A moment-convergence method for stochastic analysis of biochemical reaction networks

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in...

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Vydáno v:The Journal of chemical physics Ročník 144; číslo 19; s. 194109
Hlavní autoři: Zhang, Jiajun, Nie, Qing, Zhou, Tianshou
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States 21.05.2016
Témata:
Algorithms
Biochemical Phenomena
Computer Simulation
Gene Expression
Gene Regulatory Networks
Kinetics
Mathematical Concepts
Metabolic Networks and Pathways
Models, Biological
Models, Chemical
Probability
Stochastic Processes
ISSN:1089-7690, 1089-7690
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Shrnutí:Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.
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ISSN:1089-7690
1089-7690
DOI:10.1063/1.4950767