Dynamic response of a cricadian pacemaker

The term cell assembly, first introduced by D. O. Hebb, is defined in the framework of graph theory. This definition leads to some beautiful problems concerning the number and size of cell assemblies in large graphs. Some approaches to solve these problems are presented. In particular, the graphs K_nxK_m are constructed that have n·m points, n+m-2 connections per point, and at least 2ⁿ+2^m-4 assemblies. Several new notions of connectivity in directed graphs are introduced and their relationships are investigated. The insight into these notions and their relationships will be helpful for further construction of graphs with many assemblies and/or high connectivity. The resulting graphs are not only important for the idea of cell assemblies in the context of neurodynamics, they may also find applications in the construction of communication networks and associative memories.     

Dynamic resetting of the human circadian pacemaker by intermittent bright light

In humans, experimental studies of circadian resetting typically have been limited to lengthy episodes of exposure to continuous bright light. To evaluate the time course of the human endogenous circadian pacemaker's resetting response to brief episodes of intermittent bright light, we studied 16 subjects assigned to one of two intermittent lighting conditions in which the subjects were presented with intermittent episodes of bright-light exposure at 25- or 90-min intervals. The effective duration of bright-light exposure was 31% or 63% compared with a continuous 5-h bright-light stimulus. Exposure to intermittent bright light elicited almost as great a resetting response compared with 5 h of continuous bright light. We conclude that exposure to intermittent bright light produces robust phase shifts of the endogenous circadian pacemaker. Furthermore, these results demonstrate that humans, like other species, exhibit an enhanced sensitivity to the initial minutes of bright-light exposure.     

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.     

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     

Developmental manipulation of the circadian pacemaker in the cockroach: relationship between pacemaker period and response to light

Abstract Previous research has shown that fundamental properties of the circadian pacemaker that drives the rhythm of locomotor activity in the cockroach Leucophaea maderae L. are permanently altered by exposure of animals to 22 or 26 h light cycles during post-embryonic development (Barrett & Page, 1989; Page & Barrett, 1989). The present results document differences between animals exposed to either constant darkness (DD) or constant light (LL) during postembryonic development in the free-running period, the phase shifting response to light pulses, and the response to an LL to DD transition of the adult pacemaker. In addition, the changes in pacemaker period and in the phase shifting response that result from raising animals in several different lighting conditions are shown to be strongly correlated. The data suggest there is a developmentally labile interdependence between the period of the pacemaker and its sensitivity to light.     

Delay model of the circadian pacemaker

We present a simple and realistic model of the circadian pacemaker that can be interpreted in molecular terms. The model, which consists of a single time-delay differential equation, simulates the expression of a generic clock protein that inhibits its own expression through a feedback mechanism. Despite its simplicity, this model fulfils most of the necessary characteristics of a realistic representation of natural circadian clocks: robust and stable oscillations with circadian free-running periods, typical phase response curves and entrainment to environmental zeitgebers. The present model reduces the molecular mechanism necessary to sustain stable oscillations to its bare bones, suggesting that the essential factor is the time-delayed negative feedback of the oscillating protein on its own expression.     

Internal noise enhanced oscillation in a delayed circadian pacemaker

The effect of internal noise in a delayed circadian oscillator is studied by using both chemical Langevin equations and stochastic normal form theory. It is found that internal noise can induce circadian oscillation even if the delay time τ is below the deterministic Hopf bifurcation τ_h. We use signal-to-noise ratio (SNR) to quantitatively characterize the performance of such noise induced oscillations and a threshold value of SNR is introduced to define the so-called effective oscillation. Interestingly, the τ-range for effective stochastic oscillation, denoted as Δτ_EO, shows a bell-shaped dependence on the intensity of internal noise which is inversely proportional to the system size. We have also investigated how the rates of synthesis and degradation of the clock protein influence the SNR and thus Δτ_EO. The decay rate K_d could significantly affect Δτ_EO, while varying the gene expression rate K_e has no obvious effect if K_e is not too small. Stochastic normal form analysis and numerical simulations are in good consistency with each other. This work provides us comprehensive understandings of how internal noise and time delay work cooperatively to influence the dynamics of circadian oscillations.     

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.     

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.     

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.     

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.     

Probing the circadian pacemaker of a mouse using two light pulses

In two separate sets of experiments, the phases of the locomotor activity rhythm of the nocturnal field mouse Mus booduga were probed using two light pulses (LPs). In the first set of experiments, the circadian pacemaker underlying the locomotor activity rhythm was perturbed at circadian time 14 (CT 14) using a resetting light pulse LP1 of 1000 lux intensity and 15 min duration. The phases of the resetting pacemaker were then probed at all even CTs between CT 16 and CT 14 using a PRC probing light pulse LP2 of equal strength. The "LP2 PRC" thus obtained was then compared with the single light pulse PRC in terms of the area under delay (D) and advance (A) zones of the PRCs. The time course and waveform of the two LP PRCs suggest that the LP2 PRC resembled the single LP PRC, displaced by 2 h toward the right. The LP1 PRC had smaller D compared to the single LP PRC (p = 0.007), whereas both the PRCs had A of equal magnitude (p = 0.23). This suggests that the pacemaker phase shifts rapidly after LP perturbations. In the second set of experiments, the LP1 was administered at CT 14. The phase of the pacemaker was then perturbed on day 1 (next cycle after LP1) either 2 h after activity onset (at ca. CT 14 of the transient cycle) or 8 h after activity onset (at ca. CT 20 of the transient cycle) using an LP2 of equal strength. It was observed that the steady-state phase shifts evoked by positioning an LP2, 2 h after activity onset, were positively correlated with the phase shifts observed on day 1. The steady-state phase shifts observed, when the LP2 was positioned, 8 h after activity onset, were negatively correlated with the phase shifts observed on day 1. These results suggest that the transient cycles do not mirror the state of the pacemaker oscillator.     

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.     

Genetic evidence for a neurovestibular influence on the mammalian circadian pacemaker

The mammalian circadian timing system (CTS) exerts endogenous temporal control over virtually every biochemical, physiological, and neurobiological process. Recent studies have suggested an interrelationship between the neurovestibular system, specifically the macular otoconial gravity receptors, and the CTS. To test for a functional relationship between these 2 seemingly disparate neuronal systems, the authors performed a study to evaluate the influence of the vestibular system on 3 fundamental properties of the CTS: entrainment, photic modulation, and period. The present study used a nonrecombinant mutant mouse, the head-tilt mouse (abbr. het), which lacks otoconia and hence gravity reception, to evaluate CTS function in mice lacking vestibular inputs. Circadian rhythms of body temperature (Tb) and locomotor activity (ACT) were recorded continuously by biotelemetry in het mice as well as wild-type (PWT) controls during exposure to 4 photic regimens: 12:12 LD, DD (0 micromoles s(-1) m(-2)), constant bright light (LL(B); 0.5 micromoles s(-1) m(-2)), and constant dim light (LL(D); 0.02 micromoles s(-1) m(-2)). In DD, the circadian period of the Tb and ACT rhythms was significantly longer (p < 0.001) in het than in PWT mice. In addition, the circadian period of Tb and ACT was significantly longer (p < 0.01) in LL(B) than in DD for both the het and PWT groups, although increasing ambient illuminance (i.e., DD to LL(B)) had a significantly greater (p < 0.01) period-lengthening effect in the PWT group than in the het group. The results of the present study demonstrate for the first time that the vestibular macular gravity receptors influence 2 fundamental properties of the mammalian CTS: (1) the intrinsic circadian pacemaker period and (2) the period-altering response to changes in tonic light intensity. The results of the present study thus provide the first neurobehavioral evidence for a vestibular-circadian interrelationship as well as suggest a novel mechanism underlying the signaling of activity-based nonphotic stimuli to the CTS.     

A new (and different) circadian pacemaker

Comment on: Mohawk JA, Baer ML, Menaker M. The methamphetamine-sensitive circadian oscillator does not employ canonical clock genes. Proc Natl Acad Sci U S A 2009; 106:3519-24.