A practical guide to stochastic simulations of reaction-diffusion processes

TL;DR

This paper provides a comprehensive, accessible introduction to stochastic simulation methods for reaction-diffusion processes, covering classical algorithms, molecular diffusion, and advanced techniques with illustrative examples.

Contribution

It offers a practical, step-by-step guide to stochastic reaction-diffusion modeling, connecting stochastic and deterministic approaches for researchers and students.

Findings

Explains Gillespie algorithm for chemical reactions

Introduces stochastic algorithms for molecular diffusion

Provides overview of advanced stochastic methods

Abstract

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.