dorsal/arxiv
View SchemaRealistic boundary conditions for stochastic simulations of reaction-diffusion processes
| Authors | Radek Erban, S. Jonathan Chapman |
|---|---|
| Categories | |
| ArXiv ID | physics/0611251 |
| URL | https://arxiv.org/abs/physics/0611251 |
| DOI | 10.1088/1478-3975/4/1/003 |
Abstract
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.
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"abstract": "Many cellular and subcellular biological processes can be described in terms\nof diffusing and chemically reacting species (e.g. enzymes). Such\nreaction-diffusion processes can be mathematically modelled using either\ndeterministic partial-differential equations or stochastic simulation\nalgorithms. The latter provide a more detailed and precise picture, and several\nstochastic simulation algorithms have been proposed in recent years. Such\nmodels typically give the same description of the reaction-diffusion processes\nfar from the boundary of the simulated domain, but the behaviour close to a\nreactive boundary (e.g. a membrane with receptors) is unfortunately\nmodel-dependent. In this paper, we study four different approaches to\nstochastic modelling of reaction-diffusion problems and show the correct choice\nof the boundary condition for each model. The reactive boundary is treated as\npartially reflective, which means that some molecules hitting the boundary are\nadsorbed (e.g. bound to the receptor) and some molecules are reflected. The\nprobability that the molecule is adsorbed rather than reflected depends on the\nreactivity of the boundary (e.g. on the rate constant of the adsorbing chemical\nreaction and on the number of available receptors), and on the stochastic model\nused. This dependence is derived for each model.",
"arxiv_id": "physics/0611251",
"authors": [
"Radek Erban",
"S. Jonathan Chapman"
],
"categories": [
"physics.bio-ph",
"q-bio.QM"
],
"doi": "10.1088/1478-3975/4/1/003",
"title": "Realistic boundary conditions for stochastic simulations of reaction-diffusion processes",
"url": "https://arxiv.org/abs/physics/0611251"
},
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