<br />
\end{array} \right. $$<br />
<br />
2. Considering the backward difference for the Euler explicit method implies that the<br />
expression that refers to the current pheromone level each time step is:<br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \cdot c'(x, y, t)$$<br />
<br />
3. And now considering the spatial dimension, it is applied central differences to the Laplace operator $\Delta$, and the backward differences to the vector differential operator $\nabla$ ( in 2D and assuming equal steps in x and y directions): <br />
<br />
$$c (x, y, t) \approx c (x, y, t - dt ) + dt \left( D \cdot \nabla^2 c (x, y, t) - \nabla \vec{v} c (x, y, t) \right)$$<br />
$$ D \cdot \nabla^2 c (x, y, t) = D \left( c_{xx} + c_{yy}\right) = D \frac{c_{i,j-1} + c_{i,j+1} + c_{i-1,j } + c_{i+1,j} – 4 c_{I,j}}{s} $$<br />
$$ \nabla \vec{v} c (x, y, t) = v_{x} \cdot c_{x} + v_{y} \cdot c_{y} = v_{x} \frac{c_{i,j} – c_{i-1,j}}{h} + v_{y} \frac{c_{i,j} – c_{i,j-1}}{h} $$<br />
<br />
<br />
With respect to the boundary conditions, they are null since we are considering an opened-space. Attending to the implementation and simulation of this method, <i>dt</i> must be small enough to avoid instability.<br />
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<div id="tab3" class="tab"><br />
<br/><br />
<h3>The Idea</h3><br/><br />
<br />
<p>When one stares at moths, they apparently move with erratic flight paths. It is possibly because of predator avoiding reasons.</p><br/><br />
<br />
<p> In this frame, sex pheromones influence in moth behavior is also considered. Since these are pheromones released by females in order to attract an individual of the opposite sex, it makes sense that males respond to <span class="purple-bold">gradients of sex pheromone concentration</span>, being attracted towards the source. As soon as a flying male <span class="green-bold">randomly</span> comes into conical pheromone-effective sphere of sex pheromone released by a virgin female, the male begins to seek the females in a zigzag way, approaches to the females and finally copulates with her [1].</p><br/><br/><br/><br />
<br />
<h3>Approximation</h3><br/><br />
<br />
<img width="150px" style="float:left; margin-right: 15px; margin-bottom: 15px;" src="https://static.igem.org/mediawiki/2014/1/17/VUPVPolillita_con_vectores_v1.png" alt="moth_array"></img><br />
<br />
<p>In this project we approximate the resulting moth movement as a vectorial combination of a <span class="purple-bold">gradient vector</span> and a <span class="green-bold">random vector</span>. The magnitude of the gradient vector comes from the change in pheromone concentration level among points separated by a differential stretch in space. More precisely, the gradient points in the direction of the <b>greatest rate of increase</b> of the function and its magnitude is the slope of the graph in that direction. The <span class="green-bold">random vector</span> is restricted in this ‘moth response’ model by a fixed angle, assuming that the turning movement is relatively continuous and for example the moth can’t turn 180 relative degrees at the next instant.</p><br/><br />
<br />
<p>Since the objective of this project consists in avoiding pest damage by reaching the mating disrupting among moths, our synthetic plants are supposed to release enough sexual pheromone so as to <span class="red-bold">saturate moth perception</span>. In this sense the resulting moth vector movement will depend ultimately on the pheromone concentration levels in the field and the moth ability to follow better or worse the gradient of sex pheromone concentration.</p><br/><br />
<br />
<p>At this point, let’s highlight the three main aspects we consider for the characterization of males moth behavior:</p><br/><br />
<br />
</html><br />
[[File:Table_behavior.png|600px|center|Male moths behaviour characterization.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Male moths behaviour characterization.</p></div><br />
<br />
<p>In this context, this ensemble of behaviors could be translated in a sum of vectors in which the random vector has a constant module and changeable direction inside a range, whereas the gradient vector module is a function of the gradient in the field. The question now is: <b>how do we include the saturation effect in the resulting moth shift vector?</b></p><br/><br />
<br />
<p>With this in mind and focusing on the implementation process, our approach consists on the following:</p><br/><br />
<br />
<p>The <span class="purple-bold">gradient vector</span> instead of experiencing a change in its <b>magnitude</b>, this will be always the <b>unit</b> and its <b>direction</b> that of the <span class="purple-bold">greatest rate of increase</span> of the pheromone concentration. A <span class="green-bold">random direction vector</span> with constant module will not be literally considered, but a <span class="green-bold">random turning angle</span> starting from the gradient vector direction.</p></br/> <br />
<br />
<p>Attending to the previous question <i>how do we include the saturation effect in the resulting moth shift vector?</i>, here the answer: <b>the dependence on the</b> <span class="red-bold">moth saturation level</span> (interrelated with the pheromone concentration in the field) <b>will state in the random turning angle</b>.</p><br/><br />
<br />
</html><br />
[[File:Moth_vector.png|600px|center|Approximation of the male moths behaviour.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Table 1</span>. Approximation of the male moths behaviour.</p></div><br />
<br />
<p>This random turning angle will not follow a uniform distribution, but a Poisson distribution in which the <b>mean is zero </b>(no angle detour from the gradient vector direction) and the <b>standard-deviation</b> will be <b>inversely proportional to the intensity of the gradient of sex pheromone concentration in the field</b>. This approach will drive to a ‘sexual confusion’ of the insect as the field homogeneity increases, since the moth in its direction of displacement will fit the gradient direction with certain probabilities which depend on how saturated they are.</p><br/><br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Yoshitoshi Hirooka and Masana Suwanai. Role of Insect Sex Pheromone in Mating Behavior I. Theoretical Consideration on Release and Diffusion of Sex Pheromone in the Air. </li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues. </li><br />
</ol><br />
<p></p><br/><br />
<br />
</div><br />
<br />
<div id="tab4" class="tab"><br />
<br/><br />
<p>Using a modeling environment called Netlogo, we try to simulate the approximate moth population behavior when pheromone diffusion processes are given.</p><br/><br />
<p> <a href="http://ccl.northwestern.edu/netlogo/">Netlogo</a> simulator can be find in its website at Northwestern University.</p><br />
<p> To download the source file of our <span class="red-bold">Sexyplant</span> simlation in Netlogo click here: <br />
<a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/sexyplants.nlogo" download>sexyplants.nlogo</a><br />
<br/><br />
<h3>SETUP:</h3><br />
<ul style="list-style: disc; position: relative; left: 4%; width: 96%;"><br />
<li>We consider three <span class="black-bold">agents</span>: <span class="marron-bold">male</span> and <span class="fucsia-bold">female</span> moths, and <span class="red-bold">sexyplants</span>.</li><br />
<li>We have two kind of sexual pheromone emission sources: <span class="fucsia-bold">female</span> moths and <span class="red-bold">sexyplants</span>. </li><br />
<li>Our scenario is an opened crop field where <span class="red-bold">sexyplants</span> are intercropped and moths fly following different patterns depending on its sex.</li><br />
</ul><br />
<p><span class="fucsia-bold">Females</span>, apart from emitting sexual pheromones, they move with erratic random flight paths. After mating, females are 2 hours in which they are not emitting pheromone.</p><br />
<br />
<p><span class="marron-bold">Males</span> also move randomly while they are under its detection threshold. But when they detect a certain pheromone concentration, they start to follow the pheromone concentration gradients until its saturation threshold is reached. </p><br />
<br />
<p> <span class="red-bold">sexyplants</span> act as continuously- emitting sources and their activity is regulated by a <span class="black-bold">Switch</span>.</p><br/><br />
<br />
<p> On the side of <span class="black-bold">pheromone diffusion</span> process, it is simulated in Netlogo by implementing the <span class="black-bold">Euler explicit</span> method. </p><br/><br />
</html><br />
[[File:Upv_simu1.png|600px|center|Figure 1. NETLOGO Simulation environment.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 1</span>. NETLOGO Simulation environment.</p></div><br />
<br />
<h3>GO!</h3><br />
<p>When <span class="red-bold">sexyplants</span> are switched-off, <span class="marron-bold">males</span> move randomly until they detect pheromone traces from <span class="fucsia-bold">females</span>, in that case they follow them. </p><br />
<p>When <span class="red-bold">sexyplants</span> are switched-on, the pheromone starts to diffuse from them, rising up the concentration levels in the field. At first, the <span class="red-bold">sexyplants</span> have an effect of pheromone traps on the <span class="marron-bold">male</span> moths.</p><br/><br />
<br />
<br />
</html><br />
[[File:VUPV_Polillas.png|600px|center|Figure 2. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 2</span>. On the left: sexyplants are switched-off and a male moth follows the pheromone trace from a female. On the right: sexyplants are switched on and a male moth go towards the static source like it happens with synthetic pheromone traps.</p></div><br />
<br />
<p>As the concentration rises in the field, it becomes more homogeneous. Remember that the <span class="green-bold">random turning angle</span> of the insect follows a Poisson distribution, in which the standard-deviation is inversely proportional to the intensity of the <span class="purple-bold">gradient</span>. Thus, the probability of the insect to take a <span class="black-bold">bigger</span> detour from the faced gradient vector direction is higher. This means that it is <span class="black-bold">less able</span> to follow pheromone concentration gradients, so <span class="black-bold">‘sexual confusion’ is induced</span>.</p><br />
<br />
</html><br />
[[File:Upv_simu3.png|450px|center|Figure 3. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.]]<br />
<html><br />
<div align="center"><p style="text-align: justify; font-style: italic; font-size: 0.9em; width: 700px;"><span class="black-bold">Figure 3</span>. NETLOGO Simulation of the field: sexyplants, female moths, pheromone diffusion and male moths.</p></div><br />
<br />
<h3> Parameters</h3><br />
<p><br />
The parameters of this model are not as well-characterized as we expected at first. Finding the accurate values of these parameters is not a trivial task, in the literature it is difficult to find a number experimentally obtained.</p><br />
<p>So we decided to take an <span class="black-bold">inverse engineering approach</span>. Doing a model parameters swept, we simulate many possible scenarios, and then we come up with values of parameters corresponding to our desired one: insects get confused. This will be useful to know the limitations of our system and to help to decide the final distribution of our plants in the crop field. </p> <br/><br />
<br />
<dl><br />
<dt>Diffusion coefficient</dt><br />
<dd>Range of search: 0.01-0.2 cm^2/s <br/><br />
References: [1], [2], [3], [5]</dd><br />
<dt>Release rate (female)</dt><br />
<dd>Range of search: 0.02-1 µg/h <br/><br />
References: [4], [5]</dd><br />
<dt>Release rate (sexyplant)</dt><br />
<dd>The range of search that we have considered is a little wider than the one for the release rate of females. <br/><br />
References: It generally has been found that pheromone dispensers releasing the<br />
chemicals above a certain emission rate will catch fewer males. The optimum release<br />
rate or dispenser load for trap catch varies greatly among species [4]. This certain emission rate above which male start to get confused could be the release rate from females.</dd><br />
<dt>Detection threshold</dt><br />
<dd>Range of search: 0.001-1 [Mass]/[Distante]^2</dd><br/><br />
<dt>Saturation threshold </dt><br />
<dd>Range of search: 1-5[Mass]/[ Distante]^2</dd><br/><br />
<dt>Moth sensitivity</dt><br />
<dd>This is a parameter referred to the capability of the insect to detect changes in pheromone concentration in the patch it is located and the neighbor patch. When the field becomes more homogeneous, an insect with higher sensitivity will be more able to follow the gradients.<br/><br />
Range: 0-0.0009 <br/><br />
(The maximum level of moth sensitivity has to be less than the minimum level of release rate of females, since this parameter is obtained from the difference)</dd><br />
<dt>Wind force</dt><br />
<dd>Range: -0.1 – 0.1 cm/sec <br/><br />
References: [7] (700cm/sec!!!)</dd><br />
<dt>Population</dt><br />
<dd>The number of males and females can be selected by the observer.</dd><br />
</dl><br />
<br />
<br/><br />
<br/><br />
<h3>Ticks (time step) !!!</h3><br />
<p>We’ll consider the equivalence 20 ticks= 1 hour. That is 1 tick = 3 minutes.</p><br />
<br/><br />
<h3>Patches !!!</h3><br />
<p>The approximate velocity of a male moth flying towards the female in natural environment is 0.3 m/sec [6]. Each moth moves 1 patch per tick, so if 1 tick is equal to 3 minutes (180 sec), the patch is 54 meter long to get that velocity.</p><br />
<p>One can modify the number of patches that conform the field so as to analyze its own case. </p><br />
<br />
<br/><br />
<br />
<br />
<h3>References:</h3><br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>Wilson et al.1969, Hirooka and Suwanai, 1976.</li><br />
<li>Monchich abd Mauson, 1961, Lugs, 1968.</li><br />
<li>G. A. Lugg. Diffusion Coefficients of Some Organic and Other Vapors in Air.</li><br />
<li>W. L. Roelofs and R. T. Carde. Responses of Lepidoptera to Synthetic Sex Pheromone Chemicals and their Analogues, Page 386. </li><br />
<li>R.W. Mankiny, K.W. Vick, M.S. Mayer, J.A. Coeffelt and P.S. Callahan (1980) Models For Dispersal Of Vapors in Open and Confined Spaces: Applications to Sex Pheromone Trapping in a Warehouse, Page 932, 940.</li><br />
<li> Tal Hadad, Ally Harari, Alex Liberzon, Roi Gurka (2013) On the correlation of moth flight to characteristics of a turbulent plume. </li><br />
<li> Average Weather For Valencia, Manises, Costa del Azahar, Spain. </li><br />
</ol><br />
<br/><br/><br />
</div><br />
<br />
<br />
<div id="tab5" class="tab"><br />
<br/><br />
<br />
<p><br />
The aim consists of reducing the possibility of meeting among moths of opposite sex. Thus, we will analyze the number of meetings in the three following cases:<br />
</p><br />
<br />
<ol style="position: relative; left: 4%; width: 90%;"><br />
<li>When sexyplants are switched-off and males only interact with females.</li><br />
<li>When sexyplants are switched-on and have an effect of trapping males.</li><br />
<li>When sexyplants are swiched-on and males get confused when the concentration of pheromone level is higher than their saturation threshold.</li><br />
</ol><br />
<br />
<p><br />
It is also interesting to analyze a fourth case, what does it happen if females wouldn’t emit pheromones and males just move randomly through the field? :</p><br />
<ol start="4" style="position: relative; left: 4%; width: 90%;"><br />
<li>Males and females move randomly. How much would our results differ from the rest of cases? </li><br />
</ol><br />
<br />
<p><br />
What is important is that between the first and the third case, the number of meetings should be less in the latter than in the former. Then we are closer to our objective fulfillment.<br />
</p><br/><br />
</div><br />
</div><br />
<br/><br/><br/><br />
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Valencia UPV iGEM team participated in the communication and diffusion activity called <i>Generación Espontanea</i> (translated as Spontaneous). Twenty-four teams of students showed their projects related to different areas: engineering, social, computing, architecture and culture. We presented our <span class="red-bold">Sexy Plant</span>, and made diffusion of Synthetic Biology. <i>Generación Espontanea</i> was organized by UPV and Dr. Larisa Dunai, who was awarded by MIT Technology Review with the <b>MIT Young Innovator under 35 Award</b> of this year. </p><br />
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Valencia UPV iGEM team introduced The Sexy Plant Project to students between 10 -15 years old, during this summer. Besides, we organised an activity for students to learn the pH scale using a natural indicator based on anthocyanins obtained from plants. Around one hundred students extrated anthocyanins from a red cabagge, and created a natural pH indicator. </p> <br />
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Valencia UPV iGEM team participated in the communication and diffusion activity called <i>Generación Espontanea</i> (translated as Spontaneous). Twenty-four teams of students showed their projects related to different areas: engineering, social, computing, architecture and culture. We presented our <span class="red-bold">Sexy Plant</span>, and made diffusion of Synthetic Biology. <i>Generación Espontanea</i> was organized by UPV and Dr. Larisa Dunai, who was awarded by MIT Technology Review with the <b>MIT Young Innovator under 35 Award</b> of this year. </p><br />
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Valencia UPV iGEM team participated in the communication and diffusion activity called <i>Generación Espontanea</i> (translated as Spontaneous). Twenty-four teams of students showed their projects related to different areas: engineering, social, computing, architecture and culture. We presented our <span class="red-bold">Sexy Plant</span>, and made diffusion of Synthetic Biology. <i>Generación Espontanea</i> was organized by UPV and Dr. Larisa Dunai, who was awarded by MIT Technology Review with the <b>MIT Young Innovator under 35 Award</b> of this year. </p><br />
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<h3><i>“Generacion Espontánea UPV” </i></h3><br />
<p><br />
Valencia UPV iGEM team participated in the communication and diffusion activity called <i>Generación Espontanea</i> (translated as Spontaneous). Twenty-four teams of students showed their projects related to different areas: engineering, social, computing, architecture and culture. We presented our <span class="red-bold">Sexy Plant</span>, and made diffusion of Synthetic Biology. <i>Generación Espontanea</i> was organized by UPV and Dr. Larisa Dunai, who was awarded by MIT Technology Review with the <b>MIT Young Innovator under 35 Award</b> of this year. </p><br />
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<p><br />
Valencia UPV iGEM team introduced The Sexy Plant Project to students between 10 -15 years old, during this summer. Besides, we organised an activity for students to learn the pH scale using a natural indicator based on anthocyanins obtained from plants. Around one hundred students extrated anthocyanins from a red cabagge, and created a natural pH indicator. </p> <br />
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<h3>Workshop</h3><br />
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<h3><i>“Generacion Espontánea UPV” </i></h3><br />
<p><br />
Valencia UPV iGEM team participated in the communication and diffusion activity called <i>Generación Espontanea</i> (translated as Spontaneous). Twenty-four teams of students showed their projects related to different areas: engineering, social, computing, architecture and culture. We presented our <span class="red-bold">Sexy Plant</span>, and made diffusion of Synthetic Biology. <i>Generación Espontanea</i> was organized by UPV and Dr. Larisa Dunai, who was awarded by MIT Technology Review with the <b>MIT Young Innovator under 35 Award</b> of this year. </p><br />
<p align="right"> Valencia, October 2014</p><br />
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<h3><i>Summer 2014 School courses </i></h3><br />
<p><br />
Valencia UPV iGEM team introduced The Sexy Plant Project to students between 10 -15 years old, during this summer. Besides, we organised an activity for students to learn the pH scale using a natural indicator based on anthocyanins obtained from plants. Around one hundred students extrated anthocyanins from a red cabagge, and created a natural pH indicator. </p> <br />
<p align="right"> Valencia, from June to July 2014 </p><br />
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<h3>Lib dup</h3><br />
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src="http://www.youtube.com/v/x_uhzKFNBdk"><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:21:11Z<p>Jpico: </p>
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<div>{{:Team:Valencia_UPV/header}}<br />
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<div align="center"><div id="cn-box" align="justify"><br />
<br />
<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
<html><br />
<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
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<br/><br/><br />
<br/><br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
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<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
<br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
<html><br />
<h3><i>“Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
<br/><br/><br />
<br/><br/><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:19:58Z<p>Jpico: </p>
<hr />
<div>{{:Team:Valencia_UPV/header}}<br />
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<html><br />
<div align="center"><div id="cn-box" align="justify"><br />
<br />
<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
<html><br />
<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
<br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
<html><br />
<h3><i>“The Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
<br/><br/><br />
<br/><br/><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
<br />
<br />
<br />
</div><br />
</br></br></div><br />
<div id="space-margin"></div><br />
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</html><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:18:54Z<p>Jpico: </p>
<hr />
<div>{{:Team:Valencia_UPV/header}}<br />
<br />
<html><br />
<div align="center"><div id="cn-box" align="justify"><br />
<br />
<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
<html><br />
<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
<p align="right"> Valencia, September 2014</p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
<br />
<br/><br/><br/><br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
<html><br />
<h3><i>“The Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
<br />
<br />
<br />
</div><br />
</br></br></div><br />
<div id="space-margin"></div><br />
<br />
</html><br />
<br />
{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:16:20Z<p>Jpico: </p>
<hr />
<div>{{:Team:Valencia_UPV/header}}<br />
<br />
<html><br />
<div align="center"><div id="cn-box" align="justify"><br />
<br />
<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
<html><br />
<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
<br />
<br/><br/><br />
<br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
<p align="right"> Valencia, September 2014</p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
<br />
<br />
<br/><br/><br/><br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
<html><br />
<h3><i>“The Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:14:13Z<p>Jpico: </p>
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<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
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<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
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<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
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<br/><br/><br />
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<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
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<h3><b>Interviews</b></h3><br />
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</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the <span class="red-bold">Sexy Plant</span>, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
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<br/><br/><br/><br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
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<h3><i>“The Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/policy/activitiesTeam:Valencia UPV/policy/activities2014-10-17T17:13:20Z<p>Jpico: </p>
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<div>{{:Team:Valencia_UPV/header}}<br />
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<br />
<p><h3 class="hook" align="left"><a>Policy and Practices</a> > <a>Activities</a></h3></p><br/><br />
<br />
<div align="center"><span class="coda"><roja>A</roja>ctivities</span> </div><br/><br/><br />
<br />
<p>Policy and Practice is not just the cherry on the cake; it is an essential constituent of Synthetic Biology. Thus, it permeates the whole Sexy Plant project, conceived as a responsible research one. To start with, our motivation was to address a challenge of social relevance: protection of crops is essential for economical and social sustainability in a world with an ever-growing population. We also tried to understand the benefits and risks of our approach. Not only safety and environmental protection drove the biosafety module. To tune our project and ensure its outcome is in line with societal expectations, we engaged a wide range of social actors and stakeholders throughout the whole of it: bio-farm companies, (eco-)farmers associations, research experts, social researchers, etc. Of course, we are also enthusiast about transmitting the world of Synthetic Biology to the next generations. Thus, some activities were developed with children at our University Summer School.</p><br />
<br />
<br/><br/><br />
<h3><b>Permanent activities and meetings</b></h3><br />
<br/><br />
<h3> Center for Chemical Ecology (CEQA), Valencia.</h3><br />
<br/><br />
</html><br />
[[File:UPV_CEQA.jpg|500px|right]] <br />
<html><br />
<p><br />
CEQA has expertise in the isolation and identification of semiochemicals, the formulation of pheromone attractants and controlled rate emitters.</p><br />
<p><br />
Jaime Primo Millo is the Director of the Agricultural Center for Chemical Ecology (CEQA), and professor of organic chemistry at UPV. Jaime Primo, Ismael Navarro, Vicente Navarro and Sandra Vacas have continuously advised the Valencia UPV iGEM team since we first met them. They are developing systems to control the principal citrus pests, and their experience on “insects sexual confusion” has been invaluable for us, and has improved the achievements of our <span class="red-bold">Sexy Plant</span> as a new pest management method. <br />
</p><br />
<br />
<br/><br/><br />
<br />
<h3><i>"Projects like The Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture"</i></h3></html><br />
[[File:VUPV Bayer2.png|350px|left]] <br />
<html><br />
<br/><br />
<h3 align="right">Bayer CropScience, Valencia</h3><br />
<br/><br />
<p>Mr. Jorge Silva is the Head of Bayer CropScience Technical Department. Jorge liked <span class="red-bold">Sexy Plant</span> as a system to fight against pests. He highlighted the necessity to find new approaches in sustainable agriculture, and that our project could have future in the market. We discussed the advances in plant synthetic biology and he concluded “projects like Sexy Plant show us the importance Synthetic Biology may have in the future of agriculture”. Jorge gave us invaluable feedback on how to improve certain details to ease the commercialization of Sexy Plant in the future, and asked us to send an executive summary of our project to Bayer CropScience headquarters in Ghent. As result of the meeting, Bayer CropScience wrote an official support letter for our project, and asked to be informed about further developments of the project in the future. </p><br />
<br />
<br />
<br/><br/><br />
<br/><br/><br />
<br/><br/><br />
<h3><b>Interviews</b></h3><br />
<br/><br/><br />
</html><br />
[[Image:UPV_Cooperativa.jpg|400px|right]] <br />
<html><br />
<br />
<h3><i>“We have been using sexual confusion as a pest management method in rice crops for the last 20 years” </i></h3><br />
<p><br />
Paco Girona is agriculture engineer at Cooperatives for Agrofood industry (FECOAV). He makes efforts to extend the use of ecological pest methods over some typical crops in Valencia, Spain. </p><br />
<p><br />
Around the Albufera Natural Park in Valencia, the cycle sown rice starts in May when the farmers should start protecting their crops from the <i>Chilo</i> lepidopter (moth) pest. During the first days of May, technicians place pheromone sticks between rice plants to release the Chilo female moth pheromone into the environment. The planted area is around 15,000 Ha of crop, and they are protected by 462,960 pheromone sticks. This technique has been used for the last 20 years, and the economic losses have been cut down to approximately a mere 0.5%. Paco Girona explains that Sexy Plant coul be a wonderful alternative to chemically synthetized pheromone sticks, specially during its assembly, the most hazardous part of its production. “If you get the Sexy Plant, I take my hat off” </p><br />
<p align="right"> Valencia, October 2014</p><br />
<br />
<br />
<br/><br/><br/><br />
</html><br />
[[Image:VUPV_Coque.jpg|400px|left]] <br />
<html><br />
<h3><i>“The Sexy Plant could be a good approach to reduce the costs of pheromone production” </i></h3><br />
<br />
<p>Jose Maria Garcia Alvarez-Coque is a social researcher and Director of the Sustainable Agriculture group, at the Universitat Politècnica de Valencia (UPV). </p><br />
<p><br />
He considers the currently pheromone synthesis as an expensive method to produce insect pheromones. “Sexy Plant could be a good approach to reduce the costs of pheromone production”. This project is another ecological way to manage pests, such as the production of auxiliary insects to protect crops. In addition, Sexy Plant can be a safe, sustainable and environmentlly friendly method, as far as it respects agricultural and environmental specifications. <span class="red-bold">Sexy Plant</span> modules like Biosafety or Sterility are characteristics that assist the long-term use of this plant. </p><br/><br />
<p align="right"> Valencia, September 2014</p><br />
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</div><br />
</br></br></div><br />
<div id="space-margin"></div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T11:29:29Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
</br></br><br />
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<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
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<div class="tab-content"><br />
<div id="tab1" class="tab active"><br/><br />
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<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
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</div><br />
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<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|300px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acid exchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of rubisco</span>. This enzyme, in the presence of oxygen, reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. The action of the rubisco enzyme defines two scenarios in plant metabolism: photosynthesis, and photorespiration. During photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced, and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant. In such a case, photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production. In other words, optimizing the efflux V3 (see Figure 2) from the exchange reaction ExZ11. In addition, we must introduce the lower (lb) and upper (ub) bounds for each reaction. The bounds for the flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower flux bounds in the AraGEM model.</p><br />
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<br/><br />
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<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results for each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis, and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. During photosynthesis (Figure 4A and 4B) we see an increase of the palmitic acid exchange flux when the photons uptake is unconstrained (actually allowing it to reach the default maximum flux in COBRA, i.e. 1000). </p><br />
<p>Even when the photons flux increases freely, most palmitic acid is used for plant growth. Therefore, the new palmitic acid exchange flux only becomes 5.33 nM/seg (see Table 2). However, this low level is somehow forced by the high growth rate that was fixed according to the few existing literature references.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acid exchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acid exchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acid exchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acid exchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acid exchange, and photons uptake. Figure 4C and 4D show an imperceptible loss (2%) in the palmitic acid exchange flux. The new flux is 5.24 nM/seg, similar to the one obtained in the photosynthesis scenario.</p><br />
<p>We also performed a supplementary analysis produced using gene knockout. COBRA toolbox was used to knock out genes of the AraGEM model on a one by one basis to optimize the palmitic acid exchange flux. The Figure 5 shows the maximum palmitic acid exchange flux obtained after gene knockout of each gene. Out of 1404 knocked out genes, both at photosynthesis and photorespiration, the optimal palmitic acid exchange flux decreases in 33 cases, and does not present improvement in the remaining ones.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acid exchange flux after gene knockout. Out of 1404 genes in the AraGEM model, 33 (pink lines) genes show an influence on the optimal palmitic acid exchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acid exchange flux after gene knockout. Out of 1404 genes in the AraGEM model, 33 (pink lines) genes show an influence on the optimal palmitic acid exchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T11:23:17Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
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<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
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<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
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<br />
<br />
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<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|300px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of rubisco</span>. This enzyme, in the presence of oxygen, reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. The action of the rubisco enzyme defines two scenarios in plant metabolism: photosynthesis, and photorespiration. During photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced, and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant. In such a case, photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production. In other words, optimizing the efflux V3 (see Figure 2) from the exchange reaction ExZ11. In addition, we must introduce the lower (lb) and upper (ub) bounds for each reaction. The bounds for the flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis, and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. During photosynthesis (Figure 4A and 4B) we see an increase of the palmitic acid exchange flux when the photons uptake is unconstrained (actually allowing it to reach the default maximum flux in COBRA, i.e. 1000). </p><br />
<p>Even when the photons flux increases freely, most palmitic acid is used for plant growth. Therefore, the new palmitic acid exchange flux only becomes 5.33 nM/seg. However, this low level is somehow forced by the high growth rate that was fixed according to the few existing literature references.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acid exchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acid exchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acid exchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acid exchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acid exchange, and photons uptake. Figure 4C and 4D show an imperceptible loss (2%) in the palmitic acid exchange flux. The new flux is 5.24 nM/seg, similar to the one obtained in the photosynthesis scenario.</p><br />
<p>We also performed a supplementary analysis produced using gene knockout. COBRA toolbox was used to knock out genes of the AraGEM model on a one by one basis to optimize the palmitic acid exchange flux. The Figure 5 shows the maximum palmitic acid exchange flux obtained after gene knockout of each gene. Out of 1404 knocked out genes, both at photosynthesis and photorespiration, the optimal palmitic acid exchange flux decreases in 33 cases, and does not present improvement in the remaining ones.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acid exchange flux after gene knockout. Out of 1404 genes in the AraGEM model, 33 (pink lines) genes show an influence on the optimal palmitic acid exchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acid exchange flux after gene knockout. Out of 1404 genes in the AraGEM model, 33 (pink lines) genes show an influence on the optimal palmitic acid exchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
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<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br/><br />
<br />
<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
<br />
<br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|300px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of rubisco</span>. This enzyme, in the presence of oxygen, reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. The action of the rubisco enzyme defines two scenarios in plant metabolism: photosynthesis, and photorespiration. During photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced, and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant. In such a case, photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production. In other words, optimizing the efflux V3 (see Figure 2) from the exchange reaction ExZ11. In addition, we must introduce the lower (lb) and upper (ub) bounds for each reaction. The bounds for the flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis, and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. During photosynthesis (Figure 4A and 4B) we see an increase of the palmitic acid exchange flux when the photons uptake is unconstrained (actually allowing it to reach the default maximum flux in COBRA, i.e. 1000). </p><br />
<p>Even when the photons flux increases freely, most palmitic acid is used for plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this low level is somehow forced by the high growth rate that was fixed according to the few existing literature references.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acid exchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acid exchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acid exchange, and photons uptake. Figure 4C and 4D show an imperceptible loss (2%) in the palmitic acid exchange flux. The new flux is 5.24 nM/seg, similar to the one obtained in the photosynthesis scenario.</p><br />
<p>We also performed a supplementary analysis produced using gene knockout. COBRA toolbox was used to knock out genes of the AraGEM model on a one by one basis to optimize the palmitic acid exchange flux. The Figure 5 shows the maximum palmitic acid exchange flux obtained after gene knockout of each gene. Out of 1404 knocked out genes, both at photosynthesis and photorespiration, the optimal palmitic acid exchange flux decreases in 33 cases, and does not present improvement in the remaining ones.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acid exchange flux after gene knockout. From 1404 genes in AraGEM model, 33 (pink lines) gene show an influence over the optimal palmitic acid exchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
<br />
</ol><br />
<br />
</div><br />
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<div id="tab3" class="tab"><br />
<br />
<p><strong>NetLogo</strong> is an agent-based programming language and integrated modeling environment. <strong>NetLogo</strong> is free and open source <strong>software</strong>, under a GPL license.</p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T11:04:24Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
</br></br><br />
<br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br/><br />
<br />
<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
<br />
<br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|300px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of rubisco</span>. This enzyme, in the presence of oxygen, reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. The action of the rubisco enzyme defines two scenarios in plant metabolism: photosynthesis, and photorespiration. During photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced, and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant. In such a case, photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production. In other words, optimizing the efflux V3 (see Figure 2) from the exchange reaction ExZ11. In addition, we must introduce the lower (lb) and upper (ub) bounds for each reaction. The bounds for the flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis, and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. During photosynthesis (Figure 4A and 4B) we see an increase of the palmitic acid exchange flux when the photons uptake is unconstrained (actually allowing it to reach the default maximum flux in COBRA, i.e. 1000). </p><br />
<p>Even when the photons flux increases freely, most palmitic acid is used for plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this low level is somehow forced by the high growth rate that was fixed according to the few existing literature references.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acidexchange and photons uptake. Figure 4C and 4D shows an imperceptible loss (2%) in the palmitic acidexchange flux. The new flux is 5.24 nM/seg and its behavior is similar to the photosynthesis scenario.</p><br />
<p>We included a supplementary analysis produced by FBA optimization called Gene knockout. COBRA toolbox knock outs one by one gene of the AraGEM model to optimize the desired objective flux. The Figure 5 shows the maximum palmitic acidexchange flux obtained after gene knockout of each gene During photosynthesis or photorespiration, the optimal palmitic acidexchange flux presents a decrease when around 33 from 1404 gene were knocked out.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
<br />
</ol><br />
<br />
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<p><strong>NetLogo</strong> is an agent-based programming language and integrated modeling environment. <strong>NetLogo</strong> is free and open source <strong>software</strong>, under a GPL license.</p><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T10:50:14Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
</br></br><br />
<br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
</ul><br />
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<div class="tab-content"><br />
<div id="tab1" class="tab active"><br/><br />
<br />
<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
<br />
<br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|350px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is a generic plant cell model capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of Rubisco</span>. This enzyme in the presence of oxygen (O2) reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, the most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant, and photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production, in other words, optimizing the efflux V3 from the exchange reaction ExZ11. In addition, we must introduce the low (lb) and up (ub) bound for each reaction. In AraGEM, the bounds for flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. Photosynthesis (Figure 4A and 4B) shows an increase of the palmitic acidexchange flux, when the photons uptake are unconstraint and takes values until 1000 (default maximum flux COBRA). </p><br />
<p>Even when the photons flux freely increase, the most palmitic acid is used by the biomass or plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this level also depends of the high growth rate fixed from the literature.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acidexchange and photons uptake. Figure 4C and 4D shows an imperceptible loss (2%) in the palmitic acidexchange flux. The new flux is 5.24 nM/seg and its behavior is similar to the photosynthesis scenario.</p><br />
<p>We included a supplementary analysis produced by FBA optimization called Gene knockout. COBRA toolbox knock outs one by one gene of the AraGEM model to optimize the desired objective flux. The Figure 5 shows the maximum palmitic acidexchange flux obtained after gene knockout of each gene During photosynthesis or photorespiration, the optimal palmitic acidexchange flux presents a decrease when around 33 from 1404 gene were knocked out.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T10:46:40Z<p>Jpico: </p>
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
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<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
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<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
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<br />
<br />
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<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|400px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. </p><br />
<p> <br />
As precursor of our pathway, our efforts were aimed at the optimization of <b>palmitic acid</b>. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
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<br/><br />
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</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is a generic plant cell model capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of Rubisco</span>. This enzyme in the presence of oxygen (O2) reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, the most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant, and photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production, in other words, optimizing the efflux V3 from the exchange reaction ExZ11. In addition, we must introduce the low (lb) and up (ub) bound for each reaction. In AraGEM, the bounds for flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. Photosynthesis (Figure 4A and 4B) shows an increase of the palmitic acidexchange flux, when the photons uptake are unconstraint and takes values until 1000 (default maximum flux COBRA). </p><br />
<p>Even when the photons flux freely increase, the most palmitic acid is used by the biomass or plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this level also depends of the high growth rate fixed from the literature.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acidexchange and photons uptake. Figure 4C and 4D shows an imperceptible loss (2%) in the palmitic acidexchange flux. The new flux is 5.24 nM/seg and its behavior is similar to the photosynthesis scenario.</p><br />
<p>We included a supplementary analysis produced by FBA optimization called Gene knockout. COBRA toolbox knock outs one by one gene of the AraGEM model to optimize the desired objective flux. The Figure 5 shows the maximum palmitic acidexchange flux obtained after gene knockout of each gene During photosynthesis or photorespiration, the optimal palmitic acidexchange flux presents a decrease when around 33 from 1404 gene were knocked out.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
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<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
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<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
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<br />
<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [1]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate [2].<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [3].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM model [4], a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
<br />
<br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM [2] is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
<br/><br />
</html><br />
[[File:Precursor.png|400px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
<br/><br />
<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. <br />
<b>Coenzyme A (CoA)</b>, also present in living organisms, is bound to palmitic acid for synthesis and oxidation of several fatty acids. </p><br />
<p><br />
These two compounds react to form the first metabolite of our pathway, 16:CoA, which is generated at the endoplastic reticulum (plastid membrane). </p><br />
<p> <br />
Our efforts were aimed at the optimization of <b>palmitic acid</b>, which is the precursor of our pathway. In the AraGEM model, this is denoted as <b>Hexadecanoic acid_acc (16:0)</b> and is located in the cytosol (see Figure 1). To model the pathway, we introduced the reaction using one influx V1 and two effluxes V2, V3 (see Figure 2). The efflux V2 was incorporated as an exchange reaction, in order to generate a branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear, starting from 16:0, this new added branch represents the whole synthetic pathway of our pheromone.</p><br />
<br/><br />
<br/><br />
<br/><br />
</html><br />
[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is a generic plant cell model capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of Rubisco</span>. This enzyme in the presence of oxygen (O2) reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
<br/><br />
<br />
</html><br />
[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.</p><br />
<br/><br />
<br />
<h3>Model assumptions</h3><br />
<p>In plants, the most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant, and photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production, in other words, optimizing the efflux V3 from the exchange reaction ExZ11. In addition, we must introduce the low (lb) and up (ub) bound for each reaction. In AraGEM, the bounds for flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
<br />
</html><br />
[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
<br/><br />
<br/><br />
<br />
<h3>Optimal pheromone production using FBA </h3><br />
</html><br />
[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
<br />
<br/><br />
<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. Photosynthesis (Figure 4A and 4B) shows an increase of the palmitic acidexchange flux, when the photons uptake are unconstraint and takes values until 1000 (default maximum flux COBRA). </p><br />
<p>Even when the photons flux freely increase, the most palmitic acid is used by the biomass or plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this level also depends of the high growth rate fixed from the literature.</p><br />
<br />
</html><br />
[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange .]]<html><br />
<br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
<br />
<br/><br />
<br/><br />
<br />
<p>During photorespiration, we used FBA to optimize and analyze both palmitic acidexchange and photons uptake. Figure 4C and 4D shows an imperceptible loss (2%) in the palmitic acidexchange flux. The new flux is 5.24 nM/seg and its behavior is similar to the photosynthesis scenario.</p><br />
<p>We included a supplementary analysis produced by FBA optimization called Gene knockout. COBRA toolbox knock outs one by one gene of the AraGEM model to optimize the desired objective flux. The Figure 5 shows the maximum palmitic acidexchange flux obtained after gene knockout of each gene During photosynthesis or photorespiration, the optimal palmitic acidexchange flux presents a decrease when around 33 from 1404 gene were knocked out.</p> <br />
<br/><br />
<br/><br />
<br />
</html><br />
[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.</p><br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
<br />
</ol><br />
<br />
</div><br />
<br />
<div id="tab3" class="tab"><br />
<br />
<p><strong>NetLogo</strong> is an agent-based programming language and integrated modeling environment. <strong>NetLogo</strong> is free and open source <strong>software</strong>, under a GPL license.</p><br />
</div><br />
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{{:Team:Valencia_UPV/footer_img}}</div>Jpicohttp://2014.igem.org/Team:Valencia_UPV/Modeling/fbaTeam:Valencia UPV/Modeling/fba2014-10-17T10:07:59Z<p>Jpico: </p>
<hr />
<div>{{:Team:Valencia_UPV/header}}<br />
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<html><br />
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script><br />
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<div align="center"><div id="cn-box" align="justify"><br />
<h3 class="hook" align="left"><a href="#">Modeling</a> > <a href="https://2014.igem.org/Team:Valencia_UPV/Modeling/fba">Pheromone Production</a></h3></p></br><br />
<br />
<div align="center"><span class="coda"><roja>P</roja>heromone <roja>P</roja>roduction</span> </div><br />
</br></br><br />
<br />
<div class="tabs"><br />
<ul class="tab-links"><br />
<li class="active"><a href="#tab1">Introduction</a></li><br />
<li><a href="#tab2">FBA Analysis</a></li><br />
<!--<li><a href="#tab3">Results</a></li><br />
<li><a href="#tab4">Tab #4</a></li> --><br />
</ul><br />
<br />
<div class="tab-content"><br />
<div id="tab1" class="tab active"><br/><br />
<br />
<h3>The Idea</h3><br/><br />
<br />
<p>Pheromones production rates can be estimated using constrained-based modeling of metabolic networks.This can be useful to know the amount of pheromone that can be produced by the synthetic plant.</p><br/> <br />
<br />
<h3>Constraint-based modeling</h3><br/><br />
<br />
Constraint-based modeling use models of the cell metabolism that are derived from a metabolic network (stoichiometric models) and assume steady-state for the intracellular metabolites. These two constraints are the base of constraint-based modeling: the fact that cells are subject to constraints that limit their behaviour [Palsson06]. In principle, if all constraints operating under<br />
a given set of circumstances were known, the actual state of a metabolic network<br />
could be elucidated. So by imposing the known constraints, it is possible to determine which functional states can and cannot be achieved by a cell.<br />
</html><br />
[[File:Stoich_model.png|600px|center|Principles of the stoichiometric modeling framework. Given a metabolic network, the<br />
mass balance around each intracellular metabolite can be mathematically represented with an ordinary<br />
differential equation. If we do not consider intracellular dynamics, the mass balances can be described<br />
by a homogeneous system of linear equations: the so-called general equation. Other constraints can be<br />
also incorporated to further restrict the space of feasible flux states of cells. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br />
</p><br/> <br />
<br />
<h4>Types of contraints</h4><br/><br />
<p><br />
Constraints can be divided in two main types: non adjustable (invariant) and adjustable<br />
ones. The former are time-invariant restrictions of possible cell behaviour,<br />
whereas the latter depend on environmental conditions, may change through<br />
evolution, and may vary from one individual cell to another. Examples of non adjustable<br />
constraints are those imposed by thermodynamics (e.g, irreversibility of fluxes)<br />
and enzyme or transport capacities (e.g, maximum flux values). Enzyme kinetics,<br />
regulation, and experimental measurements are examples of adjustable constraints.<br />
To study the invariant properties of a network, only invariant constraints can be used,<br />
because they are those that are always satisfied (i.e, they limit the cell capabilities). If<br />
adjustable constraints are used, the elucidated cell states will be only valid under the<br />
particular set of circumstances in which these constraints operate.<br />
</p><br/></html><br />
[[File:Contrainedbm.png|600px|center|Space of feasible steady-state flux vectors by non-adjustable constraints. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/><br />
<br />
<h3>Flux Balance Analysis</h3><br/> <br />
<p>Flux balance analysis (FBA) is a methodology that uses optimisation to get predictions<br />
from a constraint-based model by invoking an assumption of optimal cell behaviour. Basically,<br />
one particular state among those that cells can show, accordingly to a constraint-based<br />
model, is chosen based on the assumption that cells have evolved to be optimal, i.e.,<br />
that cells regulate its fluxes toward optimal flux states.<br />
The following procedure is used to develop a flux balance analysis model:<br />
</p><br/></html><br />
[[File:FBA_steps.png|600px|center|Procedure to develop a flux balance analysis model. From: PhD Thesis. F Llaneras. UPV. 2010]]<html><br/> <br />
<p><br />
Flux balance analysis is used to investigate hypothesis (e.g., test if a<br />
reduced uptake capacity can be the cause of an unexpected cell behaviour) and to<br />
evaluate a range of possibilities (e.g, find the best combination of substrates).<br />
</p><br/> <br />
<br />
<h4>Metabolic objectives and optimization</h4><br/> <br />
<p><br />
It must be taken into account that FBA predictions, the optimal flux state, may not<br />
correspond to the actual fluxes exhibited by cells. To support the assumption of optimal<br />
behaviour, it must be hypothesised that: (i) cells, forced by evolutionary pressure,<br />
evolved to achieve an optimal behaviour with respect to certain objective, (ii) we know<br />
which this objective is, and (iii) the objective can be expressed, at least approximately,<br />
in convenient mathematical terms.</p><br />
<p><br />
Clearly, predictions of flux balance analysis are dependent on the objective function<br />
being used. To date, the most commonly used objective function has been the maximisation<br />
of biomass, which leaded to predictions consistent with experimental data<br />
for different organisms, such as <i>Escherichia coli</i> [Edwards01].</p><br/><br />
<h4>Genome-scale and plant models</h4><br/> <br />
<p><br />
FBA is widely used for predicting metabolism, in particular the genome-scale metabolic network reconstructions that have been built in the past decade. These reconstructions contain all of the known metabolic reactions in an organism, and the genes that encode each enzyme. In our case, FBA will calculate the flow of metabolites through our metabolic network to obtain the maximum production of pheromone. It must be noted that plant genome-scale models are very rare and, indeed, plant FBA is a very new research topic. One of the very few available plant models is the AraGEM, a genome-scale of <i>Arabidopsis Thaliana</i>.</p><br/><br />
<br />
</p><br/></html><br />
[[File:Aragem_excelc.png|600px|center|AraGEM: Genome-scale reconstruction network of <i>A. Thaliana</i> metabolism. From: ARAGem]]<html><br />
<br />
<br />
<p align="left"><strong>References</strong></p><br/><br />
<div style="position: relative; left: 3%; width: 96%;"><br />
<ol><br />
<li> Llaneras F, Picó J (2008). Stoichiometric Modelling of Cell Metabolism. Journal of Bioscience and Bioengineering, 105:1.</li><br />
<li> Palsson BO (2006). Systems biology: properties of reconstructed networks. New York, USA: Cambridge University Press New York.</li><br />
<li> Edwards JS, Covert M, Palsson B (2002). Metabolic modelling of microbes: the<br />
flux-balance approach. Environmental Microbiology, 4:133-140.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31. </li> <br />
</ol><br />
<br />
</div><br />
<br />
<br />
<br />
</div><br />
<br />
<div id="tab2" class="tab"><br/><br />
<h3>COBRA </h3><br/><br />
<p><br />
The COnstraints Based Reconstruction and Analysis (COBRA) approach to systems biology accepts the fact that we do not possess sufficiently detailed parameter data to precisely model, in the biophysical sense, an organism or plant at the genome scale [1].<br />
The COBRA Toolbox [2] is a freely available Matlab toolbox can be used to perform a variety of COBRA methods, including many FBA-based methods. Models for the COBRA Toolbox are saved in the Systems Biology Markup Language (SBML).<br />
</p><br/><br />
<h3> AraGEM Model </h3><br/><br />
<p><br />
AraGEM is the genome-scale metabolic network model covering primary metabolism for a compartmentalized plant cell based on the Arabidopsis (<i>Arabidopsis Thaliana</i>) genome. AraGEM is a comprehensive literature-based model, that accounts for the functions of 1,419 unique open reading frames, 1,748 metabolites, 5,253 gene-enzyme reaction-association entries, and 1,567 unique reactions compartmentalized into the cytoplasm, mitochondrion, plastid, peroxisome, and vacuole. Using efficient resource utilization as the optimality criterion, AraGEM has already been used to predict the classical photorespiratory cycle as well as known key differences between redox metabolism in photosynthetic and nonphotosynthetic plant cells.</p><br />
<p> <br />
AraGEM is a viable framework for in silico functional analysis and can be used to derive new, nontrivial hypotheses for exploring plant metabolism. We take for granted that AraGEM is the genome-scale metabolic network model that currently better approximates the metabolism model of <i>N. benthamiana.</i>. In <span class="red-bold">Sexy Plant</span> we have added <i>in silico </i> the reactions from the network of pheromone production. As optimality criterion we sought to maximize the pheromone flux produced by the plant.</p><br/><br />
<h3> Pheromone pathway location </h3><br/><br />
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[[File:Precursor.png|400px|left|Figure 1. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone. ]]<br />
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<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 1</span>. Palmitic acid is a common fatty acid in plants and animals. This metabolite is the precursor of our pheromone.</p><br />
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<p><br />
<b>Palmitic acid (16:0)</b> is the most common fatty acid (saturated) found in animals, plants and microorganisms. <br />
<b>Coenzyme A (CoA)</b> also presents in living organisms, is bound to Palmitic acid for synthesis and oxidates several fatty acids. </p><br />
<p><br />
These 2 elements reacts to form the first metabolite of our pathway 16:CoA, which is generated by the endoplastic reticulum (plastid membrane). </p><br />
<p><br />
AraGEM model is compounded by 1737 metabolites and 1601 reactions. These elements are organized in the stoichiometric matrix S[1737x1601] to use them in the FBA optimization take into account some constraints.<br />
<p> <br />
Our efforts were aimed at the optimization of <b>Palmitic Acid</b> or <b>Hexadecanoic32 Acid_acc (16:0)</b>, which is the precursor of our pathway. 16:0 is located in the cytosol and the reaction takes place using one influx V1 and two effluxes V2, V3. The efflux V2 was incorporated as an exchange reaction in order to generate branch in the original pathway of 16:0 metabolism. As our metabolic pathway is linear starting from 16:0, this new added branch represents the hole synthetic pathway of our pheromone.</p><br />
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[[File:Metabolite.png|800px|center|Figure 2. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.]]<html><br />
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<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 2</span>. In AraGEM, palmitic acid is also called Hexadecanoic32 Acid_acc. The reaction added ExZ11 produces the efflux V3 known as palmitic acidexchange.</p><br />
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<h3>Defining scenarios</h3><br/><br />
<p>AraGEM is a generic plant cell model capable of representing both photosynthetic and nonphotosynthetic cell types [1]. In order to reproduce the classical physiological scenarios of plant cell metabolism, we explored two photosynthetic scenarios: i) Photosynthesis and ii) Photorespiration. The difference comes from the <span class="black-bold">carboxylation reaction of Rubisco</span>. This enzyme in the presence of oxygen (O2) reduces the energy efficiency of photosynthetic output by 25% in C3 plants.<p><br />
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[[File:Sexy_ribusco.png|700px|center|Figure 3. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.]]<html><br />
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<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 3</span>. Rubisco enzyme action defines two scenarios in plant metabolism: Photosynthesis and Photorespiration. During Photosynthesis, the carboxylation-oxygenation ratio is +1:0 and there is no oxygenation of ribulose 1.5-bisP. Moreover, the presence of oxygen and rubisco also catalyzes an oxygen reaction, photosynthesis efficiency is reduced and the carboxylation-oxygenation ratio is +3:1.</p><br />
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<h3>Model assumptions</h3><br />
<p>In plants, the most genome-scale metabolic network reconstructions minimize the photons consumption (Ex16) while growth rate or biomass (BIO_L) rate is kept fixed. This is true if we mainly seek the survival of the plant, and photons consumption will be the optimization objective.</p> <br />
<p>In our case, the principal objective is maximizing the pheromone production, in other words, optimizing the efflux V3 from the exchange reaction ExZ11. In addition, we must introduce the low (lb) and up (ub) bound for each reaction. In AraGEM, the bounds for flux reactions Ex16, BIO_L and ExZ11 were fitted according to Table 1.</p><br />
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[[File:Tabla1.png|600px|center|Table 1.]]<html><br />
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<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 1</span>. Upper and lower bounds in AraGEM.</p><br />
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<h3>Optimal pheromone production using FBA </h3><br />
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[[File:Tabla2.png|600px|center|Table 2.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Table 2</span>. FBA results in each scenario.</p><br />
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<p>The optimum flux distribution is here defined as the flux distribution that maximizes palmitic acid flux, for a fixed rate of biomass synthesis and free photon uptake.</p><br />
<p><br />
The metabolic contrast between photosynthesis and photorespiration is illustrated in Figure 4. Photosynthesis (Figure 4A and 4B) shows an increase of the palmitic acidexchange flux, when the photons uptake are unconstraint and takes values until 1000 (default maximum flux COBRA). </p><br />
<p>Even when the photons flux freely increase, the most palmitic acid is used by the biomass or plant growth. Therefore, the new palmitic acid_{exchange} flux only becomes 5.33 nM/seg. However, this level also depends of the high growth rate fixed from the literature.</p><br />
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[[File:FBA optimization.png|600px|center|Figure 4. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange .]]<html><br />
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<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 4</span>. Optimization during photosynthesis with two different objectives fluxes A) minimizing photons uptake and B) maximizing palmitic acidexchange. During photorespiration, metabolism products decrease, such as C) photons uptake and D) palmitic acidexchange.</p><br />
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<p>During photorespiration, we used FBA to optimize and analyze both palmitic acidexchange and photons uptake. Figure 4C and 4D shows an imperceptible loss (2%) in the palmitic acidexchange flux. The new flux is 5.24 nM/seg and its behavior is similar to the photosynthesis scenario.</p><br />
<p>We included a supplementary analysis produced by FBA optimization called Gene knockout. COBRA toolbox knock outs one by one gene of the AraGEM model to optimize the desired objective flux. The Figure 5 shows the maximum palmitic acidexchange flux obtained after gene knockout of each gene During photosynthesis or photorespiration, the optimal palmitic acidexchange flux presents a decrease when around 33 from 1404 gene were knocked out.</p> <br />
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[[File:VUPV Knokout.png|600px|center|Figure 5. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.]]<html><br />
<p style="text-align: justify; font-style: italic; font-size: 0.8em; width: 700px;"><span class="black-bold">Figure 5</span>. Palmitic acidexchange flux after gene knockout. From 1404 gene in AraGEM model, 33 (pink lines) gene show an influence over the optimal Palmitic acidexchange flux.</p><br />
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<p align="left"><strong>References</strong></p><br/><br />
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<ol><br />
<li> Daniel Hyduke, Jan Schellenberger, Richard Que, Ronan Fleming, Ines Thiele, Jeffery Orth, Adam Feist, Daniel Zielinski, Aarash Bordbar, Nathan Lewis, Sorena Rahmanian, Joseph Kang & Bernhard Palsson. COBRA Toolbox 2.0 Link: http://systemsbiology.ucsd.edu/Downloads/Cobra_Toolbox.</li><br />
<li> de Oliveira Dal'Molin CG1, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK. AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. NCBI, Plant Physiol. 2010 Feb;152(2):579-89. doi: 10.1104/pp.109.148817. Epub 2009 Dec 31.</li><br />
<li> Rajib Saha,Patrick F. Suthers, Costas D. Maranas mail. Zea mays iRS1563: A Comprehensive Genome-Scale Metabolic Reconstruction of Maize Metabolism. Plos One. Published: July 06, 2011 DOI: 10.1371/journal.pone.0021784.</li><br />
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