Robust ergodicity and tracking in antithetic integral control of stochastic biochemical reaction networks

TL;DR

This paper investigates conditions for ensuring robust ergodicity and tracking in stochastic biochemical reaction networks controlled by the antithetic integral control motif, using both quantitative and qualitative verification methods.

Contribution

It introduces two novel approaches—interval matrices and sign properties—for verifying ergodicity and controllability in large reaction networks with fixed topology.

Findings

Both methods successfully verify conditions for large networks.

Results extend previous work by providing scalable verification techniques.

The approaches are grounded in control theory, linear programming, and graph theory.

Abstract

Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, the most recent one being the so-called Antithetic Integral Control (AIC) motif in Briat et al. (Cell Systems, 2016). Several favorable properties for the AIC motif have been demonstrated for classes of reaction networks that satisfy certain irreducibility, ergodicity and output controllability conditions. Here we address the problem of verifying these conditions for large sets of reaction networks with fixed topology using two different approaches. The first one is quantitative and relies on the notion of interval matrices while the second one is qualitative and is based on sign properties of matrices. The obtained results lie in the same spirit as those obtained in Briat et al. (Cell Systems, 2016) where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programming conditions and graph theoretic conditions.