Extracting Information from Stochastic Trajectories of Gene Expression

TL;DR

This paper develops a Fisher information framework for analyzing stochastic gene expression trajectories, enabling optimal experiment design and capacity estimation for biological systems modeled by continuous-time Markov processes.

Contribution

It formulates Fisher information for Markov process trajectories, applies it to gene expression models, and links it to mutual information for capacity analysis.

Findings

Validated Fisher information on gene expression models

Optimized measurement periods for microscopy experiments

Derived channel capacities for nonlinear gene regulation

Abstract

Gene expression is a stochastic process in which cells produce biomolecules essential to the function of life. Modern experimental methods allow for the measurement of biomolecules at single-cell and single-molecule resolution over time. Mathematical models are used to make sense of these experiments. The codesign of experiments and models allows one to use models to design optimal experiments, and to find experiments which provide as much information as possible about relevant model parameters. Here, we provide a formulation of Fisher information for trajectories sampled from the continuous time Markov processes often used to model biological systems, and apply the result to potentially correlated measurements of stochastic gene expression. We validate the result on two commonly used models of gene expression and show it can be used to optimize measurement periods for simulated single-cell fluorescence microscopy experiments. Finally, we use a connection between Fisher information and mutual information to derive channel capacities of nonlinearly regulated gene expression.