Paris/Stochastic model
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=== Gillespie's SSA === | === Gillespie's SSA === | ||
| + | From a computational point of view, the Gillespie SSA relies on a discrete events simulation of chemical reactions between individual molecules. A reaction <math>R_\mu</math> like | ||
| + | D’un point de vue informatique, la m´ethode de D.T. Gillespie repose sur une simulation `a | ||
| + | ´ev`enements discrets [Kre86] des r´eactions entre des mol´ecules individuelles. Une r´eaction Rμ, | ||
| + | par exemple A + B ! C, peut se produire quand les mol´ecules r´eactantes (A et B) se heurtent | ||
| + | avec suffisamment d’´energie pour cr´eer le produit (mol´ecule C). La probabilit´e P(μ, d¿) qu’une | ||
| + | r´eaction Rμ se produise durant un intervalle de temps infinit´esimal d¿ est proportionnelle `a | ||
| + | |||
| + | The algorithm developed by Gillespie consists | ||
=== Handling Membranes with SSA === | === Handling Membranes with SSA === | ||
Revision as of 15:14, 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.
Contents |
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. Extensions of Gillespie's SSA have been proposed to deal with compartments.
As our system is composed of a growing and heterogeneous population of bacteria, we propose to use this extension to simulate it. In the following paragraphs, we first detail the extended SSA we use and then we present some samples generated by our implementation using the set of parameters found in the numerical analysis of the model. Note that the main contribution here is in the development of the simulation algorithm.
Extended SSA
Gillespie's SSA
From a computational point of view, the Gillespie SSA relies on a discrete events simulation of chemical reactions between individual molecules. A reaction <math>R_\mu</math> like
D’un point de vue informatique, la m´ethode de D.T. Gillespie repose sur une simulation `a ´ev`enements discrets [Kre86] des r´eactions entre des mol´ecules individuelles. Une r´eaction Rμ, par exemple A + B ! C, peut se produire quand les mol´ecules r´eactantes (A et B) se heurtent avec suffisamment d’´energie pour cr´eer le produit (mol´ecule C). La probabilit´e P(μ, d¿) qu’une r´eaction Rμ se produise durant un intervalle de temps infinit´esimal d¿ est proportionnelle `a
The algorithm developed by Gillespie consists
Handling Membranes with SSA
Extended Algorithm
MGS Implementation
le code
