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

TL;DR

This paper develops a theoretical framework for analyzing stochastic reaction networks with arbitrary input processes, focusing on gene activation systems, and introduces a method to reconstruct input statistics from snapshot data.

Contribution

It generalizes moment equations for reaction networks with arbitrary inputs and applies spectral analysis to infer input process statistics from biological data.

Findings

Derived generalized moment equations incorporating input process statistics

Provided spectral analysis linking reaction network dynamics to linear filtering

Demonstrated input autocovariance reconstruction from simulated reporter gene data

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.