Interplay between stochasticity and negative feedback leads to pulsed dynamics and distinct gene activity patterns

Gene expression is an inherently stochastic process that depends on the structure of the biochemical regulatory network in which the gene is embedded. Here we study the dynamical consequences of the interplay between stochastic gene switching and the widespread negative feedback regulatory loop in a simple model of a biochemical regulatory network. Using a simplified hybrid simulation approach, in which only the gene activation is modeled stochastically, we find that stochasticity in gene switching by itself can induce pulses in the system, providing also analytical insights into their origin. Furthermore, we find that this simple network is able to reproduce both exponential and peaked distributions of gene active and inactive times similar to those that have been observed experimentally. This simplified hybrid simulation approach also allows us to link these patterns to the dynamics of the system for each gene state.