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The stochastic nature of chemical reactions involving randomly fluctuatingpopulation sizes has lead to a growing research interest in discrete-statestochastic models and their analysis. A widely-used approach is the descriptionof the temporal evolution of the system in terms of a chemical master equation(CME). In this paper we study two approaches for approximating the underlyingprobability distributions of the CME. The first approach is based on anintegration of the statistical moments and the reconstruction of thedistribution based on the maximum entropy principle. The second approach relieson an analytical approximation of the probability distribution of the CME usingthe system size expansion, considering higher-order terms than the linear noiseapproximation. We consider gene expression networks with unimodal andmultimodal protein distributions to compare the accuracy of the two approaches.We find that both methods provide accurate approximations to the distributionsof the CME while having different benefits and limitations in applications.

Distribution approximations for the chemical master equation: comparison of the method of moments and the system size expansion