Taking the Lag out of Jet Lag through Model-Based Schedule Design

Travel across multiple time zones results in desynchronization of environmental time cues and the sleep–wake schedule from their normal phase relationships with the endogenous circadian system. Circadian misalignment can result in poor neurobehavioral performance, decreased sleep efficiency, and inappropriately timed physiological signals including gastrointestinal activity and hormone release. Frequent and repeated transmeridian travel is associated with long-term cognitive deficits, and rodents experimentally exposed to repeated schedule shifts have increased death rates. One approach to reduce the short-term circadian, sleep–wake, and performance problems is to use mathematical models of the circadian pacemaker to design countermeasures that rapidly shift the circadian pacemaker to align with the new schedule. In this paper, the use of mathematical models to design sleep–wake and countermeasure schedules for improved performance is demonstrated. We present an approach to designing interventions that combines an algorithm for optimal placement of countermeasures with a novel mode of schedule representation. With these methods, rapid circadian resynchrony and the resulting improvement in neurobehavioral performance can be quickly achieved even after moderate to large shifts in the sleep–wake schedule. The key schedule design inputs are endogenous circadian period length, desired sleep–wake schedule, length of intervention, background light level, and countermeasure strength. The new schedule representation facilitates schedule design, simulation studies, and experiment design and significantly decreases the amount of time to design an appropriate intervention. The method presented in this paper has direct implications for designing jet lag, shift-work, and non-24-hour schedules, including scheduling for extreme environments, such as in space, undersea, or in polar regions.     

Optimal Schedules of Light Exposure for Rapidly Correcting Circadian Misalignment

Jet lag arises from a misalignment of circadian biological timing with the timing of human activity, and is caused by rapid transmeridian travel. Jet lag''s symptoms, such as depressed cognitive alertness, also arise from work and social schedules misaligned with the timing of the circadian clock. Using experimentally validated mathematical models, we develop a new methodology to find mathematically optimal schedules of light exposure and avoidance for rapidly re-entraining the human circadian system. In simulations, our schedules are found to significantly outperform other recently proposed schedules. Moreover, our schedules appear to be significantly more robust to both noise in light and to inter-individual variations in endogenous circadian period than other proposed schedules. By comparing the optimal schedules for thousands of different situations, and by using general mathematical arguments, we are also able to translate our findings into general principles of optimal circadian re-entrainment. These principles include: 1) a class of schedules where circadian amplitude is only slightly perturbed, optimal for dim light and for small shifts 2) another class of schedules where shifting occurs along the shortest path in phase-space, optimal for bright light and for large shifts 3) the determination that short light pulses are less effective than sustained light if the goal is to re-entrain quickly, and 4) the determination that length of daytime should be significantly shorter when delaying the clock than when advancing it.     

Effect of Spaceflight on the Circadian Rhythm,Lifespan and Gene Expression of Drosophila melanogaster

Space travelers are reported to experience circadian rhythm disruption during spaceflight. However, how the space environment affects circadian rhythm is yet to be determined. The major focus of this study was to investigate the effect of spaceflight on the Drosophila circadian clock at both the behavioral and molecular level. We used China’s Shenzhou-9 spaceship to carry Drosophila. After 13 days of spaceflight, behavior tests showed that the flies maintained normal locomotor activity rhythm and sleep pattern. The expression level and rhythm of major clock genes were also unaffected. However, expression profiling showed differentially regulated output genes of the circadian clock system between space flown and control flies, suggesting that spaceflight affected the circadian output pathway. We also investigated other physiological effects of spaceflight such as lipid metabolism and lifespan, and searched genes significantly affected by spaceflight using microarray analysis. These results provide new information on the effects of spaceflight on circadian rhythm, lipid metabolism and lifespan. Furthermore, we showed that studying the effect of spaceflight on gene expression using samples collected at different Zeitgeber time could obtain different results, suggesting the importance of appropriate sampling procedures in studies on the effects of spaceflight.     

Quantification of Circadian Rhythms in Single Cells

Bioluminescence techniques allow accurate monitoring of the circadian clock in single cells. We have analyzed bioluminescence data of Per gene expression in mouse SCN neurons and fibroblasts. From these data, we extracted parameters such as damping rate and noise intensity using two simple mathematical models, one describing a damped oscillator driven by noise, and one describing a self-sustained noisy oscillator. Both models describe the data well and enabled us to quantitatively characterize both wild-type cells and several mutants. It has been suggested that the circadian clock is self-sustained at the single cell level, but we conclude that present data are not sufficient to determine whether the circadian clock of single SCN neurons and fibroblasts is a damped or a self-sustained oscillator. We show how to settle this question, however, by testing the models'' predictions of different phases and amplitudes in response to a periodic entrainment signal (zeitgeber).     

The effects of a split sleep–wake schedule on neurobehavioural performance and predictions of performance under conditions of forced desynchrony

Extended wakefulness, sleep loss, and circadian misalignment are factors associated with an increased accident risk in shiftwork. Splitting shifts into multiple shorter periods per day may mitigate these risks by alleviating prior wake. However, the effect of splitting the sleep–wake schedule on the homeostatic and circadian contributions to neurobehavioural performance and subjective assessments of one’s ability to perform are not known. Twenty-nine male participants lived in a time isolation laboratory for 13?d, assigned to one of two 28-h forced desynchrony (FD) schedules. Depending on the assigned schedule, participants were provided the same total time in bed (TIB) each FD cycle, either consolidated into a single period (9.33?h TIB) or split into two equal halves (2?×?4.67?h TIB). Neurobehavioural performance was regularly assessed with a psychomotor vigilance task (PVT) and subjectively-assessed ability was measured with a prediction of performance on a visual analogue scale. Polysomnography was used to assess sleep, and core body temperature was recorded to assess circadian phase. On average, participants obtained the same amount of sleep in both schedules, but those in the split schedule obtained more slow wave sleep (SWS) on FD days. Mixed-effects ANOVAs indicated no overall difference between the standard and split schedules in neurobehavioural performance or predictions of performance. Main effects of circadian phase and prior wake were present for both schedules, such that performance and subjective ratings of ability were best around the circadian acrophase, worst around the nadir, and declined with increasing prior wake. There was a schedule by circadian phase interaction for all neurobehavioural performance metrics such that performance was better in the split schedule than the standard schedule around the nadir. There was no such interaction for predictions of performance. Performance during the standard schedule was significantly better than the split schedule at 2?h of prior wake, but declined at a steeper rate such that the schedules converged by 4.5–7?h of prior wake. Overall, the results indicate that when the total opportunity for sleep per day is satisfactory, a split sleep–wake schedule is not detrimental to sleep or performance. Indeed, though not reflected in subjective assessments of performance capacity, splitting the schedule may be of some benefit, given its reduction of neurobehavioural impairment at night and its association with increased SWS. Therefore, for some industries that require operations to be sustained around the clock, implementing a split work–rest schedule may be of assistance.     

Dosing schedule-dependent change in the disruptive effects of interferon-alpha on the circadian clock function

Altered homeostatic regulation, including the disturbance of circadian rhythms, is often observed in patients undergoing interferon (IFN) therapy. We reported previously that IFN-alpha has the ability to modulate the circadian clock function at the molecular level and that the alteration of clock function could be overcome by changing the dosing schedule. In this study, we investigated the influence of IFN-alpha on the intrinsic biological rhythms in mice by comparing two dosing schedules, continuous administration and repetitive injection. Continuous administration of IFN-alpha to mice decreased the rhythm amplitude of locomotor activity, body temperature, leukocyte counts, and plasma corticosterone levels. The treatment also suppressed the oscillation in the expression of clock genes in the liver. On the other hand, modulation effects were scarcely observed in mice treated with repetitive injection of IFN-alpha. These results indicate that treatment with IFN-alpha does not always modulate the circadian clock function. This notion was also supported by in vitro findings that the inhibitory action of IFN-alpha on the expression of clock genes was dependent on its exposure time to cells. The alteration of clock function induced by IFN-alpha could be avoided by optimizing the dosing schedule.     

The central molecular clock is robust in the face of behavioural arrhythmia in a Drosophila model of Alzheimer’s disease

Circadian behavioural deficits, including sleep irregularity and restlessness in the evening, are a distressing early feature of Alzheimer’s disease (AD). We have investigated these phenomena by studying the circadian behaviour of transgenic Drosophila expressing the amyloid beta peptide (Aβ). We find that Aβ expression results in an age-related loss of circadian behavioural rhythms despite ongoing normal molecular oscillations in the central clock neurons. Even in the absence of any behavioural correlate, the synchronised activity of the central clock remains protective, prolonging lifespan, in Aβ flies just as it does in control flies. Confocal microscopy and bioluminescence measurements point to processes downstream of the molecular clock as the main site of Aβ toxicity. In addition, there seems to be significant non-cell-autonomous Aβ toxicity resulting in morphological and probably functional signalling deficits in central clock neurons.KEY WORDS: Alzheimer’s disease, Circadian dysfunction, Non-cell-autonomous Aβ toxicity, Drosophila model, Biological clock     

Circadian phase,circadian period and chronotype are reproducible over months

The timing of the circadian clock, circadian period and chronotype varies among individuals. To date, not much is known about how these parameters vary over time in an individual. We performed an analysis of the following five common circadian clock and chronotype measures: 1) the dim light melatonin onset (DLMO, a measure of circadian phase), 2) phase angle of entrainment (the phase the circadian clock assumes within the 24-h day, measured here as the interval between DLMO and bedtime/dark onset), 3) free-running circadian period (tau) from an ultradian forced desynchrony protocol (tau influences circadian phase and phase angle of entrainment), 4) mid-sleep on work-free days (MSF from the Munich ChronoType Questionnaire; MCTQ) and 5) the score from the Morningness–Eveningness Questionnaire (MEQ). The first three are objective physiological measures, and the last two are measures of chronotype obtained from questionnaires. These data were collected from 18 individuals (10 men, eight women, ages 21–44 years) who participated in two studies with identical protocols for the first 10 days. We show how much these circadian rhythm and chronotype measures changed from the first to the second study. The time between the two studies ranged from 9 months to almost 3 years, depending on the individual. Since the full experiment required living in the laboratory for 14 days, participants were unemployed, had part-time jobs or were freelance workers with flexible hours. Thus, they did not have many constraints on their sleep schedules before the studies. The DLMO was measured on the first night in the lab, after free-sleeping at home and also after sleeping in the lab on fixed 8-h sleep schedules (loosely tailored to their sleep times before entering the laboratory) for four nights. Graphs with lines of unity (when the value from the first study is identical to the value from the second study) showed how much each variable changed from the first to the second study. The DLMO did not change more than 2 h from the first to the second study, except for two participants whose sleep schedules changed the most between studies, a change in sleep times of 3 h. Phase angle did not change by more than 2 h regardless of changes in the sleep schedule. Circadian period did not change more than 0.2 h, except for one participant. MSF did not change more than 1 h, except for two participants. MEQ did not change more than 10 points and the categories (e.g. M-type) did not change. Pearson’s correlations for the DLMO between the first and second studies increased after participants slept in the lab on their individually timed fixed 8-h sleep schedules for four nights. A longer time between the two studies did not increase the difference between any of the variables from the first to the second study. This analysis shows that the circadian clock and chronotype measures were fairly reproducible, even after many months between the two studies.     

Intrinsic period and light intensity determine the phase relationship between melatonin and sleep in humans

The internal circadian clock and sleep-wake homeostasis regulate the timing of human brain function, physiology, and behavior so that wakefulness and its associated functions are optimal during the solar day and that sleep and its related functions are optimal at night. The maintenance of a normal phase relationship between the internal circadian clock, sleep-wake homeostasis, and the light-dark cycle is crucial for optimal neurobehavioral and physiological function. Here, the authors show that the phase relationship between these factors-the phase angle of entrainment (psi)-is strongly determined by the intrinsic period (tau) of the master circadian clock and the strength of the circadian synchronizer. Melatonin was used as a marker of internal biological time, and circadian period was estimated during a forced desynchrony protocol. The authors observed relationships between the phase angle of entrainment and intrinsic period after exposure to scheduled habitual wakefulness-sleep light-dark cycle conditions inside and outside of the laboratory. Individuals with shorter circadian periods initiated sleep and awakened at a later biological time than did individuals with longer circadian periods. The authors also observed that light exposure history influenced the phase angle of entrainment such that phase angle was shorter following exposure to a moderate bright light (approximately 450 lux)-dark/wakefulness-sleep schedule for 5 days than exposure to the equivalent of an indoor daytime light (approximately 150 lux)-dark/wakefulness-sleep schedule for 2 days. These findings demonstrate that neurobiological and environmental factors interact to regulate the phase angle of entrainment in humans. This finding has important implications for understanding physiological organization by the brain's master circadian clock and may have implications for understanding mechanisms underlying circadian sleep disorders.     

Modeling the circadian regulation of the immune system: Sexually dimorphic effects of shift work

The circadian clock exerts significance influence on the immune system and disruption of circadian rhythms has been linked to inflammatory pathologies. Shift workers often experience circadian misalignment as their irregular work schedules disrupt the natural light-dark cycle, which in turn can cause serious health problems associated with alterations in genetic expressions of clock genes. In particular, shift work is associated with impairment in immune function, and those alterations are sex-specific. The goal of this study is to better understand the mechanisms that explain the weakened immune system in shift workers. To achieve that goal, we have constructed a mathematical model of the mammalian pulmonary circadian clock coupled to an acute inflammation model in the male and female rats. Shift work was simulated by an 8h-phase advance of the circadian system with sex-specific modulation of clock genes. The model reproduces the clock gene expression in the lung and the immune response to various doses of lipopolysaccharide (LPS). Under normal conditions, our model predicts that a host is more sensitive to LPS at circadian time (CT) CT12 versus CT0 due to a dynamic change of Interleukin 10 (IL-10), an anti-inflammatory cytokine. We identify REV-ERB as a key modulator of IL-10 activity throughout the circadian day. The model also predicts a reversal of the times of lowest and highest sensitivity to LPS, with males and females exhibiting an exaggerated response to LPS at CT0, which is countered by a blunted immune response at CT12. Overall, females produce fewer pro-inflammatory cytokines than males, but the extent of sequelae experienced by males and females varies across the circadian day. This model can serve as an essential component in an integrative model that will yield mechanistic understanding of how shift work-mediated circadian disruptions affect the inflammatory and other physiological responses.     

Validating and Extending the Three Process Model of Alertness in Airline Operations

Sleepiness and fatigue are important risk factors in the transport sector and bio-mathematical sleepiness, sleep and fatigue modeling is increasingly becoming a valuable tool for assessing safety of work schedules and rosters in Fatigue Risk Management Systems (FRMS). The present study sought to validate the inner workings of one such model, Three Process Model (TPM), on aircrews and extend the model with functions to model jetlag and to directly assess the risk of any sleepiness level in any shift schedule or roster with and without knowledge of sleep timings. We collected sleep and sleepiness data from 136 aircrews in a real life situation by means of an application running on a handheld touch screen computer device (iPhone, iPod or iPad) and used the TPM to predict sleepiness with varying level of complexity of model equations and data. The results based on multilevel linear and non-linear mixed effects models showed that the TPM predictions correlated with observed ratings of sleepiness, but explorative analyses suggest that the default model can be improved and reduced to include only two-processes (S+C), with adjusted phases of the circadian process based on a single question of circadian type. We also extended the model with a function to model jetlag acclimatization and with estimates of individual differences including reference limits accounting for 50%, 75% and 90% of the population as well as functions for predicting the probability of any level of sleepiness for ecological assessment of absolute and relative risk of sleepiness in shift systems for safety applications.     

Kernel Architecture of the Genetic Circuitry of the Arabidopsis Circadian System

A wide range of organisms features molecular machines, circadian clocks, which generate endogenous oscillations with ~24 h periodicity and thereby synchronize biological processes to diurnal environmental fluctuations. Recently, it has become clear that plants harbor more complex gene regulatory circuits within the core circadian clocks than other organisms, inspiring a fundamental question: are all these regulatory interactions between clock genes equally crucial for the establishment and maintenance of circadian rhythms? Our mechanistic simulation for Arabidopsis thaliana demonstrates that at least half of the total regulatory interactions must be present to express the circadian molecular profiles observed in wild-type plants. A set of those essential interactions is called herein a kernel of the circadian system. The kernel structure unbiasedly reveals four interlocked negative feedback loops contributing to circadian rhythms, and three feedback loops among them drive the autonomous oscillation itself. Strikingly, the kernel structure, as well as the whole clock circuitry, is overwhelmingly composed of inhibitory, rather than activating, interactions between genes. We found that this tendency underlies plant circadian molecular profiles which often exhibit sharply-shaped, cuspidate waveforms. Through the generation of these cuspidate profiles, inhibitory interactions may facilitate the global coordination of temporally-distant clock events that are markedly peaked at very specific times of day. Our systematic approach resulting in experimentally-testable predictions provides insights into a design principle of biological clockwork, with implications for synthetic biology.     

Circadian Regulation of Food-Anticipatory Activity in Molecular Clock–Deficient Mice

In the mammalian brain, the suprachiasmatic nucleus (SCN) of the anterior hypothalamus is considered to be the principal circadian pacemaker, keeping the rhythm of most physiological and behavioral processes on the basis of light/dark cycles. Because restriction of food availability to a certain time of day elicits anticipatory behavior even after ablation of the SCN, such behavior has been assumed to be under the control of another circadian oscillator. According to recent studies, however, mutant mice lacking circadian clock function exhibit normal food-anticipatory activity (FAA), a daily increase in locomotor activity preceding periodic feeding, suggesting that FAA is independent of the known circadian oscillator. To investigate the molecular basis of FAA, we examined oscillatory properties in mice lacking molecular clock components. Mice with SCN lesions or with mutant circadian periods were exposed to restricted feeding schedules at periods within and outside circadian range. Periodic feeding led to the entrainment of FAA rhythms only within a limited circadian range. Cry1^−/− mice, which are known to be a “short-period mutant,” entrained to a shorter period of feeding cycles than did Cry2^−/− mice. This result indicated that the intrinsic periods of FAA rhythms are also affected by Cry deficiency. Bmal1 ^−/− mice, deficient in another essential element of the molecular clock machinery, exhibited a pre-feeding increase of activity far from circadian range, indicating a deficit in circadian oscillation. We propose that mice possess a food-entrainable pacemaker outside the SCN in which canonical clock genes such as Cry1, Cry2 and Bmal1 play essential roles in regulating FAA in a circadian oscillatory manner.     

Quantifying and understanding reproductive allocation schedules in plants

A plant's reproductive allocation (RA) schedule describes the fraction of surplus energy allocated to reproduction as it increases in size. While theorists use RA schedules as the connection between life history and energy allocation, little is known about RA schedules in real vegetation. Here we review what is known about RA schedules for perennial plants using studies either directly quantifying RA or that collected data from which the shape of an RA schedule can be inferred. We also briefly review theoretical models describing factors by which variation in RA may arise. We identified 34 studies from which aspects of an RA schedule could be inferred. Within those, RA schedules varied considerably across species: some species abruptly shift all resources from growth to reproduction; most others gradually shift resources into reproduction, but under a variety of graded schedules. Available data indicate the maximum fraction of energy allocated to production ranges from 0.1 to 1 and that shorter lived species tend to have higher initial RA and increase their RA more quickly than do longer‐lived species. Overall, our findings indicate, little data exist about RA schedules in perennial plants. Available data suggest a wide range of schedules across species. Collection of more data on RA schedules would enable a tighter integration between observation and a variety of models predicting optimal energy allocation, plant growth rates, and biogeochemical cycles.     

Astronomical cycles

Abstract

Talorchestia quoyana, a sand beach amphipod, shows a rhythm of locomotor activity controlled by a circadian clock and an inhibitory circatidal clock. This article reports on an investigation of the entrainment of the circadian dock to skeleton photoperiods. Four important mathematical models for circadian rhythms are examined with respect to the results of the entrainment experiments and to predictions from the phase response curve for Talorchestia. Significant differences between the models are described, and properties of circadian rhythms not accounted for by present models are outlined.     

Relationships between the Circadian System and Alzheimer's Disease-Like Symptoms in Drosophila

Circadian clocks coordinate physiological, neurological, and behavioral functions into circa 24 hour rhythms, and the molecular mechanisms underlying circadian clock oscillations are conserved from Drosophila to humans. Clock oscillations and clock-controlled rhythms are known to dampen during aging; additionally, genetic or environmental clock disruption leads to accelerated aging and increased susceptibility to age-related pathologies. Neurodegenerative diseases, such as Alzheimer''s disease (AD), are associated with a decay of circadian rhythms, but it is not clear whether circadian disruption accelerates neuronal and motor decline associated with these diseases. To address this question, we utilized transgenic Drosophila expressing various Amyloid-β (Aβ) peptides, which are prone to form aggregates characteristic of AD pathology in humans. We compared development of AD-like symptoms in adult flies expressing Aβ peptides in the wild type background and in flies with clocks disrupted via a null mutation in the clock gene period (per⁰¹). No significant differences were observed in longevity, climbing ability and brain neurodegeneration levels between control and clock-deficient flies, suggesting that loss of clock function does not exacerbate pathogenicity caused by human-derived Aβ peptides in flies. However, AD-like pathologies affected the circadian system in aging flies. We report that rest/activity rhythms were impaired in an age-dependent manner. Flies expressing the highly pathogenic arctic Aβ peptide showed a dramatic degradation of these rhythms in tune with their reduced longevity and impaired climbing ability. At the same time, the central pacemaker remained intact in these flies providing evidence that expression of Aβ peptides causes rhythm degradation downstream from the central clock mechanism.