Cellular construction of a circadian clock: period determination in the suprachiasmatic nuclei

Modeling of Jet Lag and Searching for an Optimal Light Treatment

The role of the hierarchical organization of the suprachiasmatic nucleus (SCN) in its functioning, jet lag, and the light treatment of jet lag remains poorly understood. Using the core-shell model, we mimic collective behavior of the core and shell populations of the SCN oscillators in transient states after rapid traveling east and west. The existence of a special region of slow dynamical states of the SCN oscillators can explain phenomena such as the east-west asymmetry of jet lag, instances when entrainment to an advance is via delay shifts, and the dynamics of jet lag recovery time. If jet lag brings the SCN state into this region, it will take a long time to leave it and restore synchronization among oscillators. We show that the population of oscillators in the core responds quickly to a rapid phase shift of the light-dark cycle, in contrast to the shell, which responds slowly. A slow recovery of the synchronization among the shell oscillators in transient states may strongly affect reentrainment in peripheral tissues and behavioral rhythms. We discuss the relationship between molecular, electrical, and behavioral rhythms. We also describe how light pulses affect the SCN and analyze the efficiency of the light treatment in facilitating the adaptation of the SCN to a new time zone. Light pulses of a moderate duration and intensity reduce the recovery time after traveling east, but not west. However, long duration and high intensity of light pulses are more detrimental than beneficial for speeding up reentrainment. The results of the core-shell model are compared with experimental data and other biologically motivated models of the SCN.

A mathematical model of melatonin synthesis and interactions with the circadian clock

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.

Ticking Brain: Circadian Rhythm as a New Target for Cerebroprotection

Circadian rhythm is a master process observed in nearly every type of cell throughout the body, and it macroscopically regulates daily physiology. Recent clinical trials have revealed the effects of circadian variation on the incidence, pathophysiological processes, and prognosis of acute ischemic stroke. Furthermore, core clock genes, the cell-autonomous pacemakers of the circadian rhythm, affect the neurovascular unit-composing cells in a nonparallel manner after the same pathophysiological processes of ischemia/reperfusion. In this review, we discuss the influence of circadian rhythms and clock genes on each type of neurovascular unit cell in the pathophysiological processes of acute ischemic stroke.

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacemaker yield an internal representation of season. Output pathways of the circadian clock regulate photoperiodic responses such as flowering time in plants or hibernation in mammals. Here, we review the concepts of seasonal entrainment and photoperiodic encoding. We introduce conceptual phase oscillator models as their high level of abstraction, but, yet, intuitive interpretation of underlying parameters allows for a straightforward analysis of principles that determine entrainment characteristics. Results from this class of models are related and discussed in the context of more complex conceptual amplitude-phase oscillators as well as contextual molecular models that take into account organism, tissue, and cell-type-specific details.

Formation of recurring transient Ca2+-based intercellular communities during Drosophila hematopoiesis

Tissue development occurs through a complex interplay between many individual cells. Yet, the fundamental question of how collective tissue behavior emerges from heterogeneous and noisy information processing and transfer at the single-cell level remains unknown. Here, we reveal that tissue scale signaling regulation can arise from local gap-junction mediated cell-cell signaling through the spatiotemporal establishment of an intermediate-scale of transient multicellular communication communities over the course of tissue development. We demonstrated this intermediate scale of emergent signaling using Ca2+ signaling in the intact, ex vivo cultured, live developing Drosophila hematopoietic organ, the lymph gland. Recurrent activation of these transient signaling communities defined self-organized signaling "hotspots" that gradually formed over the course of larva development. These hotspots receive and transmit information to facilitate repetitive interactions with nonhotspot neighbors. Overall, this work bridges the scales between single-cell and emergent group behavior providing key mechanistic insight into how cells establish tissue-scale communication networks.

The Suprachiasmatic Nucleus at 50: Looking Back, Then Looking Forward

It has been 50 years since the suprachiasmatic nucleus (SCN) was first identified as the central circadian clock and 25 years since the last overview of developments in the field was published in the Journal of Biological Rhythms. Here, we explore new mechanisms and concepts that have emerged in the subsequent 25 years. Since 1997, methodological developments, such as luminescent and fluorescent reporter techniques, have revealed intricate relationships between cellular and network-level mechanisms. In particular, specific neuropeptides such as arginine vasopressin, vasoactive intestinal peptide, and gastrin-releasing peptide have been identified as key players in the synchronization of cellular circadian rhythms within the SCN. The discovery of multiple oscillators governing behavioral and physiological rhythms has significantly advanced our understanding of the circadian clock. The interaction between neurons and glial cells has been found to play a crucial role in regulating these circadian rhythms within the SCN. Furthermore, the properties of the SCN network vary across ontogenetic stages. The application of cell type-specific genetic manipulations has revealed components of the functional input-output system of the SCN and their correlation with physiological functions. This review concludes with the high-risk effort of identifying open questions and challenges that lie ahead.

Subcutaneous adipose tissue circadian gene expression: Relationship with insulin sensitivity, obesity, and the effect of weight-reducing dietary intervention

OBJECTIVE

The circadian rhythms are controlled by the central clock in the hypothalamic suprachiasmatic nuclei and by the peripheral clocks in tissues, including adipose tissue. The adipose tissue circadian clock may be associated with the regulation of insulin action; however, human data are limited. The aim of this study was to analyze the expression of subcutaneous adipose tissue circadian genes as they relate to obesity and insulin sensitivity before and after diet-induced weight loss.

METHODS

The study group comprised 38 individuals who were overweight or obese. The individuals completed a 12-wk dietary intervention program. Hyperinsulinemic-euglycemic clamp and subcutaneous adipose tissue biopsy were performed before and after the program. Sixteen normal weight individuals were examined at baseline and served as a control group.

RESULTS

At baseline, individuals who were overweight/obese had lower adipose tissue expression of NR1D1, NR1D2, DBP, PER1, and PER2 than normal weight individuals. The expression of ARNTL, CLOCK, and CRY did not differ between the groups. A weight-reducing dietary intervention resulted in an increase in the expression of adipose tissue NR1D2 and DBP, which was positively related to insulin sensitivity both before (in the entire study group and in the subgroup of overweight/obese individuals) and after the dietary intervention.

CONCLUSIONS

Adipose tissue circadian gene expression is decreased in obesity and this decrease may be partially reversed by dietary intervention. Among circadian genes, NR1D2 and DBP seem to be specifically associated with insulin action.

Weak synchronization can alter circadian period length: implications for aging and disease conditions

The synchronization of multiple oscillators serves as the central mechanism for maintaining stable circadian rhythms in physiology and behavior. Aging and disease can disrupt synchronization, leading to changes in the periodicity of circadian activities. While our understanding of the circadian clock under synchronization has advanced significantly, less is known about its behavior outside synchronization, which can also fall within a predictable domain. These states not only impact the stability of the rhythms but also modulate the period length. In C57BL/6 mice, aging, diseases, and removal of peripheral circadian oscillators often result in lengthened behavioral circadian periods. Here, we show that these changes can be explained by a surprisingly simple mathematical relationship: the frequency is the reciprocal of the period, and its distribution becomes skewed when the period distribution is symmetric. The synchronized frequency of a population in the skewed distribution and the macroscopic frequency of combined oscillators differ, accounting for some of the atypical circadian period outputs observed in networks without synchronization. Building on this finding, we investigate the dynamics of circadian outputs in the context of aging and disease, where synchronization is weakened.

In vivo recording of suprachiasmatic nucleus dynamics reveals a dominant role of arginine vasopressin neurons in circadian pacesetting

The central circadian clock of the suprachiasmatic nucleus (SCN) is a network consisting of various types of neurons and glial cells. Individual cells have the autonomous molecular machinery of a cellular clock, but their intrinsic periods vary considerably. Here, we show that arginine vasopressin (AVP) neurons set the ensemble period of the SCN network in vivo to control the circadian behavior rhythm. Artificial lengthening of cellular periods by deleting casein kinase 1 delta (CK1δ) in the whole SCN lengthened the free-running period of behavior rhythm to an extent similar to CK1δ deletion specific to AVP neurons. However, in SCN slices, PER2::LUC reporter rhythms of these mice only partially and transiently recapitulated the period lengthening, showing a dissociation between the SCN shell and core with a period instability in the shell. In contrast, in vivo calcium rhythms of both AVP and vasoactive intestinal peptide (VIP) neurons in the SCN of freely moving mice demonstrated stably lengthened periods similar to the behavioral rhythm upon AVP neuron-specific CK1δ deletion, without changing the phase relationships between each other. Furthermore, optogenetic activation of AVP neurons acutely induced calcium increase in VIP neurons in vivo. These results indicate that AVP neurons regulate other SCN neurons, such as VIP neurons, in vivo and thus act as a primary determinant of the SCN ensemble period.

Ion dynamics and the regulation of circadian cellular physiology

Circadian rhythms in physiology and behavior allow organisms to anticipate the daily environmental changes imposed by the rotation of our planet around its axis. Although these rhythms eventually manifest at the organismal level, a cellular basis for circadian rhythms has been demonstrated. Significant contributors to these cell-autonomous rhythms are daily cycles in gene expression and protein translation. However, recent data revealed cellular rhythms in other biological processes, including ionic currents, ion transport, and cytosolic ion abundance. Circadian rhythms in ion currents sustain circadian variation in action potential firing rate, which coordinates neuronal behavior and activity. Circadian regulation of metal ions abundance and dynamics is implicated in distinct cellular processes, from protein translation to membrane activity and osmotic homeostasis. In turn, studies showed that manipulating ion abundance affects the expression of core clock genes and proteins, suggestive of a close interplay. However, the relationship between gene expression cycles, ion dynamics, and cellular function is still poorly characterized. In this review, I will discuss the mechanisms that generate ion rhythms, the cellular functions they govern, and how they feed back to regulate the core clock machinery.

Circadian clock—A promising scientific target in oral science

The oral and maxillofacial organs play vital roles in chewing, maintaining facial beauty, and speaking. Almost all physiological processes display circadian rhythms that are driven by the circadian clock, allowing organisms to adapt to the changing environment. In recent years, increasing evidence has shown that the circadian clock system participates in oral and maxillofacial physiological and pathological processes, such as jaw and tooth development, salivary gland function, craniofacial malformations, oral carcinoma and other diseases. However, the roles of the circadian clock in oral science have not yet been comprehensively reviewed. Therefore, This paper provides a systematic and integrated perspective on the function of the circadian clock in the fields of oral science, reviews recent advances in terms of the circadian clock in oral and maxillofacial development and disease, dialectically analyzes the importance of the circadian clock system and circadian rhythm to the activities of oral and maxillofacial tissues, and focuses on analyzing the mechanism of the circadian clock in the maintenance of oral health, affecting the common diseases of the oral and maxillofacial region and the process of oral-related systemic diseases, sums up the chronotherapy and preventive measures for oral-related diseases based on changes in tissue activity circadian rhythms, meanwhile, comes up with a new viewpoint to promote oral health and human health.

Blast Exposure Dysregulates Nighttime Melatonin Synthesis and Signaling in the Pineal Gland: A Potential Mechanism of Blast-Induced Sleep Disruptions

Blast-induced traumatic brain injury (bTBI) frequently results in sleep-wake disturbances. However, limited studies have investigated the molecular signaling mechanisms underlying these sleep disturbances, and potentially efficacious therapies are lacking. We investigated the levels of melatonin and genes involved in melatonin synthesis pathway in the pineal glands of Sprague Dawley rats exposed to single and tightly coupled repeated blasts during the night and daytime. Rats were exposed to single and tightly coupled repeated blasts using an advanced blast simulator. The plasma, cerebrospinal fluid (CSF), and pineal gland were collected at 6 h, 24 h, or 1 month postblast at two different time points: one during the day (1000 h) and one at night (2200 h). Differential expressions of genes involved in pineal melatonin synthesis were quantified using quantitative real-time polymerase chain reaction (qRT-PCR). Plasma and CSF melatonin levels were assessed using a commercial melatonin ELISA kit. The plasma and CSF melatonin levels showed statistically significant decreases at 6 h and 24 h in the blast-exposed rats euthanized in the night (in dim light), with no significant alterations noted in rats euthanized in the morning (daylight) at all three-time points. Blast-exposed rats showed statistically significant decreases in Tph1, Aanat, Asmt, and Mtnr1b mRNA levels, along with increased Tph2 mRNA, in the pineal gland samples collected at night at 6 h and 24 h. No significant changes in the mRNA levels of these genes were noted at 1 month. These findings imply that the melatonin circadian rhythm is disrupted following blast exposure, which may be a factor in the sleep disturbances that blast victims frequently experience.

Generation and Disruption of Circadian Rhythms in the Suprachiasmatic Nucleus: A Core-Shell Model

We focus our research on how the core-shell organization controls behavior of the suprachiasmatic nucleus (SCN), how the core and shell are synchronized to the environment, what impact they have on the behavior of the SCN under different lighting conditions, and what mechanisms disrupt synchronization. To this end, we use a reduced Kuramoto model, with parameters inferred from experimental observations and calibrated for mice, and perform a detailed comparison between the model and experimental data under light-dark (LD), dark-dark (DD), and light-light (LL) conditions. The operating limits of free-running and entrained SCN activity under symmetric LD cycles are analyzed, with particular focus on the phenomena of anticipation and dissociation. Results reveal that the core-shell organization of the SCN enables anticipation of future events over circadian cycles. The model predicts the emergence of a second (dissociated) rhythm for large and small LD periods. Our results are in good qualitative and quantitative agreement with experimental observations of circadian dissociation. We further describe SCN activity under LL conditions and show that our model satisfies Aschoff’s first rule, according to which the endogenous free-running circadian period observed under complete darkness will shorten in diurnal animals and lengthen in nocturnal animals under constant light. Our results strongly suggest that the Kuramoto model captures essential features of synchronization and entrainment in the SCN. Moreover, our approach is easily extendible to an arbitrary number of groups, with dynamics described by explicit equations for the group phase and synchronization index. Viewed together, the reduced Kuramoto model presents itself as a useful tool for exploring open problems in the study of circadian rhythms, one that can account for evolving views of the circadian system’s organization, including peripheral clocks and inter-hemispheric interaction, and can be translated to other nocturnal and diurnal animals, including humans.

Stochastic synchronization in nonlinear network systems driven by intrinsic and coupling noise

In this paper, we consider a noisy network of nonlinear systems in the sense that each system is driven by two sources of state-dependent noise: (1) an intrinsic noise that can be generated by the environment or any internal fluctuations and (2) a noisy coupling which is generated by interactions with other systems. Our goal is to understand the effect of noise and coupling on synchronization behaviors of such networks. First, we assume that all the systems are driven by a common noise and show how a common noise can be detrimental or beneficial for network synchronization behavior. Then, we assume that the systems are driven by independent noise and study network approximate synchronization behavior. We numerically illustrate our results using the example of coupled Van der Pol oscillators.

Circadian rhythms and cancers: the intrinsic links and therapeutic potentials

The circadian rhythm is an evolutionarily conserved time-keeping system that comprises a wide variety of processes including sleep-wake cycles, eating-fasting cycles, and activity-rest cycles, coordinating the behavior and physiology of all organs for whole-body homeostasis. Acute disruption of circadian rhythm may lead to transient discomfort, whereas long-term irregular circadian rhythm will result in the dysfunction of the organism, therefore increasing the risks of numerous diseases especially cancers. Indeed, both epidemiological and experimental evidence has demonstrated the intrinsic link between dysregulated circadian rhythm and cancer. Accordingly, a rapidly increasing understanding of the molecular mechanisms of circadian rhythms is opening new options for cancer therapy, possibly by modulating the circadian clock. In this review, we first describe the general regulators of circadian rhythms and their functions on cancer. In addition, we provide insights into the mechanisms underlying how several types of disruption of the circadian rhythm (including sleep-wake, eating-fasting, and activity-rest) can drive cancer progression, which may expand our understanding of cancer development from the clock perspective. Moreover, we also summarize the potential applications of modulating circadian rhythms for cancer treatment, which may provide an optional therapeutic strategy for cancer patients.

Controlling The Synchronization of Molecular Oscillators Through Indirect Coupling

In this article, we study the coupling of a collection of molecular oscillators, called repressilators, interacting indirectly through enzymatic saturation. We extended a measure of autocorrelation to identify the period of the whole system and to detect coupling behaviors. We explored the parameter space of concentrations of molecular species in each oscillator versus enzymatic saturation, and observed regions of uncoupled, partially, or fully coupled systems. In particular, we found a region that provided a sharp transition between no coupling, two coupled oscillators, and full coupling. In practical applications, signals from the environment can directly affect parameters such as local enzymatic saturation, and thus switch the system from a coupled to an uncoupled regime and vice-versa. Our parameter exploration can be used to guide the design of complex molecular systems, such as active materials or molecular robot controllers.

Computational Approaches and Tools as Applied to the Study of Rhythms and Chaos in Biology

The temporal dynamics in biological systems displays a wide range of behaviors, from periodic oscillations, as in rhythms, bursts, long-range (fractal) correlations, chaotic dynamics up to brown and white noise. Herein, we propose a comprehensive analytical strategy for identifying, representing, and analyzing biological time series, focusing on two strongly linked dynamics: periodic (oscillatory) rhythms and chaos. Understanding the underlying temporal dynamics of a system is of fundamental importance; however, it presents methodological challenges due to intrinsic characteristics, among them the presence of noise or trends, and distinct dynamics at different time scales given by molecular, dcellular, organ, and organism levels of organization. For example, in locomotion circadian and ultradian rhythms coexist with fractal dynamics at faster time scales. We propose and describe the use of a combined approach employing different analytical methodologies to synergize their strengths and mitigate their weaknesses. Specifically, we describe advantages and caveats to consider for applying probability distribution, autocorrelation analysis, phase space reconstruction, Lyapunov exponent estimation as well as different analyses such as harmonic, namely, power spectrum; continuous wavelet transforms; synchrosqueezing transform; and wavelet coherence. Computational harmonic analysis is proposed as an analytical framework for using different types of wavelet analyses. We show that when the correct wavelet analysis is applied, the complexity in the statistical properties, including temporal scales, present in time series of signals, can be unveiled and modeled. Our chapter showcase two specific examples where an in-depth analysis of rhythms and chaos is performed: (1) locomotor and food intake rhythms over a 42-day period of mice subjected to different feeding regimes; and (2) chaotic calcium dynamics in a computational model of mitochondrial function.

Role of heterozygous and homozygous alleles in cryptochrome-deficient mice

The circadian rhythms of physiology and behavior are based on molecular systems at the cellular level, which are regulated by clock genes, including cryptochrome genes, Cry1 and Cry2. In mammals, the circadian pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus maintains the circadian rhythms throughout the body. Cry1 and Cry2 play distinct roles in regulating the circadian rhythm. However, the different effects of manipulating clock genes in heterozygous and homozygous alleles, Cry1 and Cry2, remain unclear. Therefore, this study aimed to understand the haplosufficiency of cryptochrome genes in regulating the circadian system. We examined wheel-running activity rhythms and PER2::LUC expression rhythms in SCN slices and pituitary explants in mice. Compared with wild-type mice, Cry1^-/- or Cry2^-/- mice had shortened or lengthened periods in free-running behavioral rhythms and PER2::LUC expression in the SCN and pituitary gland. Cry1^+/- mice had similar circadian rhythms as wild-type mice, although Cry2^+/- mice had lengthened periods. The amplitude of PER2::LUC expression exhibited faster damping in Cry1^-/- mice. Therefore, Cry1 deficiency affects the circadian period length and stability of the circadian system. A single allele of Cry2 deficiency affects the circadian rhythm, whereas that of Cry1 deficit is compensated.

Cut the noise or couple up: Coordinating circadian and synthetic clocks

Circadian clocks are important to much of life on Earth and are of inherent interest to humanity, implicated in fields ranging from agriculture and ecology to developmental biology and medicine. New techniques show that it is not simply the presence of clocks, but coordination between them that is critical for complex physiological processes across the kingdoms of life. Recent years have also seen impressive advances in synthetic biology to the point where parallels can be drawn between synthetic biological and circadian oscillators. This review will emphasize theoretical and experimental studies that have revealed a fascinating dichotomy of coupling and heterogeneity among circadian clocks. We will also consolidate the fields of chronobiology and synthetic biology, discussing key design principles of their respective oscillators.

A two-frequency-two-coupling model of coupled oscillators

We considered the phase coherence dynamics in a Two-Frequency and Two-Coupling (TFTC) model of coupled oscillators, where coupling strength and natural oscillator frequencies for individual oscillators may assume one of two values (positive/negative). The bimodal distributions for the coupling strengths and frequencies are either correlated or uncorrelated. To study how correlation affects phase coherence, we analyzed the TFTC model by means of numerical simulations and exact dimensional reduction methods allowing to study the collective dynamics in terms of local order parameters [S. Watanabe and S. H. Strogatz, Physica D 74(3-4), 197-253 (1994); E. Ott and T. M. Antonsen, Chaos 18(3), 037113 (2008)]. The competition resulting from distributed coupling strengths and natural frequencies produces nontrivial dynamic states. For correlated disorder in frequencies and coupling strengths, we found that the entire oscillator population splits into two subpopulations, both phase-locked (Lock-Lock) or one phase-locked, and the other drifting (Lock-Drift), where the mean-fields of the subpopulations maintain a constant non-zero phase difference. For uncorrelated disorder, we found that the oscillator population may split into four phase-locked subpopulations, forming phase-locked pairs which are either mutually frequency-locked (Stable Lock-Lock-Lock-Lock) or drifting (Breathing Lock-Lock-Lock-Lock), thus resulting in a periodic motion of the global synchronization level. Finally, we found for both types of disorder that a state of Incoherence exists; however, for correlated coupling strengths and frequencies, incoherence is always unstable, whereas it is only neutrally stable for the uncorrelated case. Numerical simulations performed on the model show good agreement with the analytic predictions. The simplicity of the model promises that real-world systems can be found which display the dynamics induced by correlated/uncorrelated disorder.

Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

The interaction of a large number of oscillating units can lead to the emergence of a collective, macroscopic oscillation in which many units oscillate in near-unison or near-synchrony. This has been exploited technologically, e.g., to combine many coherently interacting, individual lasers to form a single powerful laser. Collective oscillations are also important in biology. For instance, the circadian rhythm of animals is controlled by the near-synchronous dynamics of a large number of individually oscillating cells. In animals and humans brain rhythms reflect the coherent dynamics of a large number of neurons and are surmised to play an important role in the communication between different brain areas. To be functionally relevant, these rhythms have to respond to external inputs and have to be able to synchronize with each other. We show that the ubiquitous heterogeneity in the properties of the individual neurons in a network can contribute to that ability. It can allow the external inputs to modify the internal network dynamics such that the network can follow these inputs over a wider range of frequencies. Paradoxically, while an external perturbation may delay individual neurons, their ensuing within-network interaction can overcompensate this delay, leading to an overall advance of the rhythm.

Collective Oscillations in Coupled-Cell Systems

We investigate oscillations in coupled systems. The methodology is based on the Hopf bifurcation theorem and a condition extended from the Routh–Hurwitz criterion. Such a condition leads to locating the bifurcation values of the parameters. With such an approach, we analyze a single-cell system modeling the minimal genetic negative feedback loop and the coupled-cell system composed by these single-cell systems. We study the oscillatory properties for these systems and compare these properties between the model with Hill-type repression and the one with protein-sequestration-based repression. As the parameters move from the Hopf bifurcation value for single cells to the one for coupled cells, we compute the eigenvalues of the linearized systems to obtain the magnitude of the collective frequency when the periodic solution of the coupled-cell system is generated. Extending from this information on the parameter values, we further compute and compare the collective frequency for the coupled-cell system and the average frequency of the decoupled individual cells. To compare these scenarios with other biological oscillators, we perform parallel analysis and computations on a segmentation clock model.

Phase coalescence in a population of heterogeneous Kuramoto oscillators

Phase coalescence (PC) is an emerging phenomenon in an ensemble of oscillators that manifests itself as a spontaneous rise in the order parameter. This increment in the order parameter is due to the overlaying of oscillator phases to a pre-existing system state. In the current work, we present a comprehensive analysis of the phenomenon of phase coalescence observed in a population of Kuramoto phase oscillators. The given population is divided into responsive and non-responsive oscillators depending on the position of the phases of the oscillators. The responsive set of oscillators is then reset by a pulse perturbation. This resetting leads to a temporary rise in a macroscopic observable, namely, order parameter. The provoked rise thus induced in the order parameter is followed by unprovoked increments separated by a constant time τ_PC. These unprovoked increments in the order parameter are caused due to a temporary gathering of the oscillator phases in a configuration similar to the initial system state, i.e., the state of the network immediately following the perturbation. A theoretical framework corroborating this phenomenon as well as the corresponding simulation results are presented. Dependence of τ_PC and the magnitude of spontaneous order parameter augmentation on various network parameters such as coupling strength, network size, degree of the network, and frequency distribution are then explored. The size of the phase resetting region would also affect the magnitude of the order parameter at τ_PC since it directly affects the number of oscillators reset by the perturbation. Therefore, the dependence of order parameter on the size of the phase resetting region is also analyzed.

Genesis of the Master Circadian Pacemaker in Mice

The suprachiasmatic nucleus (SCN) of the hypothalamus is the central circadian clock of mammals. It is responsible for communicating temporal information to peripheral oscillators via humoral and endocrine signaling, ultimately controlling overt rhythms such as sleep-wake cycles, body temperature, and locomotor activity. Given the heterogeneity and complexity of the SCN, its genesis is tightly regulated by countless intrinsic and extrinsic factors. Here, we provide a brief overview of the development of the SCN, with special emphasis on the murine system.

Diurnal and seasonal molecular rhythms in the human brain and their relation to Alzheimer disease

Diurnal and seasonal rhythms influence many aspects of human physiology including brain function. Moreover, altered diurnal and seasonal behavioral and physiological rhythms have been linked to Alzheimer's disease and related dementias (ADRD). Understanding the molecular basis for these links may lead to identification of novel targets to mitigate the negative impact of normal and abnormal diurnal and seasonal rhythms on ADRD or to alleviate the adverse consequences of ADRD on normal diurnal and seasonal rhythms. Diurnally and seasonally rhythmic gene expression and epigenetic modification in the human neocortex may be a key mechanism underlying these links. This chapter will first review the observed epidemiological links between normal and abnormal diurnal and seasonal rhythmicity, cognitive impairment, and ADRD. Then it will review normal diurnal and seasonal rhythms of brain epigenetic modification and gene expression in model organisms. Finally, it will review evidence for diurnal and seasonal rhythms of epigenetic modification and gene expression the human brain in aging, Alzheimer's disease, and other brain disorders.

Dynamics of hierarchical weighted networks of van der Pol oscillators

We investigate the dynamics of regular fractal-like networks of hierarchically coupled van der Pol oscillators. The hierarchy is imposed in terms of the coupling strengths or link weights. We study the low frequency modes, as well as frequency and phase synchronization, in the network by a process of repeated coarse-graining of oscillator units. At any given stage of this process, we sum over the signals from the oscillator units of a clique to obtain a new oscillating unit. The frequencies and the phases for the coarse-grained oscillators are found to progressively synchronize with the number of coarse-graining steps. Furthermore, the characteristic frequency is found to decrease and finally stabilize to a value that can be tuned via the parameters of the system. We compare our numerical results with those of an approximate analytic solution and find good qualitative agreement. Our study on this idealized model shows how oscillations with a precise frequency can be obtained in systems with heterogeneous couplings. It also demonstrates the effect of imposing a hierarchy in terms of link weights instead of one that is solely topological, where the connectivity between oscillators would be the determining factor, as is usually the case.

Inferring causal networks of dynamical systems through transient dynamics and perturbation

Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the forcings are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate causal reconstructions: Granger causality (GC) with perturbations, and our proposed perturbation cascade inference (PCI). Perturbed GC is capable of inferring smaller networks under low coupling strength regimes. Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (2-5 node) and large (10-20 node) networks, with both linear and nonlinear dynamics. Thus, the ability to apply a large and diverse set of perturbations to the network is critical for successfully and accurately determining causal relations and disambiguating between various viable networks.

Seasonality and light phase-resetting in the mammalian circadian rhythm

We study the impact of light on the mammalian circadian system using the theory of phase response curves. Using a recently developed ansatz we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In particular, we find that the sensitivity of the circadian system to light may be modulated by changes in the relative coupling forces between the light sensing and non-sensing populations. Finally, we show how seasonal day-length, after-effects to light entrainment and seasonal variations in light sensitivity in the mammalian circadian clock are interrelated.

Memory and the circadian system: Identifying candidate mechanisms by which local clocks in the brain may regulate synaptic plasticity

The circadian system is an endogenous biological network responsible for coordinating near-24-h cycles in behavior and physiology with daily timing cues from the external environment. In this review, we explore how the circadian system regulates memory formation, retention, and recall. Circadian rhythms in these memory processes may arise through several endogenous pathways, and recent work highlights the importance of genetic timekeepers found locally within tissues, called local clocks. We evaluate the circadian memory literature for evidence of local clock involvement in memory, identifying potential nodes for direct interactions between local clock components and mechanisms of synaptic plasticity. Our discussion illustrates how local clocks may pervasively modulate neuronal plastic capacity, a phenomenon that we designate here as circadian metaplasticity. We suggest that this function of local clocks supports the temporal optimization of memory processes, illuminating the potential for circadian therapeutic strategies in the prevention and treatment of memory impairment.

Global sleep homeostasis reflects temporally and spatially integrated local cortical neuronal activity

Sleep homeostasis manifests as a relative constancy of its daily amount and intensity. Theoretical descriptions define 'Process S', a variable with dynamics dependent on global sleep-wake history, and reflected in electroencephalogram (EEG) slow wave activity (SWA, 0.5-4 Hz) during sleep. The notion of sleep as a local, activity-dependent process suggests that activity history must be integrated to determine the dynamics of global Process S. Here, we developed novel mathematical models of Process S based on cortical activity recorded in freely behaving mice, describing local Process S as a function of the deviation of neuronal firing rates from a locally defined set-point, independent of global sleep-wake state. Averaging locally derived Processes S and their rate parameters yielded values resembling those obtained from EEG SWA and global vigilance states. We conclude that local Process S dynamics reflects neuronal activity integrated over time, and global Process S reflects local processes integrated over space.

Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review

Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.

Epigenetic inheritance of circadian period in clonal cells

Circadian oscillations are generated via transcriptional-translational negative feedback loops. However, individual cells from fibroblast cell lines have heterogeneous rhythms, oscillating independently and with different period lengths. Here we showed that heterogeneity in circadian period is heritable and used a multi-omics approach to investigate underlying mechanisms. By examining large-scale phenotype-associated gene expression profiles in hundreds of mouse clonal cell lines, we identified and validated multiple novel candidate genes involved in circadian period determination in the absence of significant genomic variants. We also discovered differentially co-expressed gene networks that were functionally associated with period length. We further demonstrated that global differential DNA methylation bidirectionally regulated these same gene networks. Interestingly, we found that depletion of DNMT1 and DNMT3A had opposite effects on circadian period, suggesting non-redundant roles in circadian gene regulation. Together, our findings identify novel gene candidates involved in periodicity, and reveal DNA methylation as an important regulator of circadian periodicity.

Clocks in the Wild: Entrainment to Natural Light

Entrainment denotes a process of coordinating the internal circadian clock to external rhythmic time-cues (Zeitgeber), mainly light. It is facilitated by stronger Zeitgeber signals and smaller period differences between the internal clock and the external Zeitgeber. The phase of entrainment ψ is a result of this process on the side of the circadian clock. On Earth, the period of the day-night cycle is fixed to 24 h, while the periods of circadian clocks distribute widely due to natural variation within and between species. The strength and duration of light depend locally on season and geographic latitude. Therefore, entrainment characteristics of a circadian clock vary under a local light environment and distribute along geoecological settings. Using conceptual models of circadian clocks, we investigate how local conditions of natural light shape global patterning of entrainment through seasons. This clock-side entrainment paradigm enables us to predict systematic changes in the global distribution of chronotypes.

Ion Channels Controlling Circadian Rhythms in Suprachiasmatic Nucleus Excitability

Animals synchronize to the environmental day-night cycle by means of an internal circadian clock in the brain. In mammals, this timekeeping mechanism is housed in the suprachiasmatic nucleus (SCN) of the hypothalamus and is entrained by light input from the retina. One output of the SCN is a neural code for circadian time, which arises from the collective activity of neurons within the SCN circuit and comprises two fundamental components: 1) periodic alterations in the spontaneous excitability of individual neurons that result in higher firing rates during the day and lower firing rates at night, and 2) synchronization of these cellular oscillations throughout the SCN. In this review, we summarize current evidence for the identity of ion channels in SCN neurons and the mechanisms by which they set the rhythmic parameters of the time code. During the day, voltage-dependent and independent Na⁺ and Ca²⁺ currents, as well as several K⁺ currents, contribute to increased membrane excitability and therefore higher firing frequency. At night, an increase in different K⁺ currents, including Ca²⁺-activated BK currents, contribute to membrane hyperpolarization and decreased firing. Layered on top of these intrinsically regulated changes in membrane excitability, more than a dozen neuromodulators influence action potential activity and rhythmicity in SCN neurons, facilitating both synchronization and plasticity of the neural code.

The Concept of Coupling in the Mammalian Circadian Clock Network

The circadian clock network regulates daily rhythms in mammalian physiology and behavior to optimally adapt the organism to the 24-h day/night cycle. A central pacemaker, the hypothalamic suprachiasmatic nucleus (SCN), coordinates subordinate cellular oscillators in the brain, as well as in peripheral organs to align with each other and external time. Stability and coordination of this vast network of cellular oscillators is achieved through different levels of coupling. Although coupling at the molecular level and across the SCN is well established and believed to define its function as pacemaker structure, the notion of coupling in other tissues and across the whole system is less well understood. In this review, we describe the different levels of coupling in the mammalian circadian clock system - from molecules to the whole organism. We highlight recent advances in gaining knowledge of the complex organization and function of circadian network regulation and its significance for the generation of stable but plastic intrinsic 24-h rhythms.

Resetting the Aging Clock: Implications for Managing Age-Related Diseases

Worldwide, individuals are living longer due to medical and scientific advances, increased availability of medical care and changes in public health policies. Consequently, increasing attention has been focused on managing chronic conditions and age-related diseases to ensure healthy aging. The endogenous circadian system regulates molecular, physiological and behavioral rhythms orchestrating functional coordination and processes across tissues and organs. Circadian disruption or desynchronization of circadian oscillators increases disease risk and appears to accelerate aging. Reciprocally, aging weakens circadian function aggravating age-related diseases and pathologies. In this review, we summarize the molecular composition and structural organization of the circadian system in mammals and humans, and evaluate the technological and societal factors contributing to the increasing incidence of circadian disorders. Furthermore, we discuss the adverse effects of circadian dysfunction on aging and longevity and the bidirectional interactions through which aging affects circadian function using examples from mammalian research models and humans. Additionally, we review promising methods for managing healthy aging through behavioral and pharmacological reinforcement of the circadian system. Understanding age-related changes in the circadian clock and minimizing circadian dysfunction may be crucial components to promote healthy aging.

Macroscopic Models for Human Circadian Rhythms

Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.

Modeling the Influence of Synaptic Plasticity on After-effects

While circadian rhythms in physiology and behavior demonstrate remarkable day-to-day precision, they are also able to exhibit plasticity in a variety of parameters and under a variety of conditions. After-effects are one type of plasticity in which exposure to non-24-h light-dark cycles (T-cycles) will alter the animal's free-running rhythm in subsequent constant conditions. We use a mathematical model to explore whether the concept of synaptic plasticity can explain the observation of after-effects. In this model, the SCN is composed of a set of individual oscillators randomly selected from a normally distributed population. Each cell receives input from a defined set of oscillators, and the overall period of a cell is a weighted average of its own period and that of its inputs. The influence that an input has on its target's period is determined by the proximity of the input cell's period to the imposed T-cycle period, such that cells with periods near T will have greater influence. Such an arrangement is able to duplicate the phenomenon of after-effects, with relatively few inputs per cell (~4-5) being required. When the variability of periods between oscillators is low, the system is quite robust and results in minimal after-effects, while systems with greater between-cell variability exhibit greater magnitude after-effects. T-cycles that produce maximal after-effects have periods within ~2.5 to 3 h of the population period. Overall, this model demonstrates that synaptic plasticity in the SCN network could contribute to plasticity of the circadian period.

The functional changes of the circadian system organization in aging

The circadian clock drives periodic oscillations at different levels of an organism from genes to behavior. This timing system is highly conserved across species from insects to mammals and human beings. The question of how the circadian clock is involved in the aging process continues to attract more attention. We aim to characterize the detrimental impact of aging on the circadian clock organization. We review studies on different components of the circadian clock at the central and periperal levels, and their changes in aged rodents and humans, and the fruit fly Drosophila. Intracellular signaling, cellular activity and intercellular coupling in the central pacemaker have been found to decline with advancing age. Evidence of degradation of the molecular clockwork reflected by clock gene expression in both central and peripheral oscillators due to aging is inadequate. The findings on age-associated molecular and functional changes of peripheral clocks are mixed. We conclude that aging can affect the circadian clock organization at various levels, and the impairment of the central network may be a fundamental mechanism of circadian disruption seen in aged species.

Non-coding cis-element of Period2 is essential for maintaining organismal circadian behaviour and body temperature rhythmicity

Non-coding cis-regulatory elements are essential determinants of development, but their exact impacts on behavior and physiology in adults remain elusive. Cis-element-based transcriptional regulation is believed to be crucial for generating circadian rhythms in behavior and physiology. However, genetic evidence supporting this model is based on mutations in the protein-coding sequences of clock genes. Here, we report generation of mutant mice carrying a mutation only at the E'-box cis-element in the promoter region of the core clock gene Per2. The Per2 E'-box mutation abolishes sustainable molecular clock oscillations and renders circadian locomotor activity and body temperature rhythms unstable. Without the E'-box, Per2 messenger RNA and protein expression remain at mid-to-high levels. Our work delineates the Per2 E'-box as a critical nodal element for keeping sustainable cell-autonomous circadian oscillation and reveals the extent of the impact of the non-coding cis-element in daily maintenance of animal locomotor activity and body temperature rhythmicity.

From clock to functional pacemaker

In mammals, the central pacemaker that coordinates 24‐hr rhythms is located in the suprachiasmatic nucleus (SCN). Individual neurons of the SCN have a molecular basis for rhythm generation and hence, they function as cell autonomous oscillators. Communication and synchronization among these neurons are crucial for obtaining a coherent rhythm at the population level, that can serve as a pace making signal for brain and body. Hence, the ability of single SCN neurons to produce circadian rhythms is equally important as the ability of these neurons to synchronize one another, to obtain a bona fide pacemaker at the SCN tissue level. In this chapter we will discuss the mechanisms underlying synchronization, and plasticity herein, which allows adaptation to changes in day length. Furthermore, we will discuss deterioration in synchronization among SCN neurons in aging, and gain in synchronization by voluntary physical activity or exercise.

Molecular and Cellular Networks in The Suprachiasmatic Nuclei

Why do we experience the ailments of jetlag when we travel across time zones? Why is working night-shifts so detrimental to our health? In other words, why can’t we readily choose and stick to non-24 h rhythms? Actually, our daily behavior and physiology do not simply result from the passive reaction of our organism to the external cycle of days and nights. Instead, an internal clock drives the variations in our bodily functions with a period close to 24 h, which is supposed to enhance fitness to regular and predictable changes of our natural environment. This so-called circadian clock relies on a molecular mechanism that generates rhythmicity in virtually all of our cells. However, the robustness of the circadian clock and its resilience to phase shifts emerge from the interaction between cell-autonomous oscillators within the suprachiasmatic nuclei (SCN) of the hypothalamus. Thus, managing jetlag and other circadian disorders will undoubtedly require extensive knowledge of the functional organization of SCN cell networks. Here, we review the molecular and cellular principles of circadian timekeeping, and their integration in the multi-cellular complexity of the SCN. We propose that new, in vivo imaging techniques now enable to address these questions directly in freely moving animals.

Aging circadian rhythms and cannabinoids

Numerous aspects of mammalian physiology exhibit cyclic daily patterns known as circadian rhythms. However, studies in aged humans and animals indicate that these physiological rhythms are not consistent throughout the life span. The simultaneous development of disrupted circadian rhythms and age-related impairments suggests a shared mechanism, which may be amenable to therapeutic intervention. Recently, the endocannabinoid system has emerged as a complex signaling network, which regulates numerous aspects of circadian physiology relevant to the neurobiology of aging. Agonists of cannabinoid receptor-1 (CB1) have consistently been shown to decrease neuronal activity, core body temperature, locomotion, and cognitive function. Paradoxically, several lines of evidence now suggest that very low doses of cannabinoids are beneficial in advanced age. One potential explanation for this phenomenon is that these drugs exhibit hormesis-a biphasic dose-response wherein low doses produce the opposite effects of higher doses. Therefore, it is important to determine the dose-, age-, and time-dependent effects of these substances on the regulation of circadian rhythms and other processes dysregulated in aging. This review highlights 3 fields-biological aging, circadian rhythms, and endocannabinoid signaling-to critically assess the therapeutic potential of endocannabinoid modulation in aged individuals. If the hormetic properties of exogenous cannabinoids are confirmed, we conclude that precise administration of these compounds may bidirectionally entrain central and peripheral circadian clocks and benefit multiple aspects of aging physiology.

Circadian regulation of membrane physiology in neural oscillators throughout the brain

Twenty-four-hour rhythmicity in physiology and behavior are driven by changes in neurophysiological activity that vary across the light-dark and rest-activity cycle. Although this neural code is most prominent in neurons of the primary circadian pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus, there are many other regions in the brain where region-specific function and behavioral rhythmicity may be encoded by changes in electrical properties of those neurons. In this review, we explore the existing evidence for molecular clocks and/or neurophysiological rhythms (i.e., 24 hr) in brain regions outside the SCN. In addition, we highlight the brain regions that are ripe for future investigation into the critical role of circadian rhythmicity for local oscillators. For example, the cerebellum expresses rhythmicity in over 2,000 gene transcripts, and yet we know very little about how circadian regulation drives 24-hr changes in the neural coding responsible for motor coordination. Finally, we conclude with a discussion of how our understanding of circadian regulation of electrical properties may yield insight into disease mechanisms which may lead to novel chronotherapeutic strategies in the future.

Clock-Generated Temporal Codes Determine Synaptic Plasticity to Control Sleep

Neurons use two main schemes to encode information: rate coding (frequency of firing) and temporal coding (timing or pattern of firing). While the importance of rate coding is well established, it remains controversial whether temporal codes alone are sufficient for controlling behavior. Moreover, the molecular mechanisms underlying the generation of specific temporal codes are enigmatic. Here, we show in Drosophila clock neurons that distinct temporal spike patterns, dissociated from changes in firing rate, encode time-dependent arousal and regulate sleep. From a large-scale genetic screen, we identify the molecular pathways mediating the circadian-dependent changes in ionic flux and spike morphology that rhythmically modulate spike timing. Remarkably, the daytime spiking pattern alone is sufficient to drive plasticity in downstream arousal neurons, leading to increased firing of these cells. These findings demonstrate a causal role for temporal coding in behavior and define a form of synaptic plasticity triggered solely by temporal spike patterns.

Ring states in swarmalator systems

Synchronization is a universal phenomenon, occurring in systems as disparate as Japanese tree frogs and Josephson junctions. Typically, the elements of synchronizing systems adjust the phases of their oscillations, but not their positions in space. The reverse scenario is found in swarming systems, such as schools of fish or flocks of birds; now the elements adjust their positions in space, but without (noticeably) changing their internal states. Systems capable of both swarming and synchronizing, dubbed swarmalators, have recently been proposed, and analyzed in the continuum limit. Here, we extend this work by studying finite populations of swarmalators, whose phase similarity affects both their spatial attraction and repulsion. We find ring states, and compute criteria for their existence and stability. Larger populations can form annular distributions, whose density we calculate explicitly. These states may be observable in groups of Japanese tree frogs, ferromagnetic colloids, and other systems with an interplay between swarming and synchronization.

The Circadian Clock in White and Brown Adipose Tissue: Mechanistic, Endocrine, and Clinical Aspects

Obesity is a major risk factor for the development of illnesses, such as insulin resistance and hypertension, and has become a serious public health problem. Mammals have developed a circadian clock located in the hypothalamic suprachiasmatic nuclei (SCN) that responds to the environmental light-dark cycle. Clocks similar to the one located in the SCN are found in peripheral tissues, such as the kidney, liver, and adipose tissue. The circadian clock regulates metabolism and energy homeostasis in peripheral tissues by mediating activity and/or expression of key metabolic enzymes and transport systems. Knockouts or mutations in clock genes that lead to disruption of cellular rhythmicity have provided evidence to the tight link between the circadian clock and metabolism. In addition, key proteins play a dual role in regulating the core clock mechanism, as well as adipose tissue metabolism, and link circadian rhythms with lipogenesis and lipolysis. Adipose tissues are distinguished as white, brown, and beige (or brite), each with unique metabolic characteristics. Recently, the role of the circadian clock in regulating the differentiation into the different adipose tissues has been investigated. In this review, the role of clock proteins and the downstream signaling pathways in white, brown, and brite adipose tissue function and differentiation will be reviewed. In addition, chronodisruption and metabolic disorders and clinical aspects of circadian adiposity will be addressed.

Synchronization by uncorrelated noise: interacting rhythms in interconnected oscillator networks

Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. How do multiple such rhythms interact with each other? Do these collective oscillations synchronize like individual oscillators? We show that this is not the case: for strong, inhibitory coupling rhythms can become synchronized by noise. In contrast to stochastic synchronization, this new mechanism synchronizes the rhythms even if the noisy inputs to different oscillators are completely uncorrelated. Key for the synchrony across networks is the reduced synchrony within the networks: it substantially increases the frequency range across which the networks can be entrained by other networks or by periodic pacemaker-like inputs. We demonstrate this type of robust synchronization for different classes of oscillators and network connectivities. The synchronization of different population rhythms is expected to be relevant for brain rhythms.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.