A minimal activator-inhibitor-repressor model of the hepatic circadian clock

Circadian clocks rely on gene regulation networks, which generate periodic biochemical oscillations informing our cells about the time of day. Mathematical modeling has been effective in describing the dynamics of the multiple intertwined feedback loops making up circadian clocks; however, it is often delicate to adapt the complexity of the model to the question addressed and the data available. Traditionally, two main modeling approaches have been followed, using either comprehensive models recapitulating most molecular actors involved or minimal qualitative models highlighting the core mechanisms. However, analyzing the behavior of large models may be difficult, and small models often lack predictive power, questioning their relevance. Through a systematic reduction of a more complex model, we obtain a simple three-gene clock model, featuring the activator Bmal1, the repressor Reverb, and the inhibitor Cry, that accurately describes the corresponding temporal expression profiles for the mouse hepatic clock. We characterize this model by carrying out a sensitivity analysis for its limit cycle, as well as by computing phase response curves for the different possible inputs. Predictions from the model are compatible with a number of synchronizing mechanisms from the literature.