Team:Toulouse/Modelling

From 2014.igem.org

(Difference between revisions)
 
(52 intermediate revisions not shown)
Line 1: Line 1:
 +
----
{{:Team:Toulouse/template/header-base}}
{{:Team:Toulouse/template/header-base}}
<html>
<html>
-
<style type="text/css">
+
<!--/* open Sans : fonnt Google*/-->
 +
 
 +
  <link href='http://fonts.googleapis.com/css?family=Open+Sans' rel='stylesheet' type='text/css'>
 +
 
 +
  <link href='http://fonts.googleapis.com/css?family=Open+Sans:400,600' rel='stylesheet' type='text/css'>
 +
 
 +
  <link href='http://fonts.googleapis.com/css?family=Open+Sans:800' rel='stylesheet' type='text/css'>
 +
 
 +
<!--/* CSS contenu*/-->
 +
 
 +
<style type="text/css">
 +
 
 +
  .title1{color:green; font-family:'Open Sans'; font-weight:600; font-size:24px;  margin:0 0 33px 0; border:none;}
 +
 
 +
  .title2{color:#5a6060; font-family:'Open Sans'; font-weight:600; font-size:18px; margin:0 0 30px 0; border:none;}
 +
 
 +
  .title2simple{color:#5a6060; font-family:'Open Sans'; font-weight:600; font-size:18px; margin:0 0 5px 0; border:none;}
 +
 
 +
  .title3{color:#7f8c8c; font-family:'Open Sans'; font-weight:400; font-size:16px; margin:0 0 20px 0; border:none;}
 +
 
 +
  .texte{color:#5a6060; font-family:'Open Sans'; font-size:14px; margin:0 0 50px 0; line-height:24px; text-align: justify;}
 +
 
 +
  .textesimple{color:#5a6060; font-family:'Open Sans'; font-size:14px; margin:0 0 0 0; line-height:24px; text-align: justify;}
.banniere{
.banniere{
-
background: url('http://2014.igem.org/wiki/images/d/d0/Template-igem2014-slide1.jpg') no-repeat center;
+
background: url('http://2014.igem.org/wiki/images/d/de/Banniere.jpg') no-repeat center;
-webkit-background-size: cover; /* pour Chrome et Safari */
-webkit-background-size: cover; /* pour Chrome et Safari */
-moz-background-size: cover; /* pour Firefox */
-moz-background-size: cover; /* pour Firefox */
Line 17: Line 40:
.banniere-content{
.banniere-content{
-
  background-color: rgba(46,204,113, 0.6);
+
  background-color: rgba(130,196,108, 0.7);
padding:28px 28px 0;
padding:28px 28px 0;
position:absolute;
position:absolute;
Line 36: Line 59:
font-size:16px
font-size:16px
}
}
 +
 +
/*content*/
 +
 +
.Title{
 +
    text-shadow: 1px 3px 3px rgba(70, 156, 133, 0.75);
 +
    color: #2CC23E;
 +
    font-size: 50px;
 +
    text-align: center;
 +
}
 +
 +
.Sub_title{
 +
    color: #2CC23E;
 +
    font-size: 30px;
 +
}
 +
 +
.Article {
 +
    text-align: justify;
 +
    text-indent:15px;
 +
}
 +
 +
a.Link {
 +
    font-size:10pt;
 +
    color :#A4A4A4;
 +
    text-decoration:none;
 +
}
 +
 +
a.Link:hover{
 +
    text-decoration:underline;}
 +
   
 +
p.legend{color:#5a6060; font-family:'Open Sans'; font-size:14px; margin:0 0 50px 0; line-height:24px; text-align: center;}
 +
 +
ol.list1{color:#5a6060; font-family:'Open Sans'; font-size:14px; margin:0 0 50px 0; line-height:24px;}
 +
 +
ul.list2{color:#5a6060; font-family:'Open Sans'; font-size:14px; margin:0 0 50px 0; line-height:24px;}
 +
 +
li.tree {
 +
  display : list-item;
 +
list-style-image: url(http://2014.igem.org/wiki/images/a/a7/388438arbrefleurs.png);
 +
}
 +
</style>
</style>
Line 43: Line 106:
   <div class="banniere-wrapper" style="width:960px; height:100%; margin: 0 auto; position:relative;">
   <div class="banniere-wrapper" style="width:960px; height:100%; margin: 0 auto; position:relative;">
-
     <div class="attribution">
+
      
-
        <ul class="topnav" id="topnav" style="top:15px;">
+
-
                <li style="padding-right:0px"><a href="http://2014.igem.org/Team:Toulouse/Team" class="navlink" style="color:white;">ACKNOWLEGDEMENT<i style="padding-left: 10px;font-size: 14px;font-family: verdana;">></i> </a>
+
-
                    <ul class="subnav" style="background:none;">
+
-
                        <li class="lisimpledrop"><a href="http://2014.igem.org/Team:Toulouse/Team">Attribution</a></li>
+
-
                        <li class="lisimpledrop"><a href="http://igem.org/Team.cgi?year=2014&team_name=Toulouse">Sponsor</a></li>
+
-
                  </ul>
+
-
                </li>
+
-
        </ul>
+
-
    </div>
+
     <div class="banniere-content">
     <div class="banniere-content">
       <h2>Modeling</h2>
       <h2>Modeling</h2>
-
       <p>Proin sollicitudin nibh ut dapibus vulputate.</p>
+
       <p>To develop a predictive model</p>
     </div>
     </div>
   </div>
   </div>
Line 62: Line 116:
   <div class="fils-ariane" style="width:100%; height:60px; background:#ededed;">
   <div class="fils-ariane" style="width:100%; height:60px; background:#ededed;">
-
   <p style="margin:0 auto; color:#696969; width:960px; padding-top:20px; font-size:16px;"> Project&nbsp;&nbsp;&nbsp;>&nbsp;&nbsp;&nbsp;Spreading</p>
+
   <p style="margin:0 auto; color:#696969; width:960px; padding-top:20px; font-size:16px;">Results&nbsp;&nbsp;&nbsp;>&nbsp;&nbsp;&nbsp;Modeling
   </div>
   </div>
    
    
Line 69: Line 123:
       <div class="centering" style="padding-top: 85px; padding-bottom:40px;">
       <div class="centering" style="padding-top: 85px; padding-bottom:40px;">
-
<p>Fusce et fermentum nibh. Aliquam ornare venenatis odio vel interdum. Ut egestas elementum dolor, sit amet interdum metus gravida id. Morbi dictum commodo ipsum, eu maximus lectus pretium vel. Vivamus sit amet sem orci. Nulla leo ante, interdum id eros nec, rutrum suscipit sapien. Aenean posuere mauris a nisl laoreet congue. Sed aliquam vulputate risus, ut bibendum ligula consequat vel. Proin rhoncus orci eu massa dapibus elementum. Duis eu lacinia velit. Ut lacinia eu sem suscipit euismod. Proin sollicitudin nibh ut dapibus vulputate.
+
<p class="texte">
-
Quisque nec tempus mi. Sed sit amet justo tellus. Vestibulum pulvinar viverra felis sed aliquet. Suspendisse sed turpis eu justo finibus dictum quis vel nisi. Mauris quis imperdiet sem. Aenean scelerisque commodo orci a varius. Integer turpis odio, elementum a venenatis vitae, ultricies quis quam. Phasellus cursus ligula vel ex rutrum placerat. Curabitur dictum nisi risus, eu finibus ex fringilla vitae. Aenean consequat, ante elementum viverra laoreet, arcu nulla aliquam velit, pretium imperdiet neque felis a diam. Suspendisse ultricies nisi non ex finibus pharetra ac et ipsum. Nulla vulputate dolor urna, et semper nisl tempor vitae. Sed cursus dolor ut consequat posuere.
+
 
-
Ut at massa quam. Vestibulum rutrum dapibus tortor ut facilisis. Pellentesque condimentum quam id ante varius imperdiet. Quisque mauris urna, finibus in mauris vel, laoreet volutpat libero. Aliquam erat volutpat. Vivamus non imperdiet nibh. Sed fringilla tristique metus, non fermentum quam tincidunt non. Praesent dictum faucibus massa, eu bibendum sapien iaculis in. Ut porta tortor eu elementum interdum. Vivamus non tempor ligula. In accumsan ligula non ligula aliquam, at dictum dolor cursus. Ut iaculis ultrices ex et faucibus. Praesent bibendum sagittis elit, eget ultricies dolor imperdiet id.
+
Modeling is a tool used to simplify and study systems. It helps us to predict behavior of biological systems using bibliographic or experimental data.</br>
 +
 
 +
The following modelisation focuses on the development of a bacterium in trees. The bacterial growth in trees seems to be unknown, thus we must infer <i>Bacillus subtilis'</i> behavior.</p>
 +
 
 +
<p class="title1">
 +
Bacterial Growth
 +
</p>
 +
 
 +
<p class="title2">
 +
Aim
 +
</p>
 +
 
 +
<p class="texte">
 +
<i>Bacillus subtilis</i> is a tree endophyte strain. A study showed that <i>B. subtilis</i> could develop and fully colonize a tree, reaching a concentration of 10<sup>5</sup> cells per gram of fresh plant. We need to know in which conditions the growth of <i>B. subtilis</i> is optimum in a tree and if the weather can stop its development during winter. Therefore we decided to work on the growthof <i>B. subtilis'</i> in function of the temperature during the year.
 +
<br>Modeling bacterial growth in a tree section generates some difficulties. We need to know the distance between two tree extremities (treetops and root) or the speed sap flow. However the flow of speed sap can vary with temperature during the day. The composition of sap also varies due to seasons and type of container (phloem, xylem). Furthermore a tree is not an homogeneous system: its roots, trunk and branches do not contain the same amount of sap and wood. <br>The average speed of the plane tree sap is 2.4 m/h, which means that in a day the sap of a 30 m tree will flow from one extremity to the other. We thus reduced the tree to a bioreactor.
 +
</p>
 +
<p class="texte">
 +
We make the following hypothesis:</p>
 +
<ol class="list1">
 +
<li>
 +
According to the publication of <b>Xianling Ji</b> (See References), after six months of <i>B. subtilis</i> growth in a tree, bacteria cells reach a concentration of 10<sup>5</sup> cells per gram of fresh plant. We assume that 10<sup>5</sup> cells/g is the maximum concentration.
 +
</li>
 +
<li>
 +
The composition of the phloem is stable. There is no effect of depletion of the medium.
 +
</li>
 +
<li>
 +
Only temperature impacts on bacterial growth.
 +
</li>
 +
<li>
 +
It is assumed that there is no leakage of cells.
 +
</li>
 +
</ol>
 +
 
 +
 
 +
<p class="title2">
 +
Method
 +
</p>
 +
 
 +
<p class="texte">
 +
An assessment of the <i>B. subtilis</i> growth in a similar sap was performed in laboratory conditions with optimum growth medium for <i>B. subtilis</i>. The composition sap used was the one from birch sap.<br>
 +
In these conditions, the growth rate µ is optimal. From this value we can extrapolate a growth curve as a function of temperature. We used the <b>cardinal temperature model</b>: </p>
 +
 +
<center style="margin-bottom:50px;"><img style="" src="http://2014.igem.org/wiki/images/8/85/Formules_Rosso.png" alt="cardinal temperature model"></center>
 +
 
 +
 
 +
<p class="texte">
 +
T: Temperature</br>
 +
µ<sub>opt</sub>: Optimal growth rate</br>
 +
µ: growth rate at temperature T</br>
 +
T<sub>max</sub>: Maximum temperature supported by bacteria</br>
 +
T<sub>min</sub>: Minimum temperature supported by bacteria</br>
 +
T<sub>opt</sub>: Optimum temperature for the growth</br></br>
 +
 
 +
    Necessary parameters for this function are minimun temperature T<sub>min</sub> and maximum temperature T<sub>max</sub>, optimal temperature for the growth T<sub>opt</sub> and optimal growth rate µ<sub>opt</sub>.</br>
 +
</br>
 +
    T<sub>min</sub>: 10°C</br>
 +
    T<sub>max</sub>: 52°C</br>
 +
    T<sub>opt</sub>: 37°C</br>
 +
    µ<sub>opt</sub>: 8.5968 cfu/d</br></br>
 +
 
 +
The optimal growth rate (µ<sub>opt</sub>) is obtained experimentally with a similar birch sap environment.</br>
 +
The growth rate is negative below 10°C (according to growth tests performed at 10°C and 4°C under similar conditions for the measurement of µ<sub>opt</sub>), survival rate after 24h was 0.3 % at 10°C and null at 4°C.<br>
 +
Conditions applied:</p>
 +
 
 +
<p class="texte">
 +
If<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">__</span>| T<= 4°C            -> µ = -1</br>
 +
<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">____</span>| 4°C<T<= 10°C      -> µ = -0.97</br>
 +
<span style="color:#FFFFFF; font-family:'Open Sans'; font-size:14px;">____</span>| T > 10°C          -> µ = f(T) with f(T) egal to cardinal temperature model.</p>
 +
 
 +
<center style="margin-top: -52px;"><img style="" src="http://2014.igem.org/wiki/images/b/b1/Plot_growth_rate.png" alt="Figure1"></center>
 +
<p class="legend">Figure 1: Bacterial growth (µ) as a function of temperature</p>
 +
 
 +
<p class="texte"> A logistic model developed by <b>Hiroshi Fujikawa</b> (See References) is used to study bacterial growth.</p>
 +
 
 +
<p class="legend">General logistics formulas:</p>
 +
<center style="margin:-44px 0 65px;"><img style="" src="http://2014.igem.org/wiki/images/c/c3/Form_general_fonction.png" alt="General logistics formulas"></center>
 +
 
 +
 
 +
<p class="texte">
 +
In our case, the growth rate µ depends on the temperature.  
 +
<br>N corresponds to the bacterial population, N<sub>min</sub> and N<sub>max</sub> are two asymptotes.
 +
<br>The parameter m is a curvature parameter. Larger m is, smaller is the curvature of the deceleration phase with the model.
 +
<br>The parameter n is a parameter related to the period lag. Larger n is, shorter is the period of lag.
 +
<br>
 +
<br>N<sub>min</sub> is slightly lower than N<sub>0</sub>. When N is small at the initial state (N = N<sub>0</sub>) <i>i.e.</i> N is close to N<sub>min</sub>, N<sub>min</sub>/N is almost equal to 1. Therefore the term (1-(N<sub>min</sub>/N)) is nearly 0 and the growth is very slow.
 +
<br>If N decreases until it reaches N<sub>min</sub>, the term (1-(N<sub>min</sub>/N)) is equal to 0. Therefore the growth is null.
 +
<br> Similarly when N is equal to N<sub>max</sub>, the term (1-(N/N<sub>max</sub>)) is equal to 0 and the growth is blocked.</br>
 +
 
 +
To overcome this, we worked under two conditions: positive and negative growth. Theses conditions can be translated in two equations. This leads to the writing of this model:</p>
 +
<center style="margin: 65px 0;"><img style="" src="http://2014.igem.org/wiki/images/f/f8/Form_part.png" alt="model"></center>
 +
 
 +
 
 +
 
 +
 
 +
<p class="texte">
 +
with n = 1 and m = 0.5</br></br>
 +
 
 +
The term (1-(Nmin/N)) is not taken into account when there is growth. <br>The term (1-(N/Nmax)) is not taken into account when there is bacterial decay.</br>
 +
Meteorological records of the Toulouse region during the years 2011-2013 are used to calculate average daily temperatures. Thus we can determine <i>B. subtilis</i> growth in a tree located in Toulouse during a year. This values are obtained for each day by the average on the highest and the lowest temperature.
 +
</br>
 +
 
 +
The density of green wood plane is about 650 kg/m³. The average diameter of the trunks of the concerned trees is about 0.80 m and they are 15 m high. This represents a volume of 30 m³. Therefore the weight of the trunk is 19.604 kg.
 +
We need to add to this weight the weight of branches, twigs, about 25% of leaves and about 15% of roots (<a href="http://www.guichetdusavoir.org/viewtopic.php?t=25895">source-FR</a>).
 +
</br>
 +
<!--pas compris ces deux dernières phrases-->
 +
The average weight of a tree plane is 27,446kg. We inoculated 10 mL of bacterial culture at 10<sup>9</sup>cfu/mL, <i>i.e.</i> 10<sup>10</sup> bacterial cells. This represents 3.64x10<sup>2</sup>cfu/g of fresh plant (N0).
 +
</p>
 +
 
 +
<center><img style="" src="http://2014.igem.org/wiki/images/5/53/Bacterial_growth.png" alt="Figure2"></center>
 +
<p class="legend">Figure 2: (<span style="color:#000000; font-family:'Open Sans'; font-size:14px;">black</span>) <i>Bacillus subtilis</i> growth curve during one year (N is cell quantity by g of fresh plant). (<span style="color:#FF0040; font-family:'Open Sans'; font-size:14px;">red</span>) average temperature. (<span style="color:#0101DF; font-family:'Open Sans'; font-size:14px;">blue</span>) threshold at 10°C.</p>
 +
 
 +
<p class="texte">
 +
In our model, growth starts only from 10°C, which happens between March and April. This period seems to be the most suitable to administer the strain in the tree. Starting in December the temperature decreases below 4°C, corresponding to the threshold below which bacteria starts to die.  
 +
</p>
 +
 
 +
<p class="title2">
 +
Discussion
 +
</p>
 +
 
 +
<p class="texte">
 +
In practice, temperature variations are certainly lower in trees than outside, especially if roots extend very deep. Composition of the tree sap must also intervene in the growth rate and nutrient content of sap is also temperature dependent. The effects of the decrease of the temperature in winter also induces a fall of the sap and this must also be involved in the disappearance of our strain in the tree. The period of <i>B. subtilis</i> growth is certainly affected by the change of temperature, the rise of sap in the trunk and sap composition variations. All these parameters can consequently slow-down or boost the growth rate.
 +
 
 +
The modeling work is done with the programming language 'R' script attached (See Annexe).
 +
</p>
 +
 
 +
<p class="title2">
 +
References
 +
</p>
 +
 
 +
 
 +
<ul>
 +
<li class="tree"><p class="texte">
 +
Xianling Ji, Guobing Lu, Yingping Gai, Chengchao Zheng,and Zhimei Mu. (2008) <b>Biological control against bacterial wilt and colonization of mulberry by an endophytic <i>Bacillus subtilis</i> strain.</b> FEMS Microbiol Ecol 65: 565–573.
 +
</li></p>
 +
<li class="tree"><p class="texte">
 +
A. Garnier. (1977) <b>Transfert de sève brute dans le tronc des arbres aspects méthodologiques et physiologiques.</b> Ann. Sci. Foresi. 34 (1): 17-45.
 +
</li></p>
 +
<li class="tree"><p class="texte">
 +
Heikki Kallio, Tuija Teerinen, Seija Ahtonen, Meri Suihko, and Reino R. Linko. (1989) <b>Composition and properties of birch syrup (<i>Betula pubescens</i>).</b> J. Agric. Food Chem 37 (1): 51–54.
 +
</li></p>
 +
<li class="tree"><p class="texte">
 +
L. Rosso, J. R. Lobry, and J. P. Flandrois. (1992) AN <b>Unexpected Correlation between Cardinal Temperatures of Microbial Growth Highlighted by a New Model.</b> J. theor. Biol. 162 : 447-463.
 +
</li></p>
 +
<li class="tree"><p class="texte">
 +
Hiroshi Fujikawa. (2010) <b>Development of a New Logistic Model for Microbial Growth in Foods.</b> Biocontrol of Science Vol 15: 75-80.
 +
</li></p>
 +
</ul>
 +
 +
<p class="title2">
 +
Annexe
 +
</p>
 +
 
 +
<p class="texte"> To download the script and the table <a href="http://2014.igem.org/wiki/images/0/01/Annexes.zip">Click Here</a></p>
 +
 
 +
 
</p>
</p>
Line 78: Line 286:
   <div class="page-nav" style="border-top:1px solid #cccccc; padding-top:40px; margin-top:40px;">
   <div class="page-nav" style="border-top:1px solid #cccccc; padding-top:40px; margin-top:40px;">
-
     <a href="http://2014.igem.org/Team:Toulouse/Project/Spreading" class="page-nav-right" style="width:447px; float:left; display:block;text-decoration:none; color:#666; font-size:18px;">Spreading
+
     <a href="http://2014.igem.org/Team:Toulouse/Result/experimental-results" class="page-nav-right" style="width:447px; float:left; display:block;text-decoration:none; color:#666; font-size:18px;">Experimental results
       <img src="http://2014.igem.org/wiki/images/2/26/Template-igem2014-img-arrowleft.png" style="display:block; padding-top:10px;"/>
       <img src="http://2014.igem.org/wiki/images/2/26/Template-igem2014-img-arrowleft.png" style="display:block; padding-top:10px;"/>
     </a>  
     </a>  
Line 92: Line 300:
   </div>
   </div>
-
  <div class="clear"></div>
+
<div class="page-nav-center" style="width:65px; float:left;">
 +
        </div>
 +
 
 +
    <a href="http://2014.igem.org/Team:Toulouse/Result/parts" class="page-nav-left" style="width:447px; float:right; display:block; text-align:right; text-decoration:none;
 +
color:#666; font-size:18px;">Parts</br>
 +
      <img src="http://2014.igem.org/wiki/images/e/ea/Template-igem2014-img-arrowright.png" style="display:block; float:right; padding-top:10px; " />
 +
    </a>
 +
 
 +
  <div class="clear"></div>
     </div>
     </div>

Latest revision as of 03:17, 18 October 2014