Team:Grenoble/Projet/Modelling/Parameters

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    <h1>Modelling - Parameters</h1>
    <h1>Modelling - Parameters</h1>
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<div  class="blocbackground" id="Parameters">
<div  class="blocbackground" id="Parameters">
    <h2>Parameters</h2>
    <h2>Parameters</h2>
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      <a href="https://static.igem.org/mediawiki/2011/d/d1/Rapport_Equations.pdf" id="See_below">
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      <a href="http://2011..org/wiki/images/d/d1/Rapport_Equations.pdf" id="See_below">
      <img src="https://2011.igem.org/wiki/skins/common/images/icons/fileicon-pdf.png" style="float: left; height: 20px; width: auto">
      <img src="https://2011.igem.org/wiki/skins/common/images/icons/fileicon-pdf.png" style="float: left; height: 20px; width: auto">
      PDF file (detailed explanation on parameters and how we deduced them) for Toggle Switch</a>
      PDF file (detailed explanation on parameters and how we deduced them) for Toggle Switch</a>
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<p>
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Working with the aTc/TetR parameters, we needed to now if our system could work with mercury.
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In order to see if it's <a href="https://2011.igem.org/Team:Grenoble/Projet/Results/Sensitivity#Mercury">applicable to mercury</a>,
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we realized a <a href="https://2011.igem.org/Team:Grenoble/Projet/Results/Sensitivity#Robustness">sensitivity to parameters study</a>.
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</p>
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<div  class="blocbackground" id="Sensitivity">
 
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    <h2>Parameters sensitivity</h2>
 
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    <p>In order to know if an error on the parameters would induce a completely different behaviour of our system,
 
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    we studied the sensitivity of our system to a change on the parameters.
 
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    </p>
 
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    <p>
 
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    This study was performed by increasing or decreasing our parameters values by a range of percentages (from -66% to +300% for each parameter).
 
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    Then we studied the change on the output of our system, the ratio of IPTG over aTc that induces the coloration.
 
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    </p>
 
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    On the following figure one can see the influence on the output of our system (the ratio of IPTG over aTc on the interface)
 
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    for several different aTc concentrations. For these concentrations the switch is still efficient, even though the resulting
 
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    variation on the output will induce an error on our measure.
 
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    </p>
 
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    <table class="nobordure">
 
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<tr>
 
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<td>
 
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<center>
 
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<a href= "https://static.igem.org/mediawiki/2011/4/41/Parameters_sensitivity1.png"><img src="https://static.igem.org/mediawiki/2011/4/41/Parameters_sensitivity1.png" style="width: 600px;" class="centerwide"/></a>
 
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<div class="legend"><strong>Figure 1: </strong>Parameters sensitivity for 2.8e-07 M of aTc</div>
 
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</center>
 
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</td>
 
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<td>
 
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<p><strong>Note:</strong> On the next two figures the parameters are the following<br/>
 
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<table style="border: 1px;">
 
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  <tr>
 
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    <td><strong>1</strong></td>
 
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    <td>k<SUB>plac</SUB></td>
 
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  </tr>
 
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  <tr>
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    <td><strong>2</strong></td>
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    <td>V<SUB>cell</SUB></td>
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  </tr>
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  <tr>
 
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    <td><strong>3</strong></td>
 
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    <td>k<SUB>pTet <br/></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>4</strong></td>
 
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    <td>K<SUB>pLac - LacI</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>5</strong></td>
 
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    <td>K<SUB>pTet - TerR</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>6</strong></td>
 
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    <td>K<SUB>LacI - IPTG</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>7</strong></td>
 
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    <td>K<SUB>TetR - aTc</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>8</strong></td>
 
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    <td>n<SUB>plac</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>9</strong></td>
 
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    <td>n<SUB>pTet</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>10</strong></td>
 
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    <td>δ<SUB>TetR</SUB></td>
 
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  </tr>
 
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  <tr>
 
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    <td><strong>11</strong></td>
 
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    <td>δ<SUB>LacI</SUB></td>
 
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  </tr>
 
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</table>
 
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</td>
 
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</tr>
 
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    </table>
 
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    <table class="nobordure">
 
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    <tr>
 
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      <td>
 
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<a href="https://static.igem.org/mediawiki/2011/5/5b/Parameters_sensitivity2.png"><img src="https://static.igem.org/mediawiki/2011/5/5b/Parameters_sensitivity2.png" class ="centerwide" style="width: 600px;"/></a>
 
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<div class="legend"><strong>Figure 2: </strong>Parameters sensitivity for 6.3e-06 M of aTc</div>
 
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      </td>
 
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      <td> 
 
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<p>Variations from 1 to 13 : </p>
 
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<table>
 
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    <tr>
 
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      <td><strong>1</strong></td>
 
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      <td>-66%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>2</strong></td>
 
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      <td>-50%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>3</strong></td>
 
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      <td>-20%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>4</strong></td>
 
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      <td>-10%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>5</strong></td>
 
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      <td>-5%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>6</strong></td>
 
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      <td>+0%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>7</strong></td>
 
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      <td>+5%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>8</strong></td>
 
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      <td>+10%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>9</strong></td>
 
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      <td>+20%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>10</strong></td>
 
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      <td>+50%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>11</strong></td>
 
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      <td>+100%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>11</strong></td>
 
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      <td>+200%</td>
 
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    </tr>
 
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    <tr>
 
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      <td><strong>11</strong></td>
 
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      <td>+300%</td>
 
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    </tr>
 
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</table>
 
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    </td>
 
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    </tr>
 
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    </table>
 
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    <p>For low values of aTc concentration the error is too minor to perturb the mechanism of our system. If the error is
 
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    superior to -50% or +100% for parameters such as K<SUB>pLac - LacI</SUB> or K<SUB>pTet - TetR</SUB> however, it will
 
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    be impossible to predict the output. In such a case a characterization of the responsible parameter would be necessary.
 
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    </p>
 
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    <p>For higher values of aTc concentration however, the value of IPTG necessary for a switch is very high and errors on the
 
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    parameters can cause the system not to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary value
 
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    for quantification would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.
 
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    </p>
 
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    <a href="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png"><img src="https://static.igem.org/mediawiki/2011/0/01/Parameters_sensitivity3.png" class="centerwide"/></a>
 
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    <div class="legend"><strong>Figure 2: </strong>Parameters sensitivity for 6.2e-04 M of aTc</div>
 
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                                     <option value="/Deterministic#Our_EquationsTS" >Our equations - Toggle switch</option>
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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" >Our equations - Quorum sensing</option>
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                                     <option value="/Deterministic#Our_EquationsQS" >Establishment of the equation - Quorum sensing</option>
                                  
                                  
                                     <option value="/Deterministic#Our_algorithms" >Our algorithms</option>
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                                    <option value="/Deterministic#Isoclines">Isoclines and Hysteresis</option>
 
                                  
                                  
                                      
                                      
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                                     <option value="/Stochastic#Geof" >Geof's</option>
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                                     <option value="/Stochastic#Geof">Sensitivity to noise</option>
                                  
                                  
                                     <option value="/Stochastic#Gillespie_algorithm">Gillespie algorithm</option>
                                     <option value="/Stochastic#Gillespie_algorithm">Gillespie algorithm</option>
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                             <optgroup label="Parameters">
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    <option value="/Parameters" selected="selected">Our parameters</option>
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    <option value="/Parameters" selected="selected">Table of parameters</option>
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    <option value="/Parameters#Sensitivity">Parameters sensitivity</option>
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                            <optgroup label="Results">
 
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    <option value="/Results#Validation">Validation of our Network</option>
 
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    <option value="/Results#Device">Device specificities</option>
 
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Latest revision as of 03:02, 29 October 2011

Grenoble 2011, Mercuro-Coli iGEM


Modelling - Parameters

Parameters

PDF file (detailed explanation on parameters and how we deduced them) for Toggle Switch
kplac pLac production rate 600 proteins/min [1]
kpTet pTet production rate 600 proteins/min [1]
kpMer pMer production rate 600 proteins/min [1]
δLacI LacI degradation rate 4.6E-2 min−1 PDF file
δTetR TetR degradation rate 4.6E-2 min−1 PDF file
δMerR MerR degradation rate 4.6E-2 min−1 PDF file
KpLac - LacI plac - LacI dissociation constant 5.45E-7 M Kyoto 10
KpMer - MerR pMer - MerR dissociation constant 1.00E-8 M [2]
KpTet - TerR pTet - TetR dissociation constant 5.00E-8 M [3]
KLacI - IPTG LacI - IPTG dissociation constant 2.96E-5 M [4]
KTetR - aTc aTc - TetR dissociation constant 1.5E-8 M [5]
KHg2+ - MerR Hg2+ - MerR dissociation constant 1E-7 M [2]
nplac plac cooperativity number 2,3 [4]
npMer pMer cooperativity number 2,5 [6]
npTet pTet cooperativity number 3 [7]

Working with the aTc/TetR parameters, we needed to now if our system could work with mercury. In order to see if it's applicable to mercury, we realized a sensitivity to parameters study.

References

[1] Nature. 2000 Jan 20;403(6767):335-8. A synthetic oscillatory network of transcriptional regulators. Elowitz MB, Leibler S.

[2] Mol Gen Genet. 1999 Aug;262(1):154-62. Purification and characterization of MerR, the regulator of the broad-spectrum mercury resistance genes in Streptomyces lividans 1326. Rother D, Mattes R, Altenbuchner J.

[3] David Braun et al. Parameter estimation for two synthetic gene networks: A case study. IEEE 2005.

[4] Nature 403, 339-342 (20 January 2000) Construction of a genetic toggle switch in Escherichia coli. Timothy S. Gardner Charles R. Cantor & James J. Collins

[5] O. Scholz, P. Schubert, M. Kintrup and W. Hillen, Tet repressor induction without Mg2+, Biochemistry 39 (2000), pp. 10914–10920

[6] Ultrasensitivity and heavy-metal selectivity of the allosterically modulated MerR transcription complex. D M Ralston and T V O'Halloran

[7] Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. Goryachev AB, Toh DJ, Lee T.

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