Reversible phosphorylation subserves robust circadian rhythms by creating a switch in inactivating the positive element.

Reversible phosphorylation of proteins is ubiquitous in circadian systems, but the role it plays in generating rhythmicity is not completely understood. A common mechanism for most circadian rhythms involves a negative feedback loop between the positive and negative elements. Here, we built a minimal model for the Neurospora crassa circadian clock based on the core negative feedback loop and the protein FREQUENCY (FRQ)-dependent phosphorylation of the White Collar Complex (WCC). The model can reproduce basic features of the clock, such as the period length, phase relationship, and entrainment to light/dark cycles. We found that the activity of WCC can be controlled by FRQ in a switchlike manner owing to zero-order ultrasensitivity. WCC is inactivated when FRQ level crosses a threshold from below. As a result, low cooperativity in transcriptional activation is sufficient for circadian rhythms, and the level of active WCC exhibits spiky oscillations. Such oscillations are robust to molecular noise and may subserve controlling circadian output. Therefore, the core negative feedback together with phosphorylation of the positive element can ensure robust circadian rhythms. Our work provides insights into the critical roles of posttranslational modification in circadian clocks.