Novel Operon Dynamics in the Presence of State-Dependent Delays

In operon gene expression, transcription and translation processes occur with delays. Mathematical models of operon dynamics incorporating constant delays have been developed and show similar dynamics to the model without delay. Namely with constant delays, the repressible operon has a unique steady state which may undergo a Hopf bifurcation leading to a stable period orbit. In the inducible operon there is either a globally stable steady state or two locally stable steady states and an unstable intermediate steady state. Taking into account that in practice the delays are likely to be state-dependent, we extend the modeling to operon dynamics with state-dependent transcription and translation delays and explore the dynamics. Our results demonstrate that the incorporation of distributed state-dependent delays gives rise to expanded possibilities of operon dynamics. Namely, both repressible and inducible systems may display multiple steady states as well as novel bifurcations, which may result in interesting scenarios such as bistability and tristability among stable steady states and stable limit cycles.