The impact of noise and frustration on coupled genetic circuits

We consider a frequently found motif in genetic networks that consists of a self-activating species A, activating also as its own repressor, a second species B. We first summarize the phase structure of a single realization of this motif in terms of interacting proteins, where we use a deterministic description [1]. We then turn to a fully stochastic description of the same system to allow for fluctuations in the number of proteins and the reaction times. As a result we observe so-called quasicycles even deeply in the pendant of the deterministic fixed-point regime, so that the intermediate oscillatory regime is considerably enlarged [2]. Furthermore, zooming in on the genetic level, it turns out that the former effective description on the level of proteins is only adequate if the binding and unbinding rates of genes are much faster than the inverse production and decay rates of both proteins [3]. When we couple these units with frustrated bonds, we find multistable solutions [1] along with a rich dynamics that depends on the degree of frustration and the strength of the repressing couplings [4]. In an outlook we point to ongoing work on a simple mechanism for controlling pattern formation in these coupled genetic circuits. It is a single bifurcation parameter that allows for controlling the duration of collective oscillations. The patterns reflect a versatile transient dynamics of this system out-of-equilibrium.