Schnoerr David, Sanguinetti Guido, Grima Ramon
School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.
J Chem Phys. 2015 Nov 14;143(18):185101. doi: 10.1063/1.4934990.
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.
近年来，化学主方程的矩封闭近似（MAs）已成为研究化学反应系统中随机效应的一种常用方法。文献中已经提出并应用了几种不同的MA方法，但它们之间的性能表现仍不清楚。在本文中，我们通过应用正态、泊松、对数正态和中心矩忽略MAs来研究化学系统的随机性质，这些化学系统的确定性速率方程表现出双稳性、超敏感性和振荡行为。我们的结果表明，正态MA比其他研究的MA更具优势。具体而言，我们发现：（i）对于正态封闭，得到物理上有意义结果（如正均值和方差）的参数空间区域的大小，比其他三种封闭要大得多；（ii）在所有封闭都给出物理上有意义结果的参数空间区域，四种封闭预测的准确性（相对于使用随机模拟算法的模拟）相当；（iii）对于涉及分子数守恒定律的系统，泊松和对数正态MAs没有唯一的定义。我们还描述了新的软件包MOCA，它能够在图形用户界面中对各种MA方法进行自动数值分析，并用于执行本文中的比较分析。MOCA允许用户开发新的封闭方法，并且可以处理多项式、非多项式以及与时间相关的倾向函数，因此几乎适用于任何化学反应系统。
