On the origins of approximations for stochastic chemical kinetics
On the origins of approximations for stochastic chemical kinetics
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DOI：
10.1063/1.2062048
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发表时间：
2005-10-22
影响因子：
4.4
通讯作者：
Rawlings, JB
中科院分区：
文献类型：
--
作者：
Haseltine, EL;Rawlings, JB
本文考虑由离散主方程所支配的随机化学动力学近似的推导。这里，(1)基于快反应和慢反应而不是快反应和慢反应的划分以及(2)条件概率密度的概念被用来从原始的主方程推导出近似的、本质上是马尔可夫的划分的主方程。在松弛时间变量所规定的不同条件下，这种近似同时产生了平衡近似和混合(确定性或朗之万方程与离散随机模拟耦合)的近似。此外，该推导还指出了以往混合系统和平衡系统证明中的一些不足之处，并证明了原始主方程和近似主方程之间的联系。两个简单的例子说明了这两种近似方法的适用情况，并证明了这两种方法的有效性。(C)2005年美国物理研究所。
This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies. (c) 2005 American Institute of Physics.