Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments

The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach.Author Summary: Cellular reaction networks show a substantial degree of complexity, and many of the regulatory mechanisms are yet to be discovered. Therefore, building detailed mathematical models of complete networks is not only unrewarding but most often impossible. Instead, focus is put on small subnetworks such as the transcriptional circuitry associated with a few genes. Practically, those subnetworks are still embedded in the cellular environment and are consequently modulated by it. The mathematical framework that we present in this work allows to build models of such subnetworks only, while still incorporating the impact of the environment. Such models are instrumental not only for advancing our biological understanding through them, but also for the reliable forward engineering of new subnetworks in synthetic biology.