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| | <h2> Modeling Overview</h2> | | <h2> Modeling Overview</h2> |
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| - | <p>We developed models for each of the three different modules of our project: the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling #CurliMod">conductive curli module</a>, the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling #EETMod">extracellular electron transport (EET) module</a> and the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling #LandmineMod">landmine detection module</a>. <br> | + | <p>We developed models for each of the three different modules of our project: the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling /Curli">conductive curli module</a>, the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling /EET">extracellular electron transport (EET) module</a> and the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling /Landmine">landmine detection module</a>. <br> |
| | For the conductive curli module, we wanted to know if a conductive path between two electrodes of a chip filled with curli growing <i> E. coli </i> arise at a certain point in time. We also wanted to make quantitative predictions about the resistance between the two electrodes of our system in time. <br> | | For the conductive curli module, we wanted to know if a conductive path between two electrodes of a chip filled with curli growing <i> E. coli </i> arise at a certain point in time. We also wanted to make quantitative predictions about the resistance between the two electrodes of our system in time. <br> |
| | For the EET module, our goal was to investigate the carbon metabolism providing the electrons for the EET module. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Gadget">gadget section</a> of our wiki. Furthermore, in our modeling of the assembly of the EET complex, we wanted to predict how many EET complexes are formed under different initial conditions. We focused, in addition to the assembly mechanism, also on the apparent reduced cell viability.<br> | | For the EET module, our goal was to investigate the carbon metabolism providing the electrons for the EET module. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Gadget">gadget section</a> of our wiki. Furthermore, in our modeling of the assembly of the EET complex, we wanted to predict how many EET complexes are formed under different initial conditions. We focused, in addition to the assembly mechanism, also on the apparent reduced cell viability.<br> |
| | For the landmine module, we tried to find a model which would be able to reproduce the response curves of both the landmine promoters, as found in [1]. <br> | | For the landmine module, we tried to find a model which would be able to reproduce the response curves of both the landmine promoters, as found in [1]. <br> |
| - | For the EET and landmine modules, we used deterministic modeling. For the curli module, we used a stochastic modeling approach, and considered the system at the gene, cell and colony level. At the colony levvel, we employed <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#PercolationTheory">percolation theory</a> in order to predict if a conductive path between the two electrodes arise at a certain point in time and to predict at which time this happens. Our application of percolation theory to describe the formation of a conductive biological network represents a novel approach that has not been used in the literature before. | + | For the EET and landmine modules, we used deterministic modeling. For the curli module, we used a stochastic modeling approach, and considered the system at the gene, cell and colony level. At the colony levvel, we employed <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#PercolationTheory">percolation theory</a> in order to predict if a conductive path between the two electrodes arise at a certain point in time and to predict at which time this happens. Our application of percolation theory to describe the formation of a conductive biological network represents a novel approach that has not been used in the literature before. |
| | </p> | | </p> |
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| | <p> | | <p> |
| - | We used Matlab for most of the calculations; the scripts we made can be found in the <a href=" https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/CodeRepository"> code repository</a>. We had great interactions with the Life Science and Microfluidics departments, which for the conductive curli module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/curli/integration">here</a>, for the EET module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET/integration">here</a> and for the landmine detection module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/landmine/integration">here</a>. | + | We used Matlab for most of the calculations; the scripts we made can be found in the <a href="/Team:TU_Delft-Leiden/Modeling/CodeRepository"> Code Repository</a>. We had great interactions with the Life Science and Microfluidics departments, which for the conductive curli module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/curli/integration">here</a>, for the EET module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET/integration">here</a> and for the landmine detection module can be read <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/landmine/integration">here</a>. |
| | </p> | | </p> |
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| - | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling#CurliMod"> | + | <a href="/Team:TU_Delft-Leiden/Modeling/Curli"> |
| | <p>Curli Module</p> | | <p>Curli Module</p> |
| | </a> | | </a> |
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| - | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling#EETMod"> | + | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET"> |
| | <p>EET Module</p> | | <p>EET Module</p> |
| | </a> | | </a> |
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| | <li> | | <li> |
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| - | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling#FBA"> | + | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/FBA"> |
| | <p> Flux Balance Analysis of the EET Module</p> | | <p> Flux Balance Analysis of the EET Module</p> |
| | </a> | | </a> |
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| | <li> | | <li> |
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| - | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling#DeterministicMod"> | + | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/Deterministic"> |
| | <p> Deterministic Model of EET Complex Assembly</p> | | <p> Deterministic Model of EET Complex Assembly</p> |
| | </a> | | </a> |
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| | </ul> | | </ul> |
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| - | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling#LandmineMod"> | + | <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine"> |
| | <p>Landmine Module</p> | | <p>Landmine Module</p> |
| | </a> | | </a> |
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| | </div> | | </div> |
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| - | <a name="CurliMod"></a>
| + | <h3> References </h3> |
| - | <h3>Curli Module </h3> | + | |
| - | <p><i> For more information, see our entire section about <a href="/Team:TU_Delft-Leiden/Modeling/Curli">the conductive curli module </a></i>.</p>
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| - | <p>
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| - | The goal of our project for the conductive curli module is to produce a biosensor that consists of <i>E. coli</i> that are able to build a conductive biofilm, induced by any promoter, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Gadget">gadget section</a> of our wiki and the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET">extracellular electron transport (EET) module</a>. The biofilm consists of curli containing His-tags that can connect to gold nanoparticles, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/curli">conductive curli module</a>. When the curli density is sufficiently high, a dense network of connected curli fibrils is present around the cells. Further increasing the amount of curli results in a conductive pathway connecting the cells, thereby forming conductive clusters. Increasing the amount of curli even further, sufficiently curli fibrils are present to have a cluster that connects the two electrodes and thus have a conducting system. <br>
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| - | The goal of the modeling of the curli module is to prove that our biosensor system works as expected and to capture the dynamics of our system. So, we want to answer the question: "Does a conductive path between the two electrodes arise at a certain point in time and at which time does this happen?" However, we not only want to answer the question if our system works as expected qualitatively, but we also want to make quantitative predictions about the resistance between the two electrodes of our system in time.
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| - | </p>
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| - | To capture the dynamics of our system, we have implemented a three-layered model, consisting of the gene level layer, the cell level layer and the colony level layer:
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| - | <ul>
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| - | <li>
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| - | At the gene level, we calculate the curli subunits production rates and curli subunit growth that will be used in the cell level.
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| - | </li>
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| - | <li>
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| - | At the cell level, we use these production and growth rates to calculate the curli growth in time, which we will use at the colony level.
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| - | </li>
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| - | <li>
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| - | At the colony level layer, we determine if our system works as expected, ie. determine if a conductive path between the two electrodes arises at a certain point in time and at which time this happens. We also determine the change of the resistance between the two electrodes of our system in time.
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| - | </li>
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| - | </ul>
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| - | </p>
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| - | A figure of our three-layered model is displayed below.
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| - | </p>
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| - | <h3>Click in the figure to move to the corresponding page.</h3>
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| - | <figure>
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| - | <img src="https://static.igem.org/mediawiki/2014/f/fa/TU_Delft_2014_ModellingFigureCurli_small.png" width="800" height="920" usemap="#ModelMap">
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| - | <map name="ModelMap">
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| - | <area shape="rect" coords="0,0,800,296" href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Gene" alt="Gene level">
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| - | <area shape="rect" coords="0,296,800,592" href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Cell" alt="Cell level">
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| - | <area shape="rect" coords="0,592,800,920" href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Colony" alt="Colony level">
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| - | </map>
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| - | <figcaption>
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| - | Figure 1: A schematic view of our model, which is a three-layered model. Each layer determines characteristic parameters for the layer above it. At the gene level, we calculate the curli subunits production rates. At the cell level, we use these production rates to calculate the curli growth in time. At the colony level, we use the curli growth in time to determine the change of the resistance between the two electrodes of our system in time.
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| - | </figcaption>
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| - | We start with the modeling of the gene expression of proteins involved in the curli formation pathway at the gene level. In the constructs we made in the wet lab, CsgA is continuously being produced and the CsgB gene is placed under the control of a landmine promoter, activated by either TNT or DNT, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/WetLab/landmine">Landmine Detection Module</a>. So, when the cells get induced by TNT or DNT, CsgB protein production will get started and CsgA will already be present in the system, as CsgA is continuously being produced. We first modeled this system by constructing an extensive gene expression model of the curli formation pathway. Subsequently, we simplified this model, so less parameters were needed. <br>
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| - | Based on the simplified model, we made a plot of the curli growth as function of time for different initial concentrations of \(CsgA_{free}\), see figure 2. We conclude the following from this figure: </p>
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| - | Firstly, as expected, curli growth stabilizes to a rate equal to \(p_{A}\) after approximately 2 hours, independent of the initial concentration of \(CsgA_{free}\). The width of this peak is determined by the product \( k p_B\), where k is the production rate of curli and \( p_B\) is the production rate of CsgB proteins.
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| - | </li>
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| - | <li>
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| - | Secondly, increasing the initial concentration of \(CsgA_{free}\), increases the height of the peak. Even with zero initial \(CsgA_{free}\) concentration, a small peak can be found at one hour. This is a consequence of \(CsgA_{free}\) build-up when the CsgB concentration is still very small.
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| - | </li>
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| - | Thirdly, during the first two hours, few CsgB proteins are present in the system. We therefore expect that the length of the curli fibrils that started in the first few hours are much longer than the fibrils that started at later times.
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| - | </li>
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| - | </ul>
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| - | <figure>
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| - | <img src="https://static.igem.org/mediawiki/2014/e/e9/Delft2014_DifferentA0.png" width="80%" height="80%">
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| - | <figcaption>
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| - | Figure 2: The curli subunit growth in units per second for various initial concentrations \( A_0 \) of CsgA as function of time. Initial concentrations that equal 0, 5, 10 or 15 hours of CsgA production are shown.
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| - | </figcaption>
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| - | </figure>
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| - | Using the growth rate of curli and production of CsgB protein as function of time obtained from the gene level model, the conductance as a function of time can be computed for the cell. We obtained an analytical expression for \(\rho_{curli}\), which represents the density of curli fibrils around the cell. We have fitted the function
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| - | $$ \rho_n = C_{1_n} e^{-\frac{r}{C_{2_n}}} + C_{3_n} e^{-\frac{r}{C_{4_n}}} \tag{1}$$
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| - | to our curli density curves at each time \( n \), see figure 3 the red line. At first, we tried to fit our data to only one exponential term (green line). It can clearly be seen in the figure that this does not adequately capture the dynamics of the curve. However, equation 1 gives a very good fit to the curli density curves at each time \( n \). The reason for fitting such a simple function is that, in the colony level, we need to quantify the conductance between the cells. The integral for this rather complicated and we need an analytical function for \(\rho_{curli}\) to analytically solve this integral. <br>
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| - | We also calculated the conductive radius of the cell as a function of the radius, see figure 4. The conductive radius is the largest radius where \(\rho_{curli}\) is bigger than a certain threshold of curli density. We use the conductive radius in the colony level to determine when a conductive path between the two electrodes of our system arises.
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| - | </p>
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| - | <figure>
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| - | <img src="https://static.igem.org/mediawiki/2014/3/3f/TUDelft_2014_FittingCurli.png" width="80%" height="80%">
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| - | <figcaption>
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| - | Figure 3: Blue line: Right behind the red line, at t=5 hr the mean of all density curves. Green line: a weighted fit of \( \rho_n = C_{1_n} e^{-\frac{r}{C_{2_n}}} \). Red line: A fit \( \rho_n = C_{1_n} e^{-\frac{r}{C_{2_n}}} + C_{3_n} e^{-\frac{r}{C_{4_n}}} \) to the blue line.
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| - | </figcaption>
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| - | <img src="https://static.igem.org/mediawiki/2014/e/e1/TUDelft_2014_cellradius.png" width="70%" height="70%">
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| - | <figcaption>
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| - | Figure 4: The green lines are the conductive radius plotted versus the time for 100 cells with a critical density of \( \rho_{crit}=1204 \) curli subuntis \( \mu m ^{-3} \). The orange red represents the mean conductive radius and the dark blue lines represent two standard deviations from the mean.
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| - | </figcaption>
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| - | An illustrative view of what our cell looks like during the adding of curli subunits is shown in figure 5.
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| - | <img class="theimage" src="https://static.igem.org/mediawiki/2014/e/e3/TU_Delft_2014_Curli_picturestill.png" alt="meh" width="80%" height="80%"/>
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| - | <img class="theimage2 hidden" src="https://static.igem.org/mediawiki/2014/3/37/TU_Delft_2014_Curli_picture.gif" alt="meh" width="80%" height="80%"/>
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| - | <figcaption>
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| - | Figure 5: Schematic view of our cell (black sphere centred at x=y=z=0) with growing curli fibrils. The wires represent the curli fibrils. <b> Click to play!</b>
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| - | Now that we determined values for \(\rho_{curli}\) and \(r_{cond}\) at the cell level, we can finally predict if our system works as expected and capture the dynamics of our system. Firstly, we want to prove that our system works as expected. So, we want to predict if a conductive path between the two electrodes arise at a certain point in time and at which time this happens. Secondly, we not only want to answer the question if our system works as expected with a yes or no answer, but we also want to make quantitative predictions about the resistance between the two electrodes of our system in time. We do this by modeling the curli growth on the colony level; each cell is now visualized and has curli growth. Now, we have come up with two different approaches:<ul>
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| - | Firstly, we let the cells increase their conductive radius in time, according with our findings on the cellular level (figure 4). A connection is created from one electrode to the other electrode when there is a conductive path between them. Conductive paths consists of cells that have a connection between each other; cells connect when there is an overlap between their conductive radius. This problem is very similar to problems in <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#PercolationTheory">percolation theory</a>. From this, we can make conclusions about how our system works in an experimental setting.
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| - | </li>
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| - | Secondly, we also want to make quantitative predictions about the resistance between the two electrodes of our system in time. Therefore, we used <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#GraphTheory">graph theory</a> to translate the cells on the chip to a graph and used an algorithm from graph theory to calculate the resistance between the two electrodes. The conductance between the cells is computed from an integral and is equal to:
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| - | $$ \sigma (y) = \ 2 \pi \left( C_{1}^2 C_2 e^{-\frac{y}{C_2}} + C_{3}^2 C_4 e^{-\frac{y}{C_4}} + \frac{4 C_{1}C_3 C_2^2 C_4^2}{y \left( C_2^2 - C_4^2 \right)} \left( e^{-\frac{y}{C_2}} -e^{-\frac{y}{C_4}} \right) \right) \tag{1}$$
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| - | Using the first approach, a simulation of our resulting model is shown in figure 6. Percolation is computed by applying an algorithm that can find clusters of connected cells. When one of the clusters connects both electrodes, there is percolation.
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| - | <img class="theimage" src="https://static.igem.org/mediawiki/2014/1/1d/TU_Delft_2014_model_curli_colony_static.png" alt="meh" width="100%" height="100%"/>
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| - | <img class="theimage2 hidden" src="https://static.igem.org/mediawiki/2014/9/9f/TU_Delft_2014_model_curli_colony.gif" alt="meh" width="100%" height="100%"/>
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| - | <figcaption>
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| - | Figure 6: NorthWest: A visual representation of our cells on the plate. The circles represent the cells with an increasing conductive radius. In this simulation there are 5000 cells present on a chip of 500µmx500µm. NorthEast: A spy matrix of 5000x5000 where the blue dots represent connections between the individual cells. A blue dot on position x,y means that cell x is connected with y. Each cell is connected to itself (diagonal). At the point of percolation, \( \approx 0.1 \% \) of the matrix is connected, meaning that each cell is on average connected to 5 others. SouthWest: Each square of nxn represents a cluster of n connected cells. The squares are sorted from small to large. SouthEast: This figure shows the largest cluster of cells in different colors. <b> Click to play!</b>
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| - | We simulated our resulting model 100 times and for each point in time we checked the chance of percolation without variation in \(r_{cond}\) (yellow line in figure 7) and with cellular variation in \(r_{cond}\) (blue line in figure 7). Fortunately, the blue and yellow lines are very similar. This means that cellular variation has little influence on the chance of percolation at each point in time. Therefore, the results of our model are robust to cellular variation and it is likely that many factors that could increase the cellular variation, e.g. different CsgA or CsgB protein production rates, are relatively unimportant.
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| - | <img src="https://static.igem.org/mediawiki/2014/d/dc/TUDelft_2014_500x500ChipResults.png" width="60%" height="60%">
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| - | Figure 7: The chance of percolation with 5000 cells on a 500x500 \(\mu m \) chip. as function of time. The results are from 100 simulations. The yellow line represents the chance of percolation where all the cells have the same conductive radius. The blue line is the same simulation, but all cells have slightly different conductive radii. Note how there is no notable difference between the two.
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| - | As we want our system to be usable as a biosensor, it has to be strongly dependent on the analyte concentration, and therefore the CsgB production rate. From figure 8, we see that there are very distinguishable difference for different CsgB production rates. First of all, the moment of percolation differs a lot. Equally important, the transition from no percolation to percolation is much less sharper.
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| - | <img src="https://static.igem.org/mediawiki/2014/0/02/TUDelft2014_Percolation_InductionDifferences.png" width="60%" height="60%">
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| - | Figure 8: The change of induction for t=0:10 hours, when cellular differences are included in the cell level for different induction strengths. The orange line is created by reducing the promoter strength of the cyan line (\(p_B = 1.3 \cdot 10^{-13} M/s \) ) by 50%.
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| - | <p>
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| - | Using the second approach, we have calculated the conductance as function of time for different dimensions of our plate. We varied the distance between the electrodes between 210, 460 and 960 \( \mu m \). The length of the electrodes is kept at \( 500 \mu m\). The result is shown in figure 9.
| |
| - | </p>
| |
| - |
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/c/c5/TUDelft2014_Colony_DifferentSizes.png" width="80%" height="80%">
| |
| - | <figcaption>
| |
| - | Figure 9: The conductance of our system as function of time, using the results from the gene and the colony level. Different simulations have been done with different chip sizes. The length of the chips is in all cases \( 500 \mu m \). The distance between the electrodes is varied from \( 210 \mu m \) (green lines) to \( 460 \mu m \) (red lines) and \( 960 \mu m \) (blue lines). There are multiple lines for the green and red lines as we repeated the simulations multiple times. However the simulation for when the electrodes were \( 960 \mu m \) apart was only performed once.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | Another parameter we investigated is the influence of cell density on the conductivity of the system. From percolation theory we have learned that this has a strong influence on the moment of percolation. The results are shown in figure 10.
| |
| - | </p>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/f/ff/TUDelft2014_Colony_CellDens.png" width="80%" height="80%">
| |
| - | <figcaption>
| |
| - | Figure 10: The conductance of our chip ( \( 500\mu m \ by \ 500\mu m \) as function of time. Two different cell densities have been simulated. The red lines show simulations with a cell density of \( 2 \cdot 10^4 cells / mm^2\). The blue lines show the results with a cell density of \( 2.4 \cdot 10^4 cells / mm^2\)
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | The most important question of all is: Will our system work, and under what conditions? To answer this question we have done the exact same simulation for the gene level and the cell level as elsewhere, except with the only difference that we halved the promoter strength of CsgB. This simulates less CsgB protein production, which corresponds to less TNT/DNT present in the system. The results are shown in figure 11.
| |
| - | </p>
| |
| - |
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/6/6d/TUDelft2014_Colony_ActivationStrength.png" width="80%" height="80%">
| |
| - | <figcaption>
| |
| - | Figure 11: The conductance of our chip ( \( 500\mu m \ by \ 500\mu m \) as function of time. Two different activation strengths have been simulated. The red lines (same as in figure 6 and 7) show a 100% activated CsgB promoter. The blue lines show the results for a promoter that is activated for 50%.</figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | Based on the above three figures, there are a couple of recommendations we have for the design of the chip:
| |
| - | <ul>
| |
| - | <li>
| |
| - | Based on figure 6, we recommend to decrease the distance between the electrodes. This will increase the conductance without increasing the uncertainty. From the shape of the curve, we expect that we do not have to wait very long (only a couple of hours) to do a measurement. After a steep increase in conductance, the increase in conductance will be relatively small in time. Furthermore, the uncertainty due to the placement of our cells increases in time.
| |
| - | </li>
| |
| - | <li>
| |
| - | Based on figure 7, we recommend high cell density for increased signal strength of our system. However, it is crucial that the cell density is kept constant throughout the measurement. Cell density influences the conductance significantly and when the cell density is not kept constant, it will influence the conductance measurements in such a way that an increase or decrease in conductance can not only be attributed to an increase or decrease in DNT any longer.
| |
| - | </li>
| |
| - | <li>
| |
| - | From figure 8, we learned that we have to be very careful with our measurement time in order to be able to draw conclusions about the concentration of TNT/DNT. The influence of the induction strength of the CsgB promoter is very small and its influence decreases after the initial amount of CsgA protein have formed curli. A recommendation for the wet lab is to increase the waiting time prior to induction of the promoter and thereby increasing the initial amount of CsgA protein. This will increase the relative differences in conductance between different induction strengths of the CsgB promoter. In our model, this increase in relative differences in conductance happens between 0 and 2.5 hours. <br>
| |
| - | The time this increase in relative differences in conductance happens, is strongly dependent on the parameter k in our <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Curli/Gene#simplifiedgenelevel">simplified gene model</a>. For our model, we could fit this parameter to conductance curves obtained in the wet lab. Measuring conductance until observing a linear increase in time will give the most useful information for obtaining the inducer concentration, as the time of this transition depends on the strength of induction.
| |
| - | </li>
| |
| - | </ul>
| |
| - | </p>
| |
| - |
| |
| - | <a name="EETMod"></a>
| |
| - | <h3>EET Module </h3>
| |
| - | <p><i> For more information, see our entire section about <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET">the EET Module</a>. This module consists of two separate sections, <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/FBA">Flux Balance Analysis of the EET Module</a> and <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/Deterministic"> Deterministic Model of EET Complex Assembly</a>.</i></p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <a name="FBA"></a>
| |
| - | <h4> Flux Balance Analysis of the EET Module </h4>
| |
| - | <p><i> For more information, see our entire section about <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/FBA">Flux Balance Analysis of the EET Module</a></i>.</p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | In the wet lab, we integrated the Extracellular Electron Transport (EET) module of <i>S. oneidensis</i> into <i>E. coli</i>, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET">extracellular electron transport (EET) module</a>. For the modeling of the EET module, we wanted at first to gain insight in the consequences of the integration of the EET module into <i>E. coli</i>. To achieve this, we simulated the cell metabolism of <i>E. coli</i> including the EET module using the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#FBATheory">Flux Balance Analysis (FBA) method</a>. Our goal was to investigate the carbon metabolism providing the electrons for the EET module, see <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET/theory#CM">Carbon Metabolism and Electron Transport</a>. Also, we want the EET pathway used by the cells in order to have a measurable electrical signal for our biosensor, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Gadget">gadget section</a> of our wiki.
| |
| - | </p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | From the FBA method, we conclude that in aerobic conditions the cell does not use the EET pathway, but oxygen gets reduced instead, as it is a stronger oxidizing agent. However, in anaerobic growth the cell does use the EET pathway to export electrons out of the cell. When the cell is grown on glucose, the growth rate will be higher than when the cell is grown on D-lactate. <br>
| |
| - | We also conclude that in an experimental setting the EET pathway has a higher chance of being used when the cells are grown on D-lactate as the EET pathway is necessary in order for the cells to grow, while when grown on glucose and the EET pathway is turned off (represented by \(0 \ mmol \ (gDW)^{-1} \ hr^{-1}\) (per gram dry weight per hour) maximum EET flux) growth is still possible, see figure 2. From Flux Variability Analysis (FVA) we conclude that for maximum growth for each specific combination of carbon source uptake flux and maximum EET flux, only one possible EET flux is possible for both growth on glucose and growth on D-lactate, namely the EET flux shown in figure 2.
| |
| - | </p>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/9/9b/TUDelft_2014_Phase_plane%28anaerobe%29_opt_growth_v2.png" width="80%" height="80%">
| |
| - | <figcaption>
| |
| - | Figure 2: Above: Phenotypic phase planes for growth rate, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for growth. The left panel display growth on glucose, the right panel growth on D-lactate. Green means a low growth rate, yellow means a high growth rate. Regions indicated by I correspond to no growth, regions indicated by II correspond to carbon source-limited growth, regions indicated by III correspond to carbon source-limited and maximum EET flux-limited growth. Below: Phenotypic phase planes for EET flux, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for growth. The left panel display growth on glucose, the right panel growth on lactate. Green means a low EET flux, yellow means a high EET flux. Regions indicated by I correspond to no EET flux (and no growth), regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to maximum EET flux-limited EET flux.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | As performing the FBA method while maximizing the EET flux yielded no growth, we wondered if there are pathways possible that would yield growth. So, we performed FVA, the results can be found in figure 3. From this figure, we conclude that when maximizing the EET flux, there are pathways possible that yield growth, as the figure displays the difference between the optimized maximum value and the optimized minimum value of growth. We see that this value is not equal to zero everywhere in the figure, thus there are multiple pathways possible when maximizing EET flux that all yield different values for growth. Note that the EET flux is 2.8 times higher and 2 times higher in comparison to maximizing for growth rate, for glucose and D-lactate as a carbon source, respectively.
| |
| - | </p>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/0/04/TUDelft_2014_Growth_diff_phase_plane%28anaerobe%29_opt_EET_v2.png" width="80%" height="80%">
| |
| - | <figcaption>
| |
| - | Figure 3: Above: Phenotypic phase plane for EET flux, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for EET flux. The left panel display growth on glucose, the right panel growth on D-lactate. Green means a low EET flux, yellow means a high EET flux. Regions indicated by I correspond to no EET flux, regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to maximum EET flux-limited EET flux. Below: Phenotypic phase planes for growth rate, related to the maximum EET flux and carbon uptake flux, under anaerobic conditions, optimized for EET flux. The left panel display growth on glucose, the right panel growth on D-lactate. Both panels give the difference between the optimized maximum value and the optimized minimum value of growth. Green means a low growth rate, yellow means a high growth rate. Regions indicated by I correspond to no growth, regions indicated by II correspond to carbon source-limited EET flux, and regions indicated by III correspond to carbon source-limited and maximum EET flux-limited growth.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | From figures 2 and 3 we conclude that there are different regions in which the cell can operate. In an experimental setting, it can be investigated in which region the cell actually operates and if it maximizes its growth rate or its EET flux. To be able to do this, the experimental observed pathway has to be compared to the possible pathways when maximizing the EET flux and to the pathway when maximizing the growth rate. From these regions, it can be deduced if the experimentally observed EET flux and growth rate are carbon source limited or limited by the maximum possible EET flux. <br>
| |
| - | Finally, we investigated an extended model of <i>E. coli</i> metabolism. This model contains, in contrast to the previously used core model, L-lactate as a metabolite. Using the extended model, we found that for glucose and D-lactate as carbon sources, the maximized growth rate agreed quite well to the previous analysis's using the core model. Using L-lactate as a carbon source, we conclude that a steady state solution in which <i>E. coli</i> can grow on L-lactate and use the EET pathway is not possible. A possible way to obtain information about the EET flux when the cells are not in steady state as observed by Goldbeck <i>et al.</i> [2], would be by the use of dynamic flux balance analysis (dFBA), which can also model the dynamics of a system before it reaches steady state [3].
| |
| - | </p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <a name="DeterministicMod"></a>
| |
| - | <h4>Deterministic Model of EET Complex Assembly</h4>
| |
| - | <p><i> For more information, see our entire section about <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/EET/Deterministic"> Deterministic Model of EET Complex Assembly</a></i>.</p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | The EET module consists of three proteins: MtrA, a cytochrome on the inside of the outer membrane, MtrB, a β-barrel protein located in the outer membrane, and MtrC, another cytochrome, located on the cell surface. This complex enables the cell to transport electrons from the cytoplasm of the cell to the extracellular environment, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Project/Life_science/EET">extracellular electron transport (EET) module</a>. <br>
| |
| - | The assembly of the trans-membrane EET complex depends on many factors other than transcriptional and translational control, as it requires a large amount of post-translational modifications. We set up a simplified model of this assembly process, largely based on section 1.3 of the thesis of Jensen [4]. With the use of <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#DeterministicTheory">deterministic modeling methods</a>, our goal is to predict how many EET complexes are formed under different initial conditions. <br>
| |
| - | In our modeling of the assembly of the EET complex, in addition to the assembly mechanism, we also focus on the apparent reduced cell viability. Jensen [4] proposes two possible explanations for this: the formation of cytosolic aggregates and reduced membrane integrity due to the high amount of trans-membrane protein complexes.
| |
| - | </p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | We constructed two different models, one based on an extensive model of EET complex assembly, which we based upon the work of Jensen [4], the other based on a very much simplified model of EET complex assembly, which includes only the most fundamental reactions of the assembly process. <br>
| |
| - | From the extensive model, we concluded that the amount of δ-ALA (and therefore heme) is rate limiting and not the amount of available binding sites. We therefore predict that adding extra δ-ALA to the cells will increase the amount of EET complexes, see figure 4. This effect is also observed by Jensen [4].
| |
| - | </p>
| |
| - |
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/5/54/TUDelft_2014_EETvsdALA.png" width="70%" height="70%">
| |
| - | <figcaption>
| |
| - | Figure 4: The final concentration of EET complexes as a function of the initial concentration of δ-ALA.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | Although the extensive model proved to be valuable in the investigation of the mechanism which assembles the EET pathway, it is not suitable for the quantitative prediction of the amount of EET complexes. The most important reason for this is the large number of unknown parameters. Therefore we decided not to aim at enhancing this model, and rather set up a more simplified model.
| |
| - | </p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | To sidestep the difficulties experienced with the extensive model of the assembly of the EET complex, we reduced the system to a bare minimum. For this simplified model, we only included the production of MtrCAB, the formation of cytosolic aggregates and the assembly of the EET complex. <br>
| |
| - | The simplified model does not represent all the actual mechanisms of the EET complex assembly process that happens in nature, but it is able to match the experimental data of Goldbeck <i>et al.</i> [2], see figure 5. A maximum at low promoter strength is clearly visible. This corroborates the statement in [2] that maximum promoter strength does not result in maximum EET concentration due to reduced cell viability. </p>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/7/76/TUDelft_2014_EETvsk1.png" width="70%" height="70%">
| |
| - | <figcaption>
| |
| - | Figure 5: A plot of the end concentration of EET versus promoter strength using the parameters in table 3. The red circles correspond to the data points shown in figure 4a of Goldbeck et al. [2].
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | This is a confirmation that our assumptions concerning cell viability might be correct. Therefore, we conclude that reduced cell viability because of the implementation of the EET pathway is the consequence of three molecular processes, namely firstly, the amount of EET complexes reduces the transcription and translation of the MtrCAB proteins due to reduced membrane integrity, secondly, the forming of MtrCAB aggregates and thirdly, the clogging of the secretion system transporting the MtrCAB complexes.
| |
| - | </p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <a name="LandmineMod"></a>
| |
| - | <h3>Landmine Module </h3>
| |
| - | <p><i> For more information, see our entire section about <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Landmine">the landmine detection module</a></i>.</p>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <p>
| |
| - | An important part of our iGEM project is a promoter sensitive to DNT/TNT. We will use two promoters that are sensitive to DNT/TNT, namely <i>ybiJ</i> and <i>ybiFB2A1</i>, in our project, see the <a href="https://2014.igem.org/Team:TU_Delft-Leiden/WetLab/landmine">landmine detection module</a>. Of these promoters, not much is known other than the fact that they have a DNT/TNT-dependent response curve. Our goal was to find a model which would be able to reproduce the response curves of both promoters. To achieve this, we constructed two different models, both using <a href="https://2014.igem.org/Team:TU_Delft-Leiden/Modeling/Techniques#DeterministicTheory">deterministic modeling methods</a>. One model is based on a simple binding model of DNT to the promoter, the other is based on cooperative binding of DNT to the promoter. <br>
| |
| - | When based on the simple binding model, fits of promoter activation with respect to DNT concentration to the experimental data of [1] did not yield good results. However, when the fits were based on the cooperative binding model, we were able to match the experimental data in [1] really well, see figure 1. <br>
| |
| - | From the fits shown in figure 6, it is clear that both the standard and cooperative activation model fail to describe the experimental data we obtained. This might have several reasons. Firstly, the response ratio of our measurements is very small compared to the measurements in [1]. Secondly, our experimental data suggest a detrimental effect of induction with high DNT concentration. This effect is not described in [1] and we don't know its reason. It is therefore not included in our model. Thirdly, both the data set from [1] and our experimental data set are small compared to the amount of parameters. This makes finding the right model difficult. <br>
| |
| - | To improve the promoter activation model, a larger and more consistent data set has to be obtained. We need to conduct fluorescence measurements over a wide range of DNT concentrations. Besides that, possible detrimental effects of its solvent (acytonitrile) have to be investigated. Also, the induction of the N genes with rhamnose might influence the measurements in an unexpected way. Doing all this is unfortunately not possible in the time span of this iGEM project.
| |
| - | </p>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/5/59/TUDelft_2014_model_fit_tnt_promoters_coop.png" width="90%" height="90%">
| |
| - | <figcaption>
| |
| - | Figure 1: Fits of the promoter activation model described by cooperative promoter activation to the data of [1]. The left panel shows the fit for the jbiJ promoter, the right panel the fit for the yqjFB2A1 promoter. For comparison, also the fits described by the simple binding model are displayed.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <figure>
| |
| - | <img src="https://static.igem.org/mediawiki/2014/6/6b/Delft2014_Model_fit_for_jbiJ_promoter_5.png" width="48%" height="48%">
| |
| - | <img src="https://static.igem.org/mediawiki/2014/e/e4/Delft2014_Model_fit_for_yqjFB2A1_promoter_6.png" width="48%" height="48%">
| |
| - | <figcaption>
| |
| - | Figure 6: Fits of the promoter activation model described by cooperative promoter activation and by the standard activation model to our experimental data. The left panel shows the fit for the jbiJ promoter, the right panel the fit for the yqjFB2A1 promoter.
| |
| - | </figcaption>
| |
| - | </figure>
| |
| - |
| |
| - | <br>
| |
| - |
| |
| - | <h3>References </h3>
| |
| | <p> | | <p> |
| | [1] S. Yagur-Kroll, S. Belkin <i>et al.</i>, “<i>Escherichia Coli</i> bioreporters for the detection of 2,4-dinitrotoluene and 2,4,6-trinitrotoluene”, Appl. Microbiol. Biotechnol. 98, 885-895, 2014. | | [1] S. Yagur-Kroll, S. Belkin <i>et al.</i>, “<i>Escherichia Coli</i> bioreporters for the detection of 2,4-dinitrotoluene and 2,4,6-trinitrotoluene”, Appl. Microbiol. Biotechnol. 98, 885-895, 2014. |
| | </p> | | </p> |
| | | | |
| - | <p>
| |
| - | [2] C.P. Goldbeck, H.M. Jensen <i>et al.</i>, “Tuning Promoter Strengths for Improved Synthesis and Function of Electron Conduits in <i>Escherichia coli</i>”, ACS Synth. Biol. 2, 150-159, 2013.
| |
| - | </p>
| |
| - |
| |
| - | <p>
| |
| - | [3] R. Mahadevan, J.S. Edwards & F.J. Doyle, “Dynamic Flux Balanace Analysis of Diauxic Growth in <i>Escherichia coli</i>”, Biophys. J. 83, 1331-1340, 2002.
| |
| - | </p>
| |
| - |
| |
| - | <p>
| |
| - | [4] H.M. Jensen, “Engineering <i>Escherichia coli</i> for molecularly defined electron transfer to metal oxides and electrodes”, PhD Thesis Chemistry UC Berkeley, 2013.
| |
| - | </p>
| |
| | | | |
| | </div> | | </div> |
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