Robust entrainment of circadian oscillators requires specific phase response curves

The circadian clocks keeping time in many living organisms rely on self-sustained biochemical oscillations entrained by external cues, such as light, to the 24-h cycle induced by Earth's rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions, or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in the signal that entrains them. To support this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different times of the cycle. We establish a general relationship between the robustness of key entrainment properties, such as stability and oscillator phase, on the one hand, and the shape of the PRC as characterized by a specific curvature or the existence of a dead zone, on the other hand. The criteria obtained are applied to computational models of circadian clocks and account for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.     

Analysis of entrainment of respiratory rhythm by somatic afferent stimulation in cats using phase response curves

To elucidate how peripheral somatic afferents synchronize the respiratory rhythm to the exercise rhythm, the phrenic nerve activity in the vagotomized, paralyzed, and artificially ventilated cats anesthetized with chloralose-urethane was recorded during electrical stimulation of the superficial radial nerve afferents. At first, a single pulse train was given at various times of the respiratory cycle to obtain a phase-response curve (PRC). The stimulation given at mid to late expiration produced a phase advance, but the stimulation during inspiration produced no measurable phase shifts in most animals (8/10). The maximum phase advance changed depending on the stimulus intensity. The stronger the stimulus intensity, the greater became the maximum phase advance. Repetitive somatic afferent stimulation produced 1:1 entrainment of the respiratory frequency to the repetitive stimulation. Theoretical predictions on the stable entrainment phase and on the entrainment frequency range from the obtained PRC were close to the experimental results. The present study demonstrated the presence of a neuronal circuit synchronizing the respiratory rhythm to the periodic somatic afferents and the manner of how such entrainment occurs.     

Modeling circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators: phase shifts and phase response curves

Circadian rhythm generation in the suprachiasmatic nucleus was modeled by locally coupled self-sustained oscillators. The model is composed of 10,000 oscillators, arranged in a square array. Coupling between oscillators and standard deviation of (randomly determined) intrinsic oscillator periods were varied. A stable overall rhythm emerged. The model behavior was investigated for phase shifts of a 24-h zeitgeber cycle. Prolongation of either the dark or the light phase resulted in a lengthening of the period, whereas shortening of the dark or the light phase shortened the period. The model's response to shifts in the light-dark cycle was dependent only on the extent of the shift and was insensitive to changes in parameters. Phase response curves (PRC) and amplitude response curves were determined for single and triple 5-h light pulses (1000 lux). Single pulses lead to type 1 PRCs with larger phase shifts for weak coupling. Triple pulses generally evoked type 1 PRCs with the exception of weak coupling, where a type 0 PRC was observed.     

Phase sensitivity analysis of circadian rhythm entrainment

As a biological clock, circadian rhythms evolve to accomplish a stable (robust) entrainment to environmental cycles, of which light is the most obvious. The mechanism of photic entrainment is not known, but two models of entrainment have been proposed based on whether light has a continuous (parametric) or discrete (nonparametric) effect on the circadian pacemaker. A novel sensitivity analysis is developed to study the circadian entrainment in silico based on a limit cycle approach and applied to a model of Drosophila circadian rhythm. The comparative analyses of complete and skeleton photoperiods suggest a trade-off between the contribution of period modulation (parametric effect) and phase shift (nonparametric effect) in Drosophila circadian entrainment. The results also give suggestions for an experimental study to (in)validate the two models of entrainment.     

Analysis of entrainment of circadian oscillators by skeleton photoperiods using phase transition curves

A skeleton photoperiod consists of two short pulses which are applied on the circadian oscillator at times corresponding to the beginning and to the end of a continuous light stimulus. To study several problems in entrainment of circadian rhythms by skeleton photoperiods, we develop a simple diagrammatic solution of the steady state entrainment making use of phase transition curves which are directly gotten from phase response curves. The graphical method is simple and systematic to study entrainment by light cycles with various day lengths. As the method is also intuitive, we can easily examine three problems. (1) In Drosophila the phase relation (ψ) between rhythm and light cycle is a continuous function of day length of skeleton photoperiods up to about 12 h, but a marked discontinuity (ψ-jump) sets in between 13 and 14h. By the diagrammatic method we find that ψ-jump is mathematically a bifurcation phenomenon. (2) The action of photoperiods up to about 12 h is fully simulated by two 15-min skeleton pulses. Do 3-min skeleton pulses imitate the complete photoperiods? We find that pulse width is arbitrary to some extent. (3) Why skeleton photoperiods up to about 12 h are good models of complete photoperiods? The reason is the small amplitude and the nearly symmetrical form of phase response curves in the subjective day.     

Modeling light adaptation in circadian clock: prediction of the response that stabilizes entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature.     

Accuracy of circadian entrainment under fluctuating light conditions: contributions of phase and period responses.

The accuracy with which a circadian pacemaker can entrain to an environmental 24-h zeitgeber signal depends on (a) characteristics of the entraining signal and (b) response characteristics and intrinsic stability of the pacemaker itself. Position of the sun, weather conditions, shades, and behavioral variations (eye closure, burrowing) all modulate the light signal reaching the pacemaker. A simple model of a circadian pacemaker allows researchers to explore the impact of these factors on pacemaker accuracy. Accuracy is operationally defined as the reciprocal value of the day-to-day standard deviation of the clock times at which a reference phase (0) is reached. For the purpose of this exploration, the authors used a model pacemaker characterized solely by its momentary phase and momentary velocity. The average velocity determines the time needed to complete one pacemaker cycle and, therefore, is inversely proportional to pacemaker period. The model pacemaker responds to light by shifting phase and/or changing its velocity. The authors assumed further that phase and velocity show small random fluctuations and that the velocity is subject to aftereffects. Aftereffects were incorporated mathematically in a term allowing period to contract exponentially to a stable steady-state value, with a time constant of 69 d in the absence of light. The simulations demonstrate that a pacemaker reaches highest accuracy when it responds to light by simultaneous phase shifts and changes of its velocity. Phase delays need to coincide with slowing down and advances with speeding up; otherwise, no synchronization to the zeitgeber occurs. At maximal accuracy, the changes in velocity are such that the average period of the pacemaker under entrained conditions equals 24 h. The results suggest that during entrainment, the pacemaker adjusts its period to 24 h, after which daily phase shifts to compensate for differences between the periods of the zeitgeber and the clock are no longer necessary. On average, phase shifts compensate for maladjustments of phase and velocity changes compensate for maladjustments of period.     

Phase response curves for social entrainment

Summary Phase shifts in free-running activity rhythms of male golden hamsters,Mesocricetus auratus, often occur when they establish a new territory and home after a cage change. Similar shifts also often occur after pairs of animals interact with each other for half an hour. When these events take place during the middle of the hamsters' subjective day, they produce phase advances: when late in the subjective night, they produce phase delays. Repeated social interactions at the same time of day can entrain activity rhythms in a way consistent with the shape of the phase response curves. Not all individuals become entrained, as is predictable from the modest amplitude of the phase response curve. The effects of social interactions and of other disturbances may be mediated through an oscillator phased by general arousal. The present findings have implications for the interpretation of drug-induced changes in biological rhythms.     

Photobiology of the Gonyaulax circadian system. I. Different phase response curves for red and blue light

Phase responses to red and blue light pulses were measured at different times during the circadian cycle (phase response curves, PRC) in the marine unicellular dinoflagellate Gonyaulaxpolyedra Stein. Pulses were given during a 24-h period of darkness; thereafter, cultures were released into constant dim red light for the assessment of phase and period. The results confirmed earlier findings that the Gonyaulax circadian system receives light signals via two distinct input pathways. During the subjective day and for the first 3 h of the subjective night, red and blue light pulses led to identical phase responses. For the rest of the circadian cycle, however, phase responses to pulses of either red or blue light differed drastically both in their amplitude and direction (advances or delays). Thus, the Gonyaulax light PRC is generated by two distinct light responses. One of these represents responses via a light input that is responsive both to red and blue light mainly producing small delays. The other represents responses of a primarily blue-sensitive input system leading to large advances restricted to the subjective night. Via feed-back, the blue-sensitive light input appears to be under the control of the circadian system. Received: 27 November 1996/Accepted: 30 January 1997     

The circadian eclosion rhythm in Sarcophaga argyrostoma: delineation of the responsive period for entrainment

ABSTRACT. The circadian rhythm of pupal eclosion in Sarcophaga argyrostoma shows a declining responsiveness to the phase-shifting effects of single light pulses as development proceeds, the intrapuparial stages becoming largely 'insensitive'. Maximum responses occur in the intra-uterine embryos and first-instar larvae. Pharate adults, however, are responsive to single high temperature pulses. Pupae, pharate adults, and females carrying ovarian eggs, also respond to single stepwise transfers from light to dark, or vice versa, but the peaks of eclosion show a phase angle to the light which differs from that produced by transfers of embryos or larvae. The results are consistent with the view that separate 'larval' and 'adult' clocks occur at different stages of development.     

Daily exercise facilitates phase delays of circadian melatonin rhythm in very dim light

Shift workers and transmeridian travelers are exposed to abnormal work-rest cycles, inducing a change in the phase relationship between the sleep-wake cycle and the endogenous circadian timing system. Misalignment of circadian phase is associated with sleep disruption and deterioration of alertness and cognitive performance. Exercise has been investigated as a behavioral countermeasure to facilitate circadian adaptation. In contrast to previous studies where results might have been confounded by ambient light exposure, this investigation was conducted under strictly controlled very dim light (standing approximately 0.65 lux; angle of gaze) conditions to minimize the phase-resetting effects of light. Eighteen young, fit males completed a 15-day randomized clinical trial in which circadian phase was measured in a constant routine before and after exposure to a week of nightly bouts of exercise or a nonexercise control condition after a 9-h delay in the sleep-wake schedule. Plasma samples collected every 30-60 min were analyzed for melatonin to determine circadian phase. Subjects who completed three 45-min bouts of cycle ergometry each night showed a significantly greater shift in the dim light melatonin onset (DLMO(25%)), dim light melatonin offset, and midpoint of the melatonin profile compared with nonexercising controls (Student t-test; P < 0.05). The magnitude of phase delay induced by the exercise intervention was significantly dependent on the relative timing of the exercise after the preintervention DLMO(25%) (r = -0.73, P < 0.05) such that the closer to the DLMO(25%), the greater the phase shift. These data suggest that exercise may help to facilitate circadian adaptation to schedules requiring a delay in the sleep-wake cycle.     

Temperature entrainment of the circadian cuticle deposition rhythm in Drosophila melanogaster

The cuticle deposition rhythm, which is observed in the apodeme of the furca in the thorax, is controlled by a peripheral circadian clock in the epidermal cells and entrained to light-dark (LD) cycles via CRYPTOCHROME (CRY) in Drosophila melanogaster. In the present study, we examined the effects of temperature (TC) cycles and the combination of LD and TC cycles on entrainment of the cuticle deposition rhythm. The rhythm was entrained to TC cycles, whose period was 28 h. In T = 21 and 24 h, the rhythm was entrained to TC cycles in some individuals. CRY is not necessary for temperature entrainment of the cuticle deposition rhythm because the rhythm in cry(b) (lacking functional CRY) was entrained to TC cycles. Temperature entrainment of the rhythm was achieved even when the thoraxes or furcae were cultured in vitro, suggesting that the mechanism for temperature entrainment is independent of the central clock in the brain and the site of the thermoreception resides in the epidermal cells. When LD and TC cycles with different periods were applied, the rhythm was entrained to LD cycles with a slight influence of TC cycles. Thus, the LD cycle is a stronger zeitgeber than the TC cycle. The variance of the number of the cuticle layers decreased in the flies kept under LD and TC cycles with the same period in which the thermophase coincided with the photophase. Therefore, we conclude that LD and TC cycles synergistically entrain the rhythm. Synergistic effects of LD and TC cycles on entrainment were also observed even when the thoraxes were cultured in vitro, suggesting that the light and temperature information is integrated within the peripheral circadian system.     

视交叉上核的内源性昼夜节律以及光,谷氨酸和NO的调制作用

自从发现视交叉上核（ＳＣＮ）中有直接的视网膜下丘脑投射纤维以来,ＳＣＮ的内源性节律及其调节机制受到广泛重视,已成为令人感兴趣的新课题。哺乳动物的２４ｈ昼夜节律而言,ＳＣＮ是主要的启步者,但ＳＣＮ内源性的振荡节律又受到环境光暗周期、谷氨酸和一氧化氮的拖拽。     

Retinal and extraretinal photoreceptors mediate entrainment of the circadian locomotor rhythm in lizards

Summary The circadian locomotor activity rhythms of 7 species of lizards can readily be entrained (synchronized) toLD12: 12 (30–50 lux: 0) fluorescent light cycles after complete surgical removal of both eyes. Removal of the parietal eye and pineal organ does not prevent entrainment of blinded lizards. Appropriate control experiments established that lightper se, and not low amplitude temperature cycles or other obvious environmental variables, was the entraining stimulus for blinded lizards. In some cases, blocking the penetration of light to the brains of blinded lizards caused them to free-run (express their endogenous circadian rhythm) in the presence of a dim green light cycle, to which they had previously entrained, suggesting that the brain is the site of the extraretinal photoreceptor(s) mediating entrainment. The extraretinal photoreceptor(s) is capable of intensity discrimination since changing the intensity of aLD 12: 12 fluorescent light cycle caused a change in the phase-relationship between the entrained activity rhythm and the light cycle in a blinded gekko. The lateral eyes are also involved in mediating entrainment since removal of the lateral eyes of thoseSceloporus olivaceus which previously entrained to a dim green light cycle [LD 12: 12 (0.05 lux: 0)] caused them to free-run. Also, blinding had noticeable effects on the entrained activity patterns of some species of lizards.I thank Michael Menaker, Jeffrey Elliott, Sue Binkley, Joseph Silver, Ed Kluth, George Wyche, Bruee Rouse, Nancy Leshikar, Lili Mostafavi, Janet Alvis, Celeste Cromack, A. L. Mackey and Jean Rogers for their suggestions and technical assistance. Support for this work was provided by NIH grant HD-03803-02 (to M. Menaker); NSP grant GB-8138 (to M. Menaker); NSF traineeship GZ-1336 (to H. Underwood); and MH traineeship 5T01GM00836-09 (to H. Underwood).     

Accuracy of human circadian entrainment under natural light conditions: model simulations

The patterns of light intensity to which humans expose their circadian pacemakers in daily life are very irregular and vary greatly from day to day. The circadian pacemaker can adjust to such irregular exposure patterns by daily phase shifts, such as summarized in a phase response curve. It is demonstrated in this paper on the basis of computer simulations applying actually recorded human light exposure patterns that the pacemaker can substantially improve its accuracy by an additional response to light: For that purpose, it should additionally change its angular velocity (and consequently its period tau) in response to light. Reductions of tau in response to light in the morning and increases of tau in response to light in the evening can lead to an increase in entrained pacemaker accuracy with about 25%. Circadian pacemakers have evolved as accurate internal representations of external time, and investigated diurnal mammals all seem to respond to light by changing the period of their circadian pacemaker (in addition to shifting phase). The authors suggest that also human circadian systems take advantage of this possibility and that their pacemakers respond to light by shifting phase and changing period. As a consequence of this postulated mechanism, the simulations demonstrate that the period of the pacemaker under normally entrained conditions is 24 h. The maximum accuracy corresponds to a day-to-day standard deviation of the time of phase 0 of circa 15 min. This is considerably more accurate than the light signal humans usually perceive.     

Plasticity of hamster circadian entrainment patterns depends on light intensity

The multiple oscillatory basis of the mammalian circadian pacemaker is adduced by, among other phenomena, the occurrence of split locomotor activity rhythms in rodents after prolonged exposure to constant light. More recently, split rhythms entrained to a 24h light:dark:light:dark cycle have been documented following scheduled access of hamsters to a novel running wheel or by photoperiod manipulations alone. Because the incidence of constant light-induced splitting depends on light intensity, the role of this variable was assessed in this new splitting paradigm. Male Syrian hamsters, entrained to a 14h light:10h dark cycle, were transferred to individual running wheel cages 7h after light onset. Transfer coincided with the beginning of the scotophase of a new photocycle alternating between 5h of relative dark and 7h of light. For four weeks bright photophases (approximately 350 lux) were alternated with either dim (< 0.1 lux) or completely dark (0 lux) scotophases. An additional group received moderate intensity photophases (approximately 45 lux) paired with dim scotophase illumination. For an additional four weeks, all hamsters were exposed to the same bright:dim light:dark cycle. Dim light in the scotophase significantly increased the incidence of split activity rhythms relative to that observed with completely dark scotophases. Overall wheel-running rates and activity induced by a cage change were also increased in dim light-exposed animals. Group differences largely disappeared four weeks later when hamsters previously maintained in completely dark scotophases were exposed to dim scotophases. Photophase light intensity did not affect the overall incidence of splitting, but influenced the timing of activity in the afternoon scotophase. The effects of dim illumination may be mediated in part via enhanced locomotor responses to transfer to a new cage or by changes in coupling interactions between component oscillators.     

The circadian rhythm of a behavioral photoresponse in the dinoflagellate Gyrodinium dorsum

Summary The circadian rhythm of the photoresponse to blue light in the dinoflagellate Gyrodinium dorsum Kofoid was investigated by the use of a closed circuit television system. The initial cessation of movement upon stimulation (stop-response) was used as the index of light reception. Under constant dark conditions cells grown on a 12L:12D regime show an endogenous circadian rhythm in their stop-response with maximum responsiveness occurring approximately one hour before the beginning of the expected light phase. This rhythmic response was only observed if the cells were irradiated with red light (620 nm) prior to stimulation with blue light. After preirradiation both far-red reversibility and the shift in the stop-response action spectrum from 470 nm to 490 nm could also be demonstrated. These findings may be related to the diurnal migration of marine dinoflagellates.This study was supported by National Science Foundation grant GB 5137.     

Effects of induced wheel running on the circadian activity rhythms of Syrian hamsters: entrainment and phase response curve

The goal of this study was to provide an example of nonsocial and nonphotic entrainment in Syrian hamsters, together with a corresponding phase response curve (PRC). Fourteen male hamsters were given 2-hr bouts of induced activity (mostly wheel running) at 23.83-hr intervals in constant darkness (DD). The activity onsets of 10 hamsters entrained to this manipulation, with no anticipatory activity present. After entrainment, the rhythms resumed free-running from a time 0.66-3.91 hr after the onset of the last bout of induced activity. Postentrainment free-running periods were shorter than pre-entrainment values. The PRC for 2-hr pulses of induced activity in DD revealed phase advances induced in some animals between circadian time (CT) 4 and CT 11 (approximately the last half of the hamsters' rest period), and delays between CT 23 and CT 3 and between CT 17 and CT 20. The CTs for phase advances are compatible with the phase angle differences observed between rhythm and zeitgeber at the end of entrainment. Many features of the results (not all animals entraining, PRC characteristics, lack of observable anticipation to the daily stimuli, phase relationship between zeitgeber and activity rhythms) are similar to those from a previous study on social entrainment in this species (Mrosovsky, 1988). These similarities reinforce the idea that induced activity and social zeitgebers act on activity rhythms via a common mechanism.     

A comparison of light and temperature entrainment: evidence for a multioscillator circadian system

ABSTRACT. Both photoperiodic and thermoperiodic cycles synchronize circadian calling activity of male crickets, Teleogryllus commodus (Walker). Because the phase relationships between these cycles and the entrained singing activity are clearly distinguishable, we studied the relative power of these factors in affecting the circadian clock. Upon resumption of constant conditions after exposure to a thermoperiodic cycle, singing activity sometimes splits into two daily bouts, each with a distinctive period. This observation, together with results derived from simultaneous fluctuation of both factors in and out of phase, suggests that the system integrating environmental input is composed of multiple oscillators.