Ask a 70-year-old what one creak in the hallway does to their night, then ask a teenager the same question. The older sleeper may lie awake until dawn after a single disturbance; the teenager will not even stir. Narcolepsy is the mirror image of that fragility: a person who cannot hold either state for long, slipping from alertness into sleep and back again dozens of times a day. The two conditions look like separate problems, one of too little sleep stability, the other of too much. A new preprint argues they are the same geometric failure, read in opposite directions.
The thresholds that time sleep
For more than four decades, the two-process model has framed sleep as a balance between two drives: homeostatic sleep pressure, which builds the longer you stay awake, and the circadian clock, which sets the daily rhythm. Sleep begins when pressure crosses an upper boundary; wakefulness returns when it falls below a lower one. The model schedules sleep beautifully, but its boundaries have always been dialed in by hand. They are descriptive conveniences, not quantities traced back to the real neurons that generate sleep.
The new work closes that gap. Starting from the Phillips-Robinson model, which casts sleep-wake control as a mutual inhibition duel between a sleep-promoting population (the ventrolateral preoptic area) and a wake-promoting monoaminergic population, the framework gains a third player: the orexin neurons of the lateral hypothalamus, which excite the wake side during the day and are silenced during sleep. From the bifurcation geometry of this three-population system, the preprint derives closed-form expressions for a sleep-onset threshold, H+, and an awakening threshold, H-. Both are explicit functions of the clock phase, the accumulated sleep drive, and the orexinergic tone. The thresholds are no longer free parameters; they are consequences of the wiring.
Aging as a fragility regime
Aging erodes sleep along several routes, and the preprint shows each bends the threshold geometry in a distinct way. A weakened circadian rhythm compresses the corridor between the two boundaries, shifting the whole sleep window earlier and trimming its length, matching the phase advance seen in older adults. A lower ceiling on homeostatic pressure delays sleep onset and shortens the night further. The third route is the most striking: surviving orexin neurons in the aging brain do not simply fade, they become hyperexcitable.
The model treats that hyperexcitability as a dial on the maximum firing rate of the orexin population. Raising it lifts the sleep-onset threshold while barely moving the awakening threshold, so the corridor narrows from above. The consequence shows up in a simple simulated experiment: a five-minute pulse of stimulation delivered during consolidated sleep. At low orexin excitability, sleep absorbs the poke and returns within minutes. At an intermediate level, the same poke triggers a waking spell of more than an hour. At high excitability, one poke ejects the sleeper for the rest of the night.
The slide from the middle outcome to the worst is not gradual. The preprint finds a sharp boundary in excitability beyond which any transient disturbance produces irreversible awakening. Think of a thermostat whose re-engagement setpoint has drifted so high that the furnace, once off, can never climb back to its own on switch. Below the boundary, sleep repairs itself; above it, a single creak ends the night. That may be the mathematical face of a familiar clinical observation: awakenings in older adults happen more often and, critically, increasingly fail to knit back into consolidated sleep. Because the asymmetry is what makes waking easy but re-entry hard, the age-related orexin shift does not just lower the cost of waking; it makes the return to sleep disproportionately expensive.
Narcolepsy as boundary collapse
Narcolepsy type 1 is the mirror geometry of this process. Its defining lesion is the loss of orexin-producing neurons, which the model represents by weakening the coupling between orexin and the wake-promoting population. The sleep-onset threshold collapses toward the awakening threshold, and the hysteresis corridor that normally separates the two states shrinks almost to nothing. Where a healthy brain holds sleep for hours and wake for hours, the depleted system flips rapidly between states, abandoning each almost the moment it begins. H+ falls steeply while H- barely moves, the same asymmetry as aging but signed in the opposite direction.
Here is the paradox: fragmentation does not cost total sleep time. As orexin coupling weakens, the daily count of sleep-wake transitions climbs sharply, yet total sleep per 24 hours rises modestly, consistent with clinical findings that narcolepsy patients sleep slightly more, not less, than controls. Shattered architecture with preserved quantity is exactly what a compressed corridor predicts.
The model also upends a common intuition. Orexin is usually described as the molecule that holds wakefulness together, resisting unwanted sleep. The threshold analysis suggests its main job is different: orexin holds wakefulness together mainly by keeping the sleep-onset bar high enough that accumulating sleep pressure cannot spill over into sleep, not by resisting awakening. It is the height of the door, not the strength of the lock, that matters. When orexin is lost, the door gets shorter, and sleep pressure spills over it almost immediately.
Why it matters
Thresholds are the interface between sleep physiology and applied tools. Shift work fatigue models, wearable sleep trackers, and subjective sleepiness scales all assume some boundary position, but most treat it as fixed. The closed-form thresholds add the missing dimension: clock amplitude, homeostatic capacity, and orexinergic tone each deform the two boundaries in identifiable ways. In principle, that offers a mechanistic basis for personalizing fatigue prediction, for interpreting individual differences in state stability, and for asking whether a countermeasure works through the circadian, homeostatic, or orexinergic pathway. The healthy brain, in this picture, occupies a narrow corridor calibrated to be wide enough for consolidation and narrow enough for timely transitions; aging pries it open at the top, narcolepsy squeezes it shut.
Limits
The preprint is a theoretical result and has not been peer reviewed. Each brain region is modeled as a mean-field population, and the framework lumps NREM and REM together, so it cannot yet capture the sleep-onset REM episodes that characterize narcolepsy. The orexinergic influence is reduced to two scalar values, whereas real biology deploys two peptides acting on two receptor subtypes. The homeostatic process is a single exponential variable, though real sleep debt accumulates over multiple timescales. Most importantly, the quantitative predictions, including the location of the fragility boundary and its dependence on orexin excitability, have not been measured in human sleepers. Whether the sharp boundary exists in real brains, and where individual people sit relative to it, is an empirical question the model now makes testable.
Source
Yao C, Wu X, Ning Z, Yang D. Circadian-Modulated Thresholds for Sleep Patterns in Aging and Narcolepsy. bioRxiv. 2026 Aug 6. doi: 10.64898/2026.08.02.742270. Preprint, not peer reviewed.