Small-world network models of intercellular coupling predict enhanced synchronization in the suprachiasmatic nucleus

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.

Computational modeling predicts regulation of central pattern generator oscillations by size and density of the underlying heterogenous network

Central pattern generators are characterized by a heterogeneous cellular composition, with different cell types playing distinct roles in the production and transmission of rhythmic signals. However, little is known about the functional implications of individual variation in the relative distributions of cells and their connectivity patterns. Here, we addressed this question through a combination of morphological data analysis and computational modeling, using the pacemaker nucleus of the weakly electric fish Apteronotus leptorhynchus as case study. A neural network comprised of 60-110 interconnected pacemaker cells and 15-30 relay cells conveying its output to electromotoneurons in the spinal cord, this nucleus continuously generates neural signals at frequencies of up to 1 kHz with high temporal precision. We systematically explored the impact of network size and density on oscillation frequencies and their variation within and across cells. To accurately determine effect sizes, we minimized the likelihood of complex dynamics using a simplified setup precluding differential delays. To identify natural constraints, parameter ranges were extended beyond experimentally recorded numbers of cells and connections. Simulations revealed that pacemaker cells have higher frequencies and lower within-population variability than relay cells. Within-cell precision and between-cells frequency synchronization increased with the number of pacemaker cells and of connections of either type, and decreased with relay cell count in both populations. Network-level frequency-synchronized oscillations occurred in roughly half of simulations, with maximized likelihood and firing precision within biologically observed parameter ranges. These findings suggest the structure of the biological pacemaker nucleus is optimized for generating synchronized sustained oscillations.

Deciphering clock cell network morphology within the biological master clock, suprachiasmatic nucleus: From the perspective of circadian wave dynamics

The biological master clock, suprachiasmatic nucleus (of rat and mouse), is composed of ~10,000 clock cells which are heterogeneous with respect to their circadian periods. Despite this inhomogeneity, an intact SCN maintains a very good degree of circadian phase (time) coherence which is vital for sustaining various circadian rhythmic activities, and it is supposedly achieved by not just one but a few different cell-to-cell coupling mechanisms, among which action potential (AP)-mediated connectivity is known to be essential. But, due to technical difficulties and limitations in experiments, so far very little information is available about the morphology of the connectivity at a cellular scale. Building upon this limited amount of information, here we exhaustively and systematically explore a large pool (~25,000) of various network morphologies to come up with some plausible network features of SCN networks. All candidates under consideration reflect an experimentally obtained 'indegree distribution' as well as a 'physical range distribution of afferent clock cells.' Then, importantly, with a set of multitude criteria based on the properties of SCN circadian phase waves in extrinsically perturbed as well as in their natural states, we select out appropriate model networks: Some important measures are, 1) level of phase dispersal and direction of wave propagation, 2) phase-resetting ability of the model networks subject to external circadian forcing, and 3) decay rate of perturbation induced "phase-singularities." The successful, realistic networks have several common features: 1) "indegree" and "outdegree" should have a positive correlation; 2) the cells in the SCN ventrolateral region (core) have a much larger total degree than that of the dorsal medial region (shell); 3) The number of intra-core edges is about 7.5 times that of intra-shell edges; and 4) the distance probability density function for the afferent connections fits well to a beta function. We believe that these newly identified network features would be a useful guide for future explorations on the very much unknown AP-mediated clock cell connectome within the SCN.

Network rewiring and plasticity promotes synchronization of suprachiasmatic nucleus neurons

In mammals, circadian rhythms throughout the body are orchestrated by the master clock in the hypothalamic suprachiasmatic nucleus (SCN), where SCN neurons are coupled with neurotransmitters to generate a uniform circadian rhythm. How the SCN circadian rhythm is so robust and flexible is, however, unclear. In this paper, we propose a temporal SCN network model and investigate the effects of dynamical rewiring and flexible coupling due to synaptic plasticity on the synchronization of the neural network in SCN. In networks consisting of simple Poincaré oscillators and complex circadian clocks, we found that dynamical rewiring and coupling plasticity enhance the synchronization in inhomogeneous networks. We verified the effect of enhanced synchronization in different architectures of random, scale-free, and small-world networks. A simple mean-field analysis for synchronization in plastic networks is proposed. Intuitively, the synchronization is greatly enhanced because both the random rewiring and coupling plasticity in the heterogeneous network have effectively increased the coupling strength in the whole network. Our results suggest that a proper network model for the master SCN circadian rhythm needs to take into account the effects of dynamical changes in topology and plasticity in neuron interactions that could help the brain to generate a robust circadian rhythm for the whole body.

Light-induced synchronization of the SCN coupled oscillators and implications for entraining the HPA axis

The suprachiasmatic nucleus (SCN) synchronizes the physiological rhythms to the external light-dark cycle and tunes the dynamics of circadian rhythms to photoperiod fluctuations. Changes in the neuronal network topologies are suggested to cause adaptation of the SCN in different photoperiods, resulting in the broader phase distribution of neuron activities in long photoperiods (LP) compared to short photoperiods (SP). Regulated by the SCN output, the level of glucocorticoids is elevated in short photoperiod, which is associated with peak disease incidence. The underlying coupling mechanisms of the SCN and the interplay between the SCN and the HPA axis have yet to be fully elucidated. In this work, we propose a mathematical model including a multiple-cellular SCN compartment and the HPA axis to investigate the properties of the circadian timing system under photoperiod changes. Our model predicts that the probability-dependent network is more energy-efficient than the distance-dependent network. Coupling the SCN network by intra-subpopulation and inter-subpopulation forces, we identified the negative correlation between robustness and plasticity of the oscillatory network. The HPA rhythms were predicted to be strongly entrained to the SCN rhythms with a pro-inflammatory high-amplitude glucocorticoid profile under SP. The fast temporal topology switch of the SCN network was predicted to enhance synchronization when the synchronization is not complete. These synchronization and circadian dynamics alterations might govern the seasonal variation of disease incidence and its symptom severity.

Motif structure for the four subgroups within the suprachiasmatic nuclei affects its entrainment ability

Circadian rhythms of physiological and behavioral activities are regulated by a central clock. This clock is located in the bilaterally symmetrical suprachiasmatic nucleus (SCN) of mammals. Each nucleus contains a light-sensitive group of neurons, named the ventrolateral (VL) part, with the rest of the neurons being insensitive to light, named the dorsomedial (DM) group. While the coupling between the VL and DM subgroups have been investigated quite well, the communication among the four subgroups across the nuclei did not get a lot of attention. In this article, we theoretically analyzed seven motiflike connection patterns to investigate the network of the two nuclei of the SCN as a whole in relation to the function of the SCN. We investigated the entrainment ability of the SCN and found that the entrainment range is larger in the motifs containing a link between the two VL parts across the nuclei, but it is smaller in the motifs that contain a link between the two DM parts across the nuclei. The SCN may strengthen or weaken connections between the left and right nucleus to accomodate changes in external conditions, such as resynchronization after a jet lag, adjustment to photoperiod or for the aging SCN.

Network Structure of the Master Clock Is Important for Its Primary Function

A master clock located in the suprachiasmatic nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities in mammals. The SCN has two main functions in the regulation: an endogenous clock produces the endogenous rhythmic signal in body rhythms, and a calibrator synchronizes the body rhythms to the external light-dark cycle. These two functions have been determined to depend on either the dynamic behaviors of individual neurons or the whole SCN neuronal network. In this review, we first introduce possible network structures for the SCN, as revealed by time series analysis from real experimental data. It was found that the SCN network is heterogeneous and sparse, that is, the average shortest path length is very short, some nodes are hubs with large node degrees but most nodes have small node degrees, and the average node degree of the network is small. Secondly, the effects of the SCN network structure on the SCN function are reviewed based on mathematical models of the SCN network. It was found that robust rhythms with large amplitudes, a high synchronization between SCN neurons and a large entrainment ability exists mainly in small-world and scale-free type networks, but not other types. We conclude that the SCN most probably is an efficient small-world type or scale-free type network, which drives SCN function.

Modelling the functional roles of synaptic and extra-synaptic γ-aminobutyric acid receptor dynamics in circadian timekeeping

In the suprachiasmatic nucleus (SCN), γ-aminobutyric acid (GABA) is a primary neurotransmitter. GABA can signal through two types of GABAA receptor subunits, often referred to as synaptic GABAA (gamma subunit) and extra-synaptic GABAA (delta subunit). To test the functional roles of these distinct GABAA in regulating circadian rhythms, we developed a multicellular SCN model where we could separately compare the effects of manipulating GABA neurotransmitter or receptor dynamics. Our model predicted that blocking GABA signalling modestly increased synchrony among circadian cells, consistent with published SCN pharmacology. Conversely, the model predicted that lowering GABAA receptor density reduced firing rate, circadian cell fraction, amplitude and synchrony among individual neurons. When we tested these predictions, we found that the knockdown of delta GABAA reduced the amplitude and synchrony of clock gene expression among cells in SCN explants. The model further predicted that increasing gamma GABAA densities could enhance synchrony, as opposed to increasing delta GABAA densities. Overall, our model reveals how blocking GABAA receptors can modestly increase synchrony, while increasing the relative density of gamma over delta subunits can dramatically increase synchrony. We hypothesize that increased gamma GABAA density in the winter could underlie the tighter phase relationships among SCN cells.

Electrophysiological Approaches to Studying the Suprachiasmatic Nucleus

In mammals, the part of the nervous system responsible for most circadian behavior can be localized to a bilaterally paired structure in the hypothalamus known as the suprachiasmatic nucleus (SCN). Understanding the mammalian circadian system will require a detailed multilevel analysis of neural SCN circuits ex vivo and in vivo. Many of the techniques and approaches that are used for the analysis of the circuitry driving circadian oscillations in the SCN are similar to those employed in other brain regions. There is, however, one fundamental difference that needs to be taken into consideration, that is, the physiological, cell, and molecular properties of SCN neurons vary with the time of day. In this chapter, we will consider the preparations and electrophysiological techniques that we have used to analyze the SCN circuit focusing on the acute brain slice and intact, freely moving animal.

Evolutionary Constraints on Connectivity Patterns in the Mammalian Suprachiasmatic Nucleus

The mammalian suprachiasmatic nucleus (SCN) comprises about 20,000 interconnected oscillatory neurons that create and maintain a robust circadian signal which matches to external light cues. Here, we use an evolutionary game theoretic framework to explore how evolutionary constraints can influence the synchronization of the system under various assumptions on the connection topology, contributing to the understanding of the structure of interneuron connectivity. Our basic model represents the SCN as a network of agents each with two properties-a phase and a flag that determines if it communicates with its neighbors or not. Communication comes at a cost to the agent, but synchronization of phases with its neighbors bears a benefit. Earlier work shows that when we have "all-to-all" connectivity, where every agent potentially communicates with every other agent, there is often a simple trade-off that leads to complete communication and synchronization of the system: the benefit must be greater than twice the cost. This trade-off for all-to-all connectivity gives us a baseline to compare to when looking at other topologies. Using simulations, we compare three plausible topologies to the all-to-all case, finding that convergence to synchronous dynamics occurs in all considered topologies under similar benefit and cost trade-offs. Consequently, sparser, less biologically costly topologies are reasonable evolutionary outcomes for organisms that develop a synchronizable oscillatory network. Our simulations also shed light on constraints imposed by the time scale on which we observe the SCN to arise in mammals. We find two conditions that allow for a synchronizable system to arise in relatively few generations. First, the benefits of connectivity must outweigh the cost of facilitating the connectivity in the network. Second, the game at the core of the model needs to be more cooperative than antagonistic games such as the Prisoner's Dilemma. These results again imply that evolutionary pressure may have driven the system towards sparser topologies, as they are less costly to create and maintain. Last, our simulations indicate that models based on the mutualism game fare the best in uptake of communication and synchronization compared to more antagonistic games such as the Prisoner's Dilemma.

The wrinkling of time: Aging, inflammation, oxidative stress, and the circadian clock in neurodegeneration

A substantial body of research now implicates the circadian clock in the regulation of an array of diverse biological processes including glial function, metabolism, peripheral immune responses, and redox homeostasis. Sleep abnormalities and other forms of circadian disruption are common symptoms of aging and neurodegeneration. Circadian clock disruption may also influence the aging processes and the pathogenesis of neurodegenerative diseases. The specific mechanisms governing the interaction between circadian systems, aging, and the immune system are still being uncovered. Here, we review the evidence supporting a bidirectional relationship between aging and the circadian system. Further, we explore the hypothesis that age-related circadian deterioration may exacerbate multiple pathogenic processes, priming the brain for neurodegeneration.

Astrocytic Modulation of Neuronal Activity in the Suprachiasmatic Nucleus: Insights from Mathematical Modeling

The suprachiasmatic nucleus (SCN) of the hypothalamus consists of a highly heterogeneous neuronal population networked together to allow precise and robust circadian timekeeping in mammals. While the critical importance of SCN neurons in regulating circadian rhythms has been extensively studied, the roles of SCN astrocytes in circadian system function are not well understood. Recent experiments have demonstrated that SCN astrocytes are circadian oscillators with the same functional clock genes as SCN neurons. Astrocytes generate rhythmic outputs that are thought to modulate neuronal activity through pre- and postsynaptic interactions. In this study, we developed an in silico multicellular model of the SCN clock to investigate the impact of astrocytes in modulating neuronal activity and affecting key clock properties such as circadian rhythmicity, period, and synchronization. The model predicted that astrocytes could alter the rhythmic activity of neurons via bidirectional interactions at tripartite synapses. Specifically, astrocyte-regulated extracellular glutamate was predicted to increase neuropeptide signaling from neurons. Consistent with experimental results, we found that astrocytes could increase the circadian period and enhance neural synchronization according to their endogenous circadian period. The impact of astrocytic modulation of circadian rhythm amplitude, period, and synchronization was predicted to be strongest when astrocytes had periods between 0 and 2 h longer than neurons. Increasing the number of neurons coupled to the astrocyte also increased its impact on period modulation and synchrony. These computational results suggest that signals that modulate astrocytic rhythms or signaling (e.g., as a function of season, age, or treatment) could cause disruptions in circadian rhythm or serve as putative therapeutic targets.

Finite Size Effects in Networks of Coupled Neurons

We use extensive computer simulations to study synchronization phenomena in networks of biological neurons. Each individual neuron is modeled using the leaky integrate-and-fire (LIF) scheme, while many neurons are coupled nonlocally in a network. In this system chimera states develop, which are complex states consisting of coexisting synchronous and asynchronous network areas. We study the influence of the network size on the properties and the form of chimera states. We show that for constant coupling strength, the number of the synchronous/asynchronous domains depends quantitatively on the coupling ratio. This dependence allows to extract synchronization properties in large ensembles of neurons after extrapolating from simulations of small networks. Since computer simulations of even small neuron networks are highly demanding in memory and CPU time, this property is particularly important in view of the large number of neurons involved in any cognitive function. In total, the number of neurons in the human brain is of the order of 10¹⁰, and each of them is connected with an average of 10³ other neurons.

Disassortative Network Structure Improves the Synchronization between Neurons in the Suprachiasmatic Nucleus

In mammals, an endogenous clock located in the suprachiasmatic nucleus (SCN) of the brain regulates the circadian rhythms of physiological and behavioral activities. The SCN is composed of about 20,000 neurons that are autonomous oscillators with nonidentical intrinsic periods ranging from 22 h to 28 h. These neurons are coupled through neurotransmitters and synchronized to form a network, which produces a robust circadian rhythm of a uniform period. The neurons, which are the nodes in the network, are known to be heterogeneous in their characteristics, which is reflected in different phenotypes and different functionality. This heterogeneous nature of the nodes of the network leads to the question as to whether the structure of the SCN network is assortative or disassortative. Thus far, the disassortativity of the SCN network has not been assessed and neither have its effects on the collective behaviors of the SCN neurons. In the present study, we build a directed SCN network composed of hundreds of neurons for a single slice using the method of transfer entropy, based on the experimental data. Then, we measured the synchronization degree as well as the disassortativity coefficient of the network structure (calculated by either the out-degrees or the in-degrees of the nodes) and found that the network of the SCN is a disassortative network. Furthermore, a positive relationship is observed between the synchronization degree and disassortativity of the network, which is confirmed by simulations of our modeling. Our finding suggests that the disassortativity of the network structure plays a role in the synchronization between SCN neurons; that is, the synchronization degree increases with the increase of the disassortativity, which implies that a more heterogeneous coupling in the network of the SCN is important for proper function of the SCN.

Mathematical modeling of circadian rhythms

Circadian rhythms are endogenous ~24-hr oscillations usually entrained to daily environmental cycles of light/dark. Many biological processes and physiological functions including mammalian body temperature, the cell cycle, sleep/wake cycles, neurobehavioral performance, and a wide range of diseases including metabolic, cardiovascular, and psychiatric disorders are impacted by these rhythms. Circadian clocks are present within individual cells and at tissue and organismal levels as emergent properties from the interaction of cellular oscillators. Mathematical models of circadian rhythms have been proposed to provide a better understanding of and to predict aspects of this complex physiological system. These models can be used to: (a) manipulate the system in silico with specificity that cannot be easily achieved using in vivo and in vitro experimental methods and at lower cost, (b) resolve apparently contradictory empirical results, (c) generate hypotheses, (d) design new experiments, and (e) to design interventions for altering circadian rhythms. Mathematical models differ in structure, the underlying assumptions, the number of parameters and variables, and constraints on variables. Models representing circadian rhythms at different physiologic scales and in different species are reviewed to promote understanding of these models and facilitate their use. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Protein sequestration versus Hill-type repression in circadian clock models

Circadian (∼24 h) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptional-translational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, the author discusses how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modelling of transcriptional repression mechanisms in molecular circadian clocks.

Model-based Inference of a Directed Network of Circadian Neurons

The suprachiasmatic nucleus (SCN) is the master clock of the brain. It is a network of neurons that behave like biological oscillators, capable of synchronizing and maintaining daily rhythms. The detailed structure of this network is still unknown, and the role that the connectivity pattern plays in the network’s ability to generate robust oscillations has yet to be fully elucidated. In recent work, we used an information theory–based technique to infer the structure of the functional network for synchronization, from bioluminescence reporter data. Here, we propose a computational method to determine the directionality of the connections between the neurons. We find that most SCN neurons have a similar number of incoming connections, but the number of outgoing connections per neuron varies widely, with the most highly connected neurons residing preferentially in the core.

Multiplexing Visual Signals in the Suprachiasmatic Nuclei

The suprachiasmatic nuclei (SCN), the site of the mammalian circadian (daily) pacemaker, contains thousands of interconnected neurons, some of which receive direct retinal input. Here, we study the fast (<1 s) responses of SCN neurons to visual stimuli with a large-scale mathematical model tracking the ionic currents and voltage of all SCN neurons. We reconstruct the SCN network connectivity and reject 99.99% of theoretically possible SCN networks by requiring that the model reproduces experimentally determined receptive fields of SCN neurons. The model shows how the SCN neuronal network can enhance circadian entrainment by sensitizing a population of neurons in the ventral SCN to irradiance. This SCN network also increases the spatial acuity of neurons and increases the accuracy of a simulated subconscious spatial visual task. We hypothesize that much of the fast electrical activity within the SCN is related to the processing of spatial information.

Three-dimensional chimera patterns in networks of spiking neuron oscillators

We study the stable spatiotemporal patterns that arise in a three-dimensional (3D) network of neuron oscillators, whose dynamics is described by the leaky integrate-and-fire (LIF) model. More specifically, we investigate the form of the chimera states induced by a 3D coupling matrix with nonlocal topology. The observed patterns are in many cases direct generalizations of the corresponding two-dimensional (2D) patterns, e.g., spheres, layers, and cylinder grids. We also find cylindrical and "cross-layered" chimeras that do not have an equivalent in 2D systems. Quantitative measures are calculated, such as the ratio of synchronized and unsynchronized neurons as a function of the coupling range, the mean phase velocities, and the distribution of neurons in mean phase velocities. Based on these measures, the chimeras are categorized in two families. The first family of patterns is observed for weaker coupling and exhibits higher mean phase velocities for the unsynchronized areas of the network. The opposite holds for the second family, where the unsynchronized areas have lower mean phase velocities. The various measures demonstrate discontinuities, indicating criticality as the parameters cross from the first family of patterns to the second.

Dispersion of the intrinsic neuronal periods affects the relationship of the entrainment range to the coupling strength in the suprachiasmatic nucleus

Living beings on the Earth are subjected to and entrained (synchronized) to the natural 24-h light-dark cycle. Interestingly, they can also be entrained to an external artificial cycle of non-24-h periods. The range of these periods is called the entrainment range and it differs among species. In mammals, the entrainment range is regulated by a main clock located in the suprachiasmatic nucleus (SCN) which is composed of 10 000 neurons in the brain. Previous works have found that the entrainment range depends on the cellular coupling strength in the SCN. In particular, the entrainment range decreases with the increase of the cellular coupling strength, provided that all the neuronal oscillators are identical. However, the SCN neurons differ in the intrinsic periods that follow a normal distribution in a range from 22 to 28 h. In the present study, taking the dispersion of the intrinsic neuronal periods into account, we examined the relationship between the entrainment range and the coupling strength. Results from numerical simulations and theoretical analyses both show that the relationship is altered to be paraboliclike if the intrinsic neuronal periods are nonidentical, and the maximal entrainment range is obtained with a suitable coupling strength. Our results shed light on the role of the cellular coupling in the entrainment ability of the SCN network.

Calcium Circadian Rhythmicity in the Suprachiasmatic Nucleus: Cell Autonomy and Network Modulation

Circadian rhythms of mammalian physiology and behavior are coordinated by the suprachiasmatic nucleus (SCN) in the hypothalamus. Within SCN neurons, various aspects of cell physiology exhibit circadian oscillations, including circadian clock gene expression, levels of intracellular Ca²⁺ ([Ca²⁺]_i), and neuronal firing rate. [Ca²⁺]_i oscillates in SCN neurons even in the absence of neuronal firing. To determine the causal relationship between circadian clock gene expression and [Ca²⁺]_i rhythms in the SCN, as well as the SCN neuronal network dependence of [Ca²⁺]_i rhythms, we introduced GCaMP3, a genetically encoded fluorescent Ca²⁺ indicator, into SCN neurons from PER2::LUC knock-in reporter mice. Then, PER2 and [Ca²⁺]_i were imaged in SCN dispersed and organotypic slice cultures. In dispersed cells, PER2 and [Ca²⁺]_i both exhibited cell autonomous circadian rhythms, but [Ca²⁺]_i rhythms were typically weaker than PER2 rhythms. This result matches the predictions of a detailed mathematical model in which clock gene rhythms drive [Ca²⁺]_i rhythms. As predicted by the model, PER2 and [Ca²⁺]_i rhythms were both stronger in SCN slices than in dispersed cells and were weakened by blocking neuronal firing in slices but not in dispersed cells. The phase relationship between [Ca²⁺]_i and PER2 rhythms was more variable in cells within slices than in dispersed cells. Both PER2 and [Ca²⁺]_i rhythms were abolished in SCN cells deficient in the essential clock gene Bmal1. These results suggest that the circadian rhythm of [Ca²⁺]_i in SCN neurons is cell autonomous and dependent on clock gene rhythms, but reinforced and modulated by a synchronized SCN neuronal network.

The aging clock: circadian rhythms and later life

Circadian rhythms play an influential role in nearly all aspects of physiology and behavior in the vast majority of species on Earth. The biological clockwork that regulates these rhythms is dynamic over the lifespan: rhythmic activities such as sleep/wake patterns change markedly as we age, and in many cases they become increasingly fragmented. Given that prolonged disruptions of normal rhythms are highly detrimental to health, deeper knowledge of how our biological clocks change with age may create valuable opportunities to improve health and longevity for an aging global population. In this Review, we synthesize key findings from the study of circadian rhythms in later life, identify patterns of change documented to date, and review potential physiological mechanisms that may underlie these changes.

Mechanists Must be Holists Too! Perspectives from Circadian Biology

The pursuit of mechanistic explanations in biology has produced a great deal of knowledge about the parts, operations, and organization of mechanisms taken to be responsible for biological phenomena. Holist critics have often raised important criticisms of proposed mechanistic explanations, but until recently holists have not had alternative research strategies through which to advance explanations. This paper argues both that the results of mechanistic strategies has forced mechanists to confront ways in which whole systems affect their components and that new representational and modeling strategies are providing tools for understanding these effects of whole systems upon components. Drawing from research on the mechanism responsible for circadian rhythms in mammals, I develop two examples in which mechanistic analysis is being integrated into a more holist perspective: research revealing intercellular integration of circadian mechanisms with those involved in cell metabolism and research revealing that stable␣rhythms are dependent on how individual cells in the suprachiasmatic nucleus synchronize with each other to generate regular rhythms. Tools such as network diagramming and computational modeling are providing means to integrate mechanistic models into accounts of whole systems.

Coupling Controls the Synchrony of Clock Cells in Development and Knockouts

In mammals, a network of coupled neurons within the hypothalamus coordinates physiological rhythms with daily changes in the environment. In each neuron, delayed negative transcriptional feedbacks generate oscillations, albeit noisy and unreliable ones. Coupling mediated by diffusible neuropeptides lends precision and robustness to circadian rhythms. The double knockout of Cryptochrome Cry turns adult mice arrhythmic. But, remarkably, double knockout neonates continue to show robust oscillation much like wild-type neonates and appear to lose rhythmicity with development. We study quantitatively dispersed neurons and brain slices from wild-type and Cry double knockout mice to understand the links between single cell rhythmicity and intercellular coupling. We quantify oscillator properties of dispersed cells using nonlinear regression and study bifurcations diagrams of network models. We find that varying just three parameters-oscillator strength, strength of coupling, and timing of coupling-can reproduce experimentally observed features. In particular, modeling reveals that minor changes in timing of coupling can destroy synchronization as observed in adult slices from knockout mice.

The synchronization of neuronal oscillators determined by the directed network structure of the suprachiasmatic nucleus under different photoperiods

The main function of the principal clock located in the suprachiasmatic nucleus (SCN) of mammals is synchronizing the body rhythms to the 24 h light-dark cycle. Additionally, the SCN is able to adapt to the photoperiod of the cycle which varies among seasons. Under the long photoperiod (LP), the synchronization degree of the SCN neurons is lower than that under the photoperiod (SP). In the present study, a potential explanation is given for this phenomenon. We propose that the asymmetrical coupling between the light-signal-sensitive part (the ventralateral part, abbreviation: VL) and the light-signal-insensitive part (the dorsalmedial part, abbreviation: DM) of the SCN plays a role in the synchronization degree, which is reflected by the ratio of the number of the directed links from the VL neurons to the DM neurons to the total links of both directions between the VL and the DM. The ratio is assumed to characterize the directed network structure under different photoperiods, which is larger under the SP and smaller under the LP. We found that with the larger ratio in the situation of the SP, the synchronization degree is higher. Our finding may shed new light on the asymmetrical coupling between the VL and the DM, and the network structure of the SCN.

The circadian rhythm induced by the heterogeneous network structure of the suprachiasmatic nucleus

In mammals, the master clock is located in the suprachiasmatic nucleus (SCN), which is composed of about 20 000 nonidentical neuronal oscillators expressing different intrinsic periods. These neurons are coupled through neurotransmitters to form a network consisting of two subgroups, i.e., a ventrolateral (VL) subgroup and a dorsomedial (DM) subgroup. The VL contains about 25% SCN neurons that receive photic input from the retina, and the DM comprises the remaining 75% SCN neurons which are coupled to the VL. The synapses from the VL to the DM are evidently denser than that from the DM to the VL, in which the VL dominates the DM. Therefore, the SCN is a heterogeneous network where the neurons of the VL are linked with a large number of SCN neurons. In the present study, we mimicked the SCN network based on Goodwin model considering four types of networks including an all-to-all network, a Newman-Watts (NW) small world network, an Erdös-Rényi (ER) random network, and a Barabási-Albert (BA) scale free network. We found that the circadian rhythm was induced in the BA, ER, and NW networks, while the circadian rhythm was absent in the all-to-all network with weak cellular coupling, where the amplitude of the circadian rhythm is largest in the BA network which is most heterogeneous in the network structure. Our finding provides an alternative explanation for the induction or enhancement of circadian rhythm by the heterogeneity of the network structure.

Functional network inference of the suprachiasmatic nucleus

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.

Heterogeneity induces rhythms of weakly coupled circadian neurons

The main clock located in the suprachiasmatic nucleus (SCN) regulates circadian rhythms in mammals. The SCN is composed of approximately twenty thousand heterogeneous self-oscillating neurons, that have intrinsic periods varying from 22 h to 28 h. They are coupled through neurotransmitters and neuropeptides to form a network and output a uniform periodic rhythm. Previous studies found that the heterogeneity of the neurons leads to attenuation of the circadian rhythm with strong cellular coupling. In the present study, we investigate the heterogeneity of the neurons and of the network in the condition of constant darkness. Interestingly, we found that the heterogeneity of weakly coupled neurons enables them to oscillate and strengthen the circadian rhythm. In addition, we found that the period of the SCN network increases with the increase of the degree of heterogeneity. As the network heterogeneity does not change the dynamics of the rhythm, our study shows that the heterogeneity of the neurons is vitally important for rhythm generation in weakly coupled systems, such as the SCN, and it provides a new method to strengthen the circadian rhythm, as well as an alternative explanation for differences in free running periods between species in the absence of the daily cycle.

On the Inference of Functional Circadian Networks Using Granger Causality

Being able to infer one way direct connections in an oscillatory network such as the suprachiastmatic nucleus (SCN) of the mammalian brain using time series data is difficult but crucial to understanding network dynamics. Although techniques have been developed for inferring networks from time series data, there have been no attempts to adapt these techniques to infer directional connections in oscillatory time series, while accurately distinguishing between direct and indirect connections. In this paper an adaptation of Granger Causality is proposed that allows for inference of circadian networks and oscillatory networks in general called Adaptive Frequency Granger Causality (AFGC). Additionally, an extension of this method is proposed to infer networks with large numbers of cells called LASSO AFGC. The method was validated using simulated data from several different networks. For the smaller networks the method was able to identify all one way direct connections without identifying connections that were not present. For larger networks of up to twenty cells the method shows excellent performance in identifying true and false connections; this is quantified by an area-under-the-curve (AUC) 96.88%. We note that this method like other Granger Causality-based methods, is based on the detection of high frequency signals propagating between cell traces. Thus it requires a relatively high sampling rate and a network that can propagate high frequency signals.

Brain clock driven by neuropeptides and second messengers

The master circadian pacemaker in mammals is localized in a small portion of the brain called the suprachiasmatic nucleus (SCN). It is unclear how the SCN produces circadian rhythms. A common interpretation is that the SCN produces oscillations through the coupling of genetic oscillators in the neurons. The coupling is effected by a network of neuropeptides and second messengers. This network is crucial for the correct function of the SCN. However, models that study a possible oscillatory behavior of the network itself have received little attention. Here we propose and analyze a model to examine this oscillatory potential. We show that an intercellular oscillator emerges in the SCN as a result of the neuropeptide and second messenger dynamics. We find that this intercellular clock can produce circadian rhythms by itself with and without genetic clocks. We also found that the model is robust to perturbation of parameters and can be entrained by light-dark cycles.

Lhx1 controls terminal differentiation and circadian function of the suprachiasmatic nucleus

Vertebrate circadian rhythms are organized by the hypothalamic suprachiasmatic nucleus (SCN). Despite its physiological importance, SCN development is poorly understood. Here, we show that Lim homeodomain transcription factor 1 (Lhx1) is essential for terminal differentiation and function of the SCN. Deletion of Lhx1 in the developing SCN results in loss of SCN-enriched neuropeptides involved in synchronization and coupling to downstream oscillators, among other aspects of circadian function. Intact, albeit damped, clock gene expression rhythms persist in Lhx1-deficient SCN; however, circadian activity rhythms are highly disorganized and susceptible to surprising changes in period, phase, and consolidation following neuropeptide infusion. Our results identify a factor required for SCN terminal differentiation. In addition, our in vivo study of combinatorial SCN neuropeptide disruption uncovered synergies among SCN-enriched neuropeptides in regulating normal circadian function. These animals provide a platform for studying the central oscillator's role in physiology and cognition.

Timing of neuropeptide coupling determines synchrony and entrainment in the mammalian circadian clock

Robust synchronization is a critical feature of several systems including the mammalian circadian clock. The master circadian clock in mammals consists of about 20000 ‘sloppy’ neuronal oscillators within the hypothalamus that keep robust time by synchronization driven by inter-neuronal coupling. The complete understanding of this synchronization in the mammalian circadian clock and the mechanisms underlying it remain an open question. Experiments and computational studies have shown that coupling individual oscillators can achieve robust synchrony, despite heterogeneity and different network topologies. But, much less is known regarding the mechanisms and circuits involved in achieving this coupling, due to both system complexity and experimental limitations. Here, we computationally study the coupling mediated by the primary coupling neuropeptide, vasoactive intestinal peptide (VIP) and its canonical receptor, VPAC2R, using the transcriptional elements and generic mode of VIP-VPAC2R signaling. We find that synchrony is only possible if VIP (an inducer of Per expression) is released in-phase with activators of Per expression. Moreover, anti-phasic VIP release suppresses coherent rhythms by moving the network into a desynchronous state. Importantly, experimentally observed rhythms in VPAC2R have little effect on network synchronization, but can improve the amplitude of the SCN network rhythms while narrowing the network entrainment range. We further show that these findings are valid across several computational network models. Thus, we identified a general design principle to achieve robust synchronization: An activating coupling agent, such as VIP, must act in-phase with the activity of core-clock promoters. More generally, the phase of coupling is as critical as the strength of coupling from the viewpoint of synchrony and entrainment.

Synchronization among multiple oscillators is a common theme in many biological and engineered systems. Here, we look at its use by the mammalian biological clock to keep accurate time. Through biochemical interactions among a network of inaccurate neuron clocks, a strong precise clock is produced. Although we are gradually learning more about these biochemical interactions, the details still remain largely unclear. Studies, both computational and experimental, have shown that the strength of the rhythmic interaction critically decides if a system can synchronize, i.e., the interactions must be strong enough. In this work, we show that the rhythmic interaction between these neuronal clocks must be timed correctly (in the right phase) in addition to being strong enough to synchronize the network. Activating (repressing) interactions must coincide with other activators (repressors) in each neuron to achieve synchrony. Since this principle imposes certain properties on synchronizing interactions, these properties can be used to identify and understand novel interaction mechanisms. Further, these principles are applicable to interactions between cellular oscillators in other tissues and organisms.

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.

From molecules to behavior and the clinic: Integration in chronobiology

Chronobiology, especially the study of circadian rhythms, provides a model scientific field in which philosophers can study how investigators from a variety of disciplines working at different levels of organization are each contributing to a multi-level account of the responsible mechanism. I focus on how the framework of mechanistic explanation integrates research designed to decompose the mechanism with efforts directed at recomposition that relies especially on computation models. I also examine how recently the integration has extended beyond basic research to the processes through which the disruption of circadian rhythms contributes to disease, including various forms of cancer. Understanding these linkages has been facilitated by discoveries about how circadian mechanisms interact with mechanisms involved in other physiological processes, including the cell cycle and the immune system.

High-frequency stimulation of excitable cells and networks

High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks.

GABA networks destabilize genetic oscillations in the circadian pacemaker

Systems of coupled oscillators abound in nature. How they establish stable phase relationships under diverse conditions is fundamentally important. The mammalian suprachiasmatic nucleus (SCN) is a self-sustained, synchronized network of circadian oscillators that coordinates daily rhythms in physiology and behavior. To elucidate the underlying topology and signaling mechanisms that modulate circadian synchrony, we discriminated the firing of hundreds of SCN neurons continuously over days. Using an analysis method to identify functional interactions between neurons based on changes in their firing, we characterized a GABAergic network comprised of fast, excitatory, and inhibitory connections that is both stable over days and changes in strength with time of day. By monitoring PERIOD2 protein expression, we provide the first evidence that these millisecond-level interactions actively oppose circadian synchrony and inject jitter into daily rhythms. These results provide a mechanism by which circadian oscillators can tune their phase relationships under different environmental conditions.

Weakly circadian cells improve resynchrony

The mammalian suprachiasmatic nuclei (SCN) contain thousands of neurons capable of generating near 24-h rhythms. When isolated from their network, SCN neurons exhibit a range of oscillatory phenotypes: sustained or damping oscillations, or arrhythmic patterns. The implications of this variability are unknown. Experimentally, we found that cells within SCN explants recover from pharmacologically-induced desynchrony by re-establishing rhythmicity and synchrony in waves, independent of their intrinsic circadian period We therefore hypothesized that a cell's location within the network may also critically determine its resynchronization. To test this, we employed a deterministic, mechanistic model of circadian oscillators where we could independently control cell-intrinsic and network-connectivity parameters. We found that small changes in key parameters produced the full range of oscillatory phenotypes seen in biological cells, including similar distributions of period, amplitude and ability to cycle. The model also predicted that weaker oscillators could adjust their phase more readily than stronger oscillators. Using these model cells we explored potential biological consequences of their number and placement within the network. We found that the population synchronized to a higher degree when weak oscillators were at highly connected nodes within the network. A mathematically independent phase-amplitude model reproduced these findings. Thus, small differences in cell-intrinsic parameters contribute to large changes in the oscillatory ability of a cell, but the location of weak oscillators within the network also critically shapes the degree of synchronization for the population.

Circadian rhythms are daily, near 24-h oscillations in biological processes that nearly all organisms on Earth experience. Single cells contain a molecular clock that drives circadian rhythms in physiology and, when many cells synchronize in a population, daily behaviors. We hypothesized that small differences in intrinsic cellular properties allow for a diversity of circadian periods and amplitudes across cells. We observed circadian cells and their synchrony before, during, and after limiting communication between cells and then compared their intrinsic properties to their resynchronization behavior. We found that arrhythmic, weakly oscillating, and self-sustained circadian cells rejoined the rhythmic population independent of their cell-intrinsic oscillations. Using a mechanistic computational model of circadian cells, we found that resynchronization could be enhanced by including more weak oscillators or by placing weak oscillators at more connected nodes in the network. We conclude that intrinsic properties (e.g. oscillator weakness and responsiveness) and network structure (e.g. positions of weak oscillators) can independently buffer tissue rhythms from perturbations. This reveals how cellular and network properties impose rules on systems of circadian cells that must achieve synchrony from a desynchronized state, for example during perinatal development or when forced to overcome societal constraints on sleep-wake behavior, such as working early or late shifts.

Modeling the seasonal adaptation of circadian clocks by changes in the network structure of the suprachiasmatic nucleus

The dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter. It has been observed experimentally, however, that the dynamics of individual neurons of the suprachiasmatic nucleus (SCN) does not change as the seasons change. Rather, the seasonal adaptation of the circadian clock is hypothesized to be a consequence of changes in the intercellular dynamics, which leads to a phase distribution of electrical activity of SCN neurons that is narrower in winter and broader during summer. Yet to understand this complex intercellular dynamics, a more thorough understanding of the impact of the network structure formed by the SCN neurons is needed. To that effect, we propose a mathematical model for the dynamics of the SCN neuronal architecture in which the structure of the network plays a pivotal role. Using our model we show that the fraction of long-range cell-to-cell connections and the seasonal changes in the daily rhythms may be tightly related. In particular, simulations of the proposed mathematical model indicate that the fraction of long-range connections between the cells adjusts the phase distribution and consequently the length of the behavioral activity as follows: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase. Our model is also able to account for the experimental observations indicating a larger light-induced phase-shift of the circadian clock during winter, which we show to be a consequence of higher synchronization between neurons. Our model thus provides evidence that the variations in the seasonal dynamics of circadian clocks can in part also be understood and regulated by the plasticity of the SCN network structure.

Circadian clocks drive the temporal coordination of internal biological processes, which in turn determine daily rhythms in physiology and behavior in the most diverse organisms. In mammals, the 24-hour timing clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN is a network of interconnected neurons that serves as a robust self-sustained circadian pacemaker. The electrical activity of these neurons and their synchronization with the 24-hour cycle is established via the environmental day and night cycles. Apart from daily luminance changes, mammals are exposed to seasonal day length changes as well. Remarkably, it has been shown experimentally that the seasonal adaptations to different photoperiods are related to the modifications of the neuronal activity of the SCN due to the plasticity of the network. In our paper, by developing a mathematical model of the SCN architecture, we explore in depth the role of the structure of this important neuronal network. We show that the redistribution of the neuronal activity during winter and summer can in part be explained by structural changes of the network. Interestingly, the alterations of the electrical activity patterns can be related with small-world properties of our proposed SCN network.

Persistent cell-autonomous circadian oscillations in fibroblasts revealed by six-week single-cell imaging of PER2::LUC bioluminescence

Biological oscillators naturally exhibit stochastic fluctuations in period and amplitude due to the random nature of molecular reactions. Accurately measuring the precision of noisy oscillators and the heterogeneity in period and strength of rhythmicity across a population of cells requires single-cell recordings of sufficient length to fully represent the variability of oscillations. We found persistent, independent circadian oscillations of clock gene expression in 6-week-long bioluminescence recordings of 80 primary fibroblast cells dissociated from PER2::LUC mice and kept in vitro for 6 months. Due to the stochastic nature of rhythmicity, the proportion of cells appearing rhythmic increases with the length of interval examined, with 100% of cells found to be rhythmic when using 3-week windows. Mean period and amplitude are remarkably stable throughout the 6-week recordings, with precision improving over time. For individual cells, precision of period and amplitude are correlated with cell size and rhythm amplitude, but not with period, and period exhibits much less cycle-to-cycle variability (CV 7.3%) than does amplitude (CV 37%). The time series are long enough to distinguish stochastic fluctuations within each cell from differences among cells, and we conclude that the cells do exhibit significant heterogeneity in period and strength of rhythmicity, which we measure using a novel statistical metric. Furthermore, stochastic modeling suggests that these single-cell clocks operate near a Hopf bifurcation, such that intrinsic noise enhances the oscillations by minimizing period variability and sustaining amplitude.

Effect of network architecture on synchronization and entrainment properties of the circadian oscillations in the suprachiasmatic nucleus

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus constitutes the central circadian pacemaker. The SCN receives light signals from the retina and controls peripheral circadian clocks (located in the cortex, the pineal gland, the liver, the kidney, the heart, etc.). This hierarchical organization of the circadian system ensures the proper timing of physiological processes. In each SCN neuron, interconnected transcriptional and translational feedback loops enable the circadian expression of the clock genes. Although all the neurons have the same genotype, the oscillations of individual cells are highly heterogeneous in dispersed cell culture: many cells present damped oscillations and the period of the oscillations varies from cell to cell. In addition, the neurotransmitters that ensure the intercellular coupling, and thereby the synchronization of the cellular rhythms, differ between the two main regions of the SCN. In this work, a mathematical model that accounts for this heterogeneous organization of the SCN is presented and used to study the implication of the SCN network topology on synchronization and entrainment properties. The results show that oscillations with larger amplitude can be obtained with scale-free networks, in contrast to random and local connections. Networks with the small-world property such as the scale-free networks used in this work can adapt faster to a delay or advance in the light/dark cycle (jet lag). Interestingly a certain level of cellular heterogeneity is not detrimental to synchronization performances, but on the contrary helps resynchronization after jet lag. When coupling two networks with different topologies that mimic the two regions of the SCN, efficient filtering of pulse-like perturbations in the entrainment pattern is observed. These results suggest that the complex and heterogeneous architecture of the SCN decreases the sensitivity of the network to short entrainment perturbations while, at the same time, improving its adaptation abilities to long term changes.

In order to adapt to their cycling environment, virtually all living organisms have developed an internal timer, the circadian clock. In mammals, the circadian pacemaker is composed of about 20,000 neurons, called the suprachiasmatic nucleus (SCN) located in the hypothalamus. The SCN receives light signals from the retina and controls peripheral circadian clocks to ensure the proper timing of physiological processes. In each SCN neuron, a genetic regulatory network enables the circadian expression of the clock genes, but individual dynamics are highly heterogeneous in dispersed cell culture: many cells present damped oscillations and the period of the oscillations varies from cell to cell. In addition, the neurotransmitters that ensure the intercellular coupling, and thereby the synchronization of the cellular rhythms, differ between the two main regions of the SCN. We present here a mathematical model that accounts for this heterogeneous organization of the SCN and study the implication of the network topology on synchronization and entrainment properties. Our results show that cellular heterogeneity may help the resynchronization after jet lag and suggest that the complex architecture of the SCN decreases the sensitivity of the network to short entrainment perturbations while, at the same time, improving its adaptation abilities to long term changes.

Modeling circadian clocks: Roles, advantages, and limitations

Circadian rhythms are endogenous oscillations characterized by a period of about 24h. They constitute the biological rhythms with the longest period known to be generated at the molecular level. The abundance of genetic information and the complexity of the molecular circuitry make circadian clocks a system of choice for theoretical studies. Many mathematical models have been proposed to understand the molecular regulatory mechanisms that underly these circadian oscillations and to account for their dynamic properties (temperature compensation, entrainment by light dark cycles, phase shifts by light pulses, rhythm splitting, robustness to molecular noise, intercellular synchronization). The roles and advantages of modeling are discussed and illustrated using a variety of selected examples. This survey will lead to the proposal of an integrated view of the circadian system in which various aspects (interlocked feedback loops, inter-cellular coupling, and stochasticity) should be considered together to understand the design and the dynamics of circadian clocks. Some limitations of these models are commented and challenges for the future identified.

A multicellular model for differential regulation of circadian signals in the core and shell regions of the suprachiasmatic nucleus

We developed a multicellular model of the mammalian circadian clock characterized by a high degree of heterogeneity with respect to single cell periodicity and behavior (intrinsic and driven oscillators), neurotransmitter release (VIP, GABA and glutamate synthesis) and spatial organization (core and shell regions), mimicking structural patterns within the suprachiasmatic nucleus (SCN) associated with distinct circadian functions. We simulated the SCN core and shell separately utilizing experimentally derived connectivity schemes for the two subdivisions as observed within the rat SCN. The core was modeled via a small world network characterized by VIP and GABA co-localization, whereas the shell was simulated as a nearest neighbor network promoting local GABAergic connections. To study the function of the axonal plexus extending from the densely innervated ventrolateral region to distal areas across the dorsomedial SCN, directed long range links from the core to the shell were gradually introduced via a probability p(cs) that ranged from 0 to 1. A probability value of 0 excluded core-shell interactions, whereas p(cs)=1 achieved maximal connectivity between the two regions. Our model exhibited a threshold in the number of core-to-shell links required for sufficient cell-to-cell coordination to maintain periodicity and rhythmic behavior across the entire model network (including both shell and core populations) in constant darkness as well as 12:12h light-dark cycles. By contrast, constant light was shown to increase phase synchronization across the shell while core populations remained poorly synchronized, suggesting differential light response across the two SCN compartments. We further simulated increasing percentages of intrinsic oscillators and demonstrated a negative correlation between the number of intrinsic oscillators distributed across the SCN and the ability of the system to produce synchronized signals. Simulations that differed with respect to the placement of intrinsic oscillators supported the hypothesis that improved synchronization is achieved with networks characterized by localized intrinsic oscillators placed exclusively within the shell versus networks containing uniformly distributed intrinsic oscillators in both SCN compartments. This study has successfully reproduced a number of spatiotemporal and behavioral attributes of the SCN, providing a useful computational tool to correlate observed circadian phenotypes with distinct chemoarchitectural properties of spatially localized neural populations.

Multicellular model for intercellular synchronization in circadian neural networks

We developed a multicellular model characterized by a high degree of heterogeneity to investigate possible mechanisms that underlie circadian network synchronization and rhythmicity in the suprachiasmatic nucleus (SCN). We populated a two-dimensional grid with 400 model neurons coupled via γ-aminobutyric acid (GABA) and vasoactive intestinal polypeptide (VIP) neurotransmitters through a putative Ca(2+) mediated signaling cascade to investigate their roles in gene expression and electrical firing activity of cell populations. As observed experimentally, our model predicted that GABA would affect the amplitude of circadian oscillations but not synchrony among individual oscillators. Our model recapitulated experimental findings of decreased synchrony and average periods, loss of rhythmicity, and reduced circadian amplitudes as VIP signaling was eliminated. In addition, simulated increases of VIP reduced periodicity and synchrony. We therefore postulated a physiological range of VIP within which the system is able to produce sustained and synchronized oscillations. Our model recapitulated experimental findings of diminished amplitudes and periodicity with decreasing intracellular Ca(2+) concentrations, suggesting that such behavior could be due to simultaneous decrease of individual oscillation amplitudes and population synchrony. Simulated increases in Cl(-) levels resulted in increased Cl(-) influx into the cytosol, a decrease of inhibitory postsynaptic currents, and ultimately a shift of GABA-elicited responses from inhibitory to excitatory. The simultaneous reduction of IPSCs and increase in membrane resting potential produced GABA dose-dependent increases in firing rates across the population, as has been observed experimentally. By integrating circadian gene regulation and electrophysiology with intracellular and intercellular signaling, we were able to develop the first (to our knowledge) multicellular model that allows the effects of clock genes, electrical firing, Ca(2+), GABA, and VIP on circadian system behavior to be predicted.

Effects of vasoactive intestinal peptide genotype on circadian gene expression in the suprachiasmatic nucleus and peripheral organs

The neuropeptide vasoactive intestinal polypeptide (VIP) has emerged as a key candidate molecule mediating the synchronization of rhythms in clock gene expression within the suprachiasmatic nucleus (SCN). In addition, neurons expressing VIP are anatomically well positioned to mediate communication between the SCN and peripheral oscillators. In this study, we examined the temporal expression profile of 3 key circadian genes: Per1, Per2 , and Bmal1 in the SCN, the adrenal glands and the liver of mice deficient for the Vip gene (VIP KO), and their wild-type counterparts. We performed these measurements in mice held in a light/dark cycle as well as in constant darkness and found that rhythms in gene expression were greatly attenuated in the VIP-deficient SCN. In the periphery, the impact of the loss of VIP varied with the tissue and gene measured. In the adrenals, rhythms in Per1 were lost in VIP-deficient mice, while in the liver, the most dramatic impact was on the phase of the diurnal expression rhythms. Finally, we examined the effects of the loss of VIP on ex vivo explants of the same central and peripheral oscillators using the PER2::LUC reporter system. The VIP-deficient mice exhibited low amplitude rhythms in the SCN as well as altered phase relationships between the SCN and the peripheral oscillators. Together, these data suggest that VIP is critical for robust rhythms in clock gene expression in the SCN and some peripheral organs and that the absence of this peptide alters both the amplitude of circadian rhythms as well as the phase relationships between the rhythms in the SCN and periphery.

Multiscale complexity in the mammalian circadian clock

The field of systems biology studies how the interactions among individual components (e.g. genes and proteins) yield interesting and complex behavior. The circadian (daily) timekeeping system in mammals is an ideal system to study complexity because of its many biological scales (from genes to animal behavior). A wealth of data at each of these scales has recently been discovered. Within each scale, modeling can advance our understanding of challenging problems that arise in studying mammalian timekeeping. However, future work must focus on bridging the multiple spatial and temporal scales in the modeling of SCN network. Here we review recent advances, and then delve into a few areas that are promising research directions. We also discuss the flavor of modeling needed (simple or detailed) as well as new techniques that are needed to meet the challenges in modeling data across scales.

The cell: locus or object of inquiry?

Research in many fields of biology has been extremely successful in decomposing biological mechanisms to discover their parts and operations. It often remains a significant challenge for scientists to recompose these mechanisms to understand how they function as wholes and interact with the environments around them. This is true of the eukaryotic cell. Although initially identified in nineteenth-century cell theory as the fundamental unit of organisms, researchers soon learned how to decompose it into its organelles and chemical constituents and have been highly successful in understanding how these carry out many operations important to life. The emphasis on decomposition is particularly evident in modern cell biology, which for the most part has viewed the cell as merely a locus of the mechanisms responsible for vital phenomena. The cell, however, is also an integrated system and for some explanatory purposes it is essential to recompose it and understand it as an organized whole. I illustrate both the virtues of decomposition (treating the cell as a locus) and recomposition (treating the cell as an object) with recent work on circadian rhythms. Circadian researchers have both identified critical intracellular operations that maintain endogenous oscillations and have also addressed the integration of cells into multicellular systems in which cells constitute units.

Chronic stimulation of the hypothalamic vasoactive intestinal peptide receptor lengthens circadian period in mice and hamsters

Evidence suggests that circadian rhythms are regulated through diffusible signals generated by the suprachiasmatic nucleus (SCN). Vasoactive intestinal peptide (VIP) is located in SCN neurons positioned to receive photic input from the retinohypothalamic tract and transmit information to other SCN cells and adjacent hypothalamic areas. Studies using knockout mice indicate that VIP is essential for synchrony among SCN cells and for the expression of normal circadian rhythms. To test the hypothesis that VIP is also an SCN output signal, we recorded wheel-running activity rhythms in hamsters and continuously infused the VIP receptor agonist BAY 55-9837 in the third ventricle for 28 days. Unlike other candidate output signals, infusion of BAY 55-9837 did not affect activity levels. Instead, BAY 55-9837 lengthened the circadian period by 0.69 +/- 0.04 h (P < 0.0002 compared with controls). Period returned to baseline after infusions. We analyzed the effect of BAY 55-9837 on cultured SCN from PER2::LUC mice to determine if lengthening of the period by BAY 55-9837 is a direct effect on the SCN. Application of 10 muM BAY 55-9837 to SCN in culture lengthened the period of PER2 luciferase expression (24.73 +/- 0.24 h) compared with control SCN (23.57 +/- 0.26, P = 0.01). In addition, rhythm amplitude was significantly increased, consistent with increased synchronization of SCN neurons. The effect of BAY 55-9837 in vivo on period is similar to the effect of constant light. The present results suggest that VIP-VPAC2 signaling in the SCN may play two roles, synchronizing SCN neurons and setting the period of the SCN as a whole.