NDLI: Method of conditional moments (MCM) for the Chemical Master Equation : A unified framework for the method of moments and hybrid stochastic-deterministic models

Content Provider	Springer Nature Link
Author	Hasenauer, J. Wolf, V. Kazeroonian, A. Theis, F. J.
Copyright Year	2013
Abstract	The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasible. In this paper we introduce the method of conditional moments (MCM), a novel approximation method for the solution of the CME. The MCM employs a discrete stochastic description for low-copy number species and a moment-based description for medium/high-copy number species. The moments of the medium/high-copy number species are conditioned on the state of the low abundance species, which allows us to capture complex correlation structures arising, e.g., for multi-attractor and oscillatory systems. We prove that the MCM provides a generalization of previous approximations of the CME based on hybrid modeling and moment-based methods. Furthermore, it improves upon these existing methods, as we illustrate using a model for the dynamics of stochastic single-gene expression. This application example shows that due to the more general structure, the MCM allows for the approximation of multi-modal distributions.
Starting Page	687
Ending Page	735
Page Count	49
File Format	PDF
ISSN	03036812
Journal	Journal of Mathematical Biology
Volume Number	69
Issue Number	3
e-ISSN	14321416
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-08-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Continuous-time discrete-state Markov process Chemical Master Equation Method of moments Hybrid stochastic-determinstic models Differential algebraic equations Gene expression Mathematical and Computational Biology Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Agricultural and Biological Sciences Modeling and Simulation

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