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Finite state projection for approximating the stationary solution to the chemical master equation using reaction rate equations.

Authors
  • Reid, Brandon M1
  • Sidje, Roger B2
  • 1 Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487, USA. Electronic address: [email protected]
  • 2 Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487, USA. Electronic address: [email protected]
Type
Published Article
Journal
Mathematical biosciences
Publication Date
Aug 23, 2019
Volume
316
Pages
108243–108243
Identifiers
DOI: 10.1016/j.mbs.2019.108243
PMID: 31449893
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

When modeling a physical system using a Markov chain, it is often instructive to compute its probability distribution at statistical equilibrium, thereby gaining insight into the stationary, or long-term, behavior of the system. Computing such a distribution directly is problematic when the state space of the system is large. Here, we look at the case of a chemical reaction system that models the dynamics of cellular processes, where it has become popular to constrain the computational burden by using a finite state projection, which aims only to capture the most likely states of the system, rather than every possible state. We propose an efficient method to further narrow these states to those that remain highly probable in the long run, after the transient behavior of the system has dissipated. Our strategy is to quickly estimate the local maxima of the stationary distribution using the reaction rate formulation, which is of considerably smaller size than the full-blown chemical master equation, and from there develop adaptive schemes to profile the distribution around the maxima. We include numerical tests that show the efficiency of our approach. Copyright © 2019. Published by Elsevier Inc.

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