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| − | {{Paris_Bettencourt/header}}
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| − | {{Paris_Bettencourt/menu}}
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| − | {{Paris_Bettencourt/modelingBanner}}
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| − | <html>
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| − |
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| − | <h3>Introduction</h3>
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| − | As explained in the <a href="https://2015.igem.org/Team:Paris_Bettencourt/Modeling" title="Modeling wiki page" >modeling page</a>, this program modelize the cells population evolution with mother cell differentiation and cell division.
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| − | <br />
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| − | We focus here on the stochastic program.
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| − | <br />
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| − |
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| − | <h3>Files</h3>
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| − | The MATLAB code is available in <a href="https://github.com/iGEMParisBettencourt2015/modeling" title="Source code in GitHub" >GitHub</a> under the GNU General Public License version 3.0.
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| − | <br />
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| − | Here is a quick explanation of the differents files <i>ie</i> the differents functions.
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| − | <h4>Stochastic algorithm</h4>
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| − | <ul>
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| − | <li>\(timeEvolutionStochastic\) : the main function to calcul the time evolution.</li>
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| − | <li>\(checkInput\) : check the input and show an error message if the input is not good.</li>
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| − | <li>\(elmPixel\) : find the coordinates of a pixel around an other pixel.</li>
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| − | <li>\(errorProgramm\) : display an error and stop the programm.</li>
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| − | <li>\(freePosition\) : create a list of free pixels around one pixel.</li>
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| − | <li>\(getComputerName\) : get the computer name.</li>
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| − | <li>\(getSizeMat\) : find the matrice size.</li>
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| − | <li>\(imageToMatrix\) : convert an image into a matrix.</li>
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| − | <li>\(initCells\) : initialization of the cells.</li>
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| − | <li>\(initialization\) : initialization of the program.</li>
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| − | <li>\(initTimeEvent\) : calcul the different time.</li>
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| − | <li>\(initVariables\) : variables initialization.</li>
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| − | <li>\(isBinary\) : check if a number is 0 or 1.</li>
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| − | <li>\(isPositiveInteger\) : check if a number is a positive integer (1) or not (0).</li>
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| − | <li>\(makeCells\) : make the cells.</li>
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| − | <li>\(randEvent\) : generate the next random event.</li>
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| − | <li>\(randPosition\) : find a free position for a cell.</li>
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| − | <li>\(saveInitialParameters\) : save the initial parameters in a text file.</li>
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| − | <li>\(saveResult\) : save and plot the results.</li>
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| − | <li>\(showAndSaveEventTimeDistribution\) : show and save the event time probability distribution.</li>
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| − | <li>\(showPopulation\) : show the cells matrix.</li>
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| − | <li>\(writeParameters\) : write a text file with the parameters.</li>
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| − | <li>\(launchStochasticProgramm\) : launch the stochastic time evoluation simulation.</li>
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| − | <li>\(k1OptimizationStochastic\) : calcul the number of differentiated cells and vitamin with differents k1 in a stochastic way.</li>
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| − | <li>\(k1OptimizationStochasticAndDeterministic\) : superimpose the deterministic and stochastic models.</li>
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| − | </ul>
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| − | <h4>Deterministic algorithm</h4>
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| − | <ul>
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| − | <li>\(timeEvolutionDeterministic\) : show the time evolution by numerical calculus and equations.</li>
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| − | <li>\(k1OptimizationDeterministic\) : calcul the number of differentiated cells with differents k1 in a deterministic way.</li>
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| − | </ul>
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| − | <h3>Input</h3>
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| − | In order to launch a simulation, you must define five variables.
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| − | <ul>
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| − | <li>cells.</li>
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| − | <li>rate constants.</li>
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| − | <li>fermentation period.</li>
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| − | <li>action.</li>
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| − | <li>folder name.</li>
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| − | </ul>
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| − | <h4>Cells input</h4>
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| − | You can choose if you prefer to generate a random or a predetermined position for the initial cells.
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| − | <br />
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| − | You have two cells types : mother cells and differentiated cells.
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| − | <h5>Random initial position</h5>
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| − | The input array must contain four integer values in this order.
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| − | <ul>
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| − | <li>\(MC_0\) : initial number of mother cells in the medium.</li>
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| − | <li>\(DC_0\) : initial number of differentiated cells in the medium.</li>
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| − | <li>\(sizeMatCell\) : cells box size (in pixels).</li>
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| − | <li>\(sizeMat\) : real box size (in pixels).</li>
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| − | </ul>
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| − | <br />
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| − | Warning : \(sizeMatCell\) must be larger than \(sizeMat\).
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| − | <br />
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| − | <br />
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| − |
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| − | In the program, the input variable has the following pattern.
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| − | <br />
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| − | \(input = [MC_0, DC_0, sizeMatCell, sizeMat]\)
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| − | <br />
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| − | <br />
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| − | Here is an example.
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| − | <br />
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| − | <ul>
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| − | <li>\(MC_0 = 5 \phantom{t} (cells)\)</li>
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| − | <li>\(DC_0 = 0 \phantom{t} (cells)\)</li>
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| − | <li>\(sizeMatCell = 100 \phantom{t} (pixels)\)</li>
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| − | <li>\(sizeMat = 250 \phantom{t} (pixels)\)</li>
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| − | </ul>
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| − |
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| − | <h5>Predetermined initial position</h5>
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| − | In order to make an easy predetermined initial position input, we wrote a code which understand images.
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| − | <br />
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| − | The input must contain the image path.
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| − | <br />
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| − | It is very easy to design a custom image <i>ie</i> a custom spatial cell distribution. You must follow these four rules (we work only with the image red component)
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| − | <ul>
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| − | <li>the image must be square and in jpeg format.</li>
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| − | <li>255 means no cell.</li>
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| − | <li>128 means one differentiated cell.</li>
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| − | <li>0 means one mother cell.</li>
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| − | </ul>
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| − | 0, 128 and 255 are red components of any colours that you want because the MATLAB code take into account only the image red component.
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| − | <br />
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| − | If you want, you can use the following hexadecimal colours codes.
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| − | <ul>
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| − | <li>#FFFFFF (white) means no cell.</li>
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| − | <li>#800000 (red) means one differentiated cell.</li>
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| − | <li>#000000 (black) means one mother cell.</li>
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| − | </ul>
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| − | <br />
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| − | Here is an example only with mother cells.
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| − | <br />
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| − | <br />
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| − | <img src="https://static.igem.org/mediawiki/2015/9/9a/IgemImg.png" style="width:20%;height:20%;" alt="Example of predetermined cells initial position with mother cells" title="Example of predetermined cells initial position with mother cells" >
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| − | <br />
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| − | Here is an other example with mother cells (black) and differentiated cells (red).
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| − | <br />
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| − | <br />
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| − | <img src="https://static.igem.org/mediawiki/2015/a/a4/IgemParisBettencourtImg.png" style="width:20%;height:20%;" alt="Example of predetermined cells initial position with mother cells (black) and differentiated cells (red)" title="Example of predetermined cells initial position with mother cells (black) and differentiated cells (red)" >
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| − | <br />
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| − |
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| − | <h4>Rate constants</h4>
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| − | You have to define seven variables.
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| − | <ul>
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| − | <li>\(\mu_{1}\) : mother cell differentiation time mean.</li>
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| − | <li>\(\sigma_{1}\) : mother cell differentiation time standard deviation.</li>
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| − | <li>\(\mu_{2}\) : mother cell doubling time mean.</li>
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| − | <li>\(\sigma_{2}\) : mother cell doubling time standard deviation.</li>
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| − | <li>\(\mu_{3}\) : differentiated cell doubling time mean.</li>
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| − | <li>\(\sigma_{3}\) : differentiated cell doubling time standard deviation.</li>
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| − | <li>\(k_{4}\) : rate constant of the differentiated cell vitamin production.</li>
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| − | </ul>
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| − | <br />
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| − | In the program, the rate constants variable has the following pattern.
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| − | <br />
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| − | \(constantRate = [\mu_{1}, \sigma_{1}, \mu_{2}, \sigma_{2}, \mu_{3}, \sigma_{3}, k_{4}]\)
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| − | <br />
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| − | <br />
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| − | Here is an example.
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| − | <br />
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| − | <ul>
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| − | <li>\(\mu_{1} = 1 \phantom{t} (hours)\)</li>
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| − | <li>\(\sigma_{1} = 0.1 \phantom{t} (hours)\)</li>
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| − | <li>\(\mu_{2} = 1.0502 \phantom{t} (hours)\)</li>
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| − | <li>\(\sigma_{2} = 0.1 \phantom{t} (hours)\)</li>
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| − | <li>\(\mu_{3} = 2.1004 \phantom{t} (hours)\)</li>
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| − | <li>\(\sigma_{3} = 0.1 \phantom{t} (hours)\)</li>
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| − | <li>\(k_{4} = 1 \phantom{t} (hours^{-1})\)</li>
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| − | </ul>
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| − |
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| − | <h4>Fermentation period</h4>
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| − | The fermentation period \(t\) is a simple scalar variable.
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| − | <br />
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| − | You can use \(t = 5 \phantom{t} (hours)\) for example.
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| − | <h4>Action</h4>
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| − | In order to choose what you want to do, you must define three booleans.
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| − | <ul>
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| − | <li>\(createFolder\) : create a folder in the disk to save informations.</li>
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| − | <li>\(showAnimation\) : show the poulation animation. Warning : require a lot of computing power.</li>
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| − | <li>\(plotGraph\) : plot the results in graphs.</li>
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| − | </ul>
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| − |
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| − | <br />
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| − | In the program, the action variable has the following pattern.
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| − | <br />
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| − | \(action = [createFolder, showAnimation, plotGraph\)]
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| − | <br />
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| − | <br />
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| − | In the following example we want to create a folder and plot the graphs.
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| − | <br />
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| − | <ul>
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| − | <li>\(createFolder = 1\)</li>
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| − | <li>\(showAnimation = 0\)</li>
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| − | <li>\(plotGraph = 1\)</li>
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| − | </ul>
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| − | <br />
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| − | In the following example we want to show the cell animation.
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| − | <br />
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| − | <ul>
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| − | <li>\(createFolder = 0\)</li>
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| − | <li>\(showAnimation = 1\)</li>
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| − | <li>\(plotGraph = 0\)</li>
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| − | </ul>
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| − | <br />
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| − | In the following example we want to show the cell animation and save the images in a folder.
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| − | <br />
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| − | With the images you can create gif animations.
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| − | <br />
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| − | <ul>
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| − | <li>\(createFolder = 1\)</li>
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| − | <li>\(showAnimation = 1\)</li>
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| − | <li>\(plotGraph = 0\)</li>
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| − | </ul>
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| − |
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| − | <h4>Folder name</h4>
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| − | The \(folderName\) variable is a string containing the folder where results folder are store in the disk.
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| − | <br />
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| − | You can use \(folderName =\) '\(Results\)' for example.
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| − |
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| − | <h3>Output</h3>
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| − | Four types of output are generated.
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| − | <ul>
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| − | <li>raw data : all the useful informations.</li>
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| − | <li>folder creation : if chosen in the \(action\) variable, a folder is created.</li>
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| − | <li>graphs : if chosen in the \(action\) variable, graphs are generated.</li>
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| − | <li>animation : if chosen in the \(action\) variable, cell animation is generated.</li>
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| − | </ul>
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| − |
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| − | <h4>Raw data</h4>
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| − | <ul>
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| − | <li>\(mainTic\) : start of the program.</li>
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| − | <li>\(MC_0\) : initial number of mother cells in the medium.</li>
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| − | <li>\(DC_0\) : initial number of differentiated cells in the medium.</li>
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| − | <li>\(pasDistributionTimeEvent\) : resolution for the graph time event distribution plot (see the \(initVariables\) function).</li>
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| − | <li>\(frameRate\) : animation framerate (see the \(initVariables\) function).</li>
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| − | <li>\(timeShowPopulation\) : simulation time between two animations (see the \(initVariables\) function).</li>
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| − | <li>\(simulationTime\) : fermentation period \(t\).</li>
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| − | <li>\(resultFolderName\) : folder where the results folder are created.</li>
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| − | <li>\(\mu_{1}\) : mother cell differentiation time mean.</li>
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| − | <li>\(\sigma_{1}\) : mother cell differentiation time standard deviation.</li>
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| − | <li>\(\mu_{2}\) : mother cell doubling time mean.</li>
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| − | <li>\(\sigma_{2}\) : mother cell doubling time standard deviation.</li>
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| − | <li>\(\mu_{3}\) : differentiated cell doubling time mean.</li>
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| − | <li>\(\sigma_{3}\) : differentiated cell doubling time standard deviation.</li>
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| − | <li>\(k_{4}\) : rate constant of the differentiated cell vitamin production.</li>
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| − | <li>\(cVitamin\) : vitamin counter.</li>
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| − | <li>\(time\) : main timer containing the simulation time.</li>
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| − | <li>\(createFolder\) : action boolean.</li>
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| − | <li>\(showPopulationBool\) : action boolean.</li>
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| − | <li>\(plotGraph\) : action boolean.</li>
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| − | <li>\(input\) : input array.</li>
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| − | <li>\(cTime1\) : time distribution counter 1 (see the \(randEvent\) function).</li>
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| − | <li>\(cTime2\) : time distribution counter 2 (see the \(randEvent\) function).</li>
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| − | <li>\(cTime3\) : time distribution counter 3 (see the \(randEvent\) function).</li>
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| − | <li>\(counterEvent\) : event counter.</li>
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| − | <li>\(timerShow\) : time animation counter.</li>
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| − | <li>\(sizeMat\) : real box size (in pixels).</li> <li>\(nextEvent\) : .</li>
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| − | <li>\(time1Array\) : time distribution array 1 (see the \(initTimeEvent\) function).</li>
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| − | <li>\(time2Array\) : time distribution array 2 (see the \(initTimeEvent\) function).</li>
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| − | <li>\(time3Array\) : time distribution array 3 (see the \(initTimeEvent\) function).</li>
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| − | <li>\(cell\) : structure containing all the cells informations.</li>
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| − | <li>\(sizeMatCell\) : cells box size (in pixels).</li>
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| − | <li>\(timeNextEvent\) : time before the next event.</li>
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| − | <li>\(saveTime\) : array containing the simulation time evolution.</li>
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| − | <li>\(saveNbrMC\) : array containing the mother cells time evolution.</li>
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| − | <li>\(saveNbrDC\) : array containing the differentiated cells time evolution.</li>
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| − | <li>\(saveNbrVitamin\) : array containing the vitamin time evolution.</li>
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| − | <li>\(folderName\) : folder where the results are stored. The pattern is the following : \(resultFolderName/DD-MM-YY\_hh\_mm\_ss\_mss\).</li>
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| − | <li>\(imgType\) : image type (see the \(initilization\) function).</li>
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| − | <li>\(parametersFileName\) : parameters file name where the parameters are saved (see the \(initilization\) function).</li>
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| − | <li>\(parametersDoc\) : file object where the parameters are saved.</li>
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| − | <li>\(maxMC\) : maximum number of mother cells.</li>
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| − | <li>\(maxDC\) : maximum number of differentiated cells.</li>
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| − | <li>\(maxVitamin\) : maximum number of vitamins.</li>
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| − | <li>\(timeSpent\) : computation time (in seconds).</li>
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| − |
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| − | </ul>
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| − | <h4>Folder creation</h4>
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| − | If the \(action\) variable \(createFolder\) is set, the program will save important results data in this folder.
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| − | <br />
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| − | <ul>
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| − | <li>\(parameters.txt\) : text file containing differents simulation parameters and results</li>
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| − | <li>\(data.mat\) : MATLAB file containing simulation the raw data structure. To load the file, use this formula : \(load('data.mat')\).</li>
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| − | </ul>
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| − |
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| − | <h4>Graphs</h4>
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| − | If the \(action\) variable \(plotGraph\) is set, the program will show the graphs.
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| − | <br />
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| − | Moreover if the \(action\) variable \(createFolder\) is set, the program will save the graphs in the folder.
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| − |
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| − | <h4>Animation</h4>
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| − | If the \(action\) variable \(showAnimation\) is set, the program will show the cell animation.
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| − | <br />
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| − | Moreover if the \(action\) variable \(createFolder\) is set, the program will save the images in the folder.
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| − |
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| − | <h3>Examples</h3>
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| − | We present here some results obtained with the program. For more details about the model see the <a href="https://2015.igem.org/Team:Paris_Bettencourt/Modeling" title="Modeling wiki page" >modeling page</a>.
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| − |
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| − | <h4>Time evolution of mother cells, differentiated cells and vitamin</h4>
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| − | <h5>Graphs</h5>
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| − | As explained in the <a href="https://2015.igem.org/Team:Paris_Bettencourt/Modeling" title="Modeling wiki page" >modeling page</a> the program give these results.
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| − | <br />
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| − | <br />
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| − | <img width="100%" src="https://static.igem.org/mediawiki/2015/1/14/StochasticEvolution.png" title="Stochastic evolution of the system" alt="Stochastic evolution of the system" style="align:center;">
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| − | <br />
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| − | <br />
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| − | <img width="100%" src="https://static.igem.org/mediawiki/2015/0/0b/OptimizeK1Stochastic.png" title="Stochastic vitamin optimization" alt="Stochastic vitamin optimization" style="align:center;">
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| − | <br />
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| − | <br />
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| − | <img width="100%" src="https://static.igem.org/mediawiki/2015/9/97/StochasticEventTimeProbabilityDistribution.png" title="Distribution of event time probability" alt="Distribution of event time probability" style="align:center;">
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| − |
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| − | <h5>Animation</h5>
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| − | Here is an example with mother cells (black) and differentiated cells (red).
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| − | <br />
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| − | This image is the cell input.
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| − | <br />
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| − | <br />
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| − | <img style="width:30%;height:30%;" src="https://static.igem.org/mediawiki/2015/a/a4/IgemParisBettencourtImg.png" alt="Example of predetermined cells initial position with mother cells (black) and differentiated cells (red)" title="Example of predetermined cells initial position with mother cells (black) and differentiated cells (red)" >
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| − | <br />
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| − | The result is the following animation after a conversion in a gif file.
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| − | <br />
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| − | The mother cells are in orange and the differentiated cells are in yellow.
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| − | <br />
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| − | <br />
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| − | <img style="width:30%;height:30%;" src="https://static.igem.org/mediawiki/2015/7/73/IgemParisBettencourtGif.gif" alt="Animation example with predetermined cells initial position with mother cells and differentiated cells" title="Animation example with predetermined cells initial position with mother cells and differentiated cells" >
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| − | <br />
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| − |
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| − | <h4>Vitamin optimization</h4>
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| − | This program is designed to maximize the vitamin production. Here are some results.
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| − | <br />
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| − | <br />
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| − | <img width="100%" src="https://static.igem.org/mediawiki/2015/0/0b/OptimizeK1Stochastic.png" title="Stochastic vitamin optimization" alt="Stochastic vitamin optimization" style="align:center;">
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| − |
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| − | <h4>Deterministic and stochastic vitamin optimization comparison</h4>
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| − | Here is a comparison between the two models.
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| − | <br />
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| − | <br />
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| − | <img width="100%" src="https://static.igem.org/mediawiki/2015/3/3c/CompareStochasticAndDeterministic.png" title="Comparison of deterministic and stochastic vitamin optimization" alt="Comparison of deterministic and stochastic vitamin optimization" style="align:center;">
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| − |
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| − | <h3>Conclusion</h3>
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| − | Feel free to use and modify this program. The source code is available in <a href="https://github.com/iGEMParisBettencourt2015/modeling" alt="Source code in GitHub"> GitHub : iGEM Paris Bettencourt 2015</a> under the <a href="http://www.gnu.org/licenses/gpl.txt" alt="GNU General Public License" >GNU General Public License version 3.0</a>.
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| − | For more informations concerning the model see the <a href="https://2015.igem.org/Team:Paris_Bettencourt/Modeling" title="Modeling wiki page" >modeling page</a>.
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| − | </html>
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| − |
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| − | {{Paris_Bettencourt/footer}}
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