Robust ergodicity and tracking in antithetic integral control of stochastic biochemical reaction networks
For researchers in systems and synthetic biology, this work provides practical tools to verify control-theoretic properties of stochastic reaction networks, though it is an incremental extension of existing methods.
The paper develops quantitative and qualitative methods to verify irreducibility, ergodicity, and output controllability conditions for large sets of stochastic reaction networks with fixed topology, enabling robust antithetic integral control. The results extend prior work by providing interval matrix and sign-based criteria.
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.