Multiple random phosphorylations provide long delays and switches in circadian clocks

Theory predicts that self-sustained oscillations require robust delays and nonlinearities (ultrasensitivity). We study the circadian rhythms in the filamentous fungus Neurospora crassa (wild type period 22.5 hours) to investigate the underlying clock mechanisms. Its transcription translation feedback loop (TTFL) includes the activator White Collar Complex (WCC), the inhibitory FFC complex, and Casein kinase 1a. Moreover, there are multiple phosphorylation sites on FRQ (around 100) and WCC (approximately 95). A phosphoswitch controls the activity status of the FFC complex. We investigate how multiple, slow and random phosphorylations govern delay and nonlinearity in a negative feedback. We model FRQ phosphorylations with turnover of FRQ and CK1a using ordinary differential equations. Our model helps to understand the underlying mechanisms leading to delays and ultrasensitivity. The model shows temporal and steady state switches for the free kinase and phosphorylated FRQ. We show that random phosphorylations and sequestration mechanisms allow high Hill coefficients required for self-sustained oscillations. Our conceptual models help to understand multiple phosphorylations dynamics and to elucidate mechanisms of delayed switch generation.