Team:Grenoble/Projet/Modelling

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<div  class="blocbackground" id="Modelling">
    <h1>Modelling</h1>
    <h1>Modelling</h1>
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<div  class="blocbackground">
 
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  <h2>Table of content</h2>
 
    <p>
    <p>
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  Our synthetic biology constructions feature tens of parameters and at this scale human brains can only guess how the whole system would work. We of course needed mathematical modelling in order to check the effectiveness of the genetic circuit.<br/><br/>
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The modelling team is responsible for:
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<ol>
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  In the particular case of our circuit and final use of the bacteria, the modelling team also had to give the specificities (size, number of bacteria, IPTG gradient specificities) of the measuring device we intend to produce.<br/><br/>
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<li><strong>Verifying that the designed genetic circuit elicits the desired behavior in <i>E coli.</i></strong>
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A deterministic model of the circuit has been developed in order to predict the dynamical
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  In the next pages we expose which algorithms we used for both deterministic modelling and stochastic modelling, explain our MATLAB scripts (available <a href="http://igemgrenoble-files.perso.sfr.fr/2011/MATLAB_Archives/">here</a>) and finally give the results of our simulations.<br/><br/>
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behavior of the circuit in the presence of a concentration gradient of IPTG and various
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concentrations of Mercury or aTc (anhydrotetracycline).</li>
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  <a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic" ><img class="icon" src="https://static.igem.org/mediawiki/2011/b/b4/Icon_deterministic.png"/></a>
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<li><strong>Providing specifications for the quantification device (size, number of bacteria, IPTG gradient).</strong>
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The apparition of the red line indicating the presence and quantity of Mercury or aTc is sensitive to
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fluctuations in the concentration of these molecules and IPTG. We took into account these fluctuations
 +
in a stochastic version of the circuit model, which we have used to determine the specifications of
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our device.</li>
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</ol>
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</p>
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    </div>
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<div  class="blocbackground" id="Content">
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<h2>Table of content</h2>
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<p>
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In the following pages, we detail the development of the deterministic and stochastic models,  
 +
together with their dynamical analysis. Solving numerically these systems required tricky calculations,
 +
since they evolve both in time and space. To help future teams with similar calculations, we explain
 +
in details the algorithms that were used and provide the scripts <a href="http://igemgrenoble-files.perso.sfr.fr/2011/MATLAB_Archives/">here</a>.
 +
The modelling results are described in the last section.<br/><br/>
 +
 +
For an introduction to the modelling of biological genetic circuit see our tutorials in the human practice
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section or  them here :
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<ul>
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<li>
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<a href="https://static.igem.org/mediawiki/2011/9/91/M_for_B.png">
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Modelling for biologist</a>
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</li>
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<li>
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<a href="https://static.igem.org/mediawiki/2011/5/54/B_for_M.png">
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Synthetic Biology for modellers</a>
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</li>
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</ul>
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<br/><br/>
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  <a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic" ><img class="icon" src="https://static.igem.org/mediawiki/2011/0/01/Bouton_model_construction.png"/></a>
     
     
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      <big><a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic" class="menu">Deterministic Modelling :</a></big><br/>
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      <big><big><a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic" class="menu">Construction of the model :</a></big></big><br/>
       
       
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<a class="menu">Our equations and how we obtained them.</a><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic#Our_EquationsTS">Establishment of the equation</a><a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic#Our_EquationsTS"> Toggle switch</a><a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic#Our_EquationsQS">Quorum sensing</a><br/>
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<a class="menu">Our algorithms</a><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Deterministic#Our_algorithms">Our algorithms</a><br/><br/><br/>
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<a class="menu">Isoclines and Hysteresis</a><br/><br/>
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  <a ><img class="icon" src="https://static.igem.org/mediawiki/2011/6/67/Icon_stochastic.png"/></a>
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  <a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Stochastic"><img class="icon" src="https://static.igem.org/mediawiki/2011/c/c7/Bouton_model_stochastic.png"/></a>
   
   
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<big><a class="menu">Stochastic Modelling :</a></big><br/>
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<big><big><a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Stochastic">Stochastic Modelling :</a></big></big><br/>
       
       
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<a class="menu">Geoffrey</a><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Stochastic#Geof">Sensitivity to noise: a first approach</a><br/>
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<a class="menu">Gillespie algorithm</a><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Stochastic#Gillespie_algorithm">Gillespie algorithm</a><br/>
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<a class="menu">Mean, standard deviation and statistical properties</a><br/><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Stochastic#Stats">Mean, standard deviation and statistical properties</a><br/><br/>
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  <a><img class="icon" src="https://static.igem.org/mediawiki/2011/3/34/Icon_parameters.png"/></a>
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  <a href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Parameters"><img class="icon" src="https://static.igem.org/mediawiki/2011/b/ba/Bouton_model_parameter.png"/></a>
   
   
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<br/><big><a class="menu">Parameters</a><br/><br/><br/><br/>
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<big><big><a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Parameters">Parameters</a></big></big><br/>
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<a class="menu" href="https://2011.igem.org/Team:Grenoble/Projet/Modelling/Parameters#Table">Table of parameters</a><br/>
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  <a><img class="icon" src="https://static.igem.org/mediawiki/2011/e/e1/Icon_results.png"/></a>
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<br/><br/>
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    </p>
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      <big><a class="menu">Results :</a></big><br/>
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      <a class="menu">Validation of our genetical network</a>
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    <p>
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      <a class="menu">Device</a>
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You can find our modelling results <a href="https://2011.igem.org/Team:Grenoble/Projet/Results">here</a>.
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    </p>
    </p>
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    <option value="#Content" selected="selected">Table of content</option>
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    <optgroup label="Construction of the model" >
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                                    <option value="/Deterministic#Our_EquationsTS" >Establishment of the equation - Toggle switch</option>
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                                    <option value="/Deterministic#Our_EquationsQS" >Establishment of the equation - Quorum sensing</option>
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                                    <option value="/Deterministic#Our_algorithms" >Our algorithms</option>
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                            <optgroup label="Stochastic Modelling">
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                                    <option value="/Stochastic#Geof">Sensitivity to noise</option>
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                                    <option value="/Stochastic#Gillespie_algorithm">Gillespie algorithm</option>
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                                    <option value="/Stochastic#Stats">Mean, standard deviation and stats</option>
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                            </optgroup>
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                            <optgroup label="Parameters">
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    <option value="/Parameters">Table of parameters</option>
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{{:Team:Grenoble/Design/pied}}

Latest revision as of 02:20, 29 October 2011

Grenoble 2011, Mercuro-Coli iGEM


Modelling

The modelling team is responsible for:

  1. Verifying that the designed genetic circuit elicits the desired behavior in E coli. A deterministic model of the circuit has been developed in order to predict the dynamical behavior of the circuit in the presence of a concentration gradient of IPTG and various concentrations of Mercury or aTc (anhydrotetracycline).
  2. Providing specifications for the quantification device (size, number of bacteria, IPTG gradient). The apparition of the red line indicating the presence and quantity of Mercury or aTc is sensitive to fluctuations in the concentration of these molecules and IPTG. We took into account these fluctuations in a stochastic version of the circuit model, which we have used to determine the specifications of our device.

Table of content

In the following pages, we detail the development of the deterministic and stochastic models, together with their dynamical analysis. Solving numerically these systems required tricky calculations, since they evolve both in time and space. To help future teams with similar calculations, we explain in details the algorithms that were used and provide the scripts here. The modelling results are described in the last section.

For an introduction to the modelling of biological genetic circuit see our tutorials in the human practice section or them here :



Construction of the model :
Establishment of the equation Toggle switchQuorum sensing
Our algorithms


Stochastic Modelling :
Sensitivity to noise: a first approach
Gillespie algorithm
Mean, standard deviation and statistical properties

Parameters
Table of parameters


You can find our modelling results here.

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