A practical guide to stochastic simulations of reaction-diffusion processes

• DOI: 10.48550/arxiv.0704.1908
• Publication Date: 2007-01-01
• Authors: Erban, R; Chapman, J; Maini, P
• Keywords: 0301 basic medicine; 03 medical and health sciences; Quantitative Biology - Subcellular Processes; Physics Education (physics.ed-ph); FOS: Biological sciences; Physics - Physics Education; FOS: Physical sciences; Quantitative Biology - Quantitative Methods; Subcellular Processes (q-bio.SC); Quantitative Methods (q-bio.QM)

35 pages<br/>A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given. Finally, basic stochastic reaction-diffusion methods are presented. The connections between stochastic simulations and deterministic models are explained and basic mathematical tools (e.g. chemical master equation) are presented. The article concludes with an overview of more advanced methods and problems.<br/>