A two-state stochastic model of REM sleep architecture in the rat

A probabilistic model for the ultradian timing of REM sleep in mice

A salient feature of mammalian sleep is the alternation between rapid eye movement (REM) and non-REM (NREM) sleep. However, how these two sleep stages influence each other and thereby regulate the timing of REM sleep episodes is still largely unresolved. Here, we developed a statistical model that specifies the relationship between REM and subsequent NREM sleep to quantify how REM sleep affects the following NREM sleep duration and its electrophysiological features in mice. We show that a lognormal mixture model well describes how the preceding REM sleep duration influences the amount of NREM sleep till the next REM sleep episode. The model supports the existence of two different types of sleep cycles: Short cycles form closely interspaced sequences of REM sleep episodes, whereas during long cycles, REM sleep is first followed by an interval of NREM sleep during which transitions to REM sleep are extremely unlikely. This refractory period is characterized by low power in the theta and sigma range of the electroencephalogram (EEG), low spindle rate and frequent microarousals, and its duration proportionally increases with the preceding REM sleep duration. Using our model, we estimated the propensity for REM sleep at the transition from NREM to REM sleep and found that entering REM sleep with higher propensity resulted in longer REM sleep episodes with reduced EEG power. Compared with the light phase, the buildup of REM sleep propensity was slower during the dark phase. Our data-driven modeling approach uncovered basic principles underlying the timing and duration of REM sleep episodes in mice and provides a flexible framework to describe the ultradian regulation of REM sleep in health and disease.

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.

Neural and Homeostatic Regulation of REM Sleep

Rapid eye movement (REM) sleep is a distinct, homeostatically controlled brain state characterized by an activated electroencephalogram (EEG) in combination with paralysis of skeletal muscles and is associated with vivid dreaming. Understanding how REM sleep is controlled requires identification of the neural circuits underlying its initiation and maintenance, and delineation of the homeostatic processes regulating its expression on multiple timescales. Soon after its discovery in humans in 1953, the pons was demonstrated to be necessary and sufficient for the generation of REM sleep. But, especially within the last decade, researchers have identified further neural populations in the hypothalamus, midbrain, and medulla that regulate REM sleep by either promoting or suppressing this brain state. The discovery of these populations was greatly facilitated by the availability of novel technologies for the dissection of neural circuits. Recent quantitative models integrate findings about the activity and connectivity of key neurons and knowledge about homeostatic mechanisms to explain the dynamics underlying the recurrence of REM sleep. For the future, combining quantitative with experimental approaches to directly test model predictions and to refine existing models will greatly advance our understanding of the neural and homeostatic processes governing the regulation of REM sleep.

The relationship between depression and chronotype: A longitudinal assessment during childhood and adolescence

BACKGROUND/OBJECTIVE

During adolescence, chronotype shifts toward "eveningness." "Eveningness" is related to negative physical and mental health outcomes. Little is known about what influences the shift in chronotype beyond pubertal status. The current study examined the influence of earlier depression predicting later individual differences in adolescent chronotype, accounting for pubertal status, and the prospective prediction of later increases in depression from earlier chronotype.

METHODS

Youth (age M = 12.06, SD = 2.35; 56.5% girls) from the community completed repeated assessments of depression, including both self-reports (14 assessments) and diagnostic interviews (eight assessments), over a 48-month period. At the 36-month timepoint, participants completed chronotype and pubertal development measures. Regression and ANOVA analyses examined: (1) the influence of earlier depression levels (baseline to 36 months) upon chronotype, and (2) chronotype (at 36 months) upon later depression (48 months).

RESULTS

Youth with higher earlier depression symptoms (β = -0.347, P < .001) and history of depression diagnosis (β = -0.13, P = .045) showed a greater eveningness preference controlling for pubertal status, age, and gender. Further, depression diagnosis history interacted with pubertal status to predict chronotype: (F(1,243) = 4.171, P = .045) such that the influence of depression on chronotype was greatest among postpubertal youth (t = 3.271, P = .002). Chronotype (greater eveningness preference) predicted prospective increases in depression symptoms (β = -0.16, P = .03) and onset of depressive episode (b = -0.085, OR = 0.92, P = .03) 1 year later.

CONCLUSION

Depression, experienced earlier in life, predicts greater preference for eveningness, especially among postpubertal youth. In turn, later depression is predicted by evening preference. These findings suggest the reciprocal interplay between mood and biological rhythms, especially depression and chronotype, during adolescence.

Significance of the zero sum principle for circadian, homeostatic and allostatic regulation of sleep-wake state in the rat

Sleep-wake behavior exhibits diurnal rhythmicity, rebound responses to acute total sleep deprivation (TSD), and attenuated rebounds following chronic sleep restriction (CSR). We investigated how these long-term patterns of behavior emerge from stochastic short-term dynamics of state transition. Male Sprague-Dawley rats were subjected to TSD (1day×24h, N=9), or CSR (10days×18h TSD, N=7) using a rodent walking-wheel apparatus. One baseline day and one recovery day following TSD and CSR were analyzed. The implications of the zero sum principle were evaluated using a Markov model of sleep-wake state transition. Wake bout duration (a combined function of the probability of wake maintenance and proportional representations of brief and long wake) was a key variable mediating the baseline diurnal rhythms and post-TSD responses of all three states, and the attenuation of the post-CSR rebounds. Post-NREM state transition trajectory was an important factor in REM rebounds. The zero sum constraint ensures that a change in any transition probability always affects bout frequency and cumulative time of at least two, and usually all three, of wakefulness, NREM and REM. Neural mechanisms controlling wake maintenance may play a pivotal role in regulation and dysregulation of all three states.

Global Functional Connectivity Differences between Sleep-Like States in Urethane Anesthetized Rats Measured by fMRI

Sleep is essential for nervous system functioning and sleep disorders are associated with several neurodegenerative diseases. However, the macroscale connectivity changes in brain networking during different sleep states are poorly understood. One of the hindering factors is the difficulty to combine functional connectivity investigation methods with spontaneously sleeping animals, which prevents the use of numerous preclinical animal models. Recent studies, however, have implicated that urethane anesthesia can uniquely induce different sleep-like brain states, resembling rapid eye movement (REM) and non-REM (NREM) sleep, in rodents. Therefore, the aim of this study was to assess changes in global connectivity and topology between sleep-like states in urethane anesthetized rats, using blood oxygenation level dependent (BOLD) functional magnetic resonance imaging. We detected significant changes in corticocortical (increased in NREM-like state) and corticothalamic connectivity (increased in REM-like state). Additionally, in graph analysis the modularity, the measure of functional integration in the brain, was higher in NREM-like state than in REM-like state, indicating a decrease in arousal level, as in normal sleep. The fMRI findings were supported by the supplementary electrophysiological measurements. Taken together, our results show that macroscale functional connectivity changes between sleep states can be detected robustly with resting-state fMRI in urethane anesthetized rats. Our findings pave the way for studies in animal models of neurodegenerative diseases where sleep abnormalities are often one of the first markers for the disorder development.

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.

Statistical properties of sleep-wake behavior in the rat and their relation to circadian and ultradian phases

STUDY OBJECTIVES

To examine the statistical characteristics of short-term sleep-wake architecture and to evaluate their dependence on ultradian and circadian phase.

DESIGN

Observational, time series.

SETTING

Laboratory.

PARTICIPANTS

Ten male adult Sprague-Dawley rats.

INTERVENTIONS

N/A.

MEASUREMENTS AND RESULTS

States of wakefulness (WAKE), rapid eye movement sleep (REM) and nonrapid eye movement sleep (NREM) were recorded in 5-sec epochs over 7 consecutive days. State bout durations were analyzed using parametric regression of survival curves, comparing exponential, biexponential, and power law models. WAKE survival curves were best fit by biexponential models, suggesting that there are two statistically distinct stochastic mechanisms generating two types of WAKE--"brief" WAKE and "long" WAKE. Exponential time constants varied as a function of circadian and ultradian phase, with "long" WAKE showing the largest effect. NREM survival curves exhibited biexponential and monoexponential distributions in light and dark, respectively, with weak effects of ultradian phase. REM survival curves approximated a monoexponential distribution that varied with circadian but not ultradian phase. χ(2) analysis was used in a three-state Markov model to evaluate whether conditional state transition probabilities exhibit the property of first-order dependence. This was partially confirmed, but only after accounting for heterogeneity associated with circadian and ultradian phase. However, there was evidence of residual second-order dependence indicating that additional sources of statistical heterogeneity may remain to be identified.

CONCLUSIONS

Sleep-wake state is regulated over short timescales by stochastic mechanisms. When the major sources of heterogeneity are taken into account, including two-component WAKE and NREM states, the sleep-wake system of the rat behaves, to a reasonable approximation, as a Markovian system that is modulated over ultradian and circadian timescales.

A hidden Markov model to assess drug-induced sleep fragmentation in the telemetered rat

Drug-induced sleep fragmentation can cause sleep disturbances either via their intended pharmacological action or as a side effect. Examples of disturbances include excessive daytime sleepiness, insomnia and nightmares. Developing drugs without these side effects requires insight into the mechanisms leading to sleep disturbance. The characterization of the circadian sleep pattern by EEG following drug exposure has improved our understanding of these mechanisms and their translatability across species. The EEG shows frequent transitions between specific sleep states leading to multiple correlated sojourns in these states. We have developed a Markov model to consider the high correlation in the data and quantitatively compared sleep disturbance in telemetered rats induced by methylphenidate, which is known to disturb sleep, and of a new chemical entity (NCE). It was assumed that these drugs could either accelerate or decelerate the transitions between the sleep states. The difference in sleep disturbance of methylphenidate and the NCE were quantitated and different mechanisms of action on rebound sleep were identified. The estimated effect showed that both compounds induce sleep fragmentation with methylphenidate being fivefold more potent compared to the NCE.

Cholinergic modulation of narcoleptic attacks in double orexin receptor knockout mice

To investigate how cholinergic systems regulate aspects of the sleep disorder narcolepsy, we video-monitored mice lacking both orexin (hypocretin) receptors (double knockout; DKO mice) while pharmacologically altering cholinergic transmission. Spontaneous behavioral arrests in DKO mice were highly similar to those reported in orexin-deficient mice and were never observed in wild-type (WT) mice. A survival analysis revealed that arrest lifetimes were exponentially distributed indicating that random, Markovian processes determine arrest lifetime. Low doses (0.01, 0.03 mg/kg, IP), but not a high dose (0.08 mg/kg, IP) of the cholinesterase inhibitor physostigmine increased the number of arrests but did not alter arrest lifetimes. The muscarinic antagonist atropine (0.5 mg/kg, IP) decreased the number of arrests, also without altering arrest lifetimes. To determine if muscarinic transmission in pontine areas linked to REM sleep control also influences behavioral arrests, we microinjected neostigmine (50 nl, 62.5 µM) or neostigmine + atropine (62.5 µM and 111 µM respectively) into the nucleus pontis oralis and caudalis. Neostigmine increased the number of arrests in DKO mice without altering arrest lifetimes but did not provoke arrests in WT mice. Co-injection of atropine abolished this effect. Collectively, our findings establish that behavioral arrests in DKO mice are similar to those in orexin deficient mice and that arrests have exponentially distributed lifetimes. We also show, for the first time in a rodent narcolepsy model, that cholinergic systems can regulate arrest dynamics. Since perturbations of muscarinic transmission altered arrest frequency but not lifetime, our findings suggest cholinergic systems influence arrest initiation without influencing circuits that determine arrest duration.

Modeling the temporal architecture of rat sleep-wake behavior

The fine architecture of sleep-wake behavior shows a distinct dynamic structure with distributions of rat sleep and wake bout durations displaying qualitatively different profiles. Wake bout durations follow a power-law relation whereas sleep bout durations are exponentially distributed. We show that a physiologically-based sleep-wake regulatory network model with an underlying deterministic structure governing neuronal interactions can generate realistic rat sleep-wake behavior as assessed by both standard summary statistics and survival analysis of bout distributions. Obtaining appropriate bout duration distributions depended on stochastic elements included in the model, the existence of multiple mechanisms for state transitions, and specific relationships among time constants governing state maintenance. This model provides a novel framework for exploring the disruptions of sleep-wake architecture associated with pharmacological, genetic, and disease states.

Multinomial logistic estimation of Markov-chain models for modeling sleep architecture in primary insomnia patients

Hypnotic drug development calls for a better understanding of sleep physiology in order to improve and differentiate novel medicines for the treatment of sleep disorders. On this basis, a proper evaluation of polysomnographic data collected in clinical trials conducted to explore clinical efficacy of novel hypnotic compounds should include the assessment of sleep architecture and its drug-induced changes. This work presents a non-linear mixed-effect Markov-chain model based on multinomial logistic functions which characterize the time course of transition probabilities between sleep stages in insomniac patients treated with placebo. Polysomnography measurements were obtained from patients during one night treatment. A population approach was used to describe the time course of sleep stages (awake stage, stage 1, stage 2, slow-wave sleep and REM sleep) using a Markov-chain model. The relationship between time and individual transition probabilities between sleep stages was modelled through piecewise linear multinomial logistic functions. The identification of the model produced a good adherence of mean post-hoc estimates to the observed transition frequencies. Parameters were generally well estimated in terms of CV, shrinkage and distribution of empirical Bayes estimates around the typical values. The posterior predictive check analysis showed good consistency between model-predicted and observed sleep parameters. In conclusion, the Markov-chain model based on multinomial logistic functions provided an accurate description of the time course of sleep stages together with an assessment of the probabilities of transition between different stages.

The time course of the probability of transition into and out of REM sleep

STUDY OBJECTIVES

A model of rapid eye movement (REM) sleep expression is proposed that assumes underlying regulatory mechanisms operating as inhomogenous Poisson processes, the overt results of which are the transitions into and out of REM sleep.

DESIGN

Based on spontaneously occurring REM sleep episodes ("Episode") and intervals without REM sleep ("Interval"), 3 variables are defined and evaluated over discrete 15-second epochs using a nonlinear logistic regression method: "Propensity" is the instantaneous rate of into-REM transition occurrence throughout an Interval, "Volatility" is the instantaneous rate of out-of-REM transition occurrence throughout an Episode, and "Opportunity" is the probability of being in non-REM (NREM) sleep at a given time throughout an Interval, a requisite for transition.

SETTING

12:12 light:dark cycle, isolated boxes.

PARTICIPANTS

Sixteen male Sprague-Dawley rats.

INTERVENTIONS

None. Spontaneous sleep cycles.

MEASUREMENTS AND RESULTS

The highest levels of volatility and propensity occur, respectively, at the very beginning of Episodes and Intervals. The new condition stabilizes rapidly, and variables reach nadirs at minute 1.25 and 2.50, respectively. Afterward, volatility increases markedly, reaching values close to the initial level. Propensity increases moderately, the increment being stronger through NREM sleep bouts occurring at the end of long Intervals. Short-term homeostasis is evidenced by longer REM sleep episodes lowering propensity in the following Interval.

CONCLUSIONS

The stabilization after transitions into Episodes or Intervals and the destabilization after remaining for some time in either condition may be described as resulting from continuous processes building up during Episodes and intervals. These processes underlie the overt occurrence of transitions.

Markov analysis of sleep dynamics

A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.

Improved sleep-wake and behavior discrimination using MEMS accelerometers

State of vigilance is determined by behavioral observations and electrophysiological activity. Here, we improve automatic state of vigilance discrimination by combining head acceleration with EEG measures. We incorporated biaxial dc-sensitive microelectromechanical system (MEMS) accelerometers into head-mounted preamplifiers in rodents. Epochs (15s) of behavioral video and EEG data formed training sets for the following states: Slow Wave Sleep, Rapid Eye Movement Sleep, Quiet Wakefulness, Feeding or Grooming, and Exploration. Multivariate linear discriminant analysis of EEG features with and without accelerometer features was used to classify behavioral state. A broad selection of EEG feature sets based on recent literature on state discrimination in rodents was tested. In all cases, inclusion of head acceleration significantly improved the discriminative capability. Our approach offers a novel methodology for determining the behavioral context of EEG in real time, and has potential application in automatic sleep-wake staging and in neural prosthetic applications for movement disorders and epileptic seizures.

Kv3 potassium channels control the duration of different arousal states by distinct stochastic and clock-like mechanisms

Sleep-wake behavior is tightly controlled in many animal species, suggesting genetically encoded, homeostatic control mechanisms that determine arousal-state dynamics. We reported that two voltage-gated potassium channels, Kv3.1 and Kv3.3, control sleep in wild-type and Kv3-mutant mice. Compared with wild-type (WT), homozygous double mutants (DKO) that lack these channels sleep 40% less in the light and 22% less in the dark. To understand how the lack of these channels affects sleep, we analysed arousal-state changes during the light period where the differences are greatest between WT and DKO. We determined the kinetic complexity of each arousal state from the episode durations of wakefulness, slow-wave sleep and rapid eye movement sleep (REMS). Based on the number of exponential components in episode-duration histograms, WT and DKO mice have several kinetically distinct states of wakefulness, and these states are longer in duration in DKO. For slow-wave sleep, WT mice have a single slow-wave sleep (SWS) state in contrast to DKO mice, which show two distinct SWS states, one that is 60% shorter than that in WT and a second that is similar in duration. Both WT and DKO mice have two kinetically distinct REMS states. DKO mice show an 84% reduction in the frequency of short REMS episodes (<45 s) without any change in the occurrence of long REMS episodes (>60 s). In contrast to the stochastic control of episode durations of wakefulness and SWS, the durations of both REMS states are normally distributed, indicating that the underlying control processes are fundamentally different.

Sleep dynamics: a self-organized critical system

In psychiatric and neurological diseases, sleep is often perturbed. Moreover, recent works on humans and animals tend to show that sleep plays a strong role in memory processes. Reciprocally, sleep dynamics following a learning task is modified [Hubert, Nature (London) 02663, 1 (2004), Peigneux, Neuron 44, 535 (2004)]. However, sleep analysis in humans and animals is often limited to the total sleep and wake duration quantification. These two parameters are not fully able to characterize the sleep dynamics. In mammals sleep presents a complex organization with an alternation of slow wave sleep (SWS) and paradoxical sleep (PS) episodes. Moreover, it has been shown recently that these sleep episodes are frequently interrupted by micro-arousal (without awakening). We present here a detailed analysis of the basal sleep properties emerging from the mechanisms underlying the vigilance states alternation in an animal model. These properties present a self-organized critical system signature and reveal the existence of two W, two SWS, and a PS structure exhibiting a criticality as met in sand piles. We propose a theoretical model of the sleep dynamics based on several interacting neuronal populations. This new model of sleep dynamics presents the same properties as experimentally observed, and explains the variability of the collected data. This experimental and theoretical study suggests that sleep dynamics shares several common features with critical systems.

Dynamics of sleep-wake cyclicity in developing rats

Adult mammals cycle between periods of sleep and wakefulness. Recent assessments of these cycles in humans and other mammals indicate that sleep bout durations exhibit an exponential distribution, whereas wake bout durations exhibit a power-law distribution. Moreover, it was found that wake bout distributions, but not sleep bout distributions, exhibit scale invariance across mammals of different body sizes. Here we test the generalizability of these findings by examining the distributions of sleep and wake bout durations in infant rats between 2 and 21 days of age. In agreement with Lo et al., we find that sleep bout durations exhibit exponential distributions at all ages examined. In contrast, however, wake bout durations also exhibit exponential distributions at the younger ages, with a clear power-law distribution only emerging at the older ages. Further analyses failed to find substantial evidence either of short- or long-term correlations in the data, thus suggesting that the durations of current sleep and wake bouts evolve through time without memory of the durations of preceding bouts. These findings further support the notion that bouts of sleep and wakefulness are regulated independently. Moreover, in light of recent evidence that developmental changes in sleep and wake bouts can be attributed in part to increasing forebrain influences, these findings suggest the possibility of identifying specific neural circuits that modulate the changing complexity of sleep and wake dynamics during development.