Reachability analysis for switched affine systems and its application to controlled stochastic biochemical reaction networks

Under suitable assumptions, the moments of a controlled stochastic biochemical reaction network can be computed as the solution of a switched affine system. Motivated by this application, we propose a new method to approximate projections of the reachable set of a switched affine system onto a plane of interest. Our method does not require the computation of the full reachable set, thus allowing us to efficiently analyze the moments of a species of interest in arbitrarily large biochemical networks. To illustrate the benefits of the proposed method we consider a controlled gene expression model involving two species: the mRNA and the corresponding protein. The proposed approach can be used to estimate the reachable set of the protein mean and variance, under less stringent assumptions than those adopted in the literature. Specifically, we address the cases of multiple controlled reactions and heterogeneous population.