Stochastic reaction networks with input processes: Analysis and application to gene expression inference

Abstract

Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and inference of these systems is addressed by parametric approaches, where the laws governing exogenous input processes, if present, are themselves fixed in advance. Motivated by reporter gene systems, widely utilized in biology to monitor gene activation at the individual cell level, we address the analysis of reaction networks with state-affine reaction rates and arbitrary input processes. We derive a generalization of the so-called moment equations where the dynamics of the network statistics are expressed as a function of the input process statistics. In stationary conditions, we provide a spectral analysis of the system and elaborate on connections with linear filtering. We then apply the theoretical results to develop a method for the reconstruction of input process statistics, namely the gene activation autocovariance function, from reporter gene population snapshot data, and demonstrate its performance on a simulated case study.

Stationary distributions and metastable behaviour for self-regulating proteins with general lifetime distributions

“…The dynamics of these processes is therefore well described by stochastic Markov processes in continuous time with discrete state space [15,22,42]. While few-component or linear-kinetics systems [16] allow for exact analysis, in more complex system one often uses approximative methods [12], such as moment closure [4], linear-noise approximation [3,9], hybrid formulations [25,26,33], and multi-scale techniques [38,39].…”