The Mathematical Institute, University of Oxford, Eprints Archive

Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions

Erban, R. and Chapman, S. J. (2009) Stochastic modelling of reaction-diffusion processes:
algorithms for bimolecular reactions.
Not specified . (Submitted)

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Abstract

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A+B → C, or A+A → C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:835
Deposited By:Dr M. Stoll
Deposited On:08 Oct 2009 17:22
Last Modified:08 Oct 2009 17:22

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