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 ribsome 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. For instance, we exemplarily formulate and solve a marginal master equation describing the protein translation and degradation in a fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio

Marginal dynamics of stochastic biochemical networks in random environments

Stochastic simulation algorithms provide a powerful means to understand complex biochemical processes as well as to solve the inverse problem of reconstructing hidden states and parameters from experimental single-cell data. At presence, a repertoire of efficient algorithms for simulating and calibrating stochastic reaction networks is available. However, most of these approaches do not account for the fact that each cell of a clonal population is exposed to a random extrinsic environment, i.e., the agglomerate of so-called extrinsic factors such as cell size, shape or cell cycle stage. We recently proposed a dynamic description of stochastic chemical kinetics in random but unknown extrinsic environments, reflected by a stochastic process where uncertain parameters are marginalized out. In this work we further investigate that process and provide additional analytical results. We demonstrate the marginalization using several biologically relevant parameter distributions and derive exact waiting-time distributions. We further show that the marginalized process model can achieve a variance reduction in the context of parameter inference