Out-of-equilibrium gene expression fluctuations in presence of extrinsic noise

Cell-to-cell variability in protein concentrations is strongly affected by extrinsic noise, especially for highly expressed genes. Extrinsic noise can be due to fluctuations of several possible cellular factors connected to cell physiology and to the level of key enzymes in the expression process. However, how to identify the predominant sources of extrinsic noise in a biological system is still an open question. This work considers a general stochastic model of gene expression with extrinsic noise represented as colored fluctuations of the different model rates, and focuses on the out-of-equilibrium expression dynamics. Combining analytical calculations with stochastic simulations, we fully characterize how extrinsic noise shapes the protein variability during gene activation or inactivation, depending on the prevailing source of extrinsic variability, on its intensity and timescale. In particular, we show that qualitatively different noise profiles can be identified depending on which are the fluctuating parameters. This indicates an experimentally accessible way to pinpoint the dominant sources of extrinsic noise using time-coarse experiments. Author summaryGenetically identical cells living in the same environment may differ in their phenotypic traits. These differences originate from the inherent stochasticity in all cellular processes, starting from the basic process of gene expression. At this level, large part of the variability comes from cell-to-cell differences in the rates of the molecular reactions due to stochasticity in the level of key enzymes or in physiological parameters such as cell volume or growth rate. Which expression rates are predominantly affected by these so-called "extrinsic" fluctuations and how they impact the level of protein concentration are still open research questions. In this work, we tackle the protein fluctuation dynamics while approaching a steady state after gene activation or repression in presence of extrinsic noise. Our analytical results and simulations show the different consequences of alternative dominant sources of extrinsic noise, thus providing an experimentally-accessible way to distinguish them in specific systems.