A probabilistic model for the ultradian timing of REM sleep in mice

A salient feature of mammalian sleep is the alternation between rapid eye movement (REM) and non-REM (NREM) sleep. However, how these two sleep stages influence each other and thereby regulate the timing of REM sleep episodes is still largely unresolved. Here, we developed a statistical model that specifies the relationship between REM and subsequent NREM sleep to quantify how REM sleep affects the following NREM sleep duration and its electrophysiological features in mice. We show that a lognormal mixture model well describes how the preceding REM sleep duration influences the amount of NREM sleep till the next REM sleep episode. The model supports the existence of two different types of sleep cycles: Short cycles form closely interspaced sequences of REM sleep episodes, whereas during long cycles, REM sleep is first followed by an interval of NREM sleep during which transitions to REM sleep are extremely unlikely. This refractory period is characterized by low power in the theta and sigma range of the electroencephalogram (EEG), low spindle rate and frequent microarousals, and its duration proportionally increases with the preceding REM sleep duration. Using our model, we estimated the propensity for REM sleep at the transition from NREM to REM sleep and found that entering REM sleep with higher propensity resulted in longer REM sleep episodes with reduced EEG power. Compared with the light phase, the buildup of REM sleep propensity was slower during the dark phase. Our data-driven modeling approach uncovered basic principles underlying the timing and duration of REM sleep episodes in mice and provides a flexible framework to describe the ultradian regulation of REM sleep in health and disease.Author summary: During sleep, the mammalian brain repeatedly alternates between two brain states: REM and NREM sleep. This ultradian oscillation constitutes a fundamental brain rhythm, the so-called sleep cycle, which is conserved across mammalian species. However, the mechanisms that generate the sleep cycle are still largely unknown. A conserved statistical feature of mammalian sleep is that the durations of REM sleep and subsequent NREM sleep are positively correlated. This correlation suggests that REM sleep impacts the amount of the following NREM sleep and thereby influences its own timing. Here, we developed a statistical model that accurately describes the relationship between the preceding REM and following NREM sleep duration during spontaneous sleep in mice. We applied this model to investigate the relationship between REM sleep and the quality of future NREM sleep, and to uncover factors that determine the timing and duration of REM sleep episodes. Using our model-based approach, we identified three major factors shaping the ultradian regulation of REM sleep: Two types of sleep cycles, a period of light NREM sleep during which transitions to REM sleep are suppressed, and a propensity that influences the subsequent REM sleep duration.