QUANTITATIVE BIOLOGY SEMINAR<br>REM/NREM Sleep Cycles Naturally Emerge from a Mathematical Model of Human Sleep
Sleep in humans follows a predictable daily pattern, including nightly cycles between rapid eye movement (REM) sleep and non-REM (NREM) sleep with a period of approximately 90 minutes. The physiological mechanisms that generate these sleep cycles are not known. However, some neural circuits involved in the regulation of sleep have been identified. We have developed an ordinary differential equation model of the dynamics of these sleep-regulatory neural populations. This model can account for normal sleep/wake cycles in both humans and other mammalian species. Interestingly, this model is mathematically equivalent to the motion of a particle in a two-well mechanical potential, with one well representing "wake" and the other representing "sleep". By extending the model to a three-well mechanical potential, with wells for "wake", "NREM sleep", and "REM sleep", we show that the REM/NREM sleep cycle can be parsimoniously accounted for by known physiological processes.