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

Pierre Degond (1) , Maxime Herda (2, 3) , Sepideh Mirrahimi (4)

1 Department of Mathematics [Imperial College London]
2 RAPSODI - Reliable numerical approximations of dissipative systems
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Gene expression; Micro RNA; Fokker-Planck Equation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Biologie cellulaire; Biologie moléculaire

Pierre Degond, Maxime Herda, Sepideh Mirrahimi. A Fokker-Planck approach to the study of robustness in gene expression. 2020. ⟨hal-02882349v1⟩