Team:Montreal/Modeling

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===Background===
===Background===
Using coupled differential equations, we are modeling the repressilator, which is a network of three genes, whose product proteins are repressing each other's growth. This cycle is taking place in each of a colony of cells, who communicate amongst themselves by exchanging an autoinducer molecule. The model attempts to take into account a sparse, heterogeneous distribution of cells with depletion of the autoinducer molecule and leakage.
Using coupled differential equations, we are modeling the repressilator, which is a network of three genes, whose product proteins are repressing each other's growth. This cycle is taking place in each of a colony of cells, who communicate amongst themselves by exchanging an autoinducer molecule. The model attempts to take into account a sparse, heterogeneous distribution of cells with depletion of the autoinducer molecule and leakage.
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For this purpose, the model is currently being coded up in Mathematica. The simulations, based on that continuous model, are generated using xCellerator and NDelayDSolve for different cell configurations; the results obtained are graphs of the concentration of molecules in the system versus time. That is, our interest lies in the phase difference between clusters of cells. As of now, a low number of cells is being used for testing, but a higher one will be reached later.
|[[Image:Theoteam1.jpg|right|frame|Theorists: Vincent Quenneville-Bélair and Alexandra Ortan]]
|[[Image:Theoteam1.jpg|right|frame|Theorists: Vincent Quenneville-Bélair and Alexandra Ortan]]
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|[[Image:visualisation.png|right|frame|Although the cells are shown using a Voronoi graph, the cells are represented internally by points.]]
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|[[Image:px.png|right|frame|Simulation using Mathematica of the Repressilator Network with four cells shown on the left. The plot shows the concentration of AI against time (in arbitrary units).]]
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Revision as of 17:31, 23 July 2008

Home The Team The Project Parts Submitted to the Registry Modeling Notebook

Background

Using coupled differential equations, we are modeling the repressilator, which is a network of three genes, whose product proteins are repressing each other's growth. This cycle is taking place in each of a colony of cells, who communicate amongst themselves by exchanging an autoinducer molecule. The model attempts to take into account a sparse, heterogeneous distribution of cells with depletion of the autoinducer molecule and leakage.

For this purpose, the model is currently being coded up in Mathematica. The simulations, based on that continuous model, are generated using xCellerator and NDelayDSolve for different cell configurations; the results obtained are graphs of the concentration of molecules in the system versus time. That is, our interest lies in the phase difference between clusters of cells. As of now, a low number of cells is being used for testing, but a higher one will be reached later.

Theorists: Vincent Quenneville-Bélair and Alexandra Ortan
Although the cells are shown using a Voronoi graph, the cells are represented internally by points.
Simulation using Mathematica of the Repressilator Network with four cells shown on the left. The plot shows the concentration of AI against time (in arbitrary units).
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