Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Visiting Professor



p.degond Website




Huxley BuildingSouth Kensington Campus






BibTex format

author = {Degond, P and Herda, M and Mirrahimi, S},
doi = {10.3934/mbe.2020338},
journal = {Mathematical Biosciences and Engineering},
pages = {6459--6486},
title = {A Fokker-Planck approach to the study of robustness in gene expression},
url = {},
volume = {17},
year = {2020}

RIS format (EndNote, RefMan)

AB - 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 μRNA content in a cell. We provide theoretical and numerical evidence that the robustness of the gene expression is increased in the presence of μRNA. At the mathematical level, increased robustness shows in a smaller coefficient of variation of the marginal density of the mRNA in the presence of μRNA. 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.
AU - Degond,P
AU - Herda,M
AU - Mirrahimi,S
DO - 10.3934/mbe.2020338
EP - 6486
PY - 2020///
SN - 1547-1063
SP - 6459
TI - A Fokker-Planck approach to the study of robustness in gene expression
T2 - Mathematical Biosciences and Engineering
UR -
UR -
VL - 17
ER -