| Sleep can be viewed as a sequence of transitions in a very complex neuronal system. Traditionally, studies of the dynamics of sleep control have focused on the circadian rhythm of sleep-wake transitions or on the ultradian rhythm of the sleep cycle. However, very little is known about the mechanisms responsible for the time structure or even the statistics of the rapid sleep-stage transitions that appear without periodicity. I study the time dynamics of sleep-wake transitions for different species, including humans, rats, and mice, and find that the wake and sleep episodes exhibit completely different behaviors: the durations of wake episodes are characterized by a scale-free power-law distribution, while the durations of sleep episodes have an exponential distribution with a characteristic time scale. The functional forms of the distributions of the sleep and wake durations hold for human subjects of different ages and for subjects with sleep apnea. They also hold for all the species I investigate. Surprisingly, all species have the same power-law exponent for the distribution of wake durations, but the exponential characteristic time of the distribution of sleep durations changes across species. I develop a stochastic model which accurately reproduces our empirical findings. The model suggests that the difference between the dynamics of the sleep and wake states arises from the constraints on the number of microstates in the sleep-wake system. I develop a measure of asymmetry in sleep-stage transitions using a transition probability matrix. I find that both normal and sleep apnea subjects are characterized by two types of asymmetric sleep-stage transition paths, and that the sleep apnea group exhibits less asymmetry in the sleep-stage transitions. |
