Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacemaker yield an internal representation of season. Output pathways of the circadian clock regulate photoperiodic responses such as flowering time in plants or hibernation in mammals. Here, we review the concepts of seasonal entrainment and photoperiodic encoding. We introduce conceptual phase oscillator models as their high level of abstraction, but, yet, intuitive interpretation of underlying parameters allows for a straightforward analysis of principles that determine entrainment characteristics. Results from this class of models are related and discussed in the context of more complex conceptual amplitude-phase oscillators as well as contextual molecular models that take into account organism, tissue, and cell-type-specific details.

Improving adjustment to daylight saving time transitions with light

Daylight saving time (DST) is currently utilized in many countries with the rationale that it enhances the alignment between daylight hours and activity peaks in the population. The act of transitioning into and out of DST introduces disruptions to the circadian rhythm, thereby impacting sleep and overall health. Despite the substantial number of individuals affected, the consequences of this circadian disruption have often been overlooked. Here, we employ a mathematical model of the human circadian pacemaker to elucidate how the biological clock interacts with daytime and evening exposures to both natural and electrical light. This interaction plays a crucial role in determining the adaptation to the 1 hour time zone shift imposed by the transition to or from DST. In global discussions about DST, there is a prevailing assumption that individuals easily adjust to DST transitions despite a few studies indicating that the human circadian system requires several days to fully adjust to a DST transition. Our study highlights that evening light exposure changes can be the main driving force for re-entrainment, with chronobiological models predicting that people with longer intrinsic period (i.e. later chronotype) entrain more slowly to transitions to or from DST as compared to people with a shorter intrinsic period (earlier chronotype). Moreover, the model forecasts large inter-individual differences in the adaptation speed, in particular during the spring transition. The predictions derived from our model offer circadian biology-based recommendations for light exposure strategies that facilitate a more rapid adaptation to DST-related transitions or travel across a single time zone. As such, our study contributes valuable insights to the ongoing discourse on DST and its implications for human circadian rhythms.

Uncovering personal circadian responses to light through particle swarm optimization

BACKGROUND AND OBJECTIVES

Kronauer's oscillator model of the human central pacemaker is one of the most commonly used approaches to study the human circadian response to light. Two sources of error when applying it to a personal light exposure have been identified: (1) as a populational model, it does not consider inter-individual variability, and (2) the initial conditions needed to integrate the model are usually unknown, and thus subjectively estimated. In this work, we evaluate the ability of particle swarm optimization (PSO) algorithms to simultaneously uncover the optimal initial conditions and individual parameters of a pre-defined Kronauer's oscillator model.

METHODS

A Canonical PSO, a Dynamic Multi-Swarm PSO and a novel modification of the latter, namely Hierarchical Dynamic Multi-Swarm PSO, are evaluated. Two different target models (under a regular and an irregular schedule) are defined, and the same realistic light profile is fed to them. Based on their output, a fitness function is proposed, which is minimized by the algorithms to find the optimum set of parameters and initial conditions of the model.

RESULTS

We demonstrate that Dynamic Multi-Swarm and Hierarchical Dynamic Multi-Swarm algorithms can accurately uncover personal circadian parameters under both regular and irregular schedules, but as expected, optimization is easier under a regular schedule. Circadian parameters play the most important role in the optimization process and should be prioritized over initial conditions, although assessment of the impact of misestimating the latter is recommended. The log-log linear relationship between mean absolute error and computational cost shows that the number of particles to use is at the discretion of the user.

CONCLUSIONS

The robustness and low errors achieved by the algorithms support their further testing, validation and systematic application to empirical data under a regular or irregular schedule. Uncovering personal circadian parameters can improve the assessment of the circadian status of a person and the applicability of personalized light therapies, as well as help to discover other factors that may lie behind the interindividual variability in the circadian response to light.

The impact of long haul travel on the sleep of elite athletes

In order to manage and implement strategies to alleviate the symptoms of jet lag it is essential to assess the impact of jet lag in athletes. The aim of this study was to assess the impact of long haul eastward travel on elite athletes' (n = 7 elite national track cyclists; male n = 3, and female n = 4) sleep. The athletes' sleep was monitored before, during and after travel using both actigraphy and self-report measures. Participants wore an activity monitor for 5 days prior to travel, during the long haul travel and 5 days upon arrival at their destination and completed a daily online sleep diary Actigraphy highlighted significant reductions in time in bed, total sleep time and sleep efficiency (%) due to long haul eastward travel, particularly in the 48 h after travel. Sleep diary data exhibited significant reductions in time in bed, total sleep time, sleep efficiency, sleep quality and a significant increase in fatigue going to bed as a result of long haul eastward travel. In order to facilitate the development of interventions to reduce the symptoms and severity of jet lag objective and subjective assessments of sleep should be coupled with assessments of chronotype and perceived sleep need.

Modeling the Effects of Napping and Non-napping Patterns of Light Exposure on the Human Circadian Oscillator

In early childhood, consolidation of sleep from a biphasic to a monophasic sleep-wake pattern, that is, the transition from sleeping during an afternoon nap and at night to sleeping only during the night, represents a major developmental milestone. Reduced napping behavior is associated with an advance in the timing of the circadian system; however, it is unknown if this advance represents a standard response of the circadian clock to altered patterns of light exposure or if it additionally reflects features of the developing circadian system. Using a mathematical model of the human circadian pacemaker, we investigated the impact of napping and non-napping patterns of light exposure on entrained circadian phases. Simulated light schedules were based on published data from 20 children (34.2 ± 2.0 months) with habitual napping or non-napping sleep patterns (15 nappers). We found the model predicted different circadian phases for napping and non-napping light patterns: both the decrease in afternoon light during the nap and the increase in evening light associated with napping toddlers' later bedtimes contributed to the observed circadian phase difference produced between napping and non-napping light schedules. We systematically quantified the effects on phase shifting of nap duration, timing, and light intensity, finding larger phase delays occurred for longer and earlier naps. In addition, we simulated phase response curves to a 1-h light pulse and 1-h dark pulse to predict phase and intensity dependence of these changes in light exposure. We found the light pulse produced larger shifts compared with the dark pulse, and we analyzed the model dynamics to identify the features contributing to this asymmetry. These findings suggest that napping status affects circadian timing due to altered patterns of light exposure, with the dynamics of the circadian clock and light processing mediating the effects of the dark pulse associated with a daytime nap.

Individual light history matters to deal with the Antarctic summer

The effect of light, main zeitgeber of the circadian system, depends on the time of day it is received. A brief trip to the Antarctic summer (ANT) allowed us to explore the impact of a sudden and synchronized increase in light exposure on activity-rest rhythms and sleep patterns of 11 Uruguayan university students, and to assess the significance of light history in determining individual circadian phase shift. Measurements collected in the peri-equinox in Montevideo, Uruguay (baseline situation, MVD) and in ANT, included sleep logs, actigraphy, and salivary melatonin to determine dim-light melatonin onset (DLMO), the most reliable marker of circadian phase. The increase in light exposure in ANT with respect to MVD (affecting both light-sensitive windows with opposite effects on the circadian phase) resulted in no net change in DLMO among participants as some participants advanced their DLMO and some others delayed it. The ultimate cause of each participant's distinctive circadian phase shift relied on the unique change in light exposure each individual was subjected to between their MVD and ANT. This study shows an association between the individual light history and the circadian phase shift.

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.

To what extent is circadian phase predictive of subjective jet lag in long-haul cabin crew pre- and post-trip?

Long-haul cabin crew regularly report misalignment between their circadian phase and the external world (i.e. jet lag). The extent to which changes in circadian phase relate to reported levels of jet lag remains unclear. The main aim of the present study was first to evaluate the relationship between objective (circadian phase) and subjective jet lag and second to explore the relative role of both subjective and objective psycho-behavioural factors in predicting the subjective experience of jet lag. Twenty-eight long-haul cabin crew completed questionnaires measuring diurnal preference, trip characteristics and subjective jet lag as a single and as a multidimensional measure. Sleep was monitored using actigraphy and urinary melatonin peak time was measured, at baseline (T1), e.g. before a long-haul trip and post-trip on the crew's first recovery day (T2). Subjective jet lag was also measured at both time points. At T1, later circadian phase related to increased unidimensional jet lag, however, a post-trip discrepancy was found between objective and subjective uni- and multidimensional jet lag measured at T2 and change from T1 to T2. After controlling for direction and size of circadian phase, increased uni- and multidimensional subjective jet lag was predicted by depressed mood states. The regression models including phase, diurnal preference, departure time on the outbound sector and arousal levels accounted for 28% of the variance in unidimensional jet lag and 53% of the variance in multidimensional jet lag. It was concluded that there is a discordance between objective and subjective jet lag post-trip. Further, subjective jet lag in long-haul cabin crew is better explained by mood impairment than circadian phase. The results are discussed with reference to the gap between subjective and objective jet lag and the role of psychology rather than just biology in the jet lag experience. The implications for improving health and safety in the workplace, through a better understanding of the role of human factors in the management of jet lag, are discussed.

Limits of entrainment of circadian neuronal networks

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes, and more. Misalignment of intrinsic neuronal oscillations with the external day-night cycle can disrupt such processes and lead to numerous disorders. In this work, we computationally determine the limits of circadian synchronization to external light signals of different frequency, duty cycle, and simulated amplitude. Instead of modeling circadian dynamics with generic oscillator models (e.g., Kuramoto-type), we use a detailed computational neuroscience model, which integrates biomolecular dynamics, neuronal electrophysiology, and network effects. This allows us to investigate the effect of small drug molecules, such as Longdaysin, and connect our results with experimental findings. To combat the high dimensionality of such a detailed model, we employ a matrix-free approach, while our entire algorithmic pipeline enables numerical continuation and construction of bifurcation diagrams using only direct simulation. We, thus, computationally explore the effect of heterogeneity in the circadian neuronal network, as well as the effect of the corrective therapeutic intervention of Longdaysin. Last, we employ unsupervised learning to construct a data-driven embedding space for representing neuronal heterogeneity.

Different levels of circadian (de)synchrony -- where does it hurt?

A network of cellular timers ensures the maintenance of homeostasis by temporal modulation of physiological processes across the day. These so-called circadian clocks are synchronized to geophysical time by external time cues (or zeitgebers). In modern societies, natural environmental cycles are disrupted by artificial lighting, around-the-clock availability of food or shiftwork. Such contradictory zeitgeber input promotes chronodisruption, i.e., the perturbation of internal circadian rhythms, resulting in adverse health outcomes. While this phenomenon is well described, it is still poorly understood at which level of organization perturbed rhythms impact on health and wellbeing. In this review, we discuss different levels of chronodisruption and what is known about their health effects. We summarize the results of disrupted phase coherence between external and internal time vs. misalignment of tissue clocks amongst each other, i.e., internal desynchrony. Last, phase incoherence can also occur at the tissue level itself. Here, alterations in phase coordination can emerge between cellular clocks of the same tissue or between different clock genes within the single cell. A better understanding of the mechanisms of circadian misalignment and its effects on physiology will help to find effective tools to prevent or treat disorders arising from modern-day chronodisruptive environments.

Different levels of circadian (de)synchrony -- where does it hurt?

A network of cellular timers ensures the maintenance of homeostasis by temporal modulation of physiological processes across the day. These so-called circadian clocks are synchronized to geophysical time by external time cues (or zeitgebers). In modern societies, natural environmental cycles are disrupted by artificial lighting, around-the-clock availability of food or shift work. Such contradictory zeitgeber input promotes chronodisruption, i.e., the perturbation of internal circadian rhythms, resulting in adverse health outcomes. While this phenomenon is well described, it is still poorly understood at which level of organization perturbed rhythms impact on health and wellbeing. In this review, we discuss different levels of chronodisruption and what is known about their health effects. We summarize the results of disrupted phase coherence between external and internal time vs. misalignment of tissue clocks amongst each other, i.e., internal desynchrony. Last, phase incoherence can also occur at the tissue level itself. Here, alterations in phase coordination can emerge between cellular clocks of the same tissue or between different clock genes within the single cell. A better understanding of the mechanisms of circadian misalignment and its effects on physiology will help to find effective tools to prevent or treat disorders arising from modern-day chronodisruptive environments.

Entrainment within hierarchical circadian oscillator networks

Circadian rhythms are endogenous oscillations, widely found across biological species, that have the capability of entraining to the 24-h light-dark cycle. Circadian systems often consist of both central oscillators that receive direct light-dark input and peripheral oscillators that receive input from the central oscillators. In this paper, we address questions related to what governs the time to and pattern of entrainment of these hierarchical circadian systems after an abrupt switch in the light-dark phasing. For a network consisting of a single central oscillator coupled to a chain of N feed-forward peripheral oscillators, we introduce a systematic way to derive an N-dimensional entrainment map whose fixed points correspond to entrained solutions. Using the map, we explain that the direction of reentrainment can involve fairly complicated phase advancing and delaying behavior as well as reentrainment times that depend sensitively on the nature of the perturbation. We also study the dynamics of a hierarchical system in which the peripheral oscillators are mutually coupled. We study how reentrainment times vary as a function of the degree to which the oscillators are desynchronized at the time of the change in light-dark phasing. We show that desynchronizing the peripheral oscillators can, in some circumstances, speed up their ultimate reentrainment following perturbations.

Human Alertness Optimization with a Three-Process Dynamic Model

Circadian rhythm is an important biological process for humans as it modulates a wide range of physiological processes, including body temperature, sleep-wake cycle, and cognitive performance. As the most powerful external stimulus of circadian rhythm, light has been studied as a zeitgeber to regulate the circadian phase and sleep. This paper addresses the human alertness optimization problem, by optimizing light exposure and sleep schedules to relieve fatigue and cognitive impairment, in cases of night-shift workers and subjects with certain mission periods based on dynamics of the circadian rhythm system. A three-process hybrid dynamic model is used for simulating the circadian rhythm and predicting subjective alertness and sleepiness. Based on interindividual difference in sleep type and living habits, we propose a tunable sleep schedule in the alertness optimization problem, which allows the appropriate tuning of sleep and wake times based on sleep propensity. Variational calculus is applied to evaluate the impacts of light and sleep schedules on the alertness and a gradient descent algorithm is proposed to determine the optimal solutions to maximize the alertness level in various cases. Numerical simulation results demonstrate that the cognitive performance during certain periods can be significantly improved by optimizing the light input and tuning sleep/wake times compared to empirical data.

The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems

Several distinct entrainment patterns can occur in the FitzHugh-Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region (monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.

Beyond the limits of circadian entrainment: Non-24-hour sleep-wake disorder, shift work, and social jet lag

While the vast majority of humans are able to entrain their circadian rhythm to the 24-hour light-dark cycle, there are numerous individuals who are not able to do so due to disease or societal reasons. We use computational and mathematical methods to analyze a well-established model of human circadian rhythms to address cases where individuals do not entrain to the 24-hour light-dark cycle, leading to misalignment of their circadian phase. For each case, we provide a mathematically justified strategy for how to minimize circadian misalignment. In the case of non-24-hour sleep-wake disorder, we show why appropriately timed bright light therapy induces entrainment. With regard to shift work, we explain why reentrainment times following transitions between day and night shifts are asymmetric, and how higher light intensity enables unusually rapid reentrainment after certain transitions. Finally, with regard to teenagers who engage in compensatory catch-up sleep on weekends, we propose a rule of thumb for sleep and wake onset times that minimizes circadian misalignment due to this type of social jet lag. In all cases, the primary mathematical approach involves understanding the dynamics of entrainment maps that measure the phase of the entrained rhythm with respect to the daily onset of lights.

Synergies of Multiple Zeitgebers Tune Entrainment

Circadian rhythms are biological rhythms with a period close to 24 h. They become entrained to the Earth's solar day via different periodic cues, so-called zeitgebers. The entrainment of circadian rhythms to a single zeitgeber was investigated in many mathematical clock models of different levels of complexity, ranging from the Poincaré oscillator and the Goodwin model to biologically more detailed models of multiple transcriptional translational feedback loops. However, circadian rhythms are exposed to multiple coexisting zeitgebers in nature. Therefore, we study synergistic effects of two coexisting zeitgebers on different components of the circadian clock. We investigate the induction of period genes by light together with modulations of nuclear receptor activities by drugs and metabolism. Our results show that the entrainment of a circadian rhythm to two coexisting zeitgebers depends strongly on the phase difference between the two zeitgebers. Synergistic interactions of zeitgebers can strengthen diurnal rhythms to reduce detrimental effects of shift-work and jet lag. Medical treatment strategies which aim for stable circadian rhythms should consider interactions of multiple zeitgebers.

Principles underlying the complex dynamics of temperature entrainment by a circadian clock

Autonomously oscillating circadian clocks resonate with daily environmental (zeitgeber) rhythms to organize physiology around the solar day. Although entrainment properties and mechanisms have been studied widely and in great detail for light-dark cycles, entrainment to daily temperature rhythms remains poorly understood despite that they are potent zeitgebers. Here we investigate the entrainment of the chronobiological model organism Neurospora crassa, subject to thermocycles of different periods and fractions of warm versus cold phases, mimicking seasonal variations. Depending on the properties of these thermocycles, regularly entrained rhythms, period-doubling (frequency demultiplication) but also irregular aperiodic behavior occurs. We demonstrate that the complex nonlinear phenomena of experimentally observed entrainment dynamics can be understood by molecular mathematical modeling.

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

The circadian rhythm, called Process C, regulates a wide range of biological processes in humans including sleep, metabolism, body temperature, and hormone secretion. Light is the dominant synchronizer of the circadian rhythm-it has been used to regulate the circadian phase to cope with jet-lag, shift work, and sleep disorder. The homeostatic oscillation of the sleep drive is called Process S. Process C and Process S together determine the sleep-wake cycle in what is known as the two-process model. This paper addresses the regulation of both Process C and Process S by scheduling light exposure and sleep based on numerical simulations of circadian rhythm and sleep mathematical models. This is a significant step beyond the existing literature that only considers the entrainment of Process C. Regulation of the two-process model poses several unique features and challenges: 1. Process S is non-smooth, i.e., the homeostatic dynamics are different in the sleep and wake regimes; 2. Light only indirectly affects Process S through Process C; 3. Light does not affect Process C during sleep. We consider two scenarios: optimizing light intensity as the control input with spontaneous (i.e., unscheduled) sleep/wake times and jointly optimizing the light intensity and the sleep/wake times, which allows limited delayed sleep and early waking as part of the decision variables. We solve the time-optimal entrainment problem for the two-process model for both scenarios using an extension of the gradient descent algorithm to non-smooth systems. To illustrate the efficacy of our time-optimal entrainment strategies, we consider two common use cases: transmeridian travelers and shift workers. For transmeridian travelers, joint optimization of the two-process model avoids the unrealistic long wake duration when only Process C is considered. The entrainment time also decreases when both the light input and the sleep schedule are optimized compared to when only the light input is optimized. For shift workers, we show that the entrainment time is significantly shortened by optimizing the night shift working light.

Changes in 24 h Rhythmicity of Spontaneous Locomotor Activity in the Triple Transgenic Mouse for Alzheimer's Disease (3xTg-AD) in a Jet Lag Protocol: Correlations with Retinal Sensitivity

The progression of amyloid plaques and neurofibrillary tangles in different brain areas is associated with the effects of Alzheimer’s disease (AD). In addition to cognitive impairment, circadian alterations in locomotor activity have also been detected, but they have not been characterized in a jet lag protocol. Therefore, the present study aimed to compare 3xTg-AD and non-transgenic mice in changes of 24 h cycles of spontaneous locomotor activity in a jet lag protocol, in an environment without a running wheel, at 3 different states of neuronal damage: early, intermediate and advanced (3, 8 and 13 months, respectively). The 3xTg-AD mice at 3 months presented differences in phase angle and acrophase, and differentially increased activity after advances more than after delays. At 13 months, a shortening of the free-running period in constant darkness was also noted. 3xTg-AD mice showed a significant increase (123%) in global activity at 8 to 13 months and in nighttime activity (153%) at 13 months. In the advance protocol (ADV), 3xTg-AD mice displayed a significant increase in global activity (171%) at 8 and 13 months. The differences in masking effect were evident at 8 months. To assess a possible retinal dysfunction that could interfere with photic entrainment as part of the neurodegenerative process, we compared electroretinogram recordings. The results showed early deterioration in the retinal response to light flashes in mesopic conditions, observed in the B-wave latency and amplitude. Thus, our study presents new behavioral and pathological characteristics of 3xTg-AD mice and reveals the usefulness of non-invasive tools in early diagnosis.

Mammalian circadian systems: Organization and modern life challenges

Humans and other mammalian species possess an endogenous circadian clock system that has evolved in adaptation to periodically reoccurring environmental changes and drives rhythmic biological functions, as well as behavioural outputs with an approximately 24-hour period. In mammals, body clocks are hierarchically organized, encompassing a so-called pacemaker clock in the hypothalamic suprachiasmatic nucleus (SCN), non-SCN brain and peripheral clocks, as well as cell-autonomous oscillators within virtually every cell type. A functional clock machinery on the molecular level, alignment among body clocks, as well as synchronization between endogenous circadian and exogenous environmental cycles has been shown to be crucial for our health and well-being. Yet, modern life constantly poses widespread challenges to our internal clocks, for example artificial lighting, shift work and trans-meridian travel, potentially leading to circadian disruption or misalignment and the emergence of associated diseases. For instance many of us experience a mismatch between sleep timing on work and free days (social jetlag) in our everyday lives without being aware of health consequences that may arise from such chronic circadian misalignment, Hence, this review provides an overview of the organization and molecular built-up of the mammalian circadian system, its interactions with the outside world, as well as pathologies arising from circadian disruption and misalignment.

Delays are Self-enhancing: An Explanation of the East-West Asymmetry in Recovery from Jetlag

There is evidence in mammals that recovering from jetlag after westward travel is faster than after eastward travel. To understand why, mathematical models have been used, along with theories of entrainment rooted in experimental evidence. The most complete understanding relies on detailed mathematical modeling, so it is helpful to develop an intuition about why there is an east-west asymmetry. One such intuition is that humans have long periods and therefore recover better when they can delay. Although this is part of the reason, it does not explain why short-period mice also recover from westward travel faster. Our goal is to provide a simple intuition consistent with detailed mathematical theories, but which does not require mathematical expertise to follow. Here, we present the intuition that westward travel is easier to recover from because of a simple principle: delays are self-enhancing.

Jet Lag Recovery and Memory Functions Are Correlated with Direct Light Effects on Locomotion

Jet lag is a circadian disruption that affects millions of people, resulting, among other things, in extreme sleepiness and memory loss. The hazardous implications of such effects are evident in situations in which focus and attention are required. Remarkably, there is a limited understanding of how jet lag recovery and associated memory loss vary year round under different photoperiods. Here we show, using different cycles representing winter, summer, and equinox in male mice, that jet lag recovery and memory vary significantly with photoperiod changes. We uncover a positive correlation of acute light effects on circadian-driven locomotion (known as negative masking) with photoentrainment speed and memory enhancement during jet lag. Specifically, we show that enhancing or reducing negative masking is correlated with better or worse memory performance, respectively. This study indicates that in addition to timed-light exposure for phase shifting, the negative masking response could also be biologically relevant when designing effective treatments of jet lag.

Recent advances in modeling sleep: from the clinic to society and disease

In the past few decades, advances in understanding sleep-wake neurophysiology have occurred hand-in-hand with advances in mathematical modeling of sleep and wake. In this review, we summarize recent updates in modeling the timing and durations of sleep and wake, the underlying neurophysiology of sleep and wake, and the application of these models in understanding cognition and disease. Throughout, we highlight the role modeling has played in developing our understanding of sleep and its underlying mechanisms. We present open questions and controversies in the field and propose the utility of individualized models of sleep for precision sleep medicine.

[The effects of quarantine for SARS-CoV-2 on sleep: An online survey]

Objectif

Déterminer l’évolution du sommeil chez les Français pendant le confinement motivé par la pandémie du SARS-CoV-2 et définir les facteurs comportementaux associés à un sommeil détérioré.

Méthodologie

Une enquête en ligne via les réseaux sociaux pendant la période de confinement. Les questions ont ciblé les conditions de confinement, les comportements relatifs au sommeil et les éléments de l’environnement potentiellement perturbateurs du sommeil (exposition à la lumière et activités sportives).

Résultats

Au total, 1777 participants ont été inclus dont 77 % femmes, 72 % âgés de 25–54 ans. Les conditions de confinement les plus fréquentes étaient en couple avec enfants (36 %) et en maison avec jardin (51 %). Quarante-sept pour cent rapportent une diminution de la qualité du sommeil en confinement. Les facteurs associés à une détérioration du sommeil retenus par l’analyse multivariée sont une diminution de la durée du sommeil (OR 15,52 — p < 0,001), un coucher plus tardif (OR 1,72 — p < 0,001), un lever plus matinal (2,18 — p = 0,01), des horaires plus irréguliers (OR 2,29 — p < 0,001), une diminution de l’exposition à la lumière du jour (OR 1,46 — p = 0,01) et une augmentation de l’utilisation des écrans le soir (OR 1,33 — p = 0,04).

Conclusion

La mauvaise qualité subjective du sommeil en confinement est associée à une modification des comportements relatifs au sommeil et de l’exposition à la lumière (moins de lumière du jour et plus d’écran le soir). Pour optimiser le sommeil en confinement, des horaires adaptés et réguliers, une exposition de plus d’une heure/jour à la lumière du jour et l’éviction des écrans le soir sont à conseiller.

A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems

Phase-amplitude reduction is of growing interest as a strategy for the reduction and analysis of oscillatory dynamical systems. Augmentation of the widely studied phase reduction with amplitude coordinates can be used to characterize transient behavior in directions transverse to a limit cycle to give a richer description of the dynamical behavior. Various definitions for amplitude coordinates have been suggested, but none are particularly well suited for implementation in experimental systems where output recordings are readily available but the underlying equations are typically unknown. In this work, a reduction framework is developed for inferring a phase-amplitude reduced model using only the observed model output from an arbitrarily high-dimensional system. This framework employs a proper orthogonal reduction strategy to identify important features of the transient decay of solutions to the limit cycle. These features are explicitly related to previously developed phase and isostable coordinates and used to define so-called data-driven phase and isostable coordinates that are valid in the entire basin of attraction of a limit cycle. The utility of this reduction strategy is illustrated in examples related to neural physiology and is used to implement an optimal control strategy that would otherwise be computationally intractable. The proposed data-driven phase and isostable coordinate system and associated reduced modeling framework represent a useful tool for the study of nonlinear dynamical systems in situations where the underlying dynamical equations are unknown and in particularly high-dimensional or complicated numerical systems for which standard phase-amplitude reduction techniques are not computationally feasible.

Time optimal entrainment control for circadian rhythm

The circadian rhythm functions as a master clock that regulates many physiological processes in humans including sleep, metabolism, hormone secretion, and neurobehavioral processes. Disruption of the circadian rhythm is known to have negative impacts on health. Light is the strongest circadian stimulus that can be used to regulate the circadian phase. In this paper, we consider the mathematical problem of time-optimal circadian (re)entrainment, i.e., computing the lighting schedule to drive a misaligned circadian phase to a reference circadian phase as quickly as possible. We represent the dynamics of the circadian rhythm using the Jewett-Forger-Kronauer (JFK) model, which is a third-order nonlinear differential equation. The time-optimal circadian entrainment problem has been previously solved in settings that involve either a reduced-order JFK model or open-loop optimal solutions. In this paper, we present (1) a general solution for the time-optimal control problem of fastest entrainment that can be applied to the full order JFK model (2) an evaluation of the impacts of model reduction on the solutions of the time-optimal control problem, and (3) optimal feedback control laws for fastest entrainment for the full order Kronauer model and evaluate their robustness under some modeling errors.

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.

Approaches to the Pharmacological Management of Jet Lag

For many years now a treatment mitigating the debilitating effects of jet lag has been sought. Rapid travel across time zones leads, in most people, to temporary symptoms, in particular poor sleep, daytime alertness and poor performance. Mis-timed circadian rhythms are considered to be the main factor underlying jet-lag symptoms, together with the sleep deprivation from long haul flights. Virtually all aspects of physiology are rhythmic, from cells to systems, and circadian rhythms are coordinated by a central pacemaker or clock in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN adapts slowly to changes in time zone, and peripheral clocks or oscillators adapt at different rates, such that the organism is in a state of desynchrony from the external environment and internally. Light exposure is the main factor controlling the circadian system and needs to be considered together with any pharmacological interventions. This review covers the relatively new chronobiotic drugs, which can hasten adaptation of the circadian system, together with drugs directly affecting alertness and sleep propensity. No current treatment can instantly shift circadian phase to a new time zone; however, adaptation can be hastened. The melatoninergic drugs are promising but larger trials in real-life situations are needed. For short stopovers it is recommended to preserve sleep and alertness without necessarily modifying the circadian system. New research suggests that modification of clock function via genetic manipulation may one day have clinical applications.

Systems approach reveals photosensitivity and PER2 level as determinants of clock-modulator efficacy

In mammals, the master circadian clock synchronizes daily rhythms of physiology and behavior with the day-night cycle. Failure of synchrony, which increases the risk for numerous chronic diseases, can be treated by phase adjustment of the circadian clock pharmacologically, for example, with melatonin, or a CK1δ/ε inhibitor. Here, using in silico experiments with a systems pharmacology model describing molecular interactions, and pharmacokinetic and behavioral experiments in cynomolgus monkeys, we find that the circadian phase delay caused by CK1δ/ε inhibition is more strongly attenuated by light in diurnal monkeys and humans than in nocturnal mice, which are common preclinical models. Furthermore, the effect of CK1δ/ε inhibition strongly depends on endogenous PER2 protein levels, which differs depending on both the molecular cause of the circadian disruption and the patient's lighting environment. To circumvent such large interindividual variations, we developed an adaptive chronotherapeutics to identify precise dosing regimens that could restore normal circadian phase under different conditions. Our results reveal the importance of photosensitivity in the clinical efficacy of clock-modulating drugs, and enable precision medicine for circadian disruption.

Optimal global synchronization of partially forced Kuramoto oscillators

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ω_i, such that a fraction of them is subject to an external periodic force with frequency Ω, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ω_i-Ω| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization is a desired property. Some properties of the optimal forced networks and their relation to recent results in the literature are also discussed.

Pharmaceutical-based entrainment of circadian phase via nonlinear model predictive control

The widespread adoption of closed-loop control in systems biology has resulted from improvements in sensors, computing, actuation, and the discovery of alternative sites of targeted drug delivery. Most control algorithms for circadian phase resetting exploit light inputs. However, recently identified small-molecule pharmaceuticals offer advantages in terms of invasiveness and potency of actuation. Herein, we develop a systematic method to control the phase of biological oscillations motivated by the recently identified small molecule circadian pharmaceutical KL001. The model-based control architecture exploits an infinitesimal parametric phase response curve (ipPRC) that is used to predict the effect of control inputs on future phase trajectories of the oscillator. The continuous time optimal control policy is first derived for phase resetting, based on the ipPRC and Pontryagin's maximum principle. Owing to practical challenges in implementing a continuous time optimal control policy, we investigate the effect of implementing the continuous time policy in a sampled time format. Specifically, we provide bounds on the errors incurred by the physiologically tractable sampled time control law. We use these results to select directions of resetting (i.e. phase advance or delay), sampling intervals, and prediction horizons for a nonlinear model predictive control (MPC) algorithm for phase resetting. The potential of this ipPRC-informed pharmaceutical nonlinear MPC is then demonstrated in silico using real-world scenarios of jet lag or rotating shift work.

Neuronal oscillations on an ultra-slow timescale: daily rhythms in electrical activity and gene expression in the mammalian master circadian clockwork

Neuronal oscillations of the brain, such as those observed in the cortices and hippocampi of behaving animals and humans, span across wide frequency bands, from slow delta waves (0.1 Hz) to ultra-fast ripples (600 Hz). Here, we focus on ultra-slow neuronal oscillators in the hypothalamic suprachiasmatic nuclei (SCN), the master daily clock that operates on interlocking transcription-translation feedback loops to produce circadian rhythms in clock gene expression with a period of near 24 h (< 0.001 Hz). This intracellular molecular clock interacts with the cell's membrane through poorly understood mechanisms to drive the daily pattern in the electrical excitability of SCN neurons, exhibiting an up-state during the day and a down-state at night. In turn, the membrane activity feeds back to regulate the oscillatory activity of clock gene programs. In this review, we emphasise the circadian processes that drive daily electrical oscillations in SCN neurons, and highlight how mathematical modelling contributes to our increasing understanding of circadian rhythm generation, synchronisation and communication within this hypothalamic region and across other brain circuits.