Mechanistic Modeling of Sleep-Wake Transitions via Circadian-Modulated Threshold Dynamics

Human sleep-wake cycles emerge from complex interactions between homeostatic sleep pressure and circadian rhythms. In this study, we extend the Phillips-Robinson model by introducing circadian-dependent dynamic thresholds for sleep and wake transitions, yielding a more physiologically grounded framework for sleep regulation. Using bifurcation analysis, we show that the transition from sustained wakefulness to rhythmic sleep-wake cycles is governed by a saddle-node on invariant circle (SNIC) bifurcation, and that these oscillations become entrained to external 24 h light-dark cues. We analytically derive circadian-modulated sleep and wake thresholds, revealing how the interaction between circadian and homeostatic drives governs sleep-wake transitions. Our model captures key physiological phenomena, including: (1) the onset and entrainment of sleep-wake rhythms, (2) immediate sleep onset and partial rebound following sleep deprivation, and (3) sleep fragmentation under shift work-like conditions. These results offer new mechanistic insights into how circadian misalignment alters sleep timing and quality. Together, our findings establish an updated theoretical framework for modeling sleep-wake regulation in both natural and disrupted environments, with implications for shift work management, sleep disorder interventions, and personalized chronotherapy. Author summarySleep and wakefulness are regulated by a complex interaction between circadian rhythms and homeostatic sleep pressure. While existing computational models have provided valuable insights, most rely on fixed or heuristic thresholds for sleep and wake transitions that lack direct physiological basis, limiting their ability to account for the full range of sleep behaviors-especially under disrupted conditions. In this study, we substantially update the computational framework in which sleep-wake transitions are governed by dynamically circadian-dependent thresholds. It captures how internal biological time shapes sleep patterns and explains key phenomena such as sleep rebound following deprivation and sleep fragmentation during shift work. It provides new insights into how circadian misalignment leads to sleep disorders and lays the groundwork for more effective, personalized interventions.