Bounding Transient Moments of Stochastic Chemical Reactions

TL;DR

This paper introduces a semidefinite programming approach to compute rigorous upper and lower bounds on transient moments in stochastic chemical reactions, addressing the lack of closed-form solutions for the chemical master equation.

Contribution

It develops a novel computational method using moment conditions and semidefinite programming to bound transient moments in stochastic chemical systems.

Findings

Method provides mathematically rigorous bounds on transient moments.

Numerical examples demonstrate effectiveness and advantages over existing methods.

Approach is computationally efficient and applicable to various reaction networks.

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 paper 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.