Protein synthesis driven by dynamical stochastic transcription

TL;DR

This paper introduces a mathematical framework that models the coupled stochastic dynamics of mRNA transcription and protein synthesis, enabling the calculation of protein density distributions from mRNA statistics.

Contribution

It presents a novel coupling of master equations and stochastic differential equations to analyze protein synthesis dynamics.

Findings

Provides analytical expressions for protein density distribution over time

Links mRNA production statistics to protein population dynamics

Offers a new approach for studying gene expression variability

Abstract

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.