A Fokker-Planck approach to the study of robustness in gene expression

TL;DR

This paper uses Fokker-Planck equations to analyze how micro RNA enhances robustness in gene expression, showing reduced variability in messenger RNA levels through theoretical and numerical methods.

Contribution

It introduces a Fokker-Planck framework to quantify gene expression robustness and provides explicit solutions and insights into parameter effects.

Findings

Micro RNA presence reduces variability in messenger RNA levels.

Explicit formulas for solutions demonstrate increased robustness.

Numerical simulations support the theoretical results.

Abstract

We study several Fokker-Planck equations arising from a stochastic chemical kinetic system modeling a gene regulatory network in biology. The densities solving the Fokker-Planck equations describe the joint distribution of the messenger RNA and micro RNA content in a cell. We provide theoretical and numerical evidences that the robustness of the gene expression is increased in the presence of micro RNA. At the mathematical level, increased robustness shows in a smaller coefficient of variation of the marginal density of the messenger RNA in the presence of micro RNA. These results follow from explicit formulas for solutions. Moreover, thanks to dimensional analyses and numerical simulations we provide qualitative insight into the role of each parameter in the model. As the increase of gene expression level comes from the underlying stochasticity in the models, we eventually discuss the choice of noise in our models and its influence on our results.