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Stochastic reaction network models are widely utilized in biology andchemistry to describe the probabilistic dynamics of biochemical systems ingeneral, and gene interaction networks in particular. Most often, statisticalanalysis and inference of these systems is addressed by parametric approaches,where the laws governing exogenous input processes, if present, are themselvesfixed in advance. Motivated by reporter gene systems, widely utilized inbiology to monitor gene activation at the individual cell level, we address theanalysis of reaction networks with state-affine reaction rates and arbitraryinput processes. We derive a generalization of the so-called moment equationswhere the dynamics of the network statistics are expressed as a function of theinput process statistics. In stationary conditions, we provide a spectralanalysis of the system and elaborate on connections with linear filtering. Wethen apply the theoretical results to develop a method for the reconstructionof input process statistics, namely the gene activation autocovariancefunction, from reporter gene population snapshot data, and demonstrate itsperformance on a simulated case study.

Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems