Team:Grenoble/Modeling/Amplification/Quorum

From 2012.igem.org

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The goal of this part was only to check the speed of the
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diffusion. We use the same model as the 2011 IGEM team of Grenoble, which is based on the Bangalore 2007 IGEM team model. We first have to add the diffusion terms in the equations thus we get:
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<center><img src="https://static.igem.org/mediawiki/2012/1/12/Eq34_grenoble.png" alt="" /></center>
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Because of the temporal and special derivatives, we couldn’t use a classic matlab solver to solve this set of equations. The approximation we used consisted in dividing the space into a grid:
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<center><img src="https://static.igem.org/mediawiki/2012/e/ef/Grid_grenoble.png" alt="" /></center>
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It is the finite difference method. We thus get:
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<center><img src="https://static.igem.org/mediawiki/2012/b/b6/Eq35_grenoble.png" alt="" /></center>
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with h=l<SUB>x</SUB>/N, where l<SUB>x</SUB> is the length of the grid and N is the number of points of discretization along x. By using the same approximation on y<SUB>i</SUB>, and assuming that l<SUB>y</SUB>=l<SUB>x</SUB>, and that we have the same number of points of discretization, we get:
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<center><img src="https://static.igem.org/mediawiki/2012/4/48/Eq36_grenoble.png" alt="" /></center>
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Revision as of 15:45, 21 September 2012

iGEM Grenoble 2012

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The goal of this part was only to check the speed of the diffusion. We use the same model as the 2011 IGEM team of Grenoble, which is based on the Bangalore 2007 IGEM team model. We first have to add the diffusion terms in the equations thus we get:



Because of the temporal and special derivatives, we couldn’t use a classic matlab solver to solve this set of equations. The approximation we used consisted in dividing the space into a grid:



It is the finite difference method. We thus get:



with h=lx/N, where lx is the length of the grid and N is the number of points of discretization along x. By using the same approximation on yi, and assuming that ly=lx, and that we have the same number of points of discretization, we get:



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