Homeostatic Forces Shaping the Daily Pattern of Sleep Propensity

The discrepancy between high sleep need and the ability to initiate sleep underlies insomnia, the most prevalent sleep disorder, whose nature remains obscure. Sleep need increases monotonically with prolonged wakefulness, as reflected in the rising intensity of sleep after varying wake intervals. In contrast, sleep propensity – the ability to transition from wake to sleep – follows a bimodal pattern, peaking in the mid-afternoon, dipping in the evening, and rising again near bedtime. Previously, we demonstrated that sleep structure dynamics can be effectively modeled using probability waves. Here, we extend this wave model of homeostatic regulation of sleep to the period of wakefulness and show that its extrapolation predicts the bimodal pattern of wake-to-sleep transitions. This pattern arises from the interplay of two key factors in state transitions: wake-state instability and interaction strength between states. While wake-state instability increases monotonically, interaction strength follows a bimodal pattern. Their combined effect produces a bimodal probability of state transitions, aligning closely with experimental data. The mid-afternoon peak corresponds to maximal interaction at the homeostatic equilibrium of sleep and wake states, whereas the evening dip reflects minimal interaction, counteracting high wake-state instability. An exponential rise in both factors by the end of the day facilitates sleep onset at bedtime. Our experimental findings on sleep deprivation support the model predictions. Understanding the relationship between sleep need and ability to initiate sleep may offer valuable insights for optimizing daytime performance and sleep quality in both health and disease.