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.     

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.     

Two coupled neural oscillators as a model of the circadian pacemaker

Pittendrigh first found that the circadian rhythm of locomotor activity in nocturnal rodents split into two components. Hoffman then reported that the splitting phenomenon was even more reproducible in the small diurnal primate Tupaia. These “splitting” experiments and many other experiments suggest that two coupled oscillators may constitute the circadian pacemaker system. Pittendrigh proposed a phenomenological two-oscillator model. Daan and Berde developed a quantitative model assuming that the interaction between the two constituent oscillators is by instantaneous resets. Their model system can simulate several qualitative features in the experimental data. As the assumption of instantaneous resets seems to be unnatural, we study two limit cycle oscillators, which are coupled continuously to each other, as a model of the circadian pacemaker. We assume the following points, (i) One oscillator in a resting state does not affect another oscillator, (ii) Two oscillators are identical, (iii) The coupling is symmetrical. By the theory of Hopf bifurcation it is found that the general two-oscillator system has two stable periodic solutions. One is the in-phase solution where the two constituent oscillators oscillate in phase synchrony. Another is the anti-phase solution where the two oscillators oscillate 180 ° out of phase. The former corresponds to a single pattern of locomotor activity and the latter corresponds to a splitting pattern. Furthermore, we study specific two-neural oscillators, which are linearly coupled to each other. By the method of secondary bifurcation we find that the model shows simultaneous stability of the two alternative phase relationships and the hysteresis phenomena found in Tupaia. A natural period of the uncoupled constituent oscillator is longer than that of the in-phase solution but it is shorter than that of the anti-phase solution. This is in agreement with the data of Tupaia.     

TheBulla ocular circadian pacemaker

We have used intracellular recording to directly measure the effects of three experimental agents, light, elevated potassium seawater, and lowered sodium seawater on the membrane potential of the putative circadian pacemaker neurons of the Bulla eye. These agents were subsequently tested for effects on the free running period of the circadian pacemaker. We report that: 1. When applied to the eye, light and elevated potassium seawater depolarized the putative pacemaker neurons, while lowered sodium seawater hyperpolarized them. The membrane potential changes induced by these agents are sustained for at least one hour, suggesting that they produce persistent changes in the average membrane potential of the putative pacemaker neurons. 2. The amplitude of the membrane potential response to the depolarizing agents varies with the phase of the circadian cycle. Depolarizations induced by light and elevated potassium seawater are twice as large during the subjective night than they are during the subjective day. No significant difference was found in the response to lowered sodium seawater at different phases. 3. Continuous application of each of these agents caused a lengthening of the free running period of the Bulla eye. Constant light increased the period by 0.9 h, while the other depolarizing treatment (elevated potassium seawater) increased the free running period by 0.6 h. Both treatments increased the mean peak impulse frequency of treated eyes. The hyperpolarizing treatment also increased the period of the ocular pacemaker (+0.8 h), but had little effect on peak impulse frequency.(ABSTRACT TRUNCATED AT 250 WORDS)     

TheBulla ocular circadian pacemaker

In an effort to understand the cellular basis of entrainment of circadian oscillators we have studied the role of membrane potential changes in the neurons which comprise the ocular circadian pacemaker of Bulla gouldiana in mediating phase shifts of the ocular circadian rhythm. We report that: 1. Intracellular recording was used to measure directly the effects of the phase shifting agents light, serotonin, and 8-bromo-cAMP on the membrane potential of the basal retinal neurons. We found that light pulses evoke a transient depolarization followed by a smaller sustained depolarization. Application of serotonin produced a biphasic response; a transient depolarization followed by a sustained hyperpolarization. Application of a membrane permeable analog of the intracellular second messenger cAMP, 8-bromo-cAMP, elicited sustained hyperpolarization, and occasionally a weak phasic depolarization. 2. Changing the membrane potential of the basal retinal neurons directly and selectively with intracellularly injected current phase shifts the ocular circadian rhythm. Both depolarizing and hyperpolarizing current can shift the phase of the circadian oscillator. Depolarizing current mimics the phase shifting action of light, while hyperpolarizing current produces phase shifts which are transposed approximately 180 degrees in circadian time to depolarization. 3. Altering BRN membrane potential with ionic treatments, depolarizing with elevated K+ seawater or hyperpolarizing with lowered Na+ seawater, produces phase shifts similar to current injection. 4. The light-induced depolarization of the basal retinal neurons is necessary for phase shifts by light. Suppressing the light-induced depolarization with injected current inhibits light-induced phase shifts. 5. The ability of membrane potential changes to shift oscillator phase is dependent on extracellular calcium. Reducing extracellular free Ca++ from 10 mM to 1.3 X 10(-7) M inhibits light-induced phase shifts without blocking the photic response of the BRNs. The results indicate that changes in the membrane potential of the pacemaker neurons play a critical role in phase shifting the circadian rhythm, and imply that a voltage-dependent and calcium-dependent process, possibly Ca++ influx, shifts oscillator phase in response to light.     

Electrophysiology of the circadian pacemaker in mammals

The neurons of the mammalian suprachiasmatic nuclei (SCN) control circadian rhythms in molecular, physiological, endocrine, and behavioral functions. In the SCN, circadian rhythms are generated at the level of individual neurons. The last decade has provided a wealth of information on the genetic basis for circadian rhythm generation. In comparison, a modest but growing number of studies have investigated how the molecular rhythm is translated into neuronal function. Neuronal attributes have been measured at the cellular and tissue level with a variety of electrophysiological techniques. We have summarized electrophysiological research on neurons that constitute the SCN in an attempt to provide a comprehensive view on the current state of the art.     

Delay model of circadian gene expression with two negative feedback loops

In this theoretical paper we propose a quantitative minimal model for circadian gene expression based on two negative feedback loops. We perform numerical simulations to analyse its dynamics and parameter sensitivities in free-running conditions, and verify the entrainability by a single periodic driver. We furthermore apply two simultaneously acting external drivers, leading to aperiodic oscillations in the case of a single-loop system. These can be turned into regular periodic oscillations by introduction of a second loop. Our studies confirm the increasing evidence that multiple feedback loops increase the robustness of regulatory systems, and stress the particular situation of systems that are close to transition from free-running oscillation to steady-state behaviour. We discuss possible molecular realisations of the featured feedback loops and suggest the application of complex patterns of external stimulation as a generally useful approach to assess the functionality of models of circadian systems.     

Dynamic response of a circadian pacemaker

The Culex circadian pacemaker's response to phase-resetting light signals was studied in the first 3 cycles of darkness following a 12h light exposure. (1) In both cycles 1 and 2 there is a clear change from type 1 to type 0 phase-resetting as the resetting signal is prologed (Fig. 2). (2) Mosquitoes in cycle 1 are about half as sensitive to phase-resetting as those in cycles 2 or 3 (the criterion being the minimum pulse duration required to produce type 0 phase-resetting) (Fig. 2). (3) Each cycle appears to have a corkscrew-shaped phaseresetting surface and a phase singularity (Figs. 4, 5, and 7). The hypothesis that the Culex pacemaker reaches a stable limit cycle within the first cycle leads to an economical explanation of the results.     

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.     

The Drosophila melanogaster circadian pacemaker circuit

As an experimental model system, the fruit fly Drosophila melanogaster has been seminal in shaping our understanding of the circadian clockwork. The wealth of genetic tools at our disposal over the past four decades has enabled discovery of the genetic and molecular bases of circadian rhythmicity. More recently, detailed investigation leading to the anatomical, neuro-chemical and electrophysiological characterization of the various neuronal subgroups that comprise the circadian machinery has revealed pathways through which these neurons come together to act as a neuronal circuit. Thus the D. melanogaster circadian pacemaker circuit presents a relatively simple and attractive model for the study of neuronal circuits and their functions.     

Seasonal encoding by the circadian pacemaker of the SCN

The circadian pacemaker of the suprachiasmatic nucleus (SCN) functions as a seasonal clock through its ability to encode day length [1-6]. To investigate the mechanism by which SCN neurons code for day length, we housed mice under long (LD 16:8) and short (LD 8:16) photoperiods. Electrophysiological recordings of multiunit activity (MUA) in the SCN of freely moving mice revealed broad activity profiles in long days and compressed activity profiles in short days. The patterns remained consistent after release of the mice in constant darkness. Recordings of MUA in acutely prepared hypothalamic slices showed similar differences between the SCN electrical activity patterns in vitro in long and short days. In vitro recordings of neuronal subpopulations revealed that the width of the MUA activity profiles was determined by the distribution of phases of contributing units within the SCN. The subpopulation patterns displayed a significantly broader distribution in long days than in short days. Long-term recordings of single-unit activity revealed short durations of elevated activity in both short and long days (3.48 and 3.85 hr, respectively). The data indicate that coding for day length involves plasticity within SCN neuronal networks in which the phase distribution of oscillating neurons carries information on the photoperiod's duration.     

Effects of light on circadian pacemaker development

1. The effects of raising cockroaches, Leucophaea maderae, in non-24 h light cycles on circadian rhythms in adults were examined. The average period (tau) of freerunning rhythms of locomotor activity of animals exposed to LD 11:11 (T22) during post-embryonic development was significantly shorter (tau = 22.8 +/- 0.47 SD, n = 85) than that of animals raised in LD 12:12 (T24) (tau = 23.7 +/- 0.20 h, n = 142), while animals raised in LD 13:13 (T26) had significantly longer periods (tau = 24.3 +/- 0.21 h, n = 65). Animals raised in constant darkness (DD) had a significantly shorter period (tau = 23.5 +/- 0.21 h, n = 13) than siblings raised in constant light (LL) (tau = 24.0 +/- 0.15 h, n = 10). 2. The differences in tau between animals raised in T22 and T24 were found to be stable in DD for at least 7 months and could not be reversed by exposing animals to LD 12:12 or LD 6:18. 3. Animals raised in either T24 or DD and then exposed as adults to T22 exhibited average freerunning periods that were not different from animals not exposed to T22. 4. Measurement of freerunning periods at different temperatures of animals raised in T22, T24, or T26 showed that the temperature compensation of tau was not affected by the developmental light cycle. These results indicate that the lighting conditions during post-embryonic development can permanently alter the freerunning period of the circadian system in the cockroach, but do not affect its temperature compensation.     

Effects of light on circadian pacemaker development

The effects of raising cockroaches, Leucophaea maderae, in non-24-h light cycles on the response of the circadian system to light was examined. 1. Phase response curves (PRC) were measured for 6-h light pulses for animals raised in LD 11:11 (T22), LD 12:12 (T24), and LD 13:13 (T26). The delay portion of the PRC was found to be significantly reduced in T22 animals (compared to T24 animals) while the advance portion of the PRC was reduced in T26 animals. Compared to T26 animals, phase shifts were more positive at every phase for animals raised in T22. 2. When transferred from constant darkness (DD) to constant light (LL) the freerunning period lengthened significantly less for T22 animals than T24 animals, and in some cases tau in LL was actually shorter than tau in DD in T22 animals. Animals raised in LL were inactive when exposed to LL as adults, and unlike T24 animals, were consistently reset to the beginning of the subjective night (near CT 12) when transferred to DD. 3. Roaches raised in T22 would entrain to LD 6:18, but a few animals exhibited periods of relative coordination indicating that the 24-h light cycle was near the limits of entrainment. These results indicate that the circadian system's responsiveness to light, as well as its freerunning period (Barrett and Page 1989), is dependent on the lighting conditions to which the animals are exposed during development.     

Resilience of circadian pacemaker development in hamsters

Disruptions of circadian rhythms have been linked to a wide range of pathologies from sleep disorders to cancer. The extent to which disruptions of circadian rhythms during development contribute to later conditions is not known. The present study tested the hypothesis that functional properties of the central circadian pacemaker, the suprachiasmatic nucleus (SCN), are affected by abnormal entrainment during development. The SCN is specialized for the generation of robust rhythms, for direct and indirect output to physiological and behavioral systems, and for entrainment to light/dark cycles via direct retinal input. It consists of thousands of neurons and glia with distinct phenotypes and has subdivisions delineated by both anatomical and functional criteria. In rodents, SCN rhythms develop within days after SCN cells are produced and before many other aspects of differentiation, such as synaptogenesis, are complete. We demonstrated that around the time of birth, the hamster SCN in vivo can undergo repeated phase shifts by a dopamine D(1) receptor agonist (SKF-38393). For 2 days before and 2 days after birth, one group of hamsters received regular exposure to the drug at the same time of day, while another group was exposed at varying times to induce repeated phase shifts. Free-running and entrained activity rhythms were compared between the groups at different ages after weaning. Repeated phase shifts during SCN development had a significant effect on free-running period measured immediately after weaning. This effect was eliminated by subsequent entrainment to a light/dark cycle, indicating that the effect was not permanent. These and other results suggest that SCN development required for functional properties such as free-running period is resilient to perturbation.     

Characteristics of a circadian pacemaker in the suprachiasmatic nucleus

Summary The nature of the circadian rhythms of the SCN in a hypothalamic island was examined in male rats by recording multiple unit activity from the SCN for longer durations. Successful continuous recording lasted up to 35 days. Neural activity of the SCN inside the island showed free-running rhythms whose periods were slightly longer than 24 h (Figs. 2, 3, Table 1). When the retino-hypothalamic pathway was spared, re-entrainment to a displaced light and dark cycle was attained following a transition period of a few days (Fig. 4). Phases of the rhythms shifted in a phase-dependent manner in response to single light pulses interrupting constant darkness (Fig. 5 and Fig. 6). These results suggest an endogenous nature of the circadian rhythm of the SCN within the hypothalamic island. Thus, neurons or neuronal networks in the SCN may have not only an inherent ability to generate a circadian rhythm, but also an intricate machinery to regulate its phase. Simultaneous recordings from the left and right SCN showed a slight but visible discrepancy in their phases between the two rhythms in 3 out of 12 cases (Fig. 7).Abbreviations LL constant light - LD light-dark - DD constant darkness - SCN Suprachiasmatic nucleus     

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.     

Reentrainment of the circadian pacemaker through three distinct stages

Circadian rhythms are endogenously generated by a central pacemaker and are synchronized to the environmental LD cycle. The rhythms can be resynchronized, or reentrained, after a shift of the LD cycle, as in traveling across time zones. The authors have performed high-resolution mapping of the pacemaker to analyze the reentrainment process using rat pineal melatonin onset (MT(on)) and melatonin offset (MT(off)) rhythms as markers. Following LD (12:12) delays of 3, 6, and 12 h, MT(on) was phase locked immediately, whereas MT(off) shifted rapidly during the initial 1 through 3 cycles. In all animals, the MT(off) shifted beyond their expected phase positions in the new LD cycle, which resulted in a transient expansion of melatonin secretion duration for several cycles. It took MT(off) only 1, 2, or 3 cycles to complete most of the required phase shifts after 3, 6, or 12 h of the LD cycle delays, respectively. However, the final stabilization of phase relationships of both MT(on) and MT(off) required at least 6 cycles for rats experiencing a 3-h LD delay and much longer for the rest. These results reaffirmed the notion that both onset and offset phases of melatonin rhythms are important markers for the pacemaker and demonstrated that the reentrainment of the central pacemaker to a delay shift of the LD cycle is a 3-step process: an immediate phase lock of onset and a rapid delay shift of offset rhythms, overshoot of the offset, and, finally, a slow adjustment of both onset and offset phases. This study represents the 1st detailed analysis of the pacemaker behavior during reentrainment using melatonin and supports the notion that the eventual adaptation of the circadian pacemaker to a new time zone is a time-consuming process.