Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Degond, P and Herda, M and Mirrahimi, S},
journal = {Mathematical Biosciences and Engineering},
title = {A Fokker-Planck approach to the study of robustness in gene expression},
url = {},

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. Thedensities solving the Fokker-Planck equations describe the joint distribution ofthe mRNA and µRNA content in a cell. We provide theoretical and numericalevidence that the robustness of the gene expression is increased in the presenceof µRNA. At the mathematical level, increased robustness shows in a smallercoefficient of variation of the marginal density of the mRNA in the presenceof 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 ofgene expression level comes from the underlying stochasticity in the models,we eventually discuss the choice of noise in our models and its influence on ourresults.
AU - Degond,P
AU - Herda,M
AU - Mirrahimi,S
SN - 1547-1063
TI - A Fokker-Planck approach to the study of robustness in gene expression
T2 - Mathematical Biosciences and Engineering
UR -
ER -