Abstract
<title>Abstract</title> <p>The two-process model has long served as the canonical framework for understanding sleep regulation , describing the interplay between homeostatic sleep pressure (Process S) and the circadian rhythm (Process C). However, by representing sleep–wake switching as phenomenological threshold crossings, it offers limited mechanistic insight into the underlying neural circuitry and cannot account for how specific neuromodulatory nuclei shape the timing, depth, and stability of sleep. To address this, we extend the Phillips–Robinson model to incorporate the locus coeruleus (LC), yielding a new two-process model in which the circadian wakefulness and sleep thresholds emerge analytically from the neural dynamics. This framework offers three key predictive capabilities. (i) First, it explains analytically how neuromodulatory activity governs sleep timing and duration. LC activity asymmetrically sculpts the thresholds: increasing LC-to-monoaminergic excitation selectively elevates the sleep threshold while leaving the wakefulness threshold largely unaffected, thereby delaying sleep onset and shortening sleep duration. (ii) It explains how LC activity shapes the brain’s response to a brief stimulus, distinguishing among brief awakening, prolonged awakening , and sustained wakefulness. (iii) We quantify sleepiness as the geometric distance between homeostatic pressure and the sleep threshold. This metric captures subjective sleepiness well, exhibiting a linear relationship with Karolinska Sleepiness Scale measurements. Through this lens, we further reveal that higher LC activity reduces sleepiness by elevating the sleep threshold and thereby widening the distance to it. Together, these capabilities establish the new model as a unified, analytically tractable mechanistic framework that integrates sleep timing, homeostatic sleepiness, and arousal susceptibility—revealing the neural mechanisms that classical thresholds leave unexplained.</p>