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A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

Bronstein, L. and Koeppl, H. :
A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks.
[Online-Edition: http://aip.scitation.org/doi/10.1063/1.5003892]
In: The Journal of Chemical Physics, 148 (1) ISSN 00219606
[Article] , (2018)

Official URL: http://aip.scitation.org/doi/10.1063/1.5003892

Abstract

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.

Item Type: Article
Erschienen: 2018
Creators: Bronstein, L. and Koeppl, H.
Title: A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks
Language: English
Abstract:

Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.

Journal or Publication Title: The Journal of Chemical Physics
Volume: 148
Number: 1
Publisher: American Institute of Physics (AIP)
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
18 Department of Electrical Engineering and Information Technology
Date Deposited: 02 Mar 2018 08:23
DOI: 10.1063/1.5003892
Official URL: http://aip.scitation.org/doi/10.1063/1.5003892
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