Comparison of different moment-closure approximations for stochastic chemical kinetics
Comparison of different moment-closure approximations for stochastic chemical kinetics
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DOI：
10.1063/1.4934990
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发表时间：
2015-11-14
影响因子：
4.4
通讯作者：
Grima, Ramon
中科院分区：
文献类型：
--
作者：
Schnoerr, David;Sanguinetti, Guido;Grima, Ramon
近年来，化学主方程的矩封闭近似法已成为研究化学反应体系中随机效应的一种常用方法。几种不同的MA方法已被提出并应用于文献中，但目前仍不清楚它们如何相互执行。在本文中，我们研究了正常的，泊松，对数正态分布，和中心矩忽略MA通过应用它们来了解化学系统的随机特性，其确定性速率方程的双稳态，超灵敏度和振荡行为的属性。我们的研究结果表明，正常的MA是有利的其他研究的MA。特别地，我们发现（i）参数空间的区域的大小，其中闭包给出物理上有意义的结果，例如，正均值和方差，是相当大的正常封闭比其他三个封闭，（ii）的准确性预测的四个封闭（相对于使用随机模拟算法的模拟）在所有闭包都给出物理上有意义的结果的参数空间区域中是相当的，Poisson和对数正态MA对于涉及分子数守恒律的系统不是唯一定义的。我们还描述了新的软件包莫卡，它使各种MA方法的自动数值分析在图形用户界面，并用于执行本文提出的比较分析。莫卡允许用户开发新的闭合方法，并可以处理多项式，非多项式，以及时间依赖的倾向函数，从而适用于几乎任何化学反应系统。(C)2015年作者。
In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system. (C) 2015 Author(s).