Protein Synthesis Driven by Dynamical Stochastic Transcription
In this manuscript, we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations, while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time-dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.
KeywordsGene expression Stochasticity Exact solutions Dynamics
Mathematics Subject Classification92B05
We would like to thank the referees for their insights. Work supported by FAPESP, SP, Brazil (G. I., contract 2012/04723-4) and CNPq, Brazil (G. I., contract 202238/2014-8; M. F., contract 307238/2011-3; F. A., contract 306362/2012-0). O. R. thanks CNRS and LABEX Epigenmed for support.