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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

Topics:
Biology and other natural sciences, Probability theory and stochastic processes

Year: 2007

DOI identifier: 10.1088/1478-3975/4/1/003

OAI identifier:
oai:generic.eprints.org:592/core69

Provided by:
Mathematical Institute Eprints Archive

Downloaded from
http://eprints.maths.ox.ac.uk/592/1/ph7_1_003.pdf

- (1974). A stochastic model related to the telegrapher’s equation Rocky Mt.
- (2007). Dynamics of polydisperse irreversible adsorption: a pharmacological example Math. Models Methods Appl. Sci. at press (Preprint org/physics/0602001)
- (1977). Exact stochastic simulation of coupled chemical
- (2005). Faciliated transport of a Dpp/Scw heterodimer by Sog/Tsg leads to robust patterning of the Drosophila blastoderm embryo
- (2004). From individual to collective behaviour in bacterial chemotaxis
- (2006). Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations
- (1995). Introduction to Perturbation Methods
- (2007). On chemisorption of polymers to solid surfaces
- (1993). Random and cooperative sequential adsorption Rev.
- (1983). Random Walks in Biology (Princeton:
- (1982). Reduction of the Fokker–Planck equation with an adsorbing or reflecting boundary to the diffusion equation and the radiation boundary condition Phys.
- (1979). Simple chemical reaction systems with limit cycle behaviour
- (2006). Spatially distributed stochastic systems: equation-free and equation-assisted preconditioned computation
- (1943). Stochastic problems in physics and astronomy Rev.
- (2005). Stochastic reaction– diffusion simulation with
- (2004). Stochastic simulation of chemical reactions with spatial resolution and single molecule detail Phys.
- (1996). Stochastic simulation of coupled reaction–diffusion processes
- (1989). The Fokker–Planck Equation, Methods of Solution and Applications
- (1975). The Mathematics of Diffusion (Oxford:
- (2007). Time scale of random sequential adsorption Phys.

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