Comparison of amplitude recovery dynamics of two limit cycle oscillator models of the human circadian pacemaker

At an organism level, the mammalian circadian pacemaker is a two-dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures--including plasma cortisol, plasma melatonin, and core body temperature (CBT)--all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A = 1), but are markedly different in the prediction of recovery rates when A < 0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaike's Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.     

Characterizing the amplitude dynamics of the human core-temperature circadian rhythm using a stochastic-dynamic model

Two measures, amplitude and phase, have been used to describe the characteristics of the endogenous human circadian pacemaker, a biological clock located in the hypothalamus. Although many studies of change in circadian phase with respect to different stimuli have been conducted, the physiologic implications of the amplitude changes (dynamics) of the pacemaker are unknown. It is known that phase changes of the human circadian pacemaker have a significant impact on sleep timing and content, hormone secretion, subjective alertness and neurobehavioral performance. However, the changes in circadian amplitude with respect to different stimuli are less well documented. Although amplitude dynamics of the human circadian pacemaker are observed in physiological rhythms such as plasma cortisol, plasma melatonin and core temperature data, currently methods are not available to accurately characterize the amplitude dynamics from these rhythms. Of the three rhythms core temperature is the only reliable variable that can be monitored continuously in real time with a high sampling rate. To characterize the amplitude dynamics of the circadian pacemaker we propose a stochastic-dynamic model of core temperature data that contains both stochastic and dynamic characteristics. In this model the circadian component that has a dynamic characteristic is represented as a perturbation solution of the van der Pol equation and the thermoregulatory response in the data that has a stochastic characteristic is represented as a first-order autoregressive process. The model parameters are estimated using data with a maximum likelihood procedure and the goodness-of-fit measures along with the associated standard error of the estimated parameters provided inference about the amplitude dynamics of the pacemaker. Using this model we analysed core temperature data from an experiment designed to exhibit amplitude dynamics. We found that the circadian pacemaker recovers slowly to an equilibrium level following amplitude suppression. In humans this reaction to perturbation from equilibrium value has potential physiological implications.     

Revised limit cycle oscillator model of human circadian pacemaker

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.     

Comparisons of the variability of three markers of the human circadian pacemaker

A circadian pacemaker within the central nervous system regulates the approximately 24-h physiologic rhythms in sleep cycles, hormone secretion, and other physiologic functions. Because the pacemaker cannot be examined directly in humans, markers of pacemaker function must be used to study the pacemaker and its response to environmental stimuli. Core body temperature (CBT), plasma cortisol, and plasma melatonin are three marker variables frequently used to estimate the phase of the human pacemaker. Measurements of circadian phase using markers can contain variability due to the circadian pacemaker itself, the intrinsic variability of the marker relative to the pacemaker, the method of analysis of the marker, and the marker assay. For this report, we compared the mathematical variability of a number of methods of identifying circadian phase from CBT, plasma cortisol, and plasma melatonin data collected in a protocol in which pacemaker variability was minimized using low light levels and regular timing of both the light pattern and the rest/activity schedule. We hoped to assess the relative variabilities of the different physiological markers and the analysis methods. Methods were based on the crossing of an absolute threshold, on the crossing of a relative threshold, or on fitting a curve to all data points. All methods of calculating circadian phase from plasma melatonin data were less variable than those calculated using CBT or cortisol data. The standard deviation for the phase estimates using CBT data was 0.78 h, using cortisol data was 0.65 h, and for the eight analysis methods using melatonin data was 0.23 to 0.35 h. While the variability for these markers might be different for other subject populations and/or less stringent study conditions, assessment of the intrinsic variability of the different calculations of circadian phase can be applied to allow inference of the statistical significance of phase and phase shift calculations, as well as estimation of sample size or statistical power for the number of subjects within an experimental protocol.     

Development of a two-dimension manifold to represent high dimension mathematical models of the intracellular Mammalian circadian clock

A new focus for mathematical models of the circadian pacemaker involves the encapsulation within the models of detailed biological processes responsible for generating those circadian rhythms. Representing greater biological detail requires more mathematical equations, which pose a greater challenge for the analysis of such systems. Development of a method that retains the predominant dynamics while still providing biologically detailed information is advantageous. Two high-dimension mathematical models of intracellular mammalian circadian pacemakers, Leloup-Goldbeter and Forger-Peskin, with 19 and 73 differential equations, respectively, have been published. The authors projected each of these high-dimension models onto their respective manifold using proper orthogonal functions (POFs) obtained from the empirical decomposition of the model's phase space to obtain a 2-dimension model. The resulting 2-dimension model, represented by 2 differential equations, predicts most of the salient characteristics of a biological clock including approximately 24-h oscillations, entrainment to an LD cycle, phase response curves, and the amplitude recovery dynamics that emerge following amplitude suppression. The manifold representation simplifies the mathematical analysis, since only 2 variables need to be observed and analyzed to understand the behavior of the biological clock. This reduced model derived from a model based on biological variables can be used for the development and analysis of mathematical models of the coupled mammalian oscillators to understand the dynamics of the integrated circadian pacemaker.     

Linear demasking techniques are unreliable for estimating the circadian phase of ambulatory temperature data.

Clinical investigators often use ambulatory temperature monitoring to assess the endogenous phase and amplitude of an individual's circadian pacemaker for diagnostic and research purposes. However, an individual's daily schedule includes changes in levels of activity, in posture, and in sleep-wake state, all of which are known to have masking or evoked effects on core body temperature (CBT) data. To compensate for or to correct these masking effects, many investigators have developed "demasking" techniques to extract the underlying circadian phase and amplitude data. However, the validity of these methods is uncertain. Therefore, the authors tested a variety of analytic methods on two different ambulatory data sets from two different studies in which the endogenous circadian pacemaker was not synchronized to the sleep-wake schedule. In both studies, circadian phase estimates calculated from CBT collected when each subject was ambulatory (i.e., free to perform usual daily activities) were compared to those calculated during the same study when the same subject's activities were controlled. In the first study, 24 sighted young and older subjects living on a 28-h scheduled "day" protocol were studied for approximately 21 to 25 cycles of 28-h each. In the second study, a blind man whose endogenous circadian rhythms were not synchronized to the 24-h day despite his maintenance of a regular 24-h sleep-wake schedule was studied for more than 80 consecutive 24-h days. During both studies, the relative phase of the endogenous (circadian) and evoked (scheduled activity-rest) components of the ambulatory temperature data changed progressively and relatively slowly, enabling analysis of the CBT rhythm at nearly all phase relationships between the two components. The analyses of the ambulatory temperature data demonstrate that the masking of the CBT rhythm evoked by changes in activity levels, posture, or sleep-wake state associated with the evoked schedule of activity and rest can significantly obscure the endogenous circadian component of the signal, the object of study. In addition, the masking effect of these evoked responses on temperature depends on the circadian phase at which they occur. These nonlinear interactions between circadian phase and sleep-wake schedule render ambulatory temperature data unreliable for the assessment of endogenous circadian phase. Even when proposed algebraic demasking techniques are used in an attempt to reveal the endogenous temperature rhythm, the phase estimates remain severely compromised.     

CONTRIBUTION OF CIRCADIAN PHYSIOLOGY AND SLEEP HOMEOSTASIS TO AGE-RELATED CHANGES IN HUMAN SLEEP

The circadian pacemaker and sleep homeostasis play pivotal roles in vigilance state control. It has been hypothesized that age-related changes in the human circadian pacemaker, as well as sleep homeostatic mechanisms, contribute to the hallmarks of age-related changes in sleep, that is, earlier wake time and reduced sleep consolidation. Assessments of circadian parameters in healthy young (～20–30 years old) and older people (～65–75 years old)—in the absence of the confounding effects of sleep, changes in posture, and light exposure—have demonstrated that an earlier wake time in older people is accompanied by about a 1h advance of the rhythms of core body temperature and melatonin. In addition, older people wake up at an earlier circadian phase of the body temperature and plasma melatonin rhythm. The amplitude of the endogenous circadian component of the core body temperature rhythm assessed during constant routine and forced desynchrony protocols is reduced by 20–30% in older people. Recent assessments of the intrinsic period of the human circadian pacemaker in the absence of the confounding effects of light revealed no age-related reduction of this parameter in both sighted and blind individuals. Wake maintenance and sleep initiation are not markedly affected by age except that sleep latencies are longer in older people when sleep initiation is attempted in the early morning. In contrast, major age-related reductions in the consolidation and duration of sleep occur at all circadian phases. Sleep of older people is particularly disrupted when scheduled on the rising limb of the temperature rhythm, indicating that the sleep of older people is more susceptible to arousal signals genernpated by the circadian pacemaker. Sleep-homeostatic mechanisms, as assayed by the sleep-deprivation–induced increase of EEG slow-wave activity (SWA), are operative in older people, although during both baseline sleep and recovery sleep SWA in older people remains at lower levels. The internal circadian phase advance of awakening, as well as the age-related reduction in sleep consolidation, appears related to an age-related reduction in the promotion of sleep by the circadian pacemaker during the biological night in combination with a reduced homeostatic pressure for sleep. Early morning light exposure associated with this advance of awakening in older people could reinforce the advanced circadian phase. Quantification of the interaction between sleep homeostasis and circadian rhythmicity contributes to understanding age-related changes in sleep timing and quality. (Chronobiology International, 17(3), 285–311, 2000)     

Melatonin rhythm observed throughout a three-cycle bright-light stimulus designed to reset the human circadian pacemaker.

Exposure to light and darkness can rapidly induce phase shifts of the human circadian pacemaker. A type 0 phase response curve (PRC) to light that has been reported for humans was based on circadian phase data collected from constant routines performed before and after a three-cycle light stimulus, but resetting data observed throughout the entire resetting protocol have not been previously reported. Pineal melatonin secretion is governed by the hypothalamic circadian pacemaker via a well-defined neural pathway and is reportedly less subject to the masking effects of sleep and activity than body temperature. The authors reasoned that observation of the melatonin rhythm throughout the three-cycle light resetting trials could provide daily phase-resetting information, allowing a dynamic view of the resetting response of the circadian pacemaker to light. Subjects (n = 12) living in otherwise dim light (approximately 10-15 lux) were exposed to a noncritical stimulus of three cycles of bright light (approximately 9500 lux for 5 h per day) timed to phase advance or phase delay the human circadian pacemaker; control subjects (n = 11) were scheduled to the same protocols but exposed to three 5-h darkness cycles instead of light. Subjects underwent initial and final constant routine phase assessments; hourly melatonin samples and body temperature data were collected throughout the protocol. Average daily phase shifts of 1 to 3 h were observed in 11 of 12 subjects receiving the bright light, supporting predictions obtained using Kronauer's phase-amplitude model of the resetting response of the human circadian pacemaker. The melatonin rhythm in the 12th subject progressively attenuated in amplitude throughout the resetting trial, becoming undetectable for >32 hours preceding an abrupt reappearance of the rhythm at a shifted phase with a recovered amplitude. The data from control subjects who remained in dim lighting and darkness delayed on average -0.2 h per day, consistent with the daily delay expected due to the longer than 24-h intrinsic period of the human circadian pacemaker. Both temperature and melatonin rhythms shifted by equivalent amounts in both bright light-treated and control subjects (R = 0.968; p<0.0001; n = 23). Observation of the melatonin rhythm throughout a three-cycle resetting trial has provided a dynamic view of the daily phase-resetting response of the human circadian pacemaker. Taken together with the observation of strong type 0 resetting in humans in response to the same three-cycle stimulus applied at a critical phase, these data confirm the importance of considering both phase and amplitude when describing the resetting of the human circadian pacemaker by light.     

Addition of a non-photic component to a light-based mathematical model of the human circadian pacemaker

Mathematical models have become vital to the study of many biological processes in humans due to the complexity of the physiological mechanisms underlying these processes and systems. While our current mathematical representation of the human circadian pacemaker has proven useful in many experimental situations, it uses as input only a direct effect of light on the circadian pacemaker. Although light (a photic stimulus) has been shown to be the primary synchronizer of the circadian pacemaker across a number of species, studies in both animals and humans have confirmed the existence of non-photic effects that also contribute to phase shifting and entrainment. We modified our light-based circadian mathematical model to reflect evidence from these studies that the sleep-wake cycle and/or associated behaviors have a non-photic effect on the circadian pacemaker. In our representation, the sleep-wake cycle and its associated behaviors provides a non-photic drive on the circadian pacemaker that acts both independently and concomitantly with light stimuli. Further experiments are required to validate fully our model and to understand the exact effect of the sleep-wake cycle as a non-photic stimulus for the human circadian pacemaker.     

Efficacy of a single sequence of intermittent bright light pulses for delaying circadian phase in humans

It has been shown in animal studies that exposure to brief pulses of bright light can phase shift the circadian pacemaker and that the resetting action of light is most efficient during the first minutes of light exposure. In humans, multiple consecutive days of exposure to brief bright light pulses have been shown to phase shift the circadian pacemaker. The aim of the present study was to determine whether a single sequence of brief bright light pulses administered during the early biological night would phase delay the human circadian pacemaker. Twenty-one healthy young subjects underwent a 6.5-h light exposure session in one of three randomly assigned conditions: 1) continuous bright light of approximately 9,500 lux, 2) intermittent bright light (six 15-min bright light pulses of approximately 9,500 lux separated by 60 min of very dim light of <1 lux), and 3) continuous very dim light of <1 lux. Twenty subjects were included in the analysis. Core body temperature (CBT) and melatonin were used as phase markers of the circadian pacemaker. Phase delays of CBT and melatonin rhythms in response to intermittent bright light pulses were comparable to those measured after continuous bright light exposure, even though the total exposure to the intermittent bright light represented only 23% of the 6.5-h continuous exposure. These results demonstrate that a single sequence of intermittent bright light pulses can phase delay the human circadian pacemaker and show that intermittent pulses have a greater resetting efficacy on a per minute basis than does continuous exposure.     

Acute exposure to 2G phase shifts the rat circadian timing system

The circadian timing system (CTS) provides internal and external temporal coordination of an animal's physiology and behavior. In mammals, the generation and coordination of these circadian rhythms is controlled by a neural pacemaker, the suprachiasmatic nucleus (SCN), located within the hypothalamus. The pacemaker is synchronized to the 24 hour day by time cues (zeitgebers) such as the light/dark cycle. When an animal is exposed to an environment without time cues, the circadian rhythms maintain internal temporal coordination but exhibit a "free-running" condition in which the period length is determined by the internal pacemaker. Maintenance of internal and external temporal coordination are critical for normal physiological and psychological function in human and non-human primates. Exposure to altered gravitational environments has been shown to affect the amplitude, mean, and timing of circadian rhythms in species ranging from unicellular organisms to man. However, it has not been determined whether altered gravitational fields have a direct effect on the neural pacemaker, or affect peripheral physiological systems that express these circadian parameters. In previous studies, the ability of a stimulus to phase shift circadian rhythms was used to determine whether a stimulus has a direct effect on the neural pacemaker. The present experiment was performed in order to determine whether acute exposure to a hyperdynamic field could phase shift circadian rhythms.     

Development and validation of computational models for mammalian circadian oscillators

Circadian rhythms are endogenous rhythms with a cycle length of approximately 24 h. Rhythmic production of specific proteins within pacemaker structures is the basis for these physiological and behavioral rhythms. Prior work on mathematical modeling of molecular circadian oscillators has focused on the fruit fly, Drosophila melanogaster. Recently, great advances have been made in our understanding of the molecular basis of circadian rhythms in mammals. Mathematical models of the mammalian circadian oscillator are needed to piece together diverse data, predict experimental results, and help us understand the clock as a whole. Our objectives are to develop mathematical models of the mammalian circadian oscillator, generate and test predictions from these models, gather information on the parameters needed for model development, integrate the molecular model with an existing model of the influence of light and rhythmicity on human performance, and make models available in BioSpice so that they can be easily used by the general community. Two new mammalian models have been developed, and experimental data are summarized. These studies have the potential to lead to new strategies for resetting the circadian clock. Manipulations of the circadian clock can be used to optimize performance by promoting alertness and physiological synchronization.     

A forced desynchrony study of circadian pacemaker characteristics in seasonal affective disorder

The circadian pacemaker is an endogenous clock that regulates oscillations in most physiological and psychological processes with a near 24-h period. In many species, this pacemaker triggers seasonal changes in behavior. The seasonality of symptoms and the efficacy of light therapy suggest involvement of the circadian pacemaker in seasonal affective disorder (SAD), winter type. In this study, circadian pacemaker characteristics of SAD patients were compared with those of controls. Seven SAD patients and matched controls were subjected to a 120-h forced desynchrony protocol, in which core body temperature and melatonin secretion profiles were measured for the characterization of circadian pacemaker parameters. During this protocol, which enables the study of unmasked circadian pacemaker characteristics, subjects were exposed to six 20-h days in time isolation. Patients participated twice in winter (while depressed and while remitted after light therapy) and once in summer. Controls participated once in winter and once in summer. Between the SAD patients and controls, no significant differences were observed in the melatonin-derived period or in the phase of the endogenous circadian temperature rhythm. The amplitude of this rhythm was significantly smaller in depressed and remitted SAD patients than in controls. No abnormalities of the circadian pacemaker were observed in SAD patients. A disturbance in thermoregulatory processes might explain the smaller circadian temperature amplitude in SAD patients during winter.     

Analysis method and experimental conditions affect computed circadian phase from melatonin data

Accurate determination of circadian phase is necessary for research and clinical purposes because of the influence of the master circadian pacemaker on multiple physiologic functions. Melatonin is presently the most accurate marker of the activity of the human circadian pacemaker. Current methods of analyzing the plasma melatonin rhythm can be grouped into three categories: curve-fitting, threshold-based and physiologically-based linear differential equations. To determine which method provides the most accurate assessment of circadian phase, we compared the ability to fit the data and the variability of phase estimates for seventeen different markers of melatonin phase derived from these methodological categories. We used data from three experimental conditions under which circadian rhythms - and therefore calculated melatonin phase - were expected to remain constant or progress uniformly. Melatonin profiles from older subjects and subjects with lower melatonin amplitude were less likely to be fit by all analysis methods. When circadian drift over multiple study days was algebraically removed, there were no significant differences between analysis methods of melatonin onsets (P = 0.57), but there were significant differences between those of melatonin offsets (P<0.0001). For a subset of phase assessment methods, we also examined the effects of data loss on variability of phase estimates by systematically removing data in 2-hour segments. Data loss near onset of melatonin secretion differentially affected phase estimates from the methods, with some methods incorrectly assigning phases too early while other methods assigning phases too late; missing data at other times did not affect analyses of the melatonin profile. We conclude that melatonin data set characteristics, including amplitude and completeness of data collection, differentially affect the results depending on the melatonin analysis method used.     

Statistical model building and model criticism for human circadian data

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.     

A simpler model of the human circadian pacemaker

Numerous studies have used the classic van der Pol oscillator, which contains a cubic nonlinearity, to model the effect of light on the human circadian pacemaker. Jewett and Kronauer demonstrated that Aschoff's rule could be incorporated into van der Pol type models and used a van der Pol type oscillator with higher order nonlinearities. Kronauer, Forger, and Jewett have proposed a model for light preprocessing, Process L, representing a biochemical process that converts a light signal into an effective drive on the circadian pacemaker. In the paper presented here, the authors use the classic van der Pol oscillator with Process L and Jewett and Kronauer's model of Aschoff's rule to model the human circadian pacemaker. This simpler cubic model predicts the results of a three-pulse human phase response curve experiment and a two-pulse amplitude reduction study with as much, or more, accuracy as the models of Jewett and Kronauer and Kronauer, Forger, and Jewett, which both employ a nonlinearity of degree 7. This suggests that this simpler cubic model should be considered as a potential alternative to other models of the human circadian system currently available.     

Phase Shift Effects in the Kalanchoë Petal Rhythm due to Two or More Light Pulses

The circadian petal rhythm of Kalanchoë blossfeldiana Poellniz was studied theoretically and experimentally. Results of experiments in which (i) two light pulses and (ii) repeated light pulses were given to the flowers are compared with predictions based on a previously published feedback model. In this model both the amplitude and the phase of the rhythm are affected by light pulses. Results from the present phase shift studies are shown to be in good agreement with the model. The results are also discussed in relation to a constant amplitude model like that suggested by Pittendrigh for the eclosion rhythm of Drosophila.     

Two Steady‐Entrainment Phases and Graded Masking Effects by Light Generate Different Circadian Chronotypes in Octodon degus

Processes involved in the operation of the circadian pacemaker are well characterized; however; little is known about what mechanisms drive the overt diurnal, nocturnal, or crepuscular behavior in a species. In this context, dual‐phasing rodents, such as Octodon degus, emerge as a useful model to decipher these keys. Two main chronotypes, nocturnal and diurnal, have been traditionally described in laboratory‐housed degus based on the percentage of activity displayed by the animals during the scotophase or photophase. However, if one considers also the entrainment phase angle during the first days following a change from LD to DD conditions, a third chronotype (intermediate)—or more properly, a continuous grading of circadian expressions between diurnal and nocturnal chronotype—can be observed. Our experiments suggest the pacemaker of the diurnal animal is entrained to the photophase, and light does not exert a negative masking effect. The pacemaker of the nocturnal degus, on the other hand, is entrained to the scotophase, and light exerts a strong negative masking effect. Finally, the intermediate chronotype is characterized by variable negative masking effect of light overlapping a pacemaker entrained to the photophase. The phase shift inversion from diurnal to nocturnal chronotype is related to the availability of a wheel in the cage, and the effect may be located downstream from the clock. However, body temperature rhythm recordings, less affected by masking effects, point to an involvement of the circadian pacemaker in chronotype differentiation, as transient entrainment cycles, and not an abrupt phase shift, were detected after providing access to the wheel. The diurnality of degus seems to be the result of a variety of mechanisms, which may explain how different processes can lead to similar chronotypes.     

The temporal ‘structure’ and function of the insect photoperiodic clock: a tribute to Colin S. Pittendrigh

In 1936, Erwin Bünning suggested that photoperiodic time measurement was a function of the circadian system. Colin Pittendrigh became an ardent supporter of Bünning's hypothesis, drawing parallels between photoperiodism and his own group's investigations of adult eclosion rhythmicity in the fruit fly Drosophila pseudoobscura. They developed several more modern versions of Bünning's general hypothesis based on the entrainment of circadian oscillations to the light cycle, including ‘external coincidence’, which is a derivation of Bünning's original model, and ‘internal coincidence’, which relied upon seasonal changes in the mutual phase relationship of oscillators within a multi‐oscillator circadian system. This review considers the experimental evidence for the central role of the circadian system in photoperiodic timing and, in some species, for both external and internal coincidence. Pittendrigh, however, pursued the idea of internal coincidence further with his analysis of the pacemaker–slave organization of eclosion rhythmicity in D. pseudoobscura and proposed a similar theoretical model for photoperiodism comprising a group of slave oscillators driven by a light‐sensitive pacemaker. In this model, the phase relationships of the slaves to the pacemaker were affected by (i) the relative periods of the pacemaker and slave(s); (ii) the strength(s) of the coupling between the two; and (iii) the dampening coefficients of the various slaves. Manipulation of these variables showed that the slaves adopted different internal phase relationships (both to each other and to the pacemaker) under the influence of changes in daily photophase, the period of the Zeitgeber and phase shifts of the entraining light cycle.     

Circadian organization inAplysia: internal desynchronization and amplitude of locomotor rhythm

Summary We have tested the hypothesis that the circadian oscillators in the eyes ofAplysia are coequal driver oscillators for the circadian locomotor rhythm. Three predictions based on this hypothesis were tested. Prediction 1: at a time when the phase difference between the eye rhythms is small, the amplitude of the locomotor rhythm in two eyed animals will be as great or greater than the amplitude in one eyed animals. Prediction 2: the amplitude of the locomotor rhythm of two eyed animals will decline under conditions in which the two eye rhythms become out of phase with each other. Prediction 3: the form of the locomotor rhythm will broaden or become biphasic in two eyed animals when the two eye rhythms become out of phase with each other.None of the predictions was confirmed. One eyedAplysia had higher amplitude locomotor rhythms than two eyedAplysia, even under conditions in which the two eye rhythms were probably not far out of phase with each other. There was no tendency for the amplitude of the locomotor rhythm of two eyed animals to decline under circumstances in which the phase difference between the two eye rhythms changes from less than 4 h to as much as 11.5 h. There was no tendency in two eyed animals for the locomotor rhythm to broaden or become biphasic as the eye rhythms became more out of phase with each other.The results led us to reject the hypothesis that the eyes are co-equal drivers for the locomotor rhythm. The ocular influence on locomotion is more likely to be mediated via mechanisms in the central nervous system that do not faithfully conserve the phase of the eye rhythms. One possibility is that the driver is a third circadian oscillator that interacts with the two eye oscillators.Abbreviations CAP compound action potentials - CC constant conditions - CT circadian time - DO driver oscillator - EO eye oscillator - RSD relative standard deviations (see Methods)