Circadian regulation of sleep-wake behaviour in nocturnal rats requires multiple signals from suprachiasmatic nucleus

Lactuca sativa L. Extract Enhances Sleep Duration Through Upregulation of Adenosine A1 Receptor and GABAA Receptors Subunits in Pentobarbital-Injected Mice

We investigated the effects of Lactuca sativa L. extracts (Lactuc) on pentobarbital-induced sleep in mice to elucidate the mechanisms underlying its impact on sleep quality. Mice were randomly assigned to five groups: control, positive control (diazepam 2 mg/kg b.w.), and three groups orally administered with Lactuc (50, 100, and 200 mg/kg b.w.). After 2 weeks of oral administration and intraperitoneal injections, the mice were killed. We found that the Lactuc-administered groups had significantly reduced sleep latency and increased sleep duration compared with the control group. Furthermore, the oral administration of Lactuc induced a significant increase in mRNA expression and protein expression of adenosine A1 receptor in the brains compared with the expressions in the control group. In addition, the Lactuc-administered groups exhibited significantly higher levels of mRNA expressions of GABAA receptors subunits α2, β2, γ1, and, γ2 in the brain tissue. Therefore, we suggest that Lactuc could be used to develop natural products that effectively improve sleep quality and duration.

NREM-REM alternation complicates transitions from napping to non-napping behavior in a three-state model of sleep-wake regulation

The temporal structure of human sleep changes across development as it consolidates from the polyphasic sleep of infants to the single nighttime sleep episode typical in adults. Experimental studies have shown that changes in the dynamics of sleep need may mediate this developmental transition in sleep patterning, however, it is unknown how sleep architecture interacts with these changes. We employ a physiologically-based mathematical model that generates wake, rapid eye movement (REM) and non-REM (NREM) sleep states to investigate how NREM-REM alternation affects the transition in sleep patterns as the dynamics of the homeostatic sleep drive are varied. To study the mechanisms producing these transitions, we analyze the bifurcations of numerically-computed circle maps that represent key dynamics of the full sleep-wake network model by tracking the evolution of sleep onsets across different circadian (∼ 24 h) phases. The maps are non-monotonic and discontinuous, being composed of branches that correspond to sleep-wake cycles containing distinct numbers of REM bouts. As the rates of accumulation and decay of the homeostatic sleep drive are varied, we identify the bifurcations that disrupt a period-adding-like behavior of sleep patterns in the transition between biphasic and monophasic sleep. These bifurcations include border collision and saddle-node bifurcations that initiate new sleep patterns, period-doubling bifurcations leading to higher-order patterns of NREM-REM alternation, and intervals of bistability of sleep patterns with different NREM-REM alternations. Furthermore, patterns of NREM-REM alternation exhibit variable behaviors in different regimes of constant sleep-wake patterns. Overall, the sequence of sleep-wake behaviors, and underlying bifurcations, in the transition from biphasic to monophasic sleep in this three-state model is more complex than behavior observed in models of sleep-wake regulation that do not consider the dynamics of NREM-REM alternation. These results suggest that interactions between the dynamics of the homeostatic sleep drive and the dynamics of NREM-REM alternation may contribute to the wide interindividual variation observed when young children transition from napping to non-napping behavior.

Modulation of melatonin to the thalamic lesion-induced pain and comorbid sleep disturbance in the animal model of the central post-stroke hemorrhage

The devastating chronic central post stroke pain is associated with variety of comorbidities. Disrupted sleep is a severe comorbidity, causing an increase in the suicide rate, due to CPSP’s pain symptom. Melatonin is a well-known jet-lag compound, which helps in entrainment of sleep cycle. Accordingly, whether melatonin as a therapeutic measurement for the regulation of sleep disturbance related to central post stroke pain remains unclear. Exogenous melatonin administration entrained the disrupted 24 h circadian cycle, more effectively after 2 and 3 week of administration. The effect of melatonin was persisted on 4th week too, when melatonin administration was discontinued. Also, melatonin ameliorated the pain due to distorted sleep-activity behavior after melatonin administration for 3 weeks. The low levels of melatonin in blood plasma due to CPSP were restored after 3 weeks of melatonin administration. After 30 mg/kg melatonin administrations for 3 weeks, all the disrupted resting and activity behaviors were reduced during light and dark periods. The results suggested that melatonin significantly ameliorated CPSP’s pain symptoms and comorbid sleep disturbance showing in activity behavior.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

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.

Pathway-Dependent Regulation of Sleep Dynamics in a Network Model of the Sleep-Wake Cycle

Sleep is a fundamental homeostatic process within the animal kingdom. Although various brain areas and cell types are involved in the regulation of the sleep-wake cycle, it is still unclear how different pathways between neural populations contribute to its regulation. Here we address this issue by investigating the behavior of a simplified network model upon synaptic weight manipulations. Our model consists of three neural populations connected by excitatory and inhibitory synapses. Activity in each population is described by a firing-rate model, which determines the state of the network. Namely wakefulness, rapid eye movement (REM) sleep or non-REM (NREM) sleep. By systematically manipulating the synaptic weight of every pathway, we show that even this simplified model exhibits non-trivial behaviors: for example, the wake-promoting population contributes not just to the induction and maintenance of wakefulness, but also to sleep induction. Although a recurrent excitatory connection of the REM-promoting population is essential for REM sleep genesis, this recurrent connection does not necessarily contribute to the maintenance of REM sleep. The duration of NREM sleep can be shortened or extended by changes in the synaptic strength of the pathways from the NREM-promoting population. In some cases, there is an optimal range of synaptic strengths that affect a particular state, implying that the amount of manipulations, not just direction (i.e., activation or inactivation), needs to be taken into account. These results demonstrate pathway-dependent regulation of sleep dynamics and highlight the importance of systems-level quantitative approaches for sleep-wake regulatory circuits.

Estimating Representative Group Intrinsic Circadian Period from Illuminance-Response Curve Data

The human circadian pacemaker entrains to the 24-h day, but interindividual differences in properties of the pacemaker, such as intrinsic period, affect chronotype and mediate responses to challenges to the circadian system, such as shift work and jet lag, and the efficacy of therapeutic interventions such as light therapy. Robust characterization of circadian properties requires desynchronization of the circadian system from the rest-activity cycle, and these forced desynchrony protocols are very time and resource intensive. However, circadian protocols designed to derive the relationship between light intensity and phase shift, which is inherently affected by intrinsic period, may be applied more broadly. To exploit this relationship, we applied a mathematical model of the human circadian pacemaker with a Markov-Chain Monte Carlo parameter estimation algorithm to estimate the representative group intrinsic period for a group of participants using their collective illuminance-response curve data. We first validated this methodology using simulated illuminance-response curve data in which the intrinsic period was known. Over a physiological range of intrinsic periods, this method accurately estimated the representative intrinsic period of the group. We also applied the method to previously published experimental data describing the illuminance-response curve for a group of healthy adult participants. We estimated the study participants' representative group intrinsic period to be 24.26 and 24.27 h using uniform and normal priors, respectively, consistent with estimates of the average intrinsic period of healthy adults determined using forced desynchrony protocols. Our results establish an approach to estimate a population's representative intrinsic period from illuminance-response curve data, thereby facilitating the characterization of intrinsic period across a broader range of participant populations than could be studied using forced desynchrony protocols. Future applications of this approach may improve the understanding of demographic differences in the intrinsic circadian period.

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 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.

Unsupervised Estimation of Mouse Sleep Scores and Dynamics Using a Graphical Model of Electrophysiological Measurements

The proportion, number of bouts, and mean bout duration of different vigilance states (Wake, NREM, REM) are useful indices of dynamics in experimental sleep research. These metrics are estimated by first scoring state, sometimes using an algorithm, based on electrophysiological measurements such as the electroencephalogram (EEG) and electromyogram (EMG), and computing their values from the score sequence. Isolated errors in the scores can lead to large discrepancies in the estimated sleep metrics. But most algorithms score sleep by classifying the state from EEG/EMG features independently in each time epoch without considering the dynamics across epochs, which could provide contextual information. The objective here is to improve estimation of sleep metrics by fitting a probabilistic dynamical model to mouse EEG/EMG data and then predicting the metrics from the model parameters. Hidden Markov models (HMMs) with multivariate Gaussian observations and Markov state transitions were fitted to unlabeled 24-h EEG/EMG feature time series from 20 mice to model transitions between the latent vigilance states; a similar model with unbiased transition probabilities served as a reference. Sleep metrics predicted from the HMM parameters did not deviate significantly from manual estimates except for rapid eye movement sleep (REM) ([Formula: see text]; Wilcoxon signed-rank test). Changes in value from Light to Dark conditions correlated well with manually estimated differences (Spearman’s rho 0.43–0.84) except for REM. HMMs also scored vigilance state with over 90% accuracy. HMMs of EEG/EMG features can therefore characterize sleep dynamics from EEG/EMG measurements, a prerequisite for characterizing the effects of perturbation in sleep monitoring and control applications.

Neural activity in the suprachiasmatic circadian clock of nocturnal mice anticipating a daytime meal

Circadian rhythms in mammals are regulated by a system of circadian oscillators that includes a light-entrainable pacemaker in the suprachiasmatic nucleus (SCN) and food-entrainable oscillators (FEOs) elsewhere in the brain and body. In nocturnal rodents, the SCN promotes sleep in the day and wake at night, while FEOs promote an active state in anticipation of a predictable daily meal. For nocturnal animals to anticipate a daytime meal, wake-promoting signals from FEOs must compete with sleep-promoting signals from the SCN pacemaker. One hypothesis is that FEOs impose a daily rhythm of inhibition on SCN output that is timed to permit the expression of activity prior to a daytime meal. This hypothesis predicts that SCN activity should decrease prior to the onset of anticipatory activity and remain suppressed through the scheduled mealtime. To assess the hypothesis, neural activity in the SCN of mice anticipating a 4-5-h daily meal in the light period was measured using FOS immunohistochemistry and in vivo multiple unit electrophysiology. SCN FOS, quantified by optical density, was significantly reduced at the expected mealtime in food-anticipating mice with access to a running disk, compared to ad libitum-fed and acutely fasted controls. Group differences were not significant when FOS was quantified by other methods, or in mice without running disks. SCN electrical activity was markedly decreased during locomotion in some mice but increased in others. Changes in either direction were concurrent with locomotion, were not specific to food anticipation, and were not sustained during longer pauses. Reduced FOS indicates a net suppression of SCN activity that may depend on the intensity or duration of locomotion. The timing of changes in SCN activity relative to locomotion suggests that any effect of FEOs on SCN output is mediated indirectly, by feedback from neural or systemic correlates of locomotion.

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.

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.

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.

Adolescent sleep patterns in humans and laboratory animals

This article is part of a Special Issue "Puberty and Adolescence". One of the defining characteristics of adolescence in humans is a large shift in the timing and structure of sleep. Some of these changes are easily observable at the behavioral level, such as a shift in sleep patterns from a relatively morning to a relatively evening chronotype. However, there are equally large changes in the underlying architecture of sleep, including a >60% decrease in slow brain wave activity, which may reflect cortical pruning. In this review we examine the developmental forces driving adolescent sleep patterns using a cross-species comparison. We find that behavioral and physiological sleep parameters change during adolescence in non-human mammalian species, ranging from primates to rodents, in a manner that is often hormone-dependent. However, the overt appearance of these changes is species-specific, with polyphasic sleepers, such as rodents, showing a phase-advance in sleep timing and consolidation of daily sleep/wake rhythms. Using the classic two-process model of sleep regulation, we demonstrate via a series of simulations that many of the species-specific characteristics of adolescent sleep patterns can be explained by a universal decrease in the build-up and dissipation of sleep pressure. Moreover, and counterintuitively, we find that these changes do not necessitate a large decrease in overall sleep need, fitting the adolescent sleep literature. We compare these results to our previous review detailing evidence for adolescent changes in the regulation of sleep by the circadian timekeeping system (Hagenauer and Lee, 2012), and suggest that both processes may be responsible for adolescent sleep patterns.

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.

Reconstructing mammalian sleep dynamics with data assimilation

Data assimilation is a valuable tool in the study of any complex system, where measurements are incomplete, uncertain, or both. It enables the user to take advantage of all available information including experimental measurements and short-term model forecasts of a system. Although data assimilation has been used to study other biological systems, the study of the sleep-wake regulatory network has yet to benefit from this toolset. We present a data assimilation framework based on the unscented Kalman filter (UKF) for combining sparse measurements together with a relatively high-dimensional nonlinear computational model to estimate the state of a model of the sleep-wake regulatory system. We demonstrate with simulation studies that a few noisy variables can be used to accurately reconstruct the remaining hidden variables. We introduce a metric for ranking relative partial observability of computational models, within the UKF framework, that allows us to choose the optimal variables for measurement and also provides a methodology for optimizing framework parameters such as UKF covariance inflation. In addition, we demonstrate a parameter estimation method that allows us to track non-stationary model parameters and accommodate slow dynamics not included in the UKF filter model. Finally, we show that we can even use observed discretized sleep-state, which is not one of the model variables, to reconstruct model state and estimate unknown parameters. Sleep is implicated in many neurological disorders from epilepsy to schizophrenia, but simultaneous observation of the many brain components that regulate this behavior is difficult. We anticipate that this data assimilation framework will enable better understanding of the detailed interactions governing sleep and wake behavior and provide for better, more targeted, therapies.

Mathematical models are developed to better understand interactions between components of a system that together govern the overall behavior. Mathematical models of sleep have helped to elucidate the neuronal cell groups that are involved in promoting sleep and wake behavior and the transitions between them. However, to be able to take full advantage of these models one must be able to estimate the value of all included variables accurately. Data assimilation refers to methods that allow the user to combine noisy measurements of just a few system variables with the mathematical model of that system to estimate all variables, including those originally inaccessible for measurement. Using these techniques we show that we can reconstruct the unmeasured variables and parameters of a mathematical model of the sleep-wake network. These reconstructed estimates can then be used to better understand the underlying neuronal behavior that results in sleep and wake activity. Because sleep is implicated in a wide array of neurological disorders from epilepsy to schizophrenia, we anticipate that this framework will enable better understanding of the link between sleep and the rest of the brain and provide for better, more targeted, therapies.

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.

A mathematical model towards understanding the mechanism of neuronal regulation of wake-NREMS-REMS states

In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.

The sleeping brain as a complex system

'Complexity science' is a rapidly developing research direction with applications in a multitude of fields that study complex systems consisting of a number of nonlinear elements with interesting dynamics and mutual interactions. This Theme Issue 'The complexity of sleep' aims at fostering the application of complexity science to sleep research, because the brain in its different sleep stages adopts different global states that express distinct activity patterns in large and complex networks of neural circuits. This introduction discusses the contributions collected in the present Theme Issue. We highlight the potential and challenges of a complex systems approach to develop an understanding of the brain in general and the sleeping brain in particular. Basically, we focus on two topics: the complex networks approach to understand the changes in the functional connectivity of the brain during sleep, and the complex dynamics of sleep, including sleep regulation. We hope that this Theme Issue will stimulate and intensify the interdisciplinary communication to advance our understanding of the complex dynamics of the brain that underlies sleep and consciousness.