Temperature effects on circadian clocks

Periodic temperature changes represent one of the most effective entraining (Zeitgeber) signals for circadian clocks in many organisms. Different constant temperatures affect the circadian amplitude and ultimately the expression of circadian clocks, while the circadian period length (tau) remains approximately constant (temperature compensation). Experimental results and theoretical models are presented that may serve to explain these effects. After introducing the physico-chemical basis of temperature on enzyme-catalyzed and physiological reactions, and after describing mechanisms for temperature adaptation of physiological reactions to different thermal environments, general effects of temperature on chemical and biological oscillators are described. Kinetic models for circadian clocks and temperature compensation are presented and compared with experimental results. Special attention is given to the question how constant but different temperature levels affect clock amplitude, period length and phase. Influences of single and periodic temperature variations (steps or pulses) on circadian clocks are presented together with models which may explain the resulting phase response curves and entrainment patterns. Because temperature compensation is only one aspect of a general homeostatic mechanism that keeps the circadian period rather constant, the influence of other environmental variables and their relationship to temperature are discussed.     

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.     

Modeling circadian clocks: Roles,advantages, and limitations

Circadian rhythms are endogenous oscillations characterized by a period of about 24h. They constitute the biological rhythms with the longest period known to be generated at the molecular level. The abundance of genetic information and the complexity of the molecular circuitry make circadian clocks a system of choice for theoretical studies. Many mathematical models have been proposed to understand the molecular regulatory mechanisms that underly these circadian oscillations and to account for their dynamic properties (temperature compensation, entrainment by light dark cycles, phase shifts by light pulses, rhythm splitting, robustness to molecular noise, intercellular synchronization). The roles and advantages of modeling are discussed and illustrated using a variety of selected examples. This survey will lead to the proposal of an integrated view of the circadian system in which various aspects (interlocked feedback loops, inter-cellular coupling, and stochasticity) should be considered together to understand the design and the dynamics of circadian clocks. Some limitations of these models are commented and challenges for the future identified.     

Period responses to Zeitgeber signals stabilize circadian clocks during entrainment

Circadian clocks with characteristic period (τ) can be entrained to light/dark (LD) cycles by means of (i) phase shifts which are due to D/L “dawn” and/or L/D “dusk” transitions, (ii) period changes associated with long-term light exposure, or (iii) by combinations of the above possibilities. Based on stability analysis of a model circadian clock it was predicted that nocturnal burrowing mammals would benefit less from period responses than their diurnal counterparts. The model further predicted that maximal stability of circadian clock is reached when the clock slightly changes both its phase and period in response to light stimuli. Analyses of empirical phase response curve (PRC) and period response curve (τRC) of some diurnal and nocturnal mammals revealed that PRCs of both diurnal and nocturnal mammals have similar waveform while τRCs of nocturnal mammals are of smaller amplitude than those of diurnal mammals. The shape of the τRC also changes with age and with increasing strength of light stimuli. During erratic fluctuations in light intensity under different weather conditions, the stability of phase of entrainment of circadian clocks appears to be achieved by an interplay between phase and period responses and the strength of light stimuli.     

Calculating activation energies for temperature compensation in circadian rhythms

Many biological species possess a circadian clock, which helps them anticipate daily variations in the environment. In the absence of external stimuli, the rhythm persists autonomously with a period of approximately 24 h. However, single pulses of light, nutrients, chemicals or temperature can shift the clock phase. In the case of light- and temperature-cycles, this allows entrainment of the clock to cycles of exactly 24 h. Circadian clocks have the remarkable property of temperature compensation, that is, the period of the circadian rhythm remains relatively constant within a physiological range of temperatures. For several organisms, temperature-regulated processes within the circadian clock have been identified in recent years. However, how these processes contribute to temperature compensation is not fully understood. Here, we theoretically investigate temperature compensation in general oscillatory systems. It is known that every oscillator can be locally temperature compensated around a reference temperature, if reactions are appropriately balanced. A balancing is always possible if the control coefficient with respect to the oscillation period of at least one reaction in the oscillator network is positive. However, for global temperature compensation, the whole physiological temperature range is relevant. Here, we use an approach which leads to an optimization problem subject to the local balancing principle. We use this approach to analyse different circadian clock models proposed in the literature and calculate activation energies that lead to temperature compensation.     

Early- and late-emerging Drosophila melanogaster fruit flies differ in their sensitivity to light during morning and evening

The authors derived early and late populations of fruit flies showing increased incidence of emergence during morning or evening hours by imposing selection for timing of emergence under 12:12 h light/dark (LD) cycles. From previous studies, it was clear that the increased incidence of adult emergence during morning and evening hours in early and late populations was a result of evolution of divergent and characteristic emergence waveforms in these populations. Such characteristic waveforms are henceforth referred to as "evolved emergence waveforms" (EEWs). The early and late populations also evolved different circadian clocks, which is evident from the divergence in their clock period (τ) and photic phase response curve (PRC). Although correlation between emergence waveforms and clock properties suggests functional significance of circadian clocks, τ and PRCs do not satisfactorily explain the early and late emergence phenotypes. In order to understand the functional significance of the PRC for early and late emergence phenotypes, the authors investigated whether circadian clocks of these flies exhibit any difference in photosensitivity under entrained conditions. Such differences would suggest that the light requirement for circadian entrainment of the emergence rhythm in early and late populations is different. To test this, they examined if early and late flies differ in their light utilization behavior, first by assaying their emergence rhythm under complete photoperiod and then in three different skeleton photoperiods. The results showed that early and late populations require different durations of light during the morning and evening to achieve their EEWs, suggesting that for the circadian entrainment of the emergence rhythm, early and late flies utilize light from different parts of the day.     

History dependence of circadian pacemaker period in the cockroach

The freerunning period of circadian clocks in constant environmental conditions can be history-dependent, and one effect of entrainment of circadian clocks by light cycles is to cause long-lasting changes in the freerunning period that are termed after-effects. We have studied after-effects of entrainment to 22-h (LD 8:14) and 26-h (LD 8:18) light cycles in the cockroach Leucophaea maderae. We find that in cockroaches, the freerunning period of the locomotor activity rhythm, measured in constant darkness (DD), is 0.7h less after entrainment to T22 than after entrainment to T26. Induction of after-effects requires several days (>1 week) entrainment, and after induction, after-effects will persist in DD for over 40 days. Further after-effects are unaltered by phase-resetting of up to 12h caused by exposure to low-temperature pulses (7 degrees C) of 24 or 48h duration. After-effects also persist through re-entrainment for 2 weeks to 24-h light cycles. These results indicate that after-effects arise from stable changes in the circadian system that are likely to be independent of phase relationships among oscillators within the circadian system. We also show that entrainment to temperature cycles does not generate after-effects indicating that light may be unique in its ability to generate lasting changes in pacemaker period.     

Cyclic presence and absence of conspecifics alters circadian clock phase but does not entrain the locomotor activity rhythm of the fruit fly Drosophila melanogaster

Circadian clocks use a wide range of environmental cues, including cycles of light, temperature, food, and social interactions, to fine-tune rhythms in behavior and physiology. Although social cues have been shown to influence circadian clocks of a variety of organisms including the fruit fly Drosophila melanogaster, their mechanism of action is still unclear. Here, the authors report the results of their study aimed at investigating if daily cycles of presence and absence (PA) of conspecific male visitors are able to entrain the circadian locomotor activity rhythm of male hosts living under constant darkness (DD). The results suggest that PA cycles may not be able to entrain circadian locomotor activity rhythms of Drosophila. The outcome does not change when male hosts are presented with female visitors, suggesting that PA cycles of either sex may not be effective in bringing about stable entrainment of circadian clocks in D. melanogaster. However, in hosts whose clock phase has already been set by light/dark (LD) cycles, daily PA cycles of visitors can cause measurable change in the phase of subsequent free-running rhythms, provided that their circadian clocks are labile. Thus, the findings of this study suggest that D. melanogaster males may not be using cyclic social cues as their primary zeitgeber (time cue) for entrainment of circadian clocks, although social cues are capable of altering the phase of their circadian rhythms.     

Modeling temperature entrainment of circadian clocks using the Arrhenius equation and a reconstructed model from Chlamydomonas reinhardtii

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.     

A phase response curve for circannual rhythm in the varied carpet beetle <Emphasis Type="Italic">Anthrenus verbasci</Emphasis>

We know that entrainment, a stable phase relationship with an environmental cycle, must be established for a biological clock to function properly. Phase response curves (PRCs), which are plots of phase shifts that result as a function of the phase of a stimulus, have been created to examine the mode of entrainment. In circadian rhythms, single-light pulse PRCs have been obtained by giving a light pulse to various phases of a free-running rhythm under continuous darkness. This successfully explains the entrainment to light-dark cycles. Some organisms show circannual rhythms. In some of these, changes in photoperiod entrain the circannual rhythms. However, no single-pulse PRCs have been created. Here we show the PRC to a long-day pulse superimposed for 4 weeks over constant short days in the circannual pupation rhythm in the varied carpet beetle Anthrenus verbasci. Because the shape of that PRC closely resembles that of the Type 0 PRC with large phase shifts in circadian rhythms, we suggest that an oscillator having a common feature in the phase response with the circadian clock, produces a circannual rhythm.     

Human Chronotypes from a Theoretical Perspective

The endogenous circadian timing system has evolved to synchronize an organism to periodically recurring environmental conditions. Those external time cues are called Zeitgebers. When entrained by a Zeitgeber, the intrinsic oscillator adopts a fixed phase relation to the Zeitgeber. Here, we systematically study how the phase of entrainment depends on clock and Zeitgeber properties. We combine numerical simulations of amplitude-phase models with predictions from analytically tractable models. In this way we derive relations between the phase of entrainment to the mismatch between the endogenous and Zeitgeber period, the Zeitgeber strength, and the range of entrainment. A core result is the “180° rule” asserting that the phase varies over a range of about 180° within the entrainment range. The 180° rule implies that clocks with a narrow entrainment range (“strong oscillators”) exhibit quite flexible entrainment phases. We argue that this high sensitivity of the entrainment phase contributes to the wide range of human chronotypes.     

Data-driven modelling captures dynamics of the circadian clock of Neurospora crassa

Eukaryotic circadian clocks are based on self-sustaining, cell-autonomous oscillatory feedback loops that can synchronize with the environment via recurrent stimuli (zeitgebers) such as light. The components of biological clocks and their network interactions are becoming increasingly known, calling for a quantitative understanding of their role for clock function. However, the development of data-driven mathematical clock models has remained limited by the lack of sufficiently accurate data. Here we present a comprehensive model of the circadian clock of Neurospora crassa that describe free-running oscillations in constant darkness and entrainment in light-dark cycles. To parameterize the model, we measured high-resolution time courses of luciferase reporters of morning and evening specific clock genes in WT and a mutant strain. Fitting the model to such comprehensive data allowed estimating parameters governing circadian phase, period length and amplitude, and the response of genes to light cues. Our model suggests that functional maturation of the core clock protein Frequency causes a delay in negative feedback that is critical for generating circadian rhythms.     

A temperature-compensated model for circadian rhythms that can be entrained by temperature cycles

From the viewpoint that reaction rates will change with temperature, we present a general method to build circadian clock models that generate circadian oscillations with almost constant period under different constant ambient temperature, and propose an algorithm estimating the parameter condition for compensated period against the change of temperature based on the PER single-feedback loop model of Goldbeter [1995. A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. London Ser. B 261, 319-324] for Drosophila. We show that the model with derived parameters can realize the temperature compensation over a wide range of temperature, and simultaneously can realize the entrainment to temperature cycles.     

Effect of Light Intensity on the Phase and Period Response Curves in the Nocturnal Field Mouse Mus booduga

The effect of light intensity on the phase response curve (PRC) and the period response curve (τRC) of the nocturnal field mouse Mus booduga was studied. PRCs and τRCs were constructed by exposing animals free-running in constant darkness (DD), to fluorescent light pulses (LPs) of 100 lux and 1000 lux intensities for 15min duration. The waveform of the PRCs and τRCs evoked by high light intensity (1000 lux) stimuli was significantly different compared to those constructed using low light intensity (100 lux). Moreover, a weak but significant correlation was observed between phase shifts and period changes when light stimuli of 1000 lux intensity were used; however, the phase shifts and period changes in the 100 lux PRC and τRC were not correlated. This suggests that the intensity of light stimuli affects both phase and period responses in the locomotor activity rhythm of the nocturnal field mouse M. booduga. These results indicate that complex mechanisms are involved in entrainment of circadian clocks, even in nocturnal rodents, in which PRC, τRC, and dose responses play a significant role.     

Entrainment of Spontaneously Hypertensive Rat Fibroblasts by Temperature Cycles

The functional state of the circadian system of spontaneously hypertensive rats (SHR) differs in several characteristics from the functional state of normotensive Wistar rats. Some of these changes might be due to the compromised ability of the central pacemaker to entrain the peripheral clocks. Daily body temperature cycles represent one of the important cues responsible for the integrity of the circadian system, because these cycles are driven by the central pacemaker and are able to entrain the peripheral clocks. This study tested the hypothesis that the aberrant peripheral clock entrainment of SHR results from a compromised peripheral clock sensitivity to the daily temperature cycle resetting. Using cultured Wistar rat and SHR fibroblasts transfected with the circadian luminescence reporter Bmal1-dLuc, we demonstrated that two consecutive square-wave temperature cycles with amplitudes of 2.5°C are necessary and sufficient to restart the dampened oscillations and entrain the circadian clocks in both Wistar rat and SHR fibroblasts. We also generated a phase response curve to temperature cycles for fibroblasts of both rat strains. Although some of the data suggested a slight resistance of SHR fibroblasts to temperature entrainment, we concluded that the overall effect it too weak to be responsible for the differences between the SHR and Wistar in vivo circadian phenotype.     

Cyclic Presence and Absence of Conspecifics Alters Circadian Clock Phase But Does Not Entrain the Locomotor Activity Rhythm of the Fruit Fly Drosophila melanogaster

Circadian clocks use a wide range of environmental cues, including cycles of light, temperature, food, and social interactions, to fine-tune rhythms in behavior and physiology. Although social cues have been shown to influence circadian clocks of a variety of organisms including the fruit fly Drosophila melanogaster, their mechanism of action is still unclear. Here, the authors report the results of their study aimed at investigating if daily cycles of presence and absence (PA) of conspecific male visitors are able to entrain the circadian locomotor activity rhythm of male hosts living under constant darkness (DD). The results suggest that PA cycles may not be able to entrain circadian locomotor activity rhythms of Drosophila. The outcome does not change when male hosts are presented with female visitors, suggesting that PA cycles of either sex may not be effective in bringing about stable entrainment of circadian clocks in D. melanogaster. However, in hosts whose clock phase has already been set by light/dark (LD) cycles, daily PA cycles of visitors can cause measurable change in the phase of subsequent free-running rhythms, provided that their circadian clocks are labile. Thus, the findings of this study suggest that D. melanogaster males may not be using cyclic social cues as their primary zeitgeber (time cue) for entrainment of circadian clocks, although social cues are capable of altering the phase of their circadian rhythms. (Author correspondence: vsharma@jncasr.ac.in, vksharmas@gmail.com)     

Photic resetting and entrainment in CLOCK-deficient mice

Mice lacking the CLOCK protein have a relatively subtle circadian phenotype, including a slightly shorter period in constant darkness, differences in phase resetting after 4-hour light pulses in the early and late night, and a variably advanced phase angle of entrainment in a light-dark (LD) cycle. The present series of experiments was conducted to more fully characterize the circadian phenotype of Clock(-/-) mice under various lighting conditions. A phase-response curve (PRC) to 4-hour light pulses in free-running mice was conducted; the results confirm that Clock(-/-) mice exhibit very large phase advances after 4-hour light pulses in the late subjective night but have relatively normal responses to light at other phases. The abnormal shape of the PRC to light may explain the tendency of CLOCK-deficient mice to begin activity before lights-out when housed in a 12-hour light:12-hour dark lighting schedule. To assess this relationship further, Clock(-/-) and wild-type control mice were entrained to skeleton lighting cycles (1L:23D and 1L:10D:1L:12D). Comparing entrainment under the 2 types of skeleton photoperiods revealed that exposure to 1-hour light in the morning leads to a phase advance of activity onset (expressed the following afternoon) in Clock(-/-) mice but not in the controls. Constant light typically causes an intensity-dependent increase in circadian period in mice, but this did not occur in CLOCK-deficient mice. The failure of Clock(-/-) mice to respond to the period-lengthening effect of constant light likely results from the increased functional impact of light falling in the phase advance zone of the PRC. Collectively, these experiments reveal that alterations in the response of CLOCK-deficient mice to light in several paradigms are likely due to an imbalance in the shape of the PRC to light.