A limit cycle mathematical model of the REM sleep oscillator system

A limit cycle mathematical model of the rapid-eye-movement (REM) sleep oscillator system has been developed from a structural model of interaction of populations of REM-on and REM-off neurons. The marked differences in latency, amplitude, and duration of the first REM sleep period seen with circadian variation and depressive pathology are modeled by beginning the REM oscillation at different initial points relative to the final position in the limit cycle. Beginning from a point that is graphically interior to the limit cycle produces a long-latency, short-duration, and less intense first REM period. Beginning from a point graphically exterior to the limit cycle produces a short-latency, long-duration, and more intense first REM period. In the model the determinant of whether the oscillation begins exterior or interior to the limit cycle is the time course of decay of the REM-off population discharge activity at sleep onset. When this time course is made to depend on circadian phase, the model produces a very close match to the empirically observed large shifts between the first and second REM periods in duration (often a 50% change) and intensity and also closely mimics the empirically observed shifts in REM latency as human sleep begins at different circadian phases. Although this variation in limit cycle entry accounts for the major changes in REM sleep over the night, the model also postulates a continuous but small circadian variation (of the order of +/- 5% change in REM parameters) acting throughout the course of a night's sleep. Because the model is derived from actual physiological data, rather than being a purely ad hoc or phenomenological construct, it offers the possibility of direct tests of its postulates through neurobiological studies in animals, by circadian phase-related manipulations of the sleep cycle, and through perturbations of the system in humans by the use of drugs. Indeed, an explicit phase-response curve of the system to cholinergic agonists has been developed; this will permit experimental tests of the model in both animals and humans.