A mathematical model of ultradian sleep-wake regulation in rodents

Rodent models are widely used for the experimental analysis of sleep. While this is motivated by similarities in brain circuitry and electrophysiological rhythms, unlike the circadian sleep-wake cycle in humans, rodent sleep is polyphasic, containing multiple bouts of sleep and wake minutes to hours in duration over the course of a day. Each sleep bout is punctuated by several brief arousals several seconds to minutes long. Physiologically motivated mathematical models replicate the shorter timescale of arousal within sleep, but not the longer one representing prolonged wakefulness. Here, we adapt a previously published "flip-flop" model of human sleep to capture the ultradian alternation of sleep and wakefulness in mice on the longer timescale. The resulting model reproduces both the mean durations of alternating sleep and wake bouts as well as the circadian trends in their bout durations documented in our experiments on mice.