Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion
Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion
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DOI：
10.1007/978-3-319-45833-5_2
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发表时间：
2017-01-01
期刊：
影响因子：
--
通讯作者：
Wolf, Verena
中科院分区：
文献类型：
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作者：
Andreychenko, Alexander;Bortolussi, Luca;Wolf, Verena
由于化学反应的随机性，离散状态随机模型及其分析成为化学反应研究的热点。一个广泛使用的方法是描述的时间演变的化学主方程（CME）的这样的系统。在本文中，我们研究了两种方法来近似CME的潜在概率分布。第一种方法是基于统计矩的整合和基于最大熵原理的分布重建。第二种方法依赖于使用系统尺寸展开的CME的概率分布的解析近似，考虑比线性噪声近似更高阶的项。我们考虑基因表达网络与单峰和多峰蛋白质分布比较的准确性，这两种方法。我们发现，这两种方法提供了准确的近似CME的分布，但有不同的优点和应用中的限制。
The stochastic nature of chemical reactions has resulted in an increasing research interest in discrete-state stochastic models and their analysis. A widely used approach is the description of the temporal evolution of such systems in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach relies on an analytical approximation of the probability distribution of the CME using the system size expansion, considering higher order terms than the linear noise approximation. We consider gene expression networks with unimodal and multimodal protein distributions to compare the accuracy of the two approaches. We find that both methods provide accurate approximations to the distributions of the CME while having different benefits and limitations in applications.