A biophysical model of the key aspects of melatonin synthesis and excretion has been developed, which is able to predict experimental dynamics of melatonin in plasma and saliva, and of its urinary metabolite 6-sulfatoxymelatonin (aMT6s). This new model is coupled to an established model of arousal dynamics, which predicts sleep and circadian dynamics based on light exposure and times of wakefulness. The combined model thus predicts melatonin levels over the sleep-wake/dark-light cycle and enables prediction of melatonin-based circadian phase markers, such as dim light melatonin onset (DLMO) and aMT6s acrophase under conditions of normal sleep and circadian misalignment. The model is calibrated and tested against group average data from 10 published experimental studies and is found to reproduce quantitatively the key dynamics of melatonin and aMT6s, including the timing of release and amplitude, as well as response to controlled lighting and shift work.

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.

The effects of permanent shift work on entrainment and sleepiness are examined using a mathematical model that combines a model of sleep-wake switch in the brain with a model of the human circadian pacemaker entrained by light and nonphotic inputs. The model is applied to 8-hour permanent shift schedules to understand the basic mechanisms underlying changes of entrainment and sleepiness. Average sleepiness is shown to increase during the first days on the night and evening schedules, that is, shift start times between 0000 to 0700 h and 1500 to 2200 h, respectively. After the initial increase, sleepiness decreases and stabilizes via circadian re-entrainment to the cues provided by the shifts. The increase in sleepiness until entrainment is achieved is strongly correlated with the phase difference between a circadian oscillator entrained to the ambient light and one entrained to the shift schedule. The higher this phase difference, the larger the initial increase in sleepiness. When entrainment is achieved, sleepiness stabilizes and is the same for different shift onsets within the night or evening schedules. The simulations reveal the presence of a critical shift onset around 2300 h that separates schedules, leading to phase advance (night shifts) and phase delay (evening shifts) of the circadian pacemaker. Shifts starting around this time take longest to entrain and are expected to be the worst for long-term sleepiness and well-being of the workers. Surprisingly, we have found that the circadian pacemaker entrains faster to night schedules than to evening ones. This is explained by the longer photoperiod on night schedules compared to evening. In practice, this phenomenon is difficult to see due to days off on which workers switch to free sleep-wake activity. With weekends, the model predicts that entrainment is never achieved on evening and night schedules unless the workers follow the same sleep routine during weekends as during work days. Overall, the model supports experimental observations, providing new insights into the mechanisms and allowing the examination of conditions that are not accessible experimentally.