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

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 mRNA and RNA content in a cell. We provide theoretical and numerical evidence that the robustness of the gene expression is increased in the presence of RNA.