A Mathematical Model of Homeostatic Regulation of Sleep-Wake Cycles by Hypocretin/Orexin

We introduce a physiology-based mathematical model of sleep-wake cycles, suggesting a novel mechanism of homeostatic regulation of sleep. In this model, the homeostatic process is determined by the neuropeptide hypocretin/orexin, which is a cotransmitter of the lateral hypothalamus. Hypocretin/orexin neurons are silent during sleep and active during wakefulness. Firing of these neurons is sustained by reciprocal excitatory synaptic connections with local glutamate interneurons. This feedback loop has been simulated with a minimal but physiologically plausible model. It includes 2 simplified Hodgkin-Huxley type neurons that are connected via glutamate synapses, one of which additionally contains hypocretin/orexin as the functionally relevant cotransmitter. During the active state (wakefulness), the synaptic efficacy of hypocretin/orexin declines as a result of the ongoing firing. It recovers during the silent (sleep) state. We demonstrate that these homeostatic changes can account for typical alterations of sleep-wake transitions, for example, introduced by napping, sleep deprivation, or alarm clock. In combination with a circadian input, the model mimics the transitions between silent and firing states in agreement with sleep-wake cycles. These simulation results support the concept of state-dependent alterations of hypocretin/orexin effects as an important homeostatic process in sleep-wake regulation, although additional mechanisms can be involved.