Title :

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

Author(s) :

Degond, Pierre [Auteur]
Department of Mathematics [Imperial College London]
Herda, Maxime [Auteur]
Reliable numerical approximations of dissipative systems [RAPSODI]
Mirrahimi, Sepideh [Auteur]
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Journal title :

Mathematical Biosciences and Engineering

Pages :

6459-6486

Publisher :

AIMS Press

Publication date :

2020-09-24

ISSN :

1547-1063

English keyword(s) :

Gene expression
Micro RNA
Fokker-Planck Equation
Inverse Gamma distribution

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Sciences du Vivant [q-bio]/Biologie cellulaire
Sciences du Vivant [q-bio]/Biochimie, Biologie Moléculaire/Biologie moléculaire

English abstract : [en]

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 ...
Show more >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 numericalsimulations 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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL