反应扩散过程的随机模拟：双分子反应的算法
Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
摘要：
最近提出了几种随机模拟算法（SSA），用于模拟细胞和分子生物学中的反应扩散过程。本文研究了两种常用的SSA。第一个SSA是由反应扩散主方程描述的格点模型。第二个SSA是一个非格点模型的基础上模拟的布朗运动的单个分子和他们的反应碰撞。在这两种情况下，它表明，通常使用的实施双分子反应（即形式A + B -> C，或A + A -> C的反应）可能会导致不正确的结果。两个SSA的改进建议，克服突出的困难。特别是，一个公式，提出了最小可能的隔间大小（格间距），可以正确地实现在第一个模型。该实施方案使用了一个新的公式，每隔室（晶格位点）的双分子反应速率。
英文摘要：
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).
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