The Mathematical Institute, University of Oxford, Eprints Archive

Reactive boundary conditions for stochastic simulations of reaction-diffusion processes

Erban, Radek and Chapman, S. J. (2007) Reactive boundary conditions for stochastic simulations of reaction-diffusion processes. Physical Biology, 4 (1). pp. 16-28. ISSN 1478-3975


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Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction–diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction–diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction–diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecules are reflected. The probability that the molecule is adsorbed rather than reflected depends on the reactivity of the boundary (e.g. on the rate constant of the adsorbing chemical reaction and on the number of available receptors), and on the stochastic model used. This dependence is derived for each model.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
O - Z > Probability theory and stochastic processes
Research Groups:Oxford Centre for Industrial and Applied Mathematics
Centre for Mathematical Biology
ID Code:592
Deposited By: Jon Chapman
Deposited On:16 May 2007
Last Modified:29 May 2015 18:25

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