The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems
The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems
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DOI：
10.1063/1.3074302
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发表时间：
2009-03-07
影响因子：
4.4
通讯作者：
Petzold, Linda R.
中科院分区：
文献类型：
--
作者：
Lampoudi, Sotiria;Gillespie, Dan T.;Petzold, Linda R.
非均质随机模拟算法(ISSA)是随机模拟算法的一种变种，在随机模拟算法中，体系的空间非均匀体积被分成均质子体积，这些子体积中的化学反应通过分子在相邻子体积之间的扩散转移来增强。当系统的扩散转移比化学反应发生得更频繁时，ISSA可能会慢得令人望而却步。本文提出了多项式模拟算法(MSA)，该算法一方面在扩散转移事件多于反应事件时优于ISSA算法，另一方面能够以比确定性-随机混合算法更高的精度处理较小的反应物群体。MSA以通常的ISSA方式处理反应，但使用适当的条件二项式随机变量来表示从任何给定子体积扩散到规定距离内的相邻分子的净数量。仿真结果表明了该算法的优越性。
The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that diffusive transfers occur much more frequently than chemical reactions. In this paper we present the Multinomial Simulation Algorithm (MSA), which is designed to, on the one hand, outperform the ISSA when diffusive transfer events outnumber reaction events, and on the other, to handle small reactant populations with greater accuracy than deterministic-stochastic hybrid algorithms. The MSA treats reactions in the usual ISSA fashion, but uses appropriately conditioned binomial random variables for representing the net numbers of molecules diffusing from any given subvolume to a neighbor within a prescribed distance. Simulation results illustrate the benefits of the algorithm.