Glucocorticoid hormones inhibit food-induced phase-shifting of peripheral circadian oscillators.

The circadian timing system in mammals is composed of a master pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus and slave clocks in most peripheral cell types. The phase of peripheral clocks can be completely uncoupled from the SCN pacemaker by restricted feeding. Thus, feeding time, while not affecting the phase of the SCN pacemaker, is a dominant Zeitgeber for peripheral circadian oscillators. Here we show that the phase resetting in peripheral clocks of nocturnal mice is slow when feeding time is changed from night to day and rapid when switched back from day to night. Unexpectedly, the inertia in daytime feeding-induced phase resetting of circadian gene expression in liver and kidney is not an intrinsic property of peripheral oscillators, but is caused by glucocorticoid signaling. Thus, glucocorticoid hormones inhibit the uncoupling of peripheral and central circadian oscillators by altered feeding time.     

Intrinsic regulation of spatiotemporal organization within the suprachiasmatic nucleus

The mammalian pacemaker in the suprachiasmatic nucleus (SCN) contains a population of neural oscillators capable of sustaining cell-autonomous rhythms in gene expression and electrical firing. A critical question for understanding pacemaker function is how SCN oscillators are organized into a coherent tissue capable of coordinating circadian rhythms in behavior and physiology. Here we undertake a comprehensive analysis of oscillatory function across the SCN of the adult PER2::LUC mouse by developing a novel approach involving multi-position bioluminescence imaging and unbiased computational analyses. We demonstrate that there is phase heterogeneity across all three dimensions of the SCN that is intrinsically regulated and extrinsically modulated by light in a region-specific manner. By investigating the mechanistic bases of SCN phase heterogeneity, we show for the first time that phase differences are not systematically related to regional differences in period, waveform, amplitude, or brightness. Furthermore, phase differences are not related to regional differences in the expression of arginine vasopressin and vasoactive intestinal polypeptide, two key neuropeptides characterizing functionally distinct subdivisions of the SCN. The consistency of SCN spatiotemporal organization across individuals and across planes of section suggests that the precise phasing of oscillators is a robust feature of the pacemaker important for its function.     

Modeling the dual pacemaker system of the tau mutant hamster

Circadian pacemakers in many animals are compound. In rodents, a two-oscillator model of the pacemaker composed of an evening (E) and a morning (M) oscillator has been proposed based on the phenomenon of "splitting" and bimodal activity peaks. The authors describe computer simulations of the pacemaker in tau mutant hamsters viewed as a system of mutually coupled E and M oscillators. These mutant animals exhibit normal type 1 PRCs when released into DD but make a transition to a type 0 PRC when held for many weeks in DD. The two-oscillator model describes particularly well some recent behavioral experiments on these hamsters. The authors sought to determine the relationships between oscillator amplitude, period, PRC, and activity duration through computer simulations. Two complementary approaches proved useful for analyzing weakly coupled oscillator systems. The authors adopted a "distinct oscillators" view when considering the component E and M oscillators and a "system" view when considering the system as a whole. For strongly coupled systems, only the system view is appropriate. The simulations lead the authors to two primary conjectures: (1) the total amplitude of the pacemaker system in tau mutant hamsters is less than in the wild-type animals, and (2) the coupling between the unit E and M oscillators is weakened during continuous exposure of hamsters to DD. As coupling strength decreases, activity duration (alpha) increases due to a greater phase difference between E and M. At the same time, the total amplitude of the system decreases, causing an increase in observable PRC amplitudes. Reduced coupling also increases the relative autonomy of the unit oscillators. The relatively autonomous phase shifts of E and M oscillators can account for both immediate compression and expansion of activity bands in tau mutant and wild-type hamsters subjected to light pulses.     

Phase angle difference alters coupling relations of functionally distinct circadian oscillators revealed by rhythm splitting

The interactions (i.e., coupling) between multiple oscillators of a circadian system determine basic properties of the integrated pacemaker. Unfortunately, there are few experimental models to investigate the putative interactions of functionally defined oscillators comprising the mammalian circadian pacemaker. Here the authors induce in hamsters a novel circadian entrainment pattern that is characterized by the daily expression of robust wheel-running activity in each scotophase of a 24-h light:dark:light:dark cycle. The daily activity bouts are mediated by 2 circadian oscillators, here designated "daytime" and "nighttime," that have been temporally dissociated under this light regime. To assess the phase dependence of interactions between oscillatory components, the phase relationship of the 2 daily scotophases was manipulated over a 4-h range, and the timing of activity of the daytime and nighttime components under entrained and probe conditions was examined. The average phase angle of entrainment and the day-to-day variability of activity onset of each activity component depended on the phase relationship of the respective scotophases and not on whether the component occurred in the daytime or the nighttime. Short-term denial of wheel access subsequently influenced amount and duration of wheel running but not timing of its onset, suggesting that only the former measures depend on a homeostatic mechanism sensitive to the time elapsed since prior intense running. Replacement of individual photophases with darkness revealed phase attraction between oscillators that was not dependent on the phase relationship of component oscillators but differed for daytime versus nighttime activity components. Entrainment patterns shown here cannot be accounted for by only nonparametric actions of light. Instead, the phase-dependent interactions of oscillators strongly influence entrainment properties, whereas intrinsic functional differences in dissociated oscillators apparently influence their attraction in darkness. This model system may be ideal for identifying genomic and physiological factors that mediate these interactions and thus contribute importantly to system properties of the mammalian circadian clock.     

Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord

The segmental locomotor network in the lamprey spinal cord was simulated on a computer using a connectionist-type neural network. The cells of the network were identical except for their excitatory levels and their synaptic connections. The synaptic connections used were based on previous experimental work. It was demonstrated that the connectivity of the circuit is capable of generating oscillatory activity with the appropriate phase relations among the cells. Intersegmental coordination was explored by coupling two identical segmental networks using only the cells of the network. Each of the possible couplings of a bilateral pair of cells in one oscillator with a bilateral pair of cells in the other oscillator produced stable phase locking of the two oscillators. The degree of phase difference was dependent upon synaptic weight, and the operating range of synaptic weights varied among the pairs of connections. The coupling was tested using several criteria from experimental work on the lamprey spinal cord. Coupling schemes involving several pairs of connecting cells were found which 1) achieved steadystate phase locking within a single cycle, 2) exhibited constant phase differences over a wide range of cycle periods, and 3) maintained stable phase locking in spite of large differences in the intrinsic frequencies of the two oscillators. It is concluded that the synaptic connectivity plays a large role in producing oscillations in this network and that it is not necessary to postulate a separate set of coordinating neurons between oscillators in order to achieve appropriate phase coupling.     

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.     

Synaptic mechanisms in invertebrate pattern generation

Although individual neurons can be intrinsically oscillatory and can be network pacemakers, motor patterns are often generated in a more distributed manner. Synaptic connections with other neurons are important because they either modify the rhythm of the pacemaker cell or are essential for pattern generation in the first place. Computational studies of half-center oscillators have made much progress in describing how neurons make transitions between active and inactive phases in these simple networks. In addition to characterizing phase transitions, recent studies have described the synaptic mechanisms that are important for the initiation and maintenance of activity in half-center oscillators.     

Entrainment of circadian clocks in mammals by arousal and food

Circadian rhythms in mammals are regulated by a system of endogenous circadian oscillators (clock cells) in the brain and in most peripheral organs and tissues. One group of clock cells in the hypothalamic SCN (suprachiasmatic nuclei) functions as a pacemaker for co-ordinating the timing of oscillators elsewhere in the brain and body. This master clock can be reset and entrained by daily LD (light-dark) cycles and thereby also serves to interface internal with external time, ensuring an appropriate alignment of behavioural and physiological rhythms with the solar day. Two features of the mammalian circadian system provide flexibility in circadian programming to exploit temporal regularities of social stimuli or food availability. One feature is the sensitivity of the SCN pacemaker to behavioural arousal stimulated during the usual sleep period, which can reset its phase and modulate its response to LD stimuli. Neural pathways from the brainstem and thalamus mediate these effects by releasing neurochemicals that inhibit retinal inputs to the SCN clock or that alter clock-gene expression in SCN clock cells. A second feature is the sensitivity of circadian oscillators outside of the SCN to stimuli associated with food intake, which enables animals to uncouple rhythms of behaviour and physiology from LD cycles and align these with predictable daily mealtimes. The location of oscillators necessary for food-entrained behavioural rhythms is not yet certain. Persistence of these rhythms in mice with clock-gene mutations that disable the SCN pacemaker suggests diversity in the molecular basis of light- and food-entrainable clocks.     

Model of bidirectional interaction between myocardial pacemakers based on the phase response curve

As a basis for the study of sinus rhythm determination, a model is proposed of bidirectionally-coupled oscillators as a system of difference equations based on the phase response curve of sinoatrial pacemaker cells. Solutions corresponding to the one-to-one synchronization of the two pacemakers are obtained, and the relation among those solutions is examined: It is revealed that two different solutions with different cycle length coexist, and the synchronized frequency can be higher or lower than the original intrinsic frequencies of the two pacemaker cells. The experimental results of the cultured cells of cardiac pacemakers are interpreted by the analytical result of the model.     

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.     

Phase Resetting Curves Allow for Simple and Accurate Prediction of Robust N:1 Phase Locking for Strongly Coupled Neural Oscillators

Existence and stability criteria for harmonic locking modes were derived for two reciprocally pulse coupled oscillators based on their first and second order phase resetting curves. Our theoretical methods are general in the sense that no assumptions about the strength of coupling, type of synaptic coupling, and model are made. These methods were then tested using two reciprocally inhibitory Wang and Buzsáki model neurons. The existence of bands of 2:1, 3:1, 4:1, and 5:1 phase locking in the relative frequency parameter space was predicted correctly, as was the phase of the slow neuron's spike within the cycle of the fast neuron in which it occurred. For weak coupling the bands are very narrow, but strong coupling broadens the bands. The predictions of the pulse coupled method agreed with weak coupling methods in the weak coupling regime, but extended predictability into the strong coupling regime. We show that our prediction method generalizes to pairs of neural oscillators coupled through excitatory synapses, and to networks of multiple oscillatory neurons. The main limitation of the method is the central assumption that the effect of each input dies out before the next input is received.     

Exploring the dynamics of collective synchronizations in large ensembles of brain signals.

Developing methods characterizing the dynamics of synchronization in large ensemble of electromagnetic brain signals has become an important issue. In this article, we review a recently introduced method for analyzing multivariate phase synchronization in brain signals. The approach is based on the equivalence between phase locking and frequency locking in narrow band signals, which allows tracking multivariate phase synchronization in the time-frequency domain as periods of common frequency among multiple channels. The method is illustrated with simulations of multivariate phase dynamics in coupled oscillators and real multichannel electro- and magnetoencephalographic data recorded prior and during epileptic seizures. The reviewed results support the relevance of this method in the context of brain synchronization, in particular to track transient collective dynamics fluctuating in time, frequency and space.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Circadian gene expression in individual fibroblasts: cell-autonomous and self-sustained oscillators pass time to daughter cells

The mammalian circadian timing system is composed of a central pacemaker in the suprachiasmatic nucleus (SCN) of the brain and subsidiary oscillators in most peripheral cell types. While oscillators in SCN neurons are known to function in a self-sustained fashion, peripheral oscillators have been thought to damp rapidly when disconnected from the control exerted by the SCN. Using two reporter systems, we monitored circadian gene expression in NIH3T3 mouse fibroblasts in real time and in individual cells. In conjunction with mathematical modeling and cell co-culture experiments, these data demonstrated that in vitro cultured fibroblasts harbor self-sustained and cell-autonomous circadian clocks similar to those operative in SCN neurons. Circadian gene expression in fibroblasts continues during cell division, and our experiments unveiled unexpected interactions between the circadian clock and the cell division clock. Specifically, the circadian oscillator gates cytokinesis to defined time windows, and mitosis elicits phase shifts in circadian cycles.     

A phase dynamics model of human circadian rhythms

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker-driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.     

Analysis of period mRNA cycling in Drosophila head and body tissues indicates that body oscillators behave differently from head oscillators.

The period (per) gene is thought to be part of the Drosophila circadian pacemaker. The circadian fluctuations in per RNA and protein that constitute the per feedback loop appear to be required for pacemaker function, and have been measured in head neuronal tissues that are necessary for locomotor activity and eclosion rhythms. The per gene is also expressed in a number of neuronal and nonneuronal body tissues for which no known circadian phenomena have been described. To determine whether per might affect some circadian function in these body tissues, per RNA cycling was examined. These studies show that per RNA cycles in the same phase and amplitude in head and body tissues during light-dark cycles. One exception to this is the lack of per RNA cycling in the ovary, which also appears to be the only tissue in which PER protein is primarily cytoplasmic. In constant darkness, however, the amplitude of per RNA cycling dampens much more quickly in bodies than in heads. Taken together, these results indicate that circadian oscillators are present in head and body tissues in which PER protein is nuclear and that these oscillators behave differently.     

Possible modes of autorhythmic activity of a single neuron

The rhythmic impulse activity of the nerve cells is one of the characteristic phenomena often registered in the experiments on different objects. According to the nature of its origination it should be distinguished the evoked rhythmic activity from autonomic. The variants of interaction of pacemaker and membrane oscillators leading to the variety of regimes of autorhythmic activity of the neuron are discussed. The interaction of several membrane oscillators without the participation of the pacemaker autogenerator may lead to the authorhythmic reverberative (extracellular) activity.