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

Bronstein, L. ; 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
[Artikel] , (2018)

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

Kurzbeschreibung (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.

Typ des Eintrags: Artikel
Erschienen: 2018
Autor(en): Bronstein, L. ; Koeppl, H.
Titel: A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks
Sprache: Englisch
Kurzbeschreibung (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.

Titel der Zeitschrift, Zeitung oder Schriftenreihe: The Journal of Chemical Physics
Band: 148
(Heft-)Nummer: 1
Verlag: American Institute of Physics (AIP)
Fachbereich(e)/-gebiet(e): 18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik > Bioinspirierte Kommunikationssysteme
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik
18 Fachbereich Elektrotechnik und Informationstechnik
Hinterlegungsdatum: 02 Mär 2018 08:23
DOI: 10.1063/1.5003892
Offizielle URL: http://aip.scitation.org/doi/10.1063/1.5003892
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