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

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Title: Distribution approximations for the chemical master equation: comparison of the method of moments and the system size expansion
Authors: Andreychenko, A
Bortolussi, L
Grima, R
Thomas, P
Wolf, V
Item Type: Chapter
Abstract: The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system 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.
Editors: Graw, F
Matthaus, F
Pahle, J
Issue Date: 9-May-2017
URI: http://hdl.handle.net/10044/1/72612
DOI: https://doi.org/10.1007/978-3-319-45833-5_2
ISBN: 978-3-319-45833-5
Publisher: Springer
Start Page: 39
End Page: 39
Journal / Book Title: Modeling Cellular Systems
Copyright Statement: © Springer International Publishing Switzerland 2017. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-45833-5_2
Keywords: q-bio.QM
q-bio.QM
cond-mat.stat-mech
math.NA
q-bio.MN
q-bio.SC
60J22, 44A60, 37N25
G.3; I.6.m
q-bio.QM
q-bio.QM
cond-mat.stat-mech
math.NA
q-bio.MN
q-bio.SC
60J22, 44A60, 37N25
G.3; I.6.m
Notes: 28 pages, 6 figures
Publication Status: Published
Online Publication Date: 2017-05-09
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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