Paris/Stochastic model
From 2007.igem.org
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| + | In this last part of the models section, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria. | ||
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| + | == Introduction == | ||
| + | In 1977, Gillespie has developed an exact ''Simulation Stochastic Algorithm'' (SSA) dedicated to the simulation of ''homogeneous'' chemical systems. This method was recently used in many applications for the simulation of biological systems. A good point of this approach is that it allows to handle biochemical systems where numbers of molecules are low and that cannot be well characterized by classical approach using differential equations and chemical concentrations. Nevertheless this method requires strong hypotheses about the spatial homogeneity of molecules distribution. As our system is composed of structured | ||
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| + | This model aims at describing the dynamic evolution of populations of germen and soma type bacteria. | ||
| + | It is based on a set of differential equations describing DAP synthesis, DAP transport, | ||
| + | differentiation of germen bacteria into soma and bacteria death. This approach differs form the precedents one by the level of description of the model | ||
| + | and the numerical analysis done on the model. | ||
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| + | By conducting robustness and optimization analysis on two different systems, | ||
| + | one with a constant rate of differentiation against one with a rate of differentiation driven by | ||
| + | the concentration of DAP, we evaluate benefits and drawbacks of both systems. | ||
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| + | We first display the consistency of the biological system by providing a set of kinetic | ||
| + | parameters such that the numerical simulation validate a given minimal behavior. | ||
| + | Then we analyze the system robustness with regard to its kinetic parameters and finally we try to optimize the system output by adjusting some biologically relevant parameters. | ||
Revision as of 14:11, 24 October 2007
In this last part of the models section, we are developing a stochastic simulation of the microscopic model. The major contribution is to handle in a stochastic context a dynamic and heterogeneous population of bacteria.
Introduction
In 1977, Gillespie has developed an exact Simulation Stochastic Algorithm (SSA) dedicated to the simulation of homogeneous chemical systems. This method was recently used in many applications for the simulation of biological systems. A good point of this approach is that it allows to handle biochemical systems where numbers of molecules are low and that cannot be well characterized by classical approach using differential equations and chemical concentrations. Nevertheless this method requires strong hypotheses about the spatial homogeneity of molecules distribution. As our system is composed of structured
This model aims at describing the dynamic evolution of populations of germen and soma type bacteria. It is based on a set of differential equations describing DAP synthesis, DAP transport, differentiation of germen bacteria into soma and bacteria death. This approach differs form the precedents one by the level of description of the model and the numerical analysis done on the model.
By conducting robustness and optimization analysis on two different systems, one with a constant rate of differentiation against one with a rate of differentiation driven by the concentration of DAP, we evaluate benefits and drawbacks of both systems.
We first display the consistency of the biological system by providing a set of kinetic parameters such that the numerical simulation validate a given minimal behavior. Then we analyze the system robustness with regard to its kinetic parameters and finally we try to optimize the system output by adjusting some biologically relevant parameters.
