Please use this identifier to cite or link to this item: doi:10.22028/D291-31039
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Title: Distribution Approximations for the Chemical Master Equation: Comparison of the Method of Moments and the System Size Expansion
Author(s): Andreychenko, Alexander
Bortolussi, Luca
Grima, Ramon
Thomas, Philipp
Wolf, Verena
Editor(s): Graw, Frederik
Matthäus, Franziska
Pahle, Jürgen
Language: English
Title: Modeling Cellular Systems
Startpage: 39
Endpage: 66
Publisher/Platform: Springer
Year of Publication: 2017
Place of publication: Cham
Publikation type: Book Chapter
Abstract: 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.
DOI of the first publication: 10.1007/978-3-319-45833-5_2
URL of the first publication:
Link to this record: hdl:20.500.11880/29191
ISBN: 978-3-319-45833-5
Date of registration: 28-May-2020
Notes: Contributions in Mathematical and Computational Sciences ; volume 11
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Professorship: MI - Prof. Dr. Verena Wolf
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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