Modeling the Behavior of Coupled Cellular Circadian Oscillators in the Suprachiasmatic Nucleus

Light entrainment of the SCN circadian clock and implications for personalized alterations of corticosterone rhythms in shift work and jet lag

The suprachiasmatic nucleus (SCN) functions as the central pacemaker aligning physiological and behavioral oscillations to day/night (activity/inactivity) transitions. The light signal entrains the molecular clock of the photo-sensitive ventrolateral (VL) core of the SCN which in turn entrains the dorsomedial (DM) shell via the neurotransmitter vasoactive intestinal polypeptide (VIP). The shell converts the VIP rhythmic signals to circadian oscillations of arginine vasopressin (AVP), which eventually act as a neurotransmitter signal entraining the hypothalamic–pituitary–adrenal (HPA) axis, leading to robust circadian secretion of glucocorticoids. In this work, we discuss a semi-mechanistic mathematical model that reflects the essential hierarchical structure of the photic signal transduction from the SCN to the HPA axis. By incorporating the interactions across the core, the shell, and the HPA axis, we investigate how these coupled systems synchronize leading to robust circadian oscillations. Our model predicts the existence of personalized synchronization strategies that enable the maintenance of homeostatic rhythms while allowing for differential responses to transient and permanent light schedule changes. We simulated different behavioral situations leading to perturbed rhythmicity, performed a detailed computational analysis of the dynamic response of the system under varying light schedules, and determined that (1) significant interindividual diversity and flexibility characterize adaptation to varying light schedules; (2) an individual’s tolerances to jet lag and alternating shift work are positively correlated, while the tolerances to jet lag and transient shift work are negatively correlated, which indicates trade-offs in an individual’s ability to maintain physiological rhythmicity; (3) weak light sensitivity leads to the reduction of circadian flexibility, implying that light therapy can be a potential approach to address shift work and jet lag related disorders. Finally, we developed a map of the impact of the synchronization within the SCN and between the SCN and the HPA axis as it relates to the emergence of circadian flexibility.

Output from VIP cells of the mammalian central clock regulates daily physiological rhythms

The suprachiasmatic nucleus (SCN) circadian clock is critical for optimising daily cycles in mammalian physiology and behaviour. The roles of the various SCN cell types in communicating timing information to downstream physiological systems remain incompletely understood, however. In particular, while vasoactive intestinal polypeptide (VIP) signalling is essential for SCN function and whole animal circadian rhythmicity, the specific contributions of VIP cell output to physiological control remains uncertain. Here we reveal a key role for SCN VIP cells in central clock output. Using multielectrode recording and optogenetic manipulations, we show that VIP neurons provide coordinated daily waves of GABAergic input to target cells across the paraventricular hypothalamus and ventral thalamus, supressing their activity during the mid to late day. Using chemogenetic manipulation, we further demonstrate specific roles for this circuitry in the daily control of heart rate and corticosterone secretion, collectively establishing SCN VIP cells as influential regulators of physiological timing.

VIP-expressing neurons play a central role in circadian timekeeping within the mammalian central clock. Here the authors use opto- and chemogenetic approaches to show that VIP neuronal activity regulates rhythmic activity in downstream hypothalamic target neurons and their physiological functions.

Aging transition in systems of oscillators with global distributed-delay coupling

We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.

Deconstructing Circadian Rhythmicity with Models and Manipulations

A master brain clock, localized to the hypothalamic suprachiasmatic nucleus (SCN), coordinates daily rhythms of physiology and behavior. Within the SCN, interconnected individual neurons are oscillators that, as an ensemble, function to send a coherent timing signal to the brain and body. However, individually, these neurons display different amplitudes, periods, and phases of oscillation. The dynamic properties of the SCN have been characterized over several spatial levels of analysis, from proteins to cells to tissues, and over several temporal ranges, from milliseconds to weeks. Modeling tools guide empirical research in this complex and multiscale spatiotemporal environment. Given that the SCN is a prototypical example of oscillating neural systems, principles of its organization hold promise as general prototypes of rhythms in other frequencies.

Coupling-induced synchronization in multicellular circadian oscillators of mammals

In mammals, circadian rhythms are controlled by the neurons located in the suprachiasmatic nucleus (SCN) of the hypothalamus. Each neuron in the SCN contains an autonomous molecular clock. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light-dark cycle in neuronal synchronization. However, in natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. In this paper, we use a model of nonidentical, globally coupled cellular clocks considered as Goodwin oscillators. We mainly study the synchronization induced by coupling from an analytical way. Our results show that the role of the coupling is to enhance the synchronization to the external forcing. The conclusion of this paper can help us better understand the mechanism of circadian rhythm.

The role of the circadian system in fractal neurophysiological control

Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation.

SYNCHRONIZATION OF CLOCKS COUPLED BY NEUROTRANSMITTER IN THE SCN

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. Each cell in the SCN contains an autonomous molecular clock, and the SCN is composed of multiple single-cell circadian oscillators. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. In natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. Though there have been a lot of works about the synchronization of circadian oscillators coupled by neurotransmitter, most of the works are based on numerical simulation with little theoretical analysis. In this paper, from the theoretical analysis, we prove that the clocks can be synchronized by the neurotransmitter with mathematical knowledge. Our results also show that the coupling among neurons can synchronize circadian oscillators but the synchronized oscillators are not with period of 24 h, which indicates that environmental cues are necessary to entrain oscillators with period of 24 h. This work can offer theoretical basis to study circadian synchronization in a numerical or experimental way.

The itty-bitty time machine genetics of the cyanobacterial circadian clock

The cyanobacterium Synechococcus elongatus PCC 7942 has been used as the prokaryotic model system for the study of circadian rhythms for the past two decades. Its genetic malleability has been instrumental in the discovery of key input, oscillator, and output components and has also provided monumental insights into the mechanism by which proteins function to maintain and dictate 24-h time. In addition, basic research into the prokaryotic system has led to interesting advances in eukaryotic circadian mechanisms. Undoubtedly, continued genetic and mutational analyses of this single-celled cyanobacterium will aid in teasing out the intricacies of the Kai-based circadian clock to advance our understanding of this system as well as other more "complex" systems.

Emergence of noise-induced oscillations in the central circadian pacemaker

Bmal1 is an essential transcriptional activator within the mammalian circadian clock. We report here that the suprachiasmatic nucleus (SCN) of Bmal1-null mutant mice, unexpectedly, generates stochastic oscillations with periods that overlap the circadian range. Dissociated SCN neurons expressed fluctuating levels of PER2 detected by bioluminescence imaging but could not generate circadian oscillations intrinsically. Inhibition of intercellular communication or cyclic-AMP signaling in SCN slices, which provide a positive feed-forward signal to drive the intracellular negative feedback loop, abolished the stochastic oscillations. Propagation of this feed-forward signal between SCN neurons then promotes quasi-circadian oscillations that arise as an emergent property of the SCN network. Experimental analysis and mathematical modeling argue that both intercellular coupling and molecular noise are required for the stochastic rhythms, providing a novel biological example of noise-induced oscillations. The emergence of stochastic circadian oscillations from the SCN network in the absence of cell-autonomous circadian oscillatory function highlights a previously unrecognized level of circadian organization.

Population robustness arising from cellular heterogeneity

Heterogeneity between individual cells is a common feature of dynamic cellular processes, including signaling, transcription, and cell fate; yet the overall tissue level physiological phenotype needs to be carefully controlled to avoid fluctuations. Here we show that in the NF-kappaB signaling system, the precise timing of a dual-delayed negative feedback motif [involving stochastic transcription of inhibitor kappaB (IkappaB)-alpha and -epsilon] is optimized to induce heterogeneous timing of NF-kappaB oscillations between individual cells. We suggest that this dual-delayed negative feedback motif enables NF-kappaB signaling to generate robust single cell oscillations by reducing sensitivity to key parameter perturbations. Simultaneously, enhanced cell heterogeneity may represent a mechanism that controls the overall coordination and stability of cell population responses by decreasing temporal fluctuations of paracrine signaling. It has often been thought that dynamic biological systems may have evolved to maximize robustness through cell-to-cell coordination and homogeneity. Our analyses suggest in contrast, that this cellular variation might be advantageous and subject to evolutionary selection. Alternative types of therapy could perhaps be designed to modulate this cellular heterogeneity.

Phase organization of circadian oscillators in extended gate and oscillator models

The suprachiasmatic nuclei (SCN) control daily oscillations in physiology and behavior. The gate-oscillator model captures functional heterogeneity in SCN and has been successful in reproducing many features of SCN. This paper investigates the mechanism of phase organization in the gate-oscillator model and finds that only stable fixed points of the phase transition function are essential to phase organization. This obvious finding forms the basis for understanding the complex phase distribution in the gate-oscillator scheme. Extending the model with a dead zone of the phase transition function and the propagation delay of the gate signal which may represent the spatial structure of SCN, the author discusses how some features of experimentally reported phase distribution, such as the existence of anti-phase neurons and fixed phase difference between neurons, could be understood in the framework of the gate-oscillator model. The extended model shows clearly the way in which the interplay between the single-cell property and the property of the network organization influence the phase distribution of SCN neurons.

Basis of robustness and resilience in the suprachiasmatic nucleus: individual neurons form nodes in circuits that cycle daily

How the cellular elements of the SCN are synchronized to each other is not well understood. We explore circadian oscillations manifest at the level of the cell, the tissue, and the whole animal to better understand intra-SCN synchrony and master clock function of the nucleus. At each level of analysis, responses to variations in operating environment (robustness), and following damage to components of the system (resilience), provide insight into the mechanisms whereby the SCN orchestrates circadian timing. Tissue level rhythmicity reveals circuits associated with an orderly spatiotemporal daily pattern of activity that is not predictable from their cellular elements. Specifically, in stable state, some SCN regions express low amplitude or undetectable rhythms in clock gene expression while others produce high amplitude oscillations. Within the SCN, clock gene expression follows a spatially ordered, repeated pattern of activation and inactivation. This pattern of activation is plastic and subserves responses to changes in external and internal conditions. Just as daily rhythms at the cellular level depend on sequential expression and interaction of clock genes, so too do rhythms at the SCN tissue level depend on sequential activation of local nodes. We hypothesize that individual neurons are organized into nodes that are themselves sequentially activated across the volume of the SCN in a cycle that repeats on a daily basis. We further propose that robustness is expressed in the ability of the SCN to sustain rhythmicity over a wide range of internal and external conditions, and that this reflects plasticity of the underlying nodes and circuits. Resilience is expressed in the ability of SCN cells to oscillate and to sustain activity-related rhythms at the behavioral level. Importantly, other aspects of pacemaker function remain to be examined.

Light-dark cycle memory in the mammalian suprachiasmatic nucleus

The mammalian circadian oscillator, or suprachiasmatic nucleus (SCN), contains several thousand clock neurons in its ventrolateral division, many of which are spontaneous oscillators with period lengths that range from 22 to 28 h. In complete darkness, this network synchronizes through the exchange of action potentials that release vasoactive intestinal polypeptide, striking a compromise, free-running period close to 24 h long. We entrained Siberian hamsters to various light-dark cycles and then tracked their activity into constant darkness to show that they retain a memory of the previous light-dark cycle before returning to their own free-running period. Employing Leloup-Goldbeter mammalian clock neurons we model the ventrolateral SCN network and show that light acting weakly upon a strongly rhythmic vasoactive intestinal polypeptide oscillation can explain the observed light-dark cycle memory. In addition, light is known to initiate a mitogen-activated protein kinase signaling cascade that induces transcription of both per and mkp1 phosphatase. We show that the ensuing phosphatase-kinase interaction can account for the dead zone in the mammalian phase response curve and hypothesize that the SCN behaves like a lock-in amplifier to entrain to the light edges of the circadian day.

Clustering predicted by an electrophysiological model of the suprachiasmatic nucleus

Despite the wealth of experimental data on the electrophysiology of individual neurons in the suprachiasmatic nuclei (SCN), the neural code of the SCN remains largely unknown. To predict the electrical activity of the SCN, the authors simulated networks of 10,000 GABAergic SCN neurons using a detailed model of the ionic currents within SCN neurons. Their goal was to understand how neuronal firing, which occurs on a time scale faster than a second, can encode a set phase of the circadian (24-h) cycle. The authors studied the effects of key network properties including: 1) the synaptic density within the SCN, 2) the magnitude of postsynaptic currents, 3) the heterogeneity of circadian phase in the neuronal population, 4) the degree of synaptic noise, and 5) the balance between excitation and inhibition. Their main result was that under a wide variety of conditions, the SCN network spontaneously organized into (typically 3) groups of synchronously firing neurons. They showed that this type of clustering can lead to the silencing of neurons whose intracellular clocks are out of circadian phase with the rest of the population. Their results provide clues to how the SCN may generate a coherent electrical output signal at the tissue level to time rhythms throughout the body.

Influence of arousal threshold and depth of sleep on respiratory stability in man: analysis using a mathematical model

We examined the effect of arousals (shifts from sleep to wakefulness) on breathing during sleep using a mathematical model. The model consisted of a description of the fluid dynamics and mechanical properties of the upper airways and lungs, as well as a controller sensitive to arterial and brain changes in CO(2), changes in arterial oxygen, and a neural input, alertness. The body was divided into multiple gas store compartments connected by the circulation. Cardiac output was constant, and cerebral blood flows were sensitive to changes in O(2) and CO(2) levels. Arousal was considered to occur instantaneously when afferent respiratory chemical and neural stimulation reached a threshold value, while sleep occurred when stimulation fell below that value. In the case of rigid and nearly incompressible upper airways, lowering arousal threshold decreased the stability of breathing and led to the occurrence of repeated apnoeas. In more compressible upper airways, to maintain stability, increasing arousal thresholds and decreasing elasticity were linked approximately linearly, until at low elastances arousal thresholds had no effect on stability. Increased controller gain promoted instability. The architecture of apnoeas during unstable sleep changed with the arousal threshold and decreases in elasticity. With rigid airways, apnoeas were central. With lower elastances, apnoeas were mixed even with higher arousal thresholds. With very low elastances and still higher arousal thresholds, sleep consisted totally of obstructed apnoeas. Cycle lengths shortened as the sleep architecture changed from mixed apnoeas to total obstruction. Deeper sleep also tended to promote instability by increasing plant gain. These instabilities could be countered by arousal threshold increases which were tied to deeper sleep or accumulated aroused time, or by decreased controller gains.

Noise-induced coherence in multicellular circadian clocks

In higher organisms, circadian rhythms are generated by a multicellular genetic clock that is entrained very efficiently to the 24-h light-dark cycle. Most studies done so far of these circadian oscillators have considered a perfectly periodic driving by light, in the form of either a square wave or a sinusoidal modulation. However, in natural conditions, organisms are subject to nonnegligible fluctuations in the light level all through the daily cycle. In this article, we investigate how the interplay between light fluctuations and intercellular coupling affects the dynamics of the collective rhythm in a large ensemble of nonidentical, globally coupled cellular clocks modeled as Goodwin oscillators. On the basis of experimental considerations, we assume an inverse dependence of the cell-cell coupling strength on the light intensity, in such a way that the larger the light intensity, the weaker the coupling. Our results show a noise-induced rhythm generation for constant light intensities at which the clock is arrhythmic in the noise-free case. Importantly, the rhythm shows a resonancelike phenomenon as a function of the noise intensity. Such improved coherence can be only observed at the level of the overt rhythm and not at the level of the individual oscillators, thus suggesting a cooperative effect of noise, coupling, and the emerging synchronization between the oscillators.

Phase shifting capacity of the circadian pacemaker determined by the SCN neuronal network organization

Background

In mammals, a major circadian pacemaker that drives daily rhythms is located in the suprachiasmatic nuclei (SCN), at the base of the hypothalamus. The SCN receive direct light input via the retino-hypothalamic tract. Light during the early night induces phase delays of circadian rhythms while during the late night it leads to phase advances. The effects of light on the circadian system are strongly dependent on the photoperiod to which animals are exposed. An explanation for this phenomenon is currently lacking.

Methodology and Principal Findings

We recorded running wheel activity in C57 mice and observed large amplitude phase shifts in short photoperiods and small shifts in long photoperiods. We investigated whether these different light responses under short and long days are expressed within the SCN by electrophysiological recordings of electrical impulse frequency in SCN slices. Application of N-methyl-D-aspartate (NMDA) induced sustained increments in electrical activity that were not significantly different in the slices from long and short photoperiods. These responses led to large phase shifts in slices from short days and small phase shifts in slices from long days. An analysis of neuronal subpopulation activity revealed that in short days the amplitude of the rhythm was larger than in long days.

Conclusions

The data indicate that the photoperiodic dependent phase responses are intrinsic to the SCN. In contrast to earlier predictions from limit cycle theory, we observed large phase shifting responses in high amplitude rhythms in slices from short days, and small shifts in low amplitude rhythms in slices from long days. We conclude that the photoperiodic dependent phase responses are determined by the SCN and propose that synchronization among SCN neurons enhances the phase shifting capacity of the circadian system.

Melatonin, consciousness, and traumatic stress

Descartes intuitively anticipated the so-called 'binding problem' of consciousness and thought that the pineal gland enables spatio-temporal integration in cognitive processing. Recent findings indicate that a major role in the process of temporal integration and binding involve neurons in suprachiasmatic nuclei, specifically targeting the pineal gland and other structures, and control the neuroendocrine rhythms. Melatonin is an endocrine output signal of the clock and provides circadian information as an endogenous synchronizer which stabilizes and reinforces circadian rhythms. This integrative process occurs at the different levels of the circadian network via gene expression in some brain regions and peripheral structures that enables integration of circadian, hormonal, and metabolic information and creating temporal order of bodily and mental experience. This specific temporal order is reflected in associative sequentiality that is necessary for cognition, behavior and all processes of memory consolidation that must preserve all information in the temporal causal order and synchrony. In this context, recent findings suggest that melatonin could be a potential regulator in the processes that contribute to memory formation, long-term potentiation, and synaptic plasticity in the hippocampus and other brain regions. There is evidence that stress disrupts normal activity and memory consolidation in the hippocampus and prefrontal cortex, and this process leads to memories that are stored without a contextual or spatiotemporal frame. These findings emphasize a specific role of melatonin in mechanisms of consciousness, memory and stress and are also consistent with reported studies that indicate melatonin alterations under stressful conditions and in mental disorders.