  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.
