Comparison of different moment-closure approximations for stochastic chemical kinetics

TL;DR

This paper compares various moment-closure approximations for stochastic chemical kinetics, finding the normal closure generally performs better in terms of physical validity and applicability across different systems.

Contribution

The study systematically evaluates normal, Poisson, log-normal, and central-moment-neglect MAs on complex chemical systems, introducing the MOCA software for automated analysis.

Findings

Normal MA has a larger valid parameter space.

Predictions of all closures are similarly accurate within valid regions.

Poisson and log-normal MAs are not well-defined with conservation laws.

Abstract

In recent years moment-closure approximations (MA) 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; (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.