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

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.

arXiv commentMinor changes and clarifications; corrected some typos

References in corpus (8)

• Comparison of different moment-closure approximations for stochastic chemical kinetics
• Action Principle in Nonequilibrium Statistical Dynamics
• Validity conditions for moment closure approximations in stochastic chemical kinetics
• Optimal Belief Approximation
• Statistical physics approaches to subnetwork dynamics in biochemical systems
• Simulation of stochastic network dynamics via entropic matching
• The Truncated Moment Problem on ${\mathbb{N}}_0$
• Approximation scheme for master equations: variational approach to multivariate case

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• Preserving Bifurcations through Moment Closures