Dynamic Bounds on Stochastic Chemical Kinetic Systems Using Semidefinite Programming

TL;DR

This paper extends the use of moment-based semidefinite programming to compute time-dependent bounds on stochastic chemical kinetic systems, providing a rigorous method for analyzing their dynamic behavior.

Contribution

It introduces a novel approach to obtain dynamic bounds on stochastic chemical systems using semidefinite programming, building on previous stationary distribution methods.

Findings

Successfully derived time-varying bounds for stochastic systems

Extended semidefinite programming techniques to dynamic problems

Provided rigorous bounds on molecular counts over time

Abstract

Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using moment-based semidefinite programs (SDPs). In particular, they showed that moment-based SDPs can be used to calculate rigorous bounds on various descriptions of the stochastic chemical kinetic system's stationary distribution(s) -- for example, mean molecular counts, variances in these counts, and so on. In this paper, we show that these ideas can be extended to the corresponding dynamic problem, calculating time-varying bounds on the same descriptions.