Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
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DOI：
10.1088/1478-3975/4/1/003
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发表时间：
2007-03-01
期刊：
影响因子：
2
通讯作者：
Chapman, S. Jonathan
中科院分区：
文献类型：
--
作者：
Erban, Radek;Chapman, S. Jonathan
许多细胞和亚细胞生物过程可以用扩散和化学反应物质（例如酶）来描述。这种反应扩散过程可以使用确定性偏微分方程或随机模拟算法进行数学建模。后者提供了更详细和精确的图像，并且近年来提出了几种随机模拟算法。这些模型通常对远离模拟域边界的反应扩散过程给出相同的描述，但不幸的是，靠近反应边界（例如带有受体的膜）的行为是依赖于模型的。在本文中，我们研究了反应扩散问题随机建模的四种不同方法，并展示了每种模型边界条件的正确选择。反应边界被视为部分反射，这意味着一些撞击边界的分子被吸附（例如与受体结合），而一些分子被反射。分子被吸附而不是反射的概率取决于边界的反应性（例如，吸附化学反应的速率常数和可用受体的数量）以及所使用的随机模型。这种依赖性是针对每个模型得出的。
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.