A mathematical model of the sleep/wake cycle

Development of the sleep-wake switch in rats during the P2-P21 early infancy period

In early infancy, rats randomly alternate between the sleeping and waking states-from postnatal day 2-10 (P2-P10), sleep and wake bouts are both exponentially distributed with increasing means, while from P10-P21 sleep and wake bout means continue to increase, though there is a striking qualitative shift in the distribution of wake bouts from exponential to power law. The behavioral states of sleep and wakefulness correspond to the activity of sleep-active and wake-active neuronal brainstem populations, with reciprocal inhibition between the two ensuring that only one population is active at a time. The locus coeruleus (LC) forms a third component of this circuit that rises in prominence during the P10-P21 period, as experimental evidence shows that an as-of-yet undeciphered interaction of the LC with sleep-active and wake-active populations is responsible for the transformation of the wake bout distribution from exponential to power law. Interestingly, the LC undergoes remarkable physiological changes during the P10-P21 period-gap junctions within the LC are pruned and network-wide oscillatory synchrony declines and vanishes. In this work, we discuss a series of models of sleep-active, wake-active, and the LC populations, and we use these models to postulate the nature of the interaction between these three populations and how these interactions explain empirical observations of sleep and wake bout dynamics. We hypothesize a circuit in which there is reciprocal excitation between the LC and wake-active population with inhibition from the sleep-active population to the LC that suppresses the LC during sleep bouts. During the P2-P10 period, we argue that a noise-based switching mechanism between the sleep-active and wake-active populations provides a simple and natural way to account for exponential bout distributions, and that the locked oscillatory state of the LC prevents it from impacting bout distributions. From P10-P21, we use our models to postulate that, as the LC gradually shifts from a state of synchronized oscillations to a state of continuous firing, reciprocal excitation between the LC and the wake-active population is able to gradually transform the wake bout distribution from exponential to power law.

Is implementing a post-lunch nap beneficial on evening performance, following two nights partial sleep restriction?

We have investigated the effects that partial-sleep-restriction (PSR0, 4-h sleep retiring at 02:30 and waking at 06:30 h for two consecutive nights) have on 07:30 and 17:00 h cognitive and submaximal weightlifting; and whether this performance improves at 17:00 h following a 13:00 h powernap (0, 30 or 60-min). Fifteen resistance-trained males participated in this study. Prior to the experimental protocol, one repetition max (1RM) bench press and back squat, normative habitual sleep and food intake were recorded. Participants were familiarised with the testing protocol, then completed three experimental conditions: (i) PSR with no nap (PSR0); (ii) PSR with a 30-min nap (PSR30) and (iii) PSR with a 60-min nap (PSR60). Conditions were separated by 7 days with trial order counterbalanced. Intra-aural temperature, Profile of Mood Scores, word-colour interference, alertness and tiredness values were measured at 07:30, 11:00, 14:00, 17:00 h on the day of exercise protocol. Following final temperature measurements at 07:30 h and 17:00 h, participants completed a 5-min active warm-up before performing three repetitions of left and right-hand grip strength, followed by three repetitions at each incremental load (40, 60 and 80% of 1RM) for bench press and back squat, with a 5-min recovery between each repetition. A linear encoder was attached perpendicular to the bar used for the exercises. Average power (AP), average velocity (AV), peak velocity (PV), displacement (D) and time-to-peak velocity (tPV) were measured (MuscleLab software) during the concentric phase of the movements. Data were analysed using general linear models with repeated measures. The main findings were that implementing a nap at 13:00 h had no effect on measures of strength (grip, bench press or back squat). There was a main effect for time of day with greatest performance at 17:00 h for measures of strength. In addition to a significant effect for "load" on the bar for bench press and back squat where AP, AV, PV, D values were greatest at 40% (P < 0.05) and decreased with increased load, whereas tPV and RPE values increased with load; despite this no interaction of "load and condition" were present. A post lunch nap of 30- and 60-minute durations improved mood state, with feelings of alertness, vigour and happiness highest at 17:00 h, in contrast to confusion, tiredness and fatigue (P < 0.05), which were greater in the morning (07:30 h). The word-colour interference test, used as an indicator of cognitive function, reported significant main effect for condition, with the highest total test score in PSR60 condition (P = 0.015). In summary, unlike strength measures the implementation of a 30 or 60-minute nap improved cognitive function when in a partially sleep restricted state, compared to no nap.

Modeling homeostatic and circadian modulation of human pain sensitivity

Introduction

Mathematical modeling has played a significant role in understanding how homeostatic sleep pressure and the circadian rhythm interact to influence sleep-wake behavior. Pain sensitivity is also affected by these processes, and recent experimental results have measured the circadian and homeostatic components of the 24 h rhythm of thermal pain sensitivity in humans. To analyze how rhythms in pain sensitivity are affected by disruptions in sleep behavior and shifts in circadian rhythms, we introduce a dynamic mathematical model for circadian and homeostatic regulation of sleep-wake states and pain intensity.

Methods

The model consists of a biophysically based, sleep-wake regulation network model coupled to data-driven functions for the circadian and homeostatic modulation of pain sensitivity. This coupled sleep-wake-pain sensitivity model is validated by comparison to thermal pain intensities in adult humans measured across a 34 h sleep deprivation protocol.

Results

We use the model to predict dysregulation of pain sensitivity rhythms across different scenarios of sleep deprivation and circadian rhythm shifts, including entrainment to new environmental light and activity timing as occurs with jet lag and chronic sleep restriction. Model results show that increases in pain sensitivity occur under conditions of increased homeostatic sleep drive with nonlinear modulation by the circadian rhythm, leading to unexpected decreased pain sensitivity in some scenarios.

Discussion

This model provides a useful tool for pain management by predicting alterations in pain sensitivity due to varying or disrupted sleep schedules.

Explosive Synchronization-Based Brain Modulation Reduces Hypersensitivity in the Brain Network: A Computational Model Study

Fibromyalgia (FM) is a chronic pain condition that is characterized by hypersensitivity to multimodal sensory stimuli, widespread pain, and fatigue. We have previously proposed explosive synchronization (ES), a phenomenon wherein a small perturbation to a network can lead to an abrupt state transition, as a potential mechanism of the hypersensitive FM brain. Therefore, we hypothesized that converting a brain network from ES to general synchronization (GS) may reduce the hypersensitivity of FM brain. To find an effective brain network modulation to convert ES into GS, we constructed a large-scale brain network model near criticality (i.e., an optimally balanced state between order and disorders), which reflects brain dynamics in conscious wakefulness, and adjusted two parameters: local structural connectivity and signal randomness of target brain regions. The network sensitivity to global stimuli was compared between the brain networks before and after the modulation. We found that only increasing the local connectivity of hubs (nodes with intense connections) changes ES to GS, reducing the sensitivity, whereas other types of modulation such as decreasing local connectivity, increasing and decreasing signal randomness are not effective. This study would help to develop a network mechanism-based brain modulation method to reduce the hypersensitivity in FM.

Integration of sleep homeostasis and navigation in Drosophila

During sleep, the brain undergoes dynamic and structural changes. In Drosophila, such changes have been observed in the central complex, a brain area important for sleep control and navigation. The connectivity of the central complex raises the question about how navigation, and specifically the head direction system, can operate in the face of sleep related plasticity. To address this question, we develop a model that integrates sleep homeostasis and head direction. We show that by introducing plasticity, the head direction system can function in a stable way by balancing plasticity in connected circuits that encode sleep pressure. With increasing sleep pressure, the head direction system nevertheless becomes unstable and a sleep phase with a different plasticity mechanism is introduced to reset network connectivity. The proposed integration of sleep homeostasis and head direction circuits captures features of their neural dynamics observed in flies and mice.

The rhythm of a preterm neonate's life: ultradian oscillations of heart rate, body temperature and sleep cycles

The objectives are to characterize oscillations of physiological functions such as heart rate and body temperature, as well as the sleep cycle from behavioral states in generally stable preterm neonates during the first 5 days of life. Heart rate, body temperature as well as behavioral states were collected during a daily 3-h observation interval in 65 preterm neonates within the first 5 days of life. Participants were born before 32 weeks of gestational age or had a birth weight below 1500 g; neonates with asphyxia, proven sepsis or malformation were excluded. In total 263 observation intervals were available. Heart rate and body temperature were analyzed with mathematical models in the context of non-linear mixed effects modeling, and the sleep cycles were characterized with signal processing methods. The average period length of an oscillation in this preterm neonate population was 159 min for heart rate, 290 min for body temperature, and the average sleep cycle duration was 19 min. Oscillation of physiological functions as well as sleep cycles can be characterized in very preterm neonates within the first few days of life. The observed parameters heart rate, body temperature and sleep are running in a seemingly uncorrelated pace at that stage of development. Knowledge about such oscillations may help to guide nursing and medical care in these neonates as they do not yet follow a circadian rhythm.

Model-based analysis and forecast of sleep-wake regulatory dynamics: Tools and applications to data

Extensive clinical and experimental evidence links sleep-wake regulation and state of vigilance (SOV) to neurological disorders including schizophrenia and epilepsy. To understand the bidirectional coupling between disease severity and sleep disturbances, we need to investigate the underlying neurophysiological interactions of the sleep-wake regulatory system (SWRS) in normal and pathological brains. We utilized unscented Kalman filter based data assimilation (DA) and physiologically based mathematical models of a sleep-wake regulatory network synchronized with experimental measurements to reconstruct and predict the state of SWRS in chronically implanted animals. Critical to applying this technique to real biological systems is the need to estimate the underlying model parameters. We have developed an estimation method capable of simultaneously fitting and tracking multiple model parameters to optimize the reconstructed system state. We add to this fixed-lag smoothing to improve reconstruction of random input to the system and those that have a delayed effect on the observed dynamics. To demonstrate application of our DA framework, we have experimentally recorded brain activity from freely behaving rodents and classified discrete SOV continuously for many-day long recordings. These discretized observations were then used as the "noisy observables" in the implemented framework to estimate time-dependent model parameters and then to forecast future state and state transitions from out-of-sample recordings.

A Focal Inactivation and Computational Study of Ventrolateral Periaqueductal Gray and Deep Mesencephalic Reticular Nucleus Involvement in Sleep State Switching and Bistability

Neurons of the ventrolateral periaqueductal gray (vlPAG) and adjacent deep mesencephalic reticular nucleus (DpMe) are implicated in the control of sleep-wake state and are hypothesized components of a flip-flop circuit that maintains sleep bistability by preventing the overexpression of non-rapid eye movement (NREM)/REM sleep intermediary states (NRt). To determine the contribution of vlPAG/DpMe neurons in maintaining sleep bistability we combined computer simulations of flip-flop circuitry with focal inactivation of vlPAG/DpMe neurons by microdialysis delivery of the GABA_A receptor agonist muscimol in freely behaving male rats (n = 25) instrumented for electroencephalographic and electromyographic recording. REM sleep was enhanced by muscimol at the vlPAG/DpMe, consistent with previous studies; however, our analyses of NRt dynamics in vivo and those produced by flop-flop circuit simulations show that current thinking is too narrowly focused on the contribution of REM sleep-inactive populations toward vlPAG/DpMe involvement in REM sleep control. We found that much of the muscimol-mediated increase in REM sleep was more appropriately classified as NRt. This loss of sleep bistability was accompanied by fragmentation of REM sleep, as evidenced by an increased number of short REM sleep bouts. REM sleep fragmentation stemmed from an increased number and duration of NRt bouts originating in REM sleep. By contrast, NREM sleep bouts were not likewise fragmented by vlPAG/DpMe inactivation. In flip-flop circuit simulations, these changes could not be replicated through inhibition of the REM sleep-inactive population alone. Instead, combined suppression of REM sleep active and inactive vlPAG/DpMe subpopulations was required to replicate the changes in NRt dynamics.

Habitual sleep duration affects recovery from acute sleep deprivation: A modeling study

Adult humans exhibit high interindividual variation in habitual sleep durations, with short sleepers typically sleeping less than 6 h per night and long sleepers typically sleeping more than 9 h per night. Analysis of the time course of homeostatic sleep drive in habitual short and long sleepers has not identified differences between these groups, leading to the hypothesis that habitual short sleep results from increased tolerance to high levels of homeostatic sleep drive. Using a physiologically-based mathematical model of the sleep-wake regulatory network, we investigate responses to acute sleep deprivation in simulated populations of habitual long, regular and short sleepers that differ in daily levels of homeostatic sleep drive. The model predicts timing and durations of wake, rapid eye movement (REM), and non-REM (NREM) sleep episodes as modulated by the homeostatic sleep drive and the circadian rhythm, which is entrained to an external light cycle. Model parameters are fit to experimental measures of baseline sleep durations to construct simulated populations of individuals of each sleeper type. The simulated populations are validated against data for responses to specific acute sleep deprivation protocols. We use the model to predict responses to a wide range of sleep deprivation durations for each sleeper type. Model results predict that all sleeper types exhibit shorter sleep durations during recovery sleep that occurs in the morning, but, for recovery sleep times occurring later in the day, long and regular sleepers show longer and more variable sleep durations, and can suffer longer lasting disruption of daily sleep patterns compared to short sleepers. Additionally, short sleepers showed more resilience to sleep deprivation with longer durations of waking episodes following recovery sleep. These results support the hypothesis that differential responses to sleep deprivation between short and long sleepers result from differences in the tolerance for homeostatic sleep pressure.

Sleep disturbance in PTSD and other anxiety-related disorders: an updated review of clinical features, physiological characteristics, and psychological and neurobiological mechanisms

The current report provides an updated review of sleep disturbance in posttraumatic stress disorder and anxiety-related disorders. First, this review provides a summary description of the unique and overlapping clinical characteristics and physiological features of sleep disturbance in specific DSM anxiety-related disorders. Second, this review presents evidence of a bidirectional relationship between sleep disturbance and anxiety-related disorders, and provides a model to explain this relationship by integrating research on psychological and neurocognitive processes with a current understanding of neurobiological pathways. A heuristic neurobiological framework for understanding the bidirectional relationship between abnormalities in sleep and anxiety-related brain pathways is presented. Directions for future research are suggested.

A Biased Diffusion Approach to Sleep Dynamics Reveals Neuronal Characteristics

We propose a biased diffusion model of accumulated subthreshold voltage fluctuations in wake-promoting neurons to account for stochasticity in sleep dynamics and to explain the occurrence of brief arousals during sleep. Utilizing this model, we derive four neurophysiological parameters related to neuronal noise level, excitability threshold, deep-sleep threshold, and sleep inertia. We provide the first analytic expressions for these parameters, and we show that there is good agreement between empirical findings from sleep recordings and our model simulation results. Our work suggests that these four parameters can be of clinical importance because we find them to be significantly altered in elderly subjects and in children with autism.

Sleep Modelling across Physiological Levels

Sleep and circadian rhythms are regulated across multiple functional, spatial and temporal levels: from genes to networks of coupled neurons and glial cells, to large scale brain dynamics and behaviour. The dynamics at each of these levels are complex and the interaction between the levels is even more so, so research have mostly focused on interactions within the levels to understand the underlying mechanisms—the so-called reductionist approach. Mathematical models were developed to test theories of sleep regulation and guide new experiments at each of these levels and have become an integral part of the field. The advantage of modelling, however, is that it allows us to simulate and test the dynamics of complex biological systems and thus provides a tool to investigate the connections between the different levels and study the system as a whole. In this paper I review key models of sleep developed at different physiological levels and discuss the potential for an integrated systems biology approach for sleep regulation across these levels. I also highlight the necessity of building mechanistic connections between models of sleep and circadian rhythms across these levels.

Mathematical modeling of circadian rhythms

Circadian rhythms are endogenous ~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

A Motor Theory of Sleep-Wake Control: Arousal-Action Circuit

Wakefulness, rapid eye movement (REM) sleep, and non-rapid eye movement (NREM) sleep are characterized by distinct electroencephalogram (EEG), electromyogram (EMG), and autonomic profiles. The circuit mechanism coordinating these changes during sleep-wake transitions remains poorly understood. The past few years have witnessed rapid progress in the identification of REM and NREM sleep neurons, which constitute highly distributed networks spanning the forebrain, midbrain, and hindbrain. Here we propose an arousal-action circuit for sleep-wake control in which wakefulness is supported by separate arousal and action neurons, while REM and NREM sleep neurons are part of the central somatic and autonomic motor circuits. This model is well supported by the currently known sleep and wake neurons. It can also account for the EEG, EMG, and autonomic profiles of wake, REM, and NREM states and several key features of their transitions. The intimate association between the sleep and autonomic/somatic motor control circuits suggests that a primary function of sleep is to suppress motor activity.

Interacting circadian and homeostatic processes with opportunity cost: A mathematical model of sleep with application to two mammalian species

This paper introduces a new model of sleep for mammals. It extends the classic ‘two-process’ model of sleep to account for differences in external circumstances. We apply this model to previously-collected data on elephants and sloths, comparing sleep patterns in the wild with sleep patterns in captivity. We find that the model does very well in explaining sleeping patterns for both types of animals, in both the captive state and in the wild state.

Spiking patterns and synchronization of thalamic neurons along the sleep-wake cycle

Spiking patterns and synchronization dynamics of thalamic neurons along the sleep-wake cycle are studied in a minimal model of four coupled conductance-based neurons. The model simulates two thalamic neurons coupled via a gap junction and driven by a synaptic input from a two-neuron model of sleep regulation by the hypothalamus. In accord with experimental data, the model shows that during sleep, when hypothalamic wake-active neurons are silent, the thalamic neurons discharge bursts of spikes. During wake, the excitatory synaptic input from the hypothalamus drives the coupled thalamic neurons to a state of tonic firing (single spikes). In the deterministic case, the thalamic neurons synchronize in-phase in the bursting regime but demonstrate multi-stability of out-of-phase, in-phase, and asynchronous states in the tonic firing. However, along the sleep-wake cycle, once the neurons synchronize in-phase during sleep (bursting), they stay synchronized in wake (tonic firing). It is thus found that noise is needed to reproduce the experimentally observed transitions between synchronized bursting during sleep and asynchronous tonic firing during wake. Overall, synchronization of bursting is found to be more robust to noise than synchronization of tonic firing, where a small disturbance is sufficient to desynchronize the thalamic neurons. The model predicts that the transitions between sleep and wake happen via chaos because a single thalamic neuron exhibits chaos between regular bursting and tonic activity. The results of this study suggest that the sleep- and wake-related dynamics in the thalamus may be generated at a level of gap junction-coupled clusters of thalamic neurons driven from the hypothalamus which would then propagate throughout the thalamus and cortex via axonal long-range connections.

Mechanisms of hysteresis in human brain networks during transitions of consciousness and unconsciousness: Theoretical principles and empirical evidence

Hysteresis, the discrepancy in forward and reverse pathways of state transitions, is observed during changing levels of consciousness. Identifying the underlying mechanism of hysteresis phenomena in the brain will enhance the ability to understand, monitor, and control state transitions related to consciousness. We hypothesized that hysteresis in brain networks shares the same underlying mechanism of hysteresis as other biological and non-biological networks. In particular, we hypothesized that the principle of explosive synchronization, which can mediate abrupt state transitions, would be critical to explaining hysteresis in the brain during conscious state transitions. We analyzed high-density electroencephalogram (EEG) that was acquired in healthy human volunteers during conscious state transitions induced by the general anesthetics sevoflurane or ketamine. We developed a novel method to monitor the temporal evolution of EEG networks in a parameter space, which consists of the strength and topography of EEG-based networks. Furthermore, we studied conditions of explosive synchronization in anatomically informed human brain network models. We identified hysteresis in the trajectory of functional brain networks during state transitions. The model study and empirical data analysis explained various hysteresis phenomena during the loss and recovery of consciousness in a principled way: (1) more potent anesthetics induce a larger hysteresis; (2) a larger range of EEG frequencies facilitates transitions into unconsciousness and impedes the return of consciousness; (3) hysteresis of connectivity is larger than that of EEG power; and (4) the structure and strength of functional brain networks reconfigure differently during the loss vs. recovery of consciousness. We conclude that the hysteresis phenomena observed during the loss and recovery of consciousness are generic network features. Furthermore, the state transitions are grounded in the same principle as state transitions in complex non-biological networks, especially during perturbation. These findings suggest the possibility of predicting and modulating hysteresis of conscious state transitions in large-scale brain networks.

Hysteresis, characterized by distinct forward and reverse phase transitions, is ubiquitous in nature. For example, there are distinct temperatures for water freezing and ice melting. Similarly, it has been found that state transitions related to consciousness exhibit hysteresis. In particular, the concentration of general anesthetics required to achieve loss of consciousness is significantly higher than the concentration at which consciousness is regained. However, it is unknown whether this is trivially reducible to the pharmacology of these drugs or if it is something related to brain function itself. In this study, we took a novel, network-based approach and hypothesized that the hysteresis observed during anesthetic state transitions shares the same underlying mechanism as that observed in non-biological networks. Our computational modeling, analytic study, and high-density human EEG analysis suggest that various hysteresis phenomena during loss and recovery of consciousness can be explained in principled ways by generic network features. Identifying these network mechanisms of hysteresis in the brain also provides a unified framework for understanding the radically different conscious state transitions associated with sleep, anesthesia, and disorders of consciousness.

Circuit mechanisms and computational models of REM sleep

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REM sleep was discovered in the 1950s.

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Many hypothalamic and brainstem areas have been found to contribute to REM sleep.

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An up-to-date picture of REM-sleep-regulating circuits is reviewed.

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A brief overview of computational models for REM sleep regulation is provided.

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Outstanding issues for future studies are discussed.

Rapid eye movement (REM) sleep or paradoxical sleep is an elusive behavioral state. Since its discovery in the 1950s, our knowledge of the neuroanatomy, neurotransmitters and neuropeptides underlying REM sleep regulation has continually evolved in parallel with the development of novel technologies. Although the pons was initially discovered to be responsible for REM sleep, it has since been revealed that many components in the hypothalamus, midbrain, pons, and medulla also contribute to REM sleep. In this review, we first provide an up-to-date overview of REM sleep-regulating circuits in the brainstem and hypothalamus by summarizing experimental evidence from neuroanatomical, neurophysiological and gain- and loss-of-function studies. Second, because quantitative approaches are essential for understanding the complexity of REM sleep-regulating circuits and because mathematical models have provided valuable insights into the dynamics underlying REM sleep genesis and maintenance, we summarize computational studies of the sleep-wake cycle, with an emphasis on REM sleep regulation. Finally, we discuss outstanding issues for future studies.

Numerical study of entrainment of the human circadian system and recovery by light treatment

Background

While the effects of light as a zeitgeber are well known, the way the effects are modulated by features of the sleep-wake system still remains to be studied in detail.

Methods

A mathematical model for disturbance and recovery of the human circadian system is presented. The model combines a circadian oscillator and a sleep-wake switch that includes the effects of orexin. By means of simulations, we characterize the period-locking zone of the model, where a stable 24-hour circadian rhythm exists, and the occurrence of circadian disruption due to both insufficient light and imbalance in orexin. We also investigate how daily bright light treatments of short duration can recover the normal circadian rhythm.

Results

It is found that the system exhibits continuous phase advance/delay at lower/higher orexin levels. Bright light treatment simulations disclose two optimal time windows, corresponding to morning and evening light treatments. Among the two, the morning light treatment is found effective in a wider range of parameter values, with shorter recovery time.

Conclusions

This approach offers a systematic way to determine the conditions under which circadian disruption occurs, and to evaluate the effects of light treatment. In particular, it could potentially offer a way to optimize light treatments for patients with circadian disruption, e.g., sleep and mood disorders, in clinical settings.

Pleasure: The missing link in the regulation of sleep

Although largely unrecognized by sleep scholars, sleeping is a pleasure. This report aims first, to fill the gap: sleep, like food, water and sex, is a primary reinforcer. The levels of extracellular mesolimbic dopamine show circadian oscillations and mark the "wanting" for pro-homeostatic stimuli. Further, the dopamine levels decrease during waking and are replenished during sleep, in opposition to sleep propensity. The wanting of sleep, therefore, may explain the homeostatic and circadian regulation of sleep. Accordingly, sleep onset occurs when the displeasure of excessive waking is maximal, coinciding with the minimal levels of mesolimbic dopamine. Reciprocally, sleep ends after having replenished the limbic dopamine levels. Given the direct relation between waking and mesolimbic dopamine, sleep must serve primarily to gain an efficient waking. Pleasant sleep (i.e. emotional sleep), can only exist in animals capable of feeling emotions. Therefore, although sleep-like states have been described in invertebrates and primitive vertebrates, the association sleep-pleasure clearly marks a difference between the sleep of homeothermic vertebrates and cool blooded animals.

A four-state Markov model of sleep-wakefulness dynamics along light/dark cycle in mice

Behavioral states alternate between wakefulness (wk), rapid eye movement (rem) and non-rem (nrem) sleep at time scale of hours i.e., light and dark cycle rhythms and from several tens of minutes to seconds (i.e., brief awakenings during sleep). Using statistical analysis of bout duration, Markov chains of sleep-wk dynamics and quantitative EEG analysis, we evaluated the influence of light/dark (ld) changes on brain function along the sleep-wk cycle. Bout duration (bd) histograms and Kaplan-Meier (km) survival curves of wk showed a bimodal statistical distribution, suggesting that two types of wk do exist: brief-wk (wkb) and long-wk (wkl). Light changes modulated specifically wkl bouts, increasing its duration during active/dark period. In contrast, wkb, nrem and rembd histograms and km curves did not change significantly along ld cycle. Hippocampal eeg of both types of wk were different: in comparison wkb showed a lower spectral power in fast gamma and fast theta bands and less emg tone. After fitting a four-states Markov chain to mice hypnograms, moreover in states transition probabilities matrix was found that: in dark/active period, state-maintenance probability of wkl increased, and probability of wkl to nrem transition decreased; the opposite was found in light period, favoring the hypothesis of the participation of brief wk into nrem-rem intrinsic sleep cycle, and the role of wkl in SWS homeostasis. In conclusion, we propose an extended Markov model of sleep using four stages (wkl, nrem, rem, wkb) as a fully adequate model accounting for both modulation of sleep-wake dynamics based on the differential regulation of long-wk (high gamma/theta) epochs during dark and light phases.

An integrated modelling framework for neural circuits with multiple neuromodulators

Neuromodulators are endogenous neurochemicals that regulate biophysical and biochemical processes, which control brain function and behaviour, and are often the targets of neuropharmacological drugs. Neuromodulator effects are generally complex partly owing to the involvement of broad innervation, co-release of neuromodulators, complex intra- and extrasynaptic mechanism, existence of multiple receptor subtypes and high interconnectivity within the brain. In this work, we propose an efficient yet sufficiently realistic computational neural modelling framework to study some of these complex behaviours. Specifically, we propose a novel dynamical neural circuit model that integrates the effective neuromodulator-induced currents based on various experimental data (e.g. electrophysiology, neuropharmacology and voltammetry). The model can incorporate multiple interacting brain regions, including neuromodulator sources, simulate efficiently and easily extendable to large-scale brain models, e.g. for neuroimaging purposes. As an example, we model a network of mutually interacting neural populations in the lateral hypothalamus, dorsal raphe nucleus and locus coeruleus, which are major sources of neuromodulator orexin/hypocretin, serotonin and norepinephrine/noradrenaline, respectively, and which play significant roles in regulating many physiological functions. We demonstrate that such a model can provide predictions of systemic drug effects of the popular antidepressants (e.g. reuptake inhibitors), neuromodulator antagonists or their combinations. Finally, we developed user-friendly graphical user interface software for model simulation and visualization for both fundamental sciences and pharmacological studies.

Role of the locus coeruleus in the emergence of power law wake bouts in a model of the brainstem sleep-wake system through early infancy

Infant rats randomly cycle between the sleeping and waking states, which are tightly correlated with the activity of mutually inhibitory brainstem sleep and wake populations. Bouts of sleep and wakefulness are random; from P2-P10, sleep and wake bout lengths are exponentially distributed with increasing means, while during P10-P21, the sleep bout distribution remains exponential while the distribution of wake bouts gradually transforms to power law. The locus coeruleus (LC), via an undeciphered interaction with sleep and wake populations, has been shown experimentally to be responsible for the exponential to power law transition. Concurrently during P10-P21, the LC undergoes striking physiological changes - the LC exhibits strong global 0.3 Hz oscillations up to P10, but the oscillation frequency gradually rises and synchrony diminishes from P10-P21, with oscillations and synchrony vanishing at P21 and beyond. In this work, we construct a biologically plausible Wilson Cowan-style model consisting of the LC along with sleep and wake populations. We show that external noise and strong reciprocal inhibition can lead to switching between sleep and wake populations and exponentially distributed sleep and wake bout durations as during P2-P10, with the parameters of inhibition between the sleep and wake populations controlling mean bout lengths. Furthermore, we show that the changing physiology of the LC from P10-P21, coupled with reciprocal excitation between the LC and wake population, can explain the shift from exponential to power law of the wake bout distribution. To our knowledge, this is the first study that proposes a plausible biological mechanism, which incorporates the known changing physiology of the LC, for tying the developing sleep-wake circuit and its interaction with the LC to the transformation of sleep and wake bout dynamics from P2-P21.

Are Individual Differences in Sleep and Circadian Timing Amplified by Use of Artificial Light Sources?

Within the human population, there is large interindividual variability in the timing of sleep and circadian rhythms. This variability has been attributed to individual differences in sleep physiology, circadian physiology, and/or light exposure. Recent experimental evidence suggests that the latter is necessary to evoke large interindividual differences in sleep and circadian timing. We used a validated model of human sleep and circadian physiology to test the hypothesis that intrinsic differences in sleep and circadian timing are amplified by self-selected use of artificial light sources. We tested the model under 2 conditions motivated by an experimental study (Wright et al., 2013): (1) a "natural" light cycle, and (2) a "realistic" light cycle that included attenuation of light due to living indoors when natural light levels are high and use of electric light when natural light levels are low. Within these conditions, we determined the relationship between intrinsic circadian period (within the range of 23.7-24.6 h) and timing of sleep onset, sleep offset, and circadian rhythms. In addition, we simulated a work week, with fixed wake time for 5 days and free sleep times on weekends. Under both conditions, a longer intrinsic period resulted in later sleep and circadian timing. Compared to the natural condition, the realistic condition evoked more than double the variation in sleep timing across the physiological range of intrinsic circadian periods. Model predictions closely matched data from the experimental study. We found that if the intrinsic circadian period was long (>24.2 h) under the realistic condition, there was significant mismatch in sleep timing between weekdays and weekends, which is known as social jetlag. These findings indicate that individual tendencies to have very delayed schedules can be greatly amplified by self-selected modifications to the natural light/dark cycle. This has important implications for therapeutic treatment of advanced or delayed sleep phase disorders.

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.

The Neural Basis for Sleep Regulation - Data Assimilation from Animal to Model

Sleep is important for normal brain function, and sleep disruption is comorbid with many neurological diseases. There is a growing mechanistic understanding of the neurological basis for sleep regulation that is beginning to lead to mechanistic mathematically described models. It is our objective to validate the predictive capacity of such models using data assimilation (DA) methods. If such methods are successful, and the models accurately describe enough of the mechanistic functions of the physical system, then they can be used as sophisticated observation systems to reveal both system changes and sources of dysfunction with neurological diseases and identify routes to intervene. Here we report on extensions to our initial efforts [1] at applying unscented Kalman Filter (UKF) to models of sleep regulation on three fronts: tools for multi-parameter fitting; a sophisticated observation model to apply the UKF for observations of behavioral state; and comparison with data recorded from brainstem cell groups thought to regulate sleep.

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

Sleep plays a pivotal role for the consolidation of memory. While REM sleep had originally been the focus of research due to its similarity with wakefulness, more recent studies suggest that different sleep stages are responsible for the consolidation of different types of memory. To better understand the changes in neuronal dynamics between the different sleep stages, neural mass models are a valuable tool, as they relate directly to the large-scale dynamics measured by an EEG. Here, we present a model of the sleeping thalamocortical system. We first show that the isolated thalamic submodule is able to generate different oscillatory behavior found in vivo. Furthermore, the full thalamocortical model reproduces the EEG of sleep stages N2 and N3 and preserves the temporal relationship between cortical K-complexes/slow oscillations and thalamic sleep spindles. A comparison with event related potential data from a recent sleep study in humans demonstrates its possible application in predicting the outcome of external stimulation on EEG rhythms. Our study shows, that a neural mass model incorporating few key mechanisms is sufficient to reproduce the complex brain dynamics observed during sleep.

Wake-sleep transition as a noisy bifurcation

A recent physiologically based model of the ascending arousal system is used to analyze the dynamics near the transition from wake to sleep, which corresponds to a saddle-node bifurcation at a critical point. A normal form is derived by approximating the dynamics by those of a particle in a parabolic potential well with dissipation. This mechanical analog is used to calculate the power spectrum of fluctuations in response to a white noise drive, and the scalings of fluctuation variance and spectral width are derived versus distance from the critical point. The predicted scalings are quantitatively confirmed by numerical simulations, which show that the variance increases and the spectrum undergoes critical slowing, both in accord with theory. These signals can thus serve as potential precursors to indicate imminent wake-sleep transition, with potential application to safety-critical occupations in transport, air-traffic control, medicine, and heavy industry.

Sleep Propensity under Forced Desynchrony in a Model of Arousal State Dynamics

An improvement to our current quantitative model of arousal state dynamics is presented that more accurately predicts sleep propensity as measured with sleep dynamics depending on circadian phase and prior wakefulness. A nonlinear relationship between the circadian variables within the dynamic circadian oscillator model is introduced to account for the skewed shape of the circadian rhythm of alertness that peaks just prior to the onset of the biological night (the “wake maintenance zone”) and has a minimum toward the end of the biological night. The revised circadian drive thus provides a strong inhibitory input to the sleep-active neuronal population in the evening, counteracting the excitatory effects of the increased homeostatic sleep drive as originally proposed in the opponent process model of sleep-wake regulation. The revised model successfully predicts the sleep propensity profile as reflected in the dynamics of the total sleep time, sleep onset latency, wake/sleep ratio, and sleep efficiency during a wide range of experimental protocols. Specifically, all of these sleep measures are predicted for forced desynchrony schedules with day lengths ranging from 1.5 to 42.85 h and scheduled time in bed from 0.5 to 14.27 h. The revised model is expected to facilitate more accurate predictions of sleep under normal conditions as well as during circadian misalignment, for example, during shiftwork and jetlag.

A Novel Population of Wake-Promoting GABAergic Neurons in the Ventral Lateral Hypothalamus

The largest synaptic input to the sleep-promoting ventrolateral preoptic area (VLPO) [1] arises from the lateral hypothalamus [2], a brain area associated with arousal [3-5]. However, the neurochemical identity of the majority of these VLPO-projecting neurons within the lateral hypothalamus (LH), as well as their function in the arousal network, remains unknown. Herein we describe a population of VLPO-projecting neurons in the LH that express the vesicular GABA transporter (VGAT; a marker for GABA-releasing neurons). In addition to the VLPO, these neurons also project to several other established sleep and arousal nodes, including the tuberomammillary nucleus, ventral periaqueductal gray, and locus coeruleus. Selective and acute chemogenetic activation of LH VGAT(+) neurons was profoundly wake promoting, whereas acute inhibition increased sleep. Because of its direct and massive inputs to the VLPO, this population may play a particularly important role in sleep-wake switching.

A Neurophysiological Approach for Evaluating Noise-Induced Sleep Disturbance: Calculating the Time Constant of the Dynamic Characteristics in the Brainstem

Chronic sleep disturbance induced by traffic noise is considered to cause environmental sleep disorder, which increases the risk of cardiovascular disease, stroke, diabetes and other stress-related diseases. However, noise indices for the evaluation of sleep disturbance are not based on the neurophysiological process of awakening regulated by the brainstem. In this study, through the neurophysiological approach, we attempted (1) to investigate the thresholds of awakening due to external stimuli in the brainstem; (2) to evaluate the dynamic characteristics in the brainstem and (3) to verify the validity of existing noise indices. Using the mathematical Phillips-Robinson model, we obtained thresholds of awakening in the brainstem for different durations of external stimuli. The analysis revealed that the brainstem seemed insensitive to short stimuli and that the response to external stimuli in the brainstem could be approximated by a first-order lag system with a time constant of 10-100 s. These results suggest that the brainstem did not integrate sound energy as external stimuli, but neuroelectrical signals from auditory nerve. To understand the awakening risk accumulated in the brainstem, we introduced a new concept of "awakening potential" instead of sound energy.

Evaluating the Evidence Surrounding Pontine Cholinergic Involvement in REM Sleep Generation

Rapid eye movement (REM) sleep - characterized by vivid dreaming, motor paralysis, and heightened neural activity - is one of the fundamental states of the mammalian central nervous system. Initial theories of REM sleep generation posited that induction of the state required activation of the "pontine REM sleep generator" by cholinergic inputs. Here, we review and evaluate the evidence surrounding cholinergic involvement in REM sleep generation. We submit that: (i) the capacity of pontine cholinergic neurotransmission to generate REM sleep has been firmly established by gain-of-function experiments, (ii) the function of endogenous cholinergic input to REM sleep generating sites cannot be determined by gain-of-function experiments; rather, loss-of-function studies are required, (iii) loss-of-function studies show that endogenous cholinergic input to the PTF is not required for REM sleep generation, and (iv) cholinergic input to the pontine REM sleep generating sites serve an accessory role in REM sleep generation: reinforcing non-REM-to-REM sleep transitions making them quicker and less likely to fail.

Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes. Here we show there are fundamental similarities between these two models. The implications are illustrated with two important sleep-wake phenomena. Firstly, we show that in the two-process model, transitions between different numbers of daily sleep episodes can be classified as grazing bifurcations. This provides the theoretical underpinning for numerical results showing that the sleep patterns of many mammals can be explained by the mutual inhibition model. Secondly, we show that when sleep deprivation disrupts the sleep-wake cycle, ostensibly different measures of sleepiness in the two models are closely related. The demonstration of the mathematical similarities of the two models is valuable because not only does it allow some features of the two-process model to be interpreted physiologically but it also means that knowledge gained from study of the two-process model can be used to inform understanding of the behaviour of the mutual inhibition model. This is important because the mutual inhibition model and its extensions are increasingly being used as a tool to understand a diverse range of sleep-wake phenomena such as the design of optimal shift-patterns, yet the values it uses for parameters associated with the circadian and homeostatic processes are very different from those that have been experimentally measured in the context of the two-process model.

Coupled flip-flop model for REM sleep regulation in the rat

Recent experimental studies investigating the neuronal regulation of rapid eye movement (REM) sleep have identified mutually inhibitory synaptic projections among REM sleep-promoting (REM-on) and REM sleep-inhibiting (REM-off) neuronal populations that act to maintain the REM sleep state and control its onset and offset. The control mechanism of mutually inhibitory synaptic interactions mirrors the proposed flip-flop switch for sleep-wake regulation consisting of mutually inhibitory synaptic projections between wake- and sleep-promoting neuronal populations. While a number of synaptic projections have been identified between these REM-on/REM-off populations and wake/sleep-promoting populations, the specific interactions that govern behavioral state transitions have not been completely determined. Using a minimal mathematical model, we investigated behavioral state transition dynamics dictated by a system of coupled flip-flops, one to control transitions between wake and sleep states, and another to control transitions into and out of REM sleep. The model describes the neurotransmitter-mediated inhibitory interactions between a wake- and sleep-promoting population, and between a REM-on and REM-off population. We proposed interactions between the wake/sleep and REM-on/REM-off flip-flops to replicate the behavioral state statistics and probabilities of behavioral state transitions measured from experimental recordings of rat sleep under ad libitum conditions and after 24 h of REM sleep deprivation. Reliable transitions from REM sleep to wake, as dictated by the data, indicated the necessity of an excitatory projection from the REM-on population to the wake-promoting population. To replicate the increase in REM-wake-REM transitions observed after 24 h REM sleep deprivation required that this excitatory projection promote transient activation of the wake-promoting population. Obtaining the reliable wake-nonREM sleep transitions observed in the data required that activity of the wake-promoting population modulated the interaction between the REM-on and REM-off populations. This analysis suggests neuronal processes to be targeted in further experimental studies of the regulatory mechanisms of REM sleep.

A physiologically based model of orexinergic stabilization of sleep and wake

The orexinergic neurons of the lateral hypothalamus (Orx) are essential for regulating sleep-wake dynamics, and their loss causes narcolepsy, a disorder characterized by severe instability of sleep and wake states. However, the mechanisms through which Orx stabilize sleep and wake are not well understood. In this work, an explanation of the stabilizing effects of Orx is presented using a quantitative model of important physiological connections between Orx and the sleep-wake switch. In addition to Orx and the sleep-wake switch, which is composed of mutually inhibitory wake-active monoaminergic neurons in brainstem and hypothalamus (MA) and the sleep-active ventrolateral preoptic neurons of the hypothalamus (VLPO), the model also includes the circadian and homeostatic sleep drives. It is shown that Orx stabilizes prolonged waking episodes via its excitatory input to MA and by relaying a circadian input to MA, thus sustaining MA firing activity during the circadian day. During sleep, both Orx and MA are inhibited by the VLPO, and the subsequent reduction in Orx input to the MA indirectly stabilizes sustained sleep episodes. Simulating a loss of Orx, the model produces dynamics resembling narcolepsy, including frequent transitions between states, reduced waking arousal levels, and a normal daily amount of total sleep. The model predicts a change in sleep timing with differences in orexin levels, with higher orexin levels delaying the normal sleep episode, suggesting that individual differences in Orx signaling may contribute to chronotype. Dynamics resembling sleep inertia also emerge from the model as a gradual sleep-to-wake transition on a timescale that varies with that of Orx dynamics. The quantitative, physiologically based model developed in this work thus provides a new explanation of how Orx stabilizes prolonged episodes of sleep and wake, and makes a range of experimentally testable predictions, including a role for Orx in chronotype and sleep inertia.

Human turnover dynamics during sleep: statistical behavior and its modeling

Turnover is a typical intermittent body movement while asleep. Exploring its behavior may provide insights into the mechanisms and management of sleep. However, little is understood about the dynamic nature of turnover in healthy humans and how it can be modified in disease. Here we present a detailed analysis of turnover signals that are collected by accelerometry from healthy elderly subjects and age-matched patients with neurodegenerative disorders such as Parkinson's disease. In healthy subjects, the time intervals between consecutive turnover events exhibit a well-separated bimodal distribution with one mode at ⩽10 s and the other at ⩾100 s, whereas such bimodality tends to disappear in neurodegenerative patients. The discovery of bimodality and fine temporal structures (⩽10 s) is a contribution that is not revealed by conventional sleep recordings with less time resolution (≈30 s). Moreover, we estimate the scaling exponent of the interval fluctuations, which also shows a clear difference between healthy subjects and patients. We incorporate these experimental results into a computational model of human decision making. A decision is to be made at each simulation step between two choices: to keep on sleeping or to make a turnover, the selection of which is determined dynamically by comparing a pair of random numbers assigned to each choice. This decision is weighted by a single parameter that reflects the depth of sleep. The resulting simulated behavior accurately replicates many aspects of observed turnover patterns, including the appearance or disappearance of bimodality and leads to several predictions, suggesting that the depth parameter may be useful as a quantitative measure for differentiating between normal and pathological sleep. These findings have significant clinical implications and may pave the way for the development of practical sleep assessment technologies.

Physiologically-based modeling of sleep-wake regulatory networks

Mathematical modeling has played a significant role in building our understanding of sleep-wake and circadian behavior. Over the past 40 years, phenomenological models, including the two-process model and oscillator models, helped frame experimental results and guide progress in understanding the interaction of homeostatic and circadian influences on sleep and understanding the generation of rapid eye movement sleep cycling. Recent advances in the clarification of the neural anatomy and physiology involved in the regulation of sleep and circadian rhythms have motivated the development of more detailed and physiologically-based mathematical models that extend the approach introduced by the classical reciprocal-interaction model. Using mathematical formalisms developed in the field of computational neuroscience to model neuronal population activity, these models investigate the dynamics of proposed conceptual models of sleep-wake regulatory networks with a focus on generating appropriate sleep and wake state transition patterns as well as simulating disease states and experimental protocols. In this review, we discuss several recent physiologically-based mathematical models of sleep-wake regulatory networks. We identify common features among these models in their network structures, model dynamics and approaches for model validation. We describe how the model analysis technique of fast-slow decomposition, which exploits the naturally occurring multiple timescales of sleep-wake behavior, can be applied to understand model dynamics in these networks. Our purpose in identifying commonalities among these models is to propel understanding of both the mathematical models and their underlying conceptual models, and focus directions for future experimental and theoretical work.

Neural circuit interactions between the dorsal raphe nucleus and the lateral hypothalamus: an experimental and computational study

Orexinergic/hypocretinergic (Ox) neurotransmission plays an important role in regulating sleep, as well as in anxiety and depression, for which the serotonergic (5-HT) system is also involved in. However, little is known regarding the direct and indirect interactions between 5-HT in the dorsal raphe nucleus (DRN) and Ox neurons in the lateral hypothalamus (LHA). In this study, we report the additional presence of 5-HT1BR, 5-HT2AR, 5-HT2CR and fast ligand-gated 5-HT3AR subtypes on the Ox neurons of transgenic Ox-enhanced green fluorescent protein (Ox-EGFP) and wild type C57Bl/6 mice using single and double immunofluorescence (IF) staining, respectively, and quantify the colocalization for each 5-HT receptor subtype. We further reveal the presence of 5-HT3AR and 5-HT1AR on GABAergic neurons in LHA. We also identify NMDAR1, OX1R and OX2R on Ox neurons, but none on adjacent GABAergic neurons. This suggests a one-way relationship between LHA's GABAergic and Ox neurons, wherein GABAergic neurons exerts an inhibitory effect on Ox neurons under partial DRN's 5-HT control. We also show that Ox axonal projections receive glutamatergic (PSD-95 immunopositive) and GABAergic (Gephyrin immunopositive) inputs in the DRN. We consider these and other available findings into our computational model to explore possible effects of neural circuit connection types and timescales on the DRN-LHA system's dynamics. We find that if the connections from 5-HT to LHA's GABAergic neurons are weakly excitatory or inhibitory, the network exhibits slow oscillations; not observed when the connection is strongly excitatory. Furthermore, if Ox directly excites 5-HT neurons at a fast timescale, phasic Ox activation can lead to an increase in 5-HT activity; no significant effect with slower timescale. Overall, our experimental and computational approaches provide insights towards a more complete understanding of the complex relationship between 5-HT in the DRN and Ox in the LHA.

The ontogeny of sleep-wake cycles in zebrafish: a comparison to humans

Zebrafish (Danio rerio) are used extensively in sleep research; both to further understanding of sleep in general and also as a model of human sleep. To date, sleep studies have been performed in larval and adult zebrafish but no efforts have been made to document the ontogeny of zebrafish sleep-wake cycles. Because sleep differs across phylogeny and ontogeny it is important to validate the use of zebrafish in elucidating the neural substrates of sleep. Here we describe the development of sleep and wake across the zebrafish lifespan and how it compares to humans. We find power-law distributions to best fit wake bout data but demonstrate that exponential distributions, previously used to describe sleep bout distributions, fail to adequately account for the data in either species. Regardless, the data reveal remarkable similarities in the ontogeny of sleep cycles in zebrafish and humans. Moreover, as seen in other organisms, zebrafish sleep levels are highest early in ontogeny and sleep and wake bouts gradually consolidate to form the adult sleep pattern. Finally, sleep percentage, bout duration, bout number, and sleep fragmentation are shown to allow for meaningful comparisons between zebrafish and human sleep.

Modeling Interindividual Differences in Spontaneous Internal Desynchrony Patterns

A physiologically based mathematical model of a putative sleep-wake regulatory network is used to investigate the transition from typical human sleep patterns to spontaneous internal desynchrony behavior observed under temporal isolation conditions. The model sleep-wake regulatory network describes the neurotransmitter-mediated interactions among brainstem and hypothalamic neuronal populations that participate in the transitions between wake, rapid eye movement (REM) sleep, and non-REM (NREM) sleep. Physiologically based interactions among these sleep-wake centers and the suprachiasmatic nucleus (SCN), whose activity is driven by an established circadian oscillator model, mediate circadian modulation of sleep-wake behavior. When the sleep-wake and circadian rhythms are synchronized, the model simulates stereotypically normal human sleep-wake behavior within the limits of individual variation, including typical NREM-REM cycling across the night. When effects of temporal isolation are simulated by increasing the period of the sleep-wake cycle, the model replicates spontaneous internal desynchrony with the appropriate dependence of multiple features of REM sleep on circadian phase. In temporal isolation experiments, subjects have exhibited different desynchronized sleep-wake behaviors. Our model can generate similar ranges of desynchronized behaviors by variations in the period of the sleep-wake cycle and the strength of interactions between the SCN and the sleep-wake centers. Analysis of the model suggests that similar mechanisms underlie several different desynchronized behaviors and that the phenomenon of phase trapping may be dependent on SCN modulation of REM sleep-promoting centers. These results provide predictions for physiologically plausible mechanisms underlying interindividual variations in sleep-wake behavior observed during temporal isolation experiments.

Mammalian rest/activity patterns explained by physiologically based modeling

Circadian rhythms are fundamental to life. In mammals, these rhythms are generated by pacemaker neurons in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is remarkably consistent in structure and function between species, yet mammalian rest/activity patterns are extremely diverse, including diurnal, nocturnal, and crepuscular behaviors. Two mechanisms have been proposed to account for this diversity: (i) modulation of SCN output by downstream nuclei, and (ii) direct effects of light on activity. These two mechanisms are difficult to disentangle experimentally and their respective roles remain unknown. To address this, we developed a computational model to simulate the two mechanisms and their influence on temporal niche. In our model, SCN output is relayed via the subparaventricular zone (SPZ) to the dorsomedial hypothalamus (DMH), and thence to ventrolateral preoptic nuclei (VLPO) and lateral hypothalamus (LHA). Using this model, we generated rich phenotypes that closely resemble experimental data. Modulation of SCN output at the SPZ was found to generate a full spectrum of diurnal-to-nocturnal phenotypes. Intriguingly, we also uncovered a novel mechanism for crepuscular behavior: if DMH/VLPO and DMH/LHA projections act cooperatively, daily activity is unimodal, but if they act competitively, activity can become bimodal. In addition, we successfully reproduced diurnal/nocturnal switching in the rodent Octodon degu using coordinated inversions in both masking and circadian modulation. Finally, the model correctly predicted the SCN lesion phenotype in squirrel monkeys: loss of circadian rhythmicity and emergence of ∼4-h sleep/wake cycles. In capturing these diverse phenotypes, the model provides a powerful new framework for understanding rest/activity patterns and relating them to underlying physiology. Given the ubiquitous effects of temporal organization on all aspects of animal behavior and physiology, this study sheds light on the physiological changes required to orchestrate adaptation to various temporal niches.

Arousal state feedback as a potential physiological generator of the ultradian REM/NREM sleep cycle

Human sleep episodes are characterized by an approximately 90-min ultradian oscillation between rapid eye movement (REM) and non-REM (NREM) sleep stages. The source of this oscillation is not known. Pacemaker mechanisms for this rhythm have been proposed, such as a reciprocal interaction network, but these fail to account for documented homeostatic regulation of both sleep stages. Here, two candidate mechanisms are investigated using a simple model that has stable states corresponding to Wake, REM sleep, and NREM sleep. Unlike other models of the ultradian rhythm, this model of sleep dynamics does not include an ultradian pacemaker, nor does it invoke a hypothetical homeostatic process that exists purely to drive ultradian rhythms. Instead, only two inputs are included: the homeostatic drive for Sleep and the circadian drive for Wake. These two inputs have been the basis for the most influential Sleep/Wake models, but have not previously been identified as possible ultradian rhythm generators. Using the model, realistic ultradian rhythms are generated by arousal state feedback to either the homeostatic or circadian drive. For the proposed 'homeostatic mechanism', homeostatic pressure increases in Wake and REM sleep, and decreases in NREM sleep. For the proposed 'circadian mechanism', the circadian drive is up-regulated in Wake and REM sleep, and is down-regulated in NREM sleep. The two mechanisms are complementary in the features they capture. The homeostatic mechanism reproduces experimentally observed rebounds in NREM sleep duration and intensity following total sleep deprivation, and rebounds in both NREM sleep intensity and REM sleep duration following selective REM sleep deprivation. The circadian mechanism does not reproduce sleep state rebounds, but more accurately reproduces the temporal patterns observed in a normal night of sleep. These findings have important implications in terms of sleep physiology and they provide a parsimonious explanation for the observed ultradian rhythm of REM/NREM sleep.