Stochastic Gene Expression in Cells: A Point Process Approach

This paper investigates the stochastic fluctuations of the number of copies of a given protein in a cell. This problem has already been addressed in the past, and closed-form expressions of the mean and variance have been obtained for a simplified stochastic model of the gene expression. These results have been obtained under the assumption that the durations of all the protein production steps are exponentially distributed. In such a case, a Markovian approach (via Fokker--Planck equations) is used to derive analytic formulas of the mean and the variance of the number of proteins at equilibrium. This assumption is, however, not totally satisfactory from a modeling point of view since the distribution of the duration of some steps is more likely to be Gaussian, if not almost deterministic. In such a setting, Markovian methods can no longer be used. A finer characterization of the fluctuations of the number of proteins is therefore of primary interest to understand the general economy of the cell. In this ...