Team:UPO-Sevilla/Modeling

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<h1>Models</h1>
<h1>Models</h1>
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The members of the dry lab are simulating the different components of the full system. Three main components can be identified:
The members of the dry lab are simulating the different components of the full system. Three main components can be identified:
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<li>The difussion of the chemoattractant through the medium. </li>
<li>The difussion of the chemoattractant through the medium. </li>
<li>The motion of the bacterias through the medium due to the gradient on the chemoattractant concentration.</li>
<li>The motion of the bacterias through the medium due to the gradient on the chemoattractant concentration.</li>
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<li>The chemoattractant generation within the bacteria. </li>
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<li>The circuits and devices for the chemoattractant generation within the bacteria. </li>
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<p>For the first two points, we have developed a simulation using Java. The explanation of the simulation can be found in the Chemotaxis link below. Moreover, you can <b>download the bacterial crowding simulation</b> <a href="https://static.igem.org/mediawiki/2010/3/3f/BacterialCrowdingSimulation.zip">here</a>
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<h2>Chemoattractant Diffusion</h2>
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The basic equations for the diffusion of the chemoattractant in the medium are the Fick laws of diffusion, which govern the variation of the concentration of a substance within a medium.
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The flux (that is, the amount of substance that flows through a given surface per unit of time $\frac{mol}{m^2 s}$) is given by:
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The circuits and transduction signals inside the cell is simulated by using Matlab's Simbiology Toolbox. The model and results can be found in the Signaling link below.
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                  <a href="https://2010.igem.org/Team:UPO-Sevilla/Modeling/Chemotaxis"> <img class="subBanner" src="https://static.igem.org/mediawiki/2010/2/24/BacterialCrowdingChemotaxis.png" alt="Chemotaxis" /></a>
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                  <a href="https://2010.igem.org/Team:UPO-Sevilla/Modeling/Signaling"><img class="subBanner" src="https://static.igem.org/mediawiki/2010/5/59/BacterialCrowdingSignaling.png" alt="Signaling" /></a>
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<img src="https://static.igem.org/mediawiki/2010/6/6f/UPO-Model-Eq1.png" width="150 "alt="First Fick Law"/>
 
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where $\phi$ is the concentration ($\frac{mol}{m^{3}}$) in a given point. $D$ is a constant called the diffusion coefficient, and that depends on the medium .
 
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Basically, the equation states that the is directed towards places with lower concentration (thus the minus sign). If the concentration is constant in the space $ \Delta \phi = \mathbf{0}$ there is no flux.
 
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If the flux is known, it is possible to determine the amount of substance that goes through a small surface $d\mathbf{S}$ and a small amount of time $dt$</p>
 
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<img src="https://static.igem.org/mediawiki/2010/f/f8/UPO-Model-Eq2.png" width="170 "alt="First Fick Law"/>
 
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In order to simulate the diffusion, we define the environment and discretize it in very small cells. Each cell determines a given volume $V$, and has a surface $\mathbf{S}$. At a given time instant, the cell has an amount of substance $c$ (and then a concentration $\frac{c}{V}$).
 
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If the cells and time step $\Delta t$ are small, we can consider that the gradient of concentration can be approximated though the differences in concentration between a cell $i$ and 4 (or 8) neighbors $j$. Thus:
 
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<img src="https://static.igem.org/mediawiki/2010/e/ea/UPO-Model-Eq3.png" width="170 "alt="First Fick Law"/>
 
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and then, the amount of substance that diffusses from $i$ to $j$:
 
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<img src="https://static.igem.org/mediawiki/2010/6/6f/UPO-Model-Eq4.png" width="170 "alt="First Fick Law"/>
 
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<h2> Bacteria motion</h2>
 
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<h2>Chemical reactions</h2>
 
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<h1>Modeling Tools</h1>
 
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Latest revision as of 20:09, 26 October 2010

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Models

The members of the dry lab are simulating the different components of the full system. Three main components can be identified:
  1. The difussion of the chemoattractant through the medium.
  2. The motion of the bacterias through the medium due to the gradient on the chemoattractant concentration.
  3. The circuits and devices for the chemoattractant generation within the bacteria.

For the first two points, we have developed a simulation using Java. The explanation of the simulation can be found in the Chemotaxis link below. Moreover, you can download the bacterial crowding simulation here

The circuits and transduction signals inside the cell is simulated by using Matlab's Simbiology Toolbox. The model and results can be found in the Signaling link below.

Chemotaxis Signaling


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