Dynamical properties of the two-process model for sleep-wake cycles in infantile autism

The two-process model is a scheme for the timing of sleep that consists of homeostatic (Process S) and circadian (Process C) variables. The two-process model exhibits abnormal sleep patterns such as internal desynchronization or sleep fragmentation. Early infants with autism often experience sleep difficulties. Large day-by-day changes are found in the sleep onset and waking times in autistic children. Frequent night waking is a prominent property of their sleep. Further, the sleep duration of autistic children is often fragmented. These sleep patterns in infants with autism are not fully understood yet. In the present study, the sleep patterns in autistic children were reproduced by a modified two-process model using nonlinear analysis. A nap term was introduced into the original two-process model to reproduce the sleep patterns in early infants. The nap term and the time course of Process S are mentioned in the present study. Those parameters led to bifurcation of the sleep-wake cycle in the modified two-process model. In a certain range of these parameter sets, a small external noise was amplified, and an irregular sleep-wake cycle appeared. The short duration of sleep led to another irregular sleep onset or waking. Consequently, an irregular sleep-wake cycle appeared in early infantile autism.     

Sleep deprivation in a quantitative physiologically based model of the ascending arousal system

A physiologically based quantitative model of the human ascending arousal system is used to study sleep deprivation after being calibrated on a small set of experimentally based criteria. The model includes the sleep-wake switch of mutual inhibition between nuclei which use monoaminergic neuromodulators, and the ventrolateral preoptic area. The system is driven by the circadian rhythm and sleep homeostasis. We use a small number of experimentally derived criteria to calibrate the model for sleep deprivation, then investigate model predictions for other experiments, demonstrating the scope of application. Calibration gives an improved parameter set, in which the form of the homeostatic drive is better constrained, and its weighting relative to the circadian drive is increased. Within the newly constrained parameter ranges, the model predicts repayment of sleep debt consistent with experiment in both quantity and distribution, asymptoting to a maximum repayment for very long deprivations. Recovery is found to depend on circadian phase, and the model predicts that it is most efficient to recover during normal sleeping phases of the circadian cycle, in terms of the amount of recovery sleep required. The form of the homeostatic drive suggests that periods of wake during recovery from sleep deprivation are phases of relative recovery, in the sense that the homeostatic drive continues to converge toward baseline levels. This undermines the concept of sleep debt, and is in agreement with experimentally restricted recovery protocols. Finally, we compare our model to the two-process model, and demonstrate the power of physiologically based modeling by correctly predicting sleep latency times following deprivation from experimental data.     

Neurobiology of the sleep-wake cycle: sleep architecture, circadian regulation, and regulatory feedback

This mini-review article presents the remarkable progress that has been made in the past decade in our understanding of the neural circuitry underlying the regulation of sleep-wake states and circadian control of behaviors. Following a brief introduction to sleep architecture and physiology, the authors describe the neural circuitry and neurotransmitters that regulate sleep and cortical arousal (i.e., wakefulness). They next examine how sleep and wakefulness are regulated by mutual inhibition between sleep-and arousal-promoting circuitry and how this interaction functions analogously to an electronic "flip-flop" switch that ensures behavioral state stability. The authors then discuss the role of circadian and homeostatic processes in the consolidation of sleep, including the physiologic basis of homeostatic sleep drive (i.e., wake-dependent increase in sleep propensity) and the role of the SCN in the circadian regulation of sleep-wake cycles. Finally, they describe the hypothalamic circuitry for the integration of photic and nonphotic environmental time cues and how this integration allows organisms to sculpt patterns of rest-activity and sleep-wake cycles that are optimally adaptive.     

Sleep homeostasis and models of sleep regulation

According to the two-process model of sleep regulation, the timing and structure of sleep are determined by the interaction of a homeostatic and a circadian process. The original qualitative model was elaborated to quantitative versions that included the ultradian dynamics of sleep in relation to the non-REM-REM sleep cycle. The time course of EEG slow-wave activity, the major marker of non-REM sleep homeostasis, as well as daytime alertness were simulated successfully for a considerable number of experimental protocols. They include sleep after partial sleep deprivation and daytime napping, sleep in habitual short and long sleepers, and alertness in a forced desynchrony protocol or during an extended photoperiod. Simulations revealed that internal desynchronization can be obtained for different shapes of the thresholds. New developments include the analysis of the waking EEG to delineate homeostatic and circadian processes, studies of REM sleep homeostasis, and recent evidence for local, use-dependent sleep processes. Moreover, nonlinear interactions between homeostatic and circadian processes were identified. In the past two decades, models have contributed considerably to conceptualizing and analyzing the major processes underlying sleep regulation, and they are likely to play an important role in future advances in the field.     

Commentary: models of sleep regulation: successes and continuing challenges

Quantitative models have been developed to describe salient aspects of human sleep regulation. The two-process model of sleep regulation and the thermoregulatory model of sleep control highlight the interaction between sleep homeostasis and circadian rhythmicity and the association between sleep and temperature regulation, respectively. These models have been successful and inspiring, but continuing progress remains dependent on rigorous testing of some of their basic assumptions. Whereas it has been established that EEG slow-wave activity is a marker of sleep homeostasis, its causal role in regulating the timing of sleep and wakefulness remains to be demonstrated conclusively. Likewise, the causal role of the temperature regulatory system in sleep timing requires further investigation. In both models, many parameters have yet to be associated with specific physiologic processes. This makes it challenging, at least within the framework of these models, to account for interindividual differences or age-related changes in such features as sleep duration and sleep timing, as well as changes in the phase angle between the sleep-wake cycle and accepted markers of the circadian pacemaker, such as the body temperature or melatonin rhythm. Although the models may describe adequately global sleep patterns and their circadian modulation, detailed modeling of the frequent short awakenings from, and the subsequent transitions back to, sleep, as well as the variation of the propensity to awaken across the ultradian non-REM-REM cycle, is not addressed. Incoporation of these aspects of sleep in mathematical models of sleep regulation may further our understanding of a key aspect of sleep regulation, that is, its timing.     

Timing and consolidation of human sleep, wakefulness, and performance by a symphony of oscillators

Daily rhythms in sleep and waking performance are generated by the interplay of multiple external and internal oscillators. These include the light-dark and social cycles, a circadian hypothalamic oscillator oscillating virtually independently of behavior, and a homeostatic oscillator driven primarily by sleep-wake behavior. Both internal oscillators contribute to variation in many aspects of sleep and wakefulness (e.g., sleep timing and duration, REM sleep, non-REM sleep, REM density, sleep spindles, slow-wave sleep, electroencephalographic oscillations during wakefulness and sleep, and performance parameters, including attention and memory). The relative contribution of the oscillators varies greatly between these variables. Sleep and performance cannot be predicted by either oscillator independently but critically depend on their phase relationship and amplitude. The homeostatic oscillator feeds back onto the central pacemaker or its outputs. Thus, the amplitude of observed circadian variation in sleep and performance depends on how long we have been asleep or awake. During entrainment to external 24-h cycles, the opposing interplay between circadian and homeostatic changes in sleep propensity consolidates sleep and wakefulness. Some physiological correlates and mediators of both the circadian process (e.g., melatonin and hypocretin rhythms) and the homeostat (e.g., EEG, slow-wave activity, and adenosine release) have been established, offering targets for the development of countermeasures for circadian sleep and performance disorders. Interindividual differences in sleep timing, duration, and morning or evening preference are associated with changes of circadian or sleep homeostatic processes or both. Molecular genetic correlates, including polymorphisms in clock genes, of some of these interindividual differences are emerging.     

A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system

A quantitative, physiology-based model of the ascending arousal system is developed, using continuum neuronal population modeling, which involves averaging properties such as firing rates across neurons in each population. The model includes the ventrolateral preoptic area (VLPO), where circadian and homeostatic drives enter the system, the monoaminergic and cholinergic nuclei of the ascending arousal system, and their interconnections. The human sleep-wake cycle is governed by the activities of these nuclei, which modulate the behavioral state of the brain via diffuse neuromodulatory projections. The model parameters are not free since they correspond to physiological observables. Approximate parameter bounds are obtained by requiring consistency with physiological and behavioral measures, and the model replicates the human sleep-wake cycle, with physiologically reasonable voltages and firing rates. Mutual inhibition between the wake-promoting monoaminergic group and sleep-promoting VLPO causes ;;flip-flop' behavior, with most time spent in 2 stable steady states corresponding to wake and sleep, with transitions between them on a timescale of a few minutes. The model predicts hysteresis in the sleep-wake cycle, with a region of bistability of the wake and sleep states. Reducing the monoaminergic-VLPO mutual inhibition results in a smaller hysteresis loop. This makes the model more prone to wake-sleep transitions in both directions and makes the states less distinguishable, as in narcolepsy. The model behavior is robust across the constrained parameter ranges, but with sufficient flexibility to describe a wide range of observed phenomena.     

Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle

Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.     

Quantitative physiologically based modeling of subjective fatigue during sleep deprivation

A quantitative physiologically based model of the sleep-wake switch is used to predict variations in subjective fatigue-related measures during total sleep deprivation. The model includes the mutual inhibition of the sleep-active neurons in the hypothalamic ventrolateral preoptic area (VLPO) and the wake-active monoaminergic brainstem populations (MA), as well as circadian and homeostatic drives. We simulate sleep deprivation by introducing a drive to the MA, which we call wake effort, to maintain the system in a wakeful state. Physiologically this drive is proposed to be afferent from the cortex or the orexin group of the lateral hypothalamus. It is hypothesized that the need to exert this effort to maintain wakefulness at high homeostatic sleep pressure correlates with subjective fatigue levels. The model's output indeed exhibits good agreement with existing clinical time series of subjective fatigue-related measures, supporting this hypothesis. Subjective fatigue, adrenaline, and body temperature variations during two 72 h sleep deprivation protocols are reproduced by the model. By distinguishing a motivation-dependent orexinergic contribution to the wake-effort drive, the model can be extended to interpret variation in performance levels during sleep deprivation in a way that is qualitatively consistent with existing, clinically derived results. The example of sleep deprivation thus demonstrates the ability of physiologically based sleep modeling to predict psychological measures from the underlying physiological interactions that produce them.     

Homeostatic regulation of sleep in arrhythmic Siberian hamsters

Sleep is regulated by independent yet interacting circadian and homeostatic processes. The present study used a novel approach to study sleep homeostasis in the absence of circadian influences by exposing Siberian hamsters to a simple phase delay of the photocycle to make them arrhythmic. Because these hamsters lacked any circadian organization, their sleep homeostasis could be studied in the absence of circadian interactions. Control animals retained circadian rhythmicity after the phase shift and re-entrained to the phase-shifted photocycle. These animals displayed robust daily sleep-wake rhythms with consolidated sleep during the light phase beginning about 1 h after light onset. This marked sleep-wake pattern was circadian in that it persisted in constant darkness. The distribution of sleep in the arrhythmic hamsters over 24 h was similar to that in the light phase of rhythmic animals. Therefore, daily sleep amounts were higher in arrhythmic animals compared with rhythmic ones. During 2- and 6-h sleep deprivations (SD), it was more difficult to keep arrhythmic hamsters awake than it was for rhythmic hamsters. Because the arrhythmic animals obtained more non-rapid eye movement sleep (NREMS) during the SD, they showed a diminished compensatory response in NREMS EEG slow-wave activity during recovery sleep. When amounts of sleep during the SD were taken into account, there were no differences in sleep homeostasis between experimental and control hamsters. Thus loss of circadian control did not alter the homeostatic response to SD. This supports the view that circadian and homeostatic influences on sleep regulation are independent processes.     

A mathematical model of the sleep/wake cycle

We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous “flip–flop” conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip–flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip–flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip–flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.     

Simulation of daytime vigilance by the additive interaction of a homeostatic and a circadian process

The two-process model of sleep regulation postulates that a homeostatic and a circadian process underlie sleep regulation. The timing of sleep and waking is accounted for by the interaction of these two processes. The assumptions of two separate processes or of a single process resulting from their additive interaction are mathematically equivalent but conceptually different. Based on an additive interaction, subjective alertness ratings in a forced desynchrony protocol and subjective sleepiness ratings in a photoperiod experiment were simulated. The correspondence between empirical and simulated data supports the basic assumption of the model. Received: 7 October 1993/Accepted in revised form: 22 January 1994     

Young women with major depression live on higher homeostatic sleep pressure than healthy controls

There is mounting evidence for the involvement of the sleep-wake cycle and the circadian system in the pathogenesis of major depression. However, only a few studies so far focused on sleep and circadian rhythms under controlled experimental conditions. Thus, it remains unclear whether homeostatic sleep pressure or circadian rhythms, or both, are altered in depression. Here, the authors aimed at quantifying homeostatic and circadian sleep-wake regulatory mechanisms in young women suffering from major depressive disorder and healthy controls during a multiple nap paradigm under constant routine conditions. After an 8-h baseline night, 9 depressed women, 8 healthy young women, and 8 healthy older women underwent a 40-h multiple nap protocol (10 short sleep-wake cycles) followed by an 8-h recovery night. Polysomnographic recordings were done continuously, and subjective sleepiness was assessed. In order to measure circadian output, salivary melatonin samples were collected during scheduled wakefulness, and the circadian modulation of sleep spindles was analyzed with reference to the timing of melatonin secretion. Sleep parameters as well as non-rapid eye movement (NREM) sleep electroencephalographic (EEG) spectra were determined for collapsed left, central, and right frontal, central, parietal, and occipital derivations for the night and nap-sleep episodes in the frequency range .75-25 Hz. Young depressed women showed higher frontal EEG delta activity, as a marker of homeostatic sleep pressure, compared to healthy young and older women across both night sleep episodes together with significantly higher subjective sleepiness. Higher delta sleep EEG activity in the naps during the biological day were observed in young depressed women along with reduced nighttime melatonin secretion as compared to healthy young volunteers. The circadian modulation of sleep spindles between the biological night and day was virtually absent in healthy older women and partially impaired in young depressed women. These data provide strong evidence for higher homeostatic sleep pressure in young moderately depressed women, along with some indications for impairment of the strength of the endogenous circadian output signal involved in sleep-wake regulation. This finding may have important repercussions on the treatment of the illness as such that a selective suppression of EEG slow-wave activity could promote acute mood improvement.     

Sleep initiation and initial sleep intensity: interactions of homeostatic and circadian mechanisms

Sleep initiation and sleep intensity in humans show a dissimilar time course. The propensity of sleep initiation (PSI), as measured by the multiple sleep latency test, remains at a relatively constant level throughout the habitual period of waking or exhibits a midafternoon peak. When waking is extended into the sleep period, PSI rises rapidly within a few hours. In contrast, sleep intensity, as measured by electroencephalographic slow-wave activity during naps, shows a gradual increase during the period of habitual waking. In the two-process model of sleep regulation, it corresponds to the rising limb of the homeostatic Process S. We propose that PSI is determined by the difference between Process S and the threshold H defining sleep onset, which is modulated by the circadian process C. In contrast to a previous version of the model, the parameters of H (amplitude, phase, skewness) differ from those of threshold L, which defines sleep termination. The present model is able to simulate the time course of PSI under baseline conditions as well as following recovery sleep after extended sleep deprivation. The simulations suggest that during the regular period of waking, a circadian process counteracts the increasing sleep propensity induced by a homeostatic process. Data obtained in the rat indicate that during the circadian period of predominant waking, a circadian process prevents a major intrusion of sleep.     

Interactive mathematical models of subjective alertness and cognitive throughput in humans

The authors present here mathematical models in which levels of subjective alertness and cognitive throughput are predicted by three components that interact with one another in a nonlinear manner. These components are (1) a homeostatic component (H) that falls in a sigmoidal manner during wake and rises in a saturating exponential manner at a rate that is determined by circadian phase during sleep; (2) a circadian component (C) that is a function of the output of our mathematical model of the effect of light on the circadian pacemaker, with the amplitude further regulated by the level of H; and (3) a sleep inertia component (W) that rises in a saturating exponential manner after waketime. The authors first construct initial models of subjective alertness and cognitive throughput based on the results of sleep inertia studies, sleep deprivation studies initiated across all circadian phases, 28-h forced desynchrony studies, and alertness and performance dose response curves to sleep. These initial models are then refined using data from nearly one hundred fifty 30- to 50-h sleep deprivation studies in which subjects woke at their habitual times. The interactive three-component models presented here are able to predict even the fine details of neurobehavioral data from sleep deprivation studies and, after further validation, may provide a powerful tool for the design of safe shift work and travel schedules, including those in which people are exposed to unusual patterns of light.     

Young Women With Major Depression Live on Higher Homeostatic Sleep Pressure Than Healthy Controls

There is mounting evidence for the involvement of the sleep-wake cycle and the circadian system in the pathogenesis of major depression. However, only a few studies so far focused on sleep and circadian rhythms under controlled experimental conditions. Thus, it remains unclear whether homeostatic sleep pressure or circadian rhythms, or both, are altered in depression. Here, the authors aimed at quantifying homeostatic and circadian sleep-wake regulatory mechanisms in young women suffering from major depressive disorder and healthy controls during a multiple nap paradigm under constant routine conditions. After an 8-h baseline night, 9 depressed women, 8 healthy young women, and 8 healthy older women underwent a 40-h multiple nap protocol (10 short sleep-wake cycles) followed by an 8-h recovery night. Polysomnographic recordings were done continuously, and subjective sleepiness was assessed. In order to measure circadian output, salivary melatonin samples were collected during scheduled wakefulness, and the circadian modulation of sleep spindles was analyzed with reference to the timing of melatonin secretion. Sleep parameters as well as non-rapid eye movement (NREM) sleep electroencephalographic (EEG) spectra were determined for collapsed left, central, and right frontal, central, parietal, and occipital derivations for the night and nap-sleep episodes in the frequency range .75–25?Hz. Young depressed women showed higher frontal EEG delta activity, as a marker of homeostatic sleep pressure, compared to healthy young and older women across both night sleep episodes together with significantly higher subjective sleepiness. Higher delta sleep EEG activity in the naps during the biological day were observed in young depressed women along with reduced nighttime melatonin secretion as compared to healthy young volunteers. The circadian modulation of sleep spindles between the biological night and day was virtually absent in healthy older women and partially impaired in young depressed women. These data provide strong evidence for higher homeostatic sleep pressure in young moderately depressed women, along with some indications for impairment of the strength of the endogenous circadian output signal involved in sleep-wake regulation. This finding may have important repercussions on the treatment of the illness as such that a selective suppression of EEG slow-wave activity could promote acute mood improvement. (Author correspondence: Christian.cajochen@upkbs.ch)     

A phase dynamics model of human circadian rhythms

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker-driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.     

Spectral EEG indicator of pressure to enter into deep sleep: its responsiveness to closing the eyes for just a few minutes exhibits a pure exponential buildup during sleep deprivation

According to the two-process model of sleep–wake regulation, a homeostatic sleep pressure, i.e. a pressure to enter into deep non-rapid eyes movement (NREM) sleep, must exhibit a purely exponential buildup during prolonged wakefulness. However, this pressure is usually measured indirectly, i.e. during the following episode of actual deep NREM sleep. The purpose of this paper was to show that, despite a prominent circadian modulation of time course of any waking EEG index, the model-postulated purely exponential buildup of the homeostatic sleep pressure can be directly confirmed. During two days of sleep deprivation experiments, the EEG of healthy adults (N = 30) was recorded every other hour throughout 5-min eyes closed relaxation. Sixteen ln-transformed single-Hz power densities (from 1 to 16 Hz) were computed for each of 5 one-min intervals. Differences between these densities obtained for the first and the following intervals were calculated and averaged. The obtained 16 values were used as the frequency weighting curve for weighting densities of each set of 16 single-Hz power densities. Summing-up of these weighted densities provided a single measure that was found to co-vary with self-rated sleepiness throughout two-day interval of sleep deprivation, thus reflecting the joint influence of the circadian and homeostatic processes. However, two-day time course of responsiveness of this measure to closing the eyes for just a few minutes exhibited a purely exponential buildup. It was concluded that this result provided a direct experimental confirmation of the model-predicted exponential buildup of the homeostatic sleep pressure across prolonged episode of wakefulness.     

Sleep rhythmicity and homeostasis in mice with targeted disruption of mPeriod genes

In mammals, sleep is regulated by circadian and homeostatic mechanisms. The circadian component, residing in the suprachiasmatic nucleus (SCN), regulates the timing of sleep, whereas homeostatic factors determine the amount of sleep. It is believed that these two processes regulating sleep are independent because sleep amount is unchanged after SCN lesions. However, because such lesions necessarily damage neuronal connectivity, it is preferable to investigate this question in a genetic model that overcomes the confounding influence of circadian rhythmicity. Mice with disruption of both mouse Period genes (mPer)1 and mPer2 have a robust diurnal sleep-wake rhythm in an entrained light-dark cycle but lose rhythmicity in a free-run condition. Here, we examine the role of the mPer genes on the rhythmic and homeostatic regulation of sleep. In entrained conditions, when averaged over the 24-h period, there were no significant differences in waking, slow-wave sleep (SWS), or rapid eye movement (REM) sleep between mPer1, mPer2, mPer3, mPer1-mPer2 double-mutant, and wild-type mice. The mice were then kept awake for 6 h (light period 6-12), and the mPer mutants exhibited increased sleep drive, indicating an intact sleep homeostatic response in the absence of the mPer genes. In free-run conditions (constant darkness), the mPer1-mPer2 double mutants became arrhythmic, but they continued to maintain their sleep levels even after 36 days in free-running conditions. Although mPer1 and mPer2 represent key elements of the molecular clock in the SCN, they are not required for homeostatic regulation of the daily amounts of waking, SWS, or REM sleep.     

A three-oscillator model of the human circadian system controlling the core temperature rhythm and the sleep-wake cycle

Even during “free-running” experiments, in which subjects lived in caves or cellars without any time cues, various circadian rhythms such as core body temperature and the sleep-wake cycle remained for a long time mutually synchronized in one group of subjects. In another group of subjects, or later in the same subjects, a number of unusually long sleep-wake cycles occurred while body temperature persisted in a near-24 hr rhythm. This has been termed “internal desynchronization” by Aschoff & Wever (1962) to emphasize the uncoupling of rhythms. Zulley (1980) and Czeisler et al. (1980) found that the duration of sleep depends regularly on the phase of the sleep onset in the body temperature rhythm, even in the apparently “random and irregular” sleep-wake pattern. The graph which plots, the sleep duration against the sleep onset phase is called sleep duration in this paper. We develop a quantitative, multi-oscillator model of human circadian system following Wever (1979) and Kronauer et al. (1982). Because the simplest model, which describes the state of each component oscillator by only one variable (ptlase) was adopted for each component oscillator, we can determine the intFraction between oscillators using sleep duration. It is found that a three-oscillator model can simulate several qualitative features of human circadian rhythms, such as an irregular free-running pattern and sleep duration. Moreover we find that the model reproduces the mysterious phenomenon of “forbidden wake up”, although we do not incorporate a priori any mechanism to explain it.