Bounding transient moments of stochastic chemical reactions

Yuta Sakurai, Yutaka Hori

Research output: Contribution to journalArticle

Abstract

The predictive ability of stochastic chemical reactions is currently limited by the lack of closed form solutions to the governing chemical master equation. To overcome this limitation, this letter proposes a computational method capable of predicting mathematically rigorous upper and lower bounds of transient moments for reactions governed by the law of mass action. We first derive an equation that transient moments must satisfy based on the moment equation. Although this equation is underdetermined, we introduce a set of semidefinite constraints known as moment condition to narrow the feasible set of the variables in the equation. Using these conditions, we formulate a semidefinite program that efficiently and rigorously computes the bounds of transient moment dynamics. The proposed method is demonstrated with illustrative numerical examples and is compared with related works to discuss advantages and limitations.

LanguageEnglish
Article number8462752
Pages290-295
Number of pages6
JournalIEEE Control Systems Letters
Volume3
Issue number2
DOIs
Publication statusPublished - 2019 Apr 1

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Chemical Reaction
Chemical reactions
Moment
Moment Equations
Semidefinite Program
Moment Conditions
Master Equation
Computational methods
Closed-form Solution
Computational Methods
Upper and Lower Bounds
Numerical Examples

Keywords

  • LMIs
  • Markov processes
  • optimization
  • Stochastic systems
  • systems biology

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

Cite this

Bounding transient moments of stochastic chemical reactions. / Sakurai, Yuta; Hori, Yutaka.

In: IEEE Control Systems Letters, Vol. 3, No. 2, 8462752, 01.04.2019, p. 290-295.

Research output: Contribution to journalArticle

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