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1 - Stochastic Simulation of Chemical Reactions

Published online by Cambridge University Press:  04 November 2019

Radek Erban  and
S. Jonathan Chapman
Radek Erban
Affiliation:
University of Oxford
S. Jonathan Chapman
Affiliation:
University of Oxford
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Summary

This chapter provides an introduction to stochastic methods for modelling spatially homogeneous systems of chemical reactions. The Gillespie stochastic simulation algorithm and the chemical master equation are presented using simple examples of chemical systems. The chemical master equation is analysed for chemical systems containing zeroth-order, first-order and second-order chemical reactions. For zeroth-order and first-order chemical reactions, the average behaviour of the stochastic chemical system is described by the ordinary differential equations (ODEs) given by the standard deterministic model. However, when we consider higher-order chemical reactions, for which the deterministic description is nonlinear, the deterministic ODE model does not provide an exact description of the average behaviour of the stochastic system.

Keywords

chemical master equationGillespie algorithmchemical reactionsprobability-generating functionpropensity functionstochastic simulation algorithmproductiondegradationdimerization
Type
Chapter
Information
Stochastic Modelling of Reaction–Diffusion Processes , pp. 1 - 32
Publisher: Cambridge University Press
Print publication year: 2020

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