Functional network inference of the suprachiasmatic nucleus

GABAA receptor subunit composition regulates circadian rhythms in rest-wake and synchrony among cells in the suprachiasmatic nucleus

The mammalian circadian clock located in the suprachiasmatic nucleus (SCN) produces robust daily rhythms including rest-wake. SCN neurons synthesize and respond to γ-aminobutyric acid (GABA), but its role remains unresolved. We tested the hypothesis that γ2- and δ-subunits of the GABAA receptor in the SCN differ in their regulation of synchrony among circadian cells. We used two approaches: 1) shRNA to knock-down (KD) the expression of either γ2 or δ subunits in the SCN or 2) knock-in mice harboring a point mutation in the M2 domains of the endogenous GABAA γ2 or δ subunits. KD of either γ2 or δ subunits in the SCN increased daytime running and reduced nocturnal running by reducing their circadian amplitude by a third. Similarly, δ subunit knock-in mice showed decreased circadian amplitude, increased duration of daily activity, and decreased total daily activity. Reduction, or mutation of either γ2 or δ subunits halved the synchrony among, and amplitude of, circadian SCN cells as measured by firing rate or expression of the PERIOD2 protein, in vitro. Surprisingly, overexpression of the γ2 subunit rescued these phenotypes following KD or mutation of the δ subunit, and overexpression of the δ subunit rescued deficiencies due to γ2 subunit KD or mutation. We conclude that γ2 and δ GABAA receptor subunits play similar roles in maintaining circadian synchrony in the SCN and amplitude of daily rest-wake rhythms, but that modulation of their relative densities can change the duration and amplitude of daily activities.

System-level time computation and representation in the suprachiasmatic nucleus revealed by large-scale calcium imaging and machine learning

The suprachiasmatic nucleus (SCN) is the mammalian central circadian pacemaker with heterogeneous neurons acting in concert while each neuron harbors a self-sustained molecular clockwork. Nevertheless, how system-level SCN signals encode time of the day remains enigmatic. Here we show that population-level Ca2+ signals predict hourly time, via a group decision-making mechanism coupled with a spatially modular time feature representation in the SCN. Specifically, we developed a high-speed dual-view two-photon microscope for volumetric Ca2+ imaging of up to 9000 GABAergic neurons in adult SCN slices, and leveraged machine learning methods to capture emergent properties from multiscale Ca2+ signals as a whole. We achieved hourly time prediction by polling random cohorts of SCN neurons, reaching 99.0% accuracy at a cohort size of 900. Further, we revealed that functional neuron subtypes identified by contrastive learning tend to aggregate separately in the SCN space, giving rise to bilaterally symmetrical ripple-like modular patterns. Individual modules represent distinctive time features, such that a module-specifically learned time predictor can also accurately decode hourly time from random polling of the same module. These findings open a new paradigm in deciphering the design principle of the biological clock at the system level.

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.

Extensive soma-soma plate-like contact sites (ephapses) connect suprachiasmatic nucleus neurons

The hypothalamic suprachiasmatic nucleus (SCN) is the central pacemaker for mammalian circadian rhythms. As such, this ensemble of cell-autonomous neuronal oscillators with divergent periods must maintain coordinated oscillations. To investigate ultrastructural features enabling such synchronization, 805 coronal ultrathin sections of mouse SCN tissue were imaged with electron microscopy and aligned into a volumetric stack, from which selected neurons within the SCN core were reconstructed in silico. We found that clustered SCN core neurons were physically connected to each other via multiple large soma-to-soma plate-like contacts. In some cases, a sliver of a glial process was interleaved. These contacts were large, covering on average ∼21% of apposing neuronal somata. It is possible that contacts may be the electrophysiological substrate for synchronization between SCN neurons. Such plate-like contacts may explain why the synchronization of SCN neurons is maintained even when chemical synaptic transmission or electrical synaptic transmission via gap junctions is blocked. Such ephaptic contact-mediated synchronization among nearby neurons may therefore contribute to the wave-like oscillations of circadian core clock genes and calcium signals observed in the SCN.

Estrogen-mediated coupling via gap junctions in the suprachiasmatic nucleus

The circadian clock orchestrates many physiological and behavioural rhythms in mammals with 24-h periodicity, through a hierarchical organisation, with the central clock located in the suprachiasmatic nucleus (SCN) in the hypothalamus. The circuits of the SCN generate circadian rhythms with precision, relying on intrinsic coupling mechanisms, for example, neurotransmitters like arginine vasopressin (AVP), vasoactive intestinal peptide (VIP), neuronal gamma-aminobutyric acid (GABA) signalling and astrocytes connected by gap junctions composed of connexins (Cx). In female rodents, the presence of estrogen receptors (ERs) in the dorsal SCN suggests an influence of estrogen (E2) on the circuit timekeeping that could regulate circadian rhythm and coupling. To investigate this, we used SCN explants together with hypothalamic neurons and astrocytes. First, we showed that E2 stabilised the circadian amplitude in the SCN when rAVPs (receptor-associated vasopressin peptides) were inhibited. However, the phase delay induced by VIPAC2 (VIP receptors) inhibition remained unaffected by E2. We then showed that E2 exerted its effects in the SCN via ERβ (estrogen receptor beta), resulting in increased expression of Cx36 and Cx43. Notably, specific inhibition of both connexins resulted in a significant reduction in circadian amplitude within the SCN. Remarkably, E2 restored the period with inhibited Cx36 but not with Cx43 inhibition. This implies that the network between astrocytes and neurons, responsible for coupling in the SCN, can be reinforced through E2. In conclusion, these findings provide new insights into how E2 regulates circadian rhythms ex vivo in an ERβ-dependent manner, underscoring its crucial role in fortifying the SCN's rhythm.

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.

Data-Efficient Inference of Nonlinear Oscillator Networks

Decoding the connectivity structure of a network of nonlinear oscillators from measurement data is a difficult yet essential task for understanding and controlling network functionality. Several data-driven network inference algorithms have been presented, but the commonly considered premise of ample measurement data is often difficult to satisfy in practice. In this paper, we propose a data-efficient network inference technique by combining correlation statistics with the model-fitting procedure. The proposed approach can identify the network structure reliably in the case of limited measurement data. We compare the proposed method with existing techniques on a network of Stuart-Landau oscillators, oscillators describing circadian gene expression, and noisy experimental data obtained from Rössler Electronic Oscillator network.

p75NTR promotes tooth rhythmic mineralization via upregulation of BMAL1/CLOCK

The circadian clock plays a critical role in dentomaxillofacial development. Tooth biomineralization is characterized by the circadian clock; however, the mechanisms underlying the coordination of circadian rhythms with tooth development and biomineralization remain unclear. The p75 neurotrophin receptor (p75NTR) is a clock factor that regulates the oscillatory components of the circadian rhythm. This study aims to investigate the impact of p75NTR on the rhythmic mineralization of teeth and elucidate its underlying molecular mechanisms. We generated p75NTR knockout mice to examine the effects of p75NTR deficiency on tooth mineralization. Ectomesenchymal stem cells (EMSCs), derived from mouse tooth germs, were used for in vitro experiments. Results showed a reduction in tooth mineral density and daily mineralization rate in p75NTR knockout mice. Deletion of p75NTR decreased the expression of DMP1, DSPP, RUNX2, and ALP in tooth germ. Odontogenic differentiation and mineralization of EMSCs were activated by p75NTR. Histological results demonstrated predominant detection of p75NTR protein in odontoblasts and stratum intermedium cells during rapid formation phases of dental hard tissue. The mRNA expression of p75NTR exhibited circadian variations in tooth germs and EMSCs, consistent with the expression patterns of the core clock genes Bmal1 and Clock. The upregulation of BMAL1/CLOCK expression by p75NTR positively regulated the mineralization ability of EMSCs, whereas BMAL1 and CLOCK exerted a negative feedback regulation on p75NTR by inhibiting its promoter activity. Our findings suggest that p75NTR is necessary to maintain normal tooth biomineralization. Odontogenic differentiation and mineralization of EMSCs is regulated by the p75NTR-BMAL1/CLOCK signaling axis. These findings offer valuable insights into the associations between circadian rhythms, tooth development, and biomineralization.

Ultrastructure of Synaptic Connectivity within Subregions of the Suprachiasmatic Nucleus Revealed by a Genetically Encoded Tag and Serial Blockface Electron Microscopy

The hypothalamic suprachiasmatic nucleus (SCN) is the central circadian pacemaker in vertebrates. The SCN receives photic information exclusively through melanopsin-expressing retinal ganglion cells (mRGCs) to synchronize circadian rhythms with the environmental light cycles. The SCN is composed of two major peptidergic neuron types in the core and shell regions of the SCN. Determining how mRGCs interact with the network of synaptic connections onto and between SCN neurons is key to understand how light regulates the circadian clock and to elucidate the relevant local circuits within the SCN. To map these connections, we used a newly developed Cre-dependent electron microscopy (EM) reporter, APEX2, to label the mitochondria of mRGC axons. Serial blockface scanning electron microscopy was then used to resolve the fine 3D structure of mRGC axons and synaptic boutons in the SCN of a male mouse. The resulting maps reveal patterns of connectomic organization in the core and shell of the SCN. We show that these regions are composed of different neuronal subtypes and differ with regard to the pattern of mRGC input, as the shell receives denser mRGC synaptic input compared with the core. This finding challenges the present view that photic information coming directly from the retina is received primarily by the core region of the SCN.

Astrocytic control of extracellular GABA drives circadian timekeeping in the suprachiasmatic nucleus

The hypothalamic suprachiasmatic nucleus (SCN) is the master mammalian circadian clock. Its cell-autonomous timing mechanism, a transcriptional/translational feedback loop (TTFL), drives daily peaks of neuronal electrical activity, which in turn control circadian behavior. Intercellular signals, mediated by neuropeptides, synchronize and amplify TTFL and electrical rhythms across the circuit. SCN neurons are GABAergic, but the role of GABA in circuit-level timekeeping is unclear. How can a GABAergic circuit sustain circadian cycles of electrical activity, when such increased neuronal firing should become inhibitory to the network? To explore this paradox, we show that SCN slices expressing the GABA sensor iGABASnFR demonstrate a circadian oscillation of extracellular GABA ([GABA]e) that, counterintuitively, runs in antiphase to neuronal activity, with a prolonged peak in circadian night and a pronounced trough in circadian day. Resolving this unexpected relationship, we found that [GABA]e is regulated by GABA transporters (GATs), with uptake peaking during circadian day, hence the daytime trough and nighttime peak. This uptake is mediated by the astrocytically expressed transporter GAT3 (Slc6a11), expression of which is circadian-regulated, being elevated in daytime. Clearance of [GABA]e in circadian day facilitates neuronal firing and is necessary for circadian release of the neuropeptide vasoactive intestinal peptide, a critical regulator of TTFL and circuit-level rhythmicity. Finally, we show that genetic complementation of the astrocytic TTFL alone, in otherwise clockless SCN, is sufficient to drive [GABA]e rhythms and control network timekeeping. Thus, astrocytic clocks maintain the SCN circadian clockwork by temporally controlling GABAergic inhibition of SCN neurons.

Partitioned estimation methodology of biological neuronal networks with topology-based module detection

Parameter estimation of neuronal networks is closely related with information processing mechanisms in neural systems. Estimation of synaptic parameters for neuronal networks was an time consuming task. Due to complex interactions between neurons, computational efficiency and accuracy of estimation methods is relatively low. Meanwhile, inherent topological properties such as core-periphery and modular structures are not fully considered in estimation. In order to improve the efficiency and accuracy of estimation, this study proposes a two-stage PartitionMLE method which introduces detected neuronal modules as topological constraints in estimation. The proposed PartitionMLE method firstly decomposes the system into multiple non-overlapping neuronal modules, by performing topology-based module detection. Dynamic parameters including intra-modular and inter-modular parameters are estimated in two stages, using detected hubs to connect non-overlapping neuronal modules. The contributions of PartitionMLE method are two-folds: reducing estimation errors and improving the model interpretability. Experiments about neuronal networks consisting of Hodgkin-Huxley (HH) and leaky integrate-and-firing (LIF) neurons validated the effectiveness of the PartitionMLE method, with comparison to the single-stage MLE method.

Hyperammonaemia disrupts daily rhythms reversibly by elevating glutamate in the central circadian pacemaker

Patients with cirrhosis exhibit features of circadian disruption. Hyperammonaemia has been suggested to impair both homeostatic and circadian sleep regulation. Here, we tested if hyperammonaemia directly disrupts circadian rhythm generation in the central pacemaker, the suprachiasmatic nuclei (SCN) of the hypothalamus. Wheel-running activity was recorded from mice fed with a hyperammonaemic or normal diet for ~35 days in a 12:12 light-dark (LD) cycle followed by ~15 days in constant darkness (DD). The expression of the clock protein PERIOD2 (PER2) was recorded from SCN explants before, during and after ammonia exposure, ±glutamate receptor antagonists. In LD, hyperammonaemic mice advanced their daily activity onset time by ~1 h (16.8 ± 0.3 vs. 18.1 ± 0.04 h, p = .009) and decreased their total activity, concentrating it during the first half of the night. In DD, hyperammonaemia reduced the amplitude of daily activity (551.5 ± 27.7 vs. 724.9 ± 59 counts, p = .007), with no changes in circadian period. Ammonia (≥0.01 mM) rapidly and significantly reduced PER2 amplitude, and slightly increased circadian period. The decrease in PER2 amplitude correlated with decreased synchrony among circadian cells in the SCN and increased extracellular glutamate, which was rescued by AMPA glutamate receptor antagonists. These data suggest that hyperammonaemia affects circadian regulation of rest-activity behaviour by increasing extracellular glutamate in the SCN.

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.

Analysis of Complex Circadian Time Series Data Using Wavelets

Experiments that compare rhythmic properties across different genetic alterations and entrainment conditions underlie some of the most important breakthroughs in circadian biology. A robust estimation of the rhythmic properties of the circadian signals goes hand in hand with these discoveries. Widely applied traditional signal analysis methods such as fitting cosine functions or Fourier transformations rely on the assumption that oscillation periods do not change over time. However, novel high-resolution recording techniques have shown that, most commonly, circadian signals exhibit time-dependent changes of periods and amplitudes which cannot be captured with the traditional approaches. In this chapter we introduce a method to determine time-dependent properties of oscillatory signals, using the novel open-source Python-based Biological Oscillations Analysis Toolkit (pyBOAT). We show with examples how to detect rhythms, compute and interpret high-resolution time-dependent spectral results, analyze the main oscillatory component, and to subsequently determine these main components' time-dependent instantaneous period, amplitude, and phase. We introduce step-by-step how such an analysis can be done by means of the easy-to-use point-and-click graphical user interface (GUI) provided by pyBOAT or executed within a Python programming environment. Concepts are explained using simulated signals as well as experimentally obtained time series.

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.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

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.

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.

Inferring causality in biological oscillators

MOTIVATION

Fundamental to biological study is identifying regulatory interactions. The recent surge in time-series data collection in biology provides a unique opportunity to infer regulations computationally. However, when components oscillate, model-free inference methods, while easily implemented, struggle to distinguish periodic synchrony and causality. Alternatively, model-based methods test the reproducibility of time series given a specific model but require inefficient simulations and have limited applicability.

RESULTS

We develop an inference method based on a general model of molecular, neuronal and ecological oscillatory systems that merges the advantages of both model-based and model-free methods, namely accuracy, broad applicability and usability. Our method successfully infers the positive and negative regulations within various oscillatory networks, e.g. the repressilator and a network of cofactors at the pS2 promoter, outperforming popular inference methods.

AVAILABILITY AND IMPLEMENTATION

We provide a computational package, ION (Inferring Oscillatory Networks), that users can easily apply to noisy, oscillatory time series to uncover the mechanisms by which diverse systems generate oscillations. Accompanying MATLAB code under a BSD-style license and examples are available at https://github.com/Mathbiomed/ION. Additionally, the code is available under a CC-BY 4.0 License at https://doi.org/10.6084/m9.figshare.16431408.v1.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

The role of circadian rhythm in choroid plexus functions

For several years, a great effort has been devoted to understand how circadian oscillations in physiological processes are determined by the circadian clock system. This system is composed by the master clock at the suprachiasmatic nucleus which sets the pace and tunes peripheral clocks in several organs. It was recently demonstrated that the choroid plexus epithelial cells that compose the blood-cerebrospinal fluid barrier hold a circadian clock which might control their multiple functions with implications for the maintenance of brain homeostasis. However, the choroid plexus activities regulated by its inner clock are still largely unknown. In this review, we propose that several choroid plexus functions might be regulated by the circadian clock, alike in other tissues. We provide evidences that the timing of cerebrospinal fluid secretion, clearance of amyloid-beta peptides and xenobiotics, and the barrier function of the blood-cerebrospinal fluid barrier are regulated by the circadian clock. These data, highlight that the circadian regulation of the blood-cerebrospinal fluid barrier must be taken into consideration for enhancing drug delivery to central nervous system disorders.

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.

Dual-Color Single-Cell Imaging of the Suprachiasmatic Nucleus Reveals a Circadian Role in Network Synchrony

The suprachiasmatic nucleus (SCN) acts as a master pacemaker driving circadian behavior and physiology. Although the SCN is small, it is composed of many cell types, making it difficult to study the roles of particular cells. Here we develop bioluminescent circadian reporter mice that are Cre dependent, allowing the circadian properties of genetically defined populations of cells to be studied in real time. Using a Color-Switch PER2::LUCIFERASE reporter that switches from red PER2::LUCIFERASE to green PER2::LUCIFERASE upon Cre recombination, we assess circadian rhythms in two of the major classes of peptidergic neurons in the SCN: AVP (arginine vasopressin) and VIP (vasoactive intestinal polypeptide). Surprisingly, we find that circadian function in AVP neurons, not VIP neurons, is essential for autonomous network synchrony of the SCN and stability of circadian rhythmicity.

Cellular coupling determines scale-invariant behavior of neurons in suprachiasmatic nucleus

The main clock in mammals, located in the suprachiasmatic nucleus (SCN) of hypothalamus, not only regulates the daily rhythms in physiological and behavioral activities, but also plays a key role as one of the control nodes in the brain regulating behavioral activity. As such, it induces scale-invariance in the temporal patterns of behavioral activity and of multi-unit neural activity of the SCN network. In particular, the scale-invariant patterns maintain across multiple time scales from 3 minutes to 10 hours, characterized by a scaling exponent around 1. Thus far, no study found the origin of the scale-invariance of the SCN network. Using the method of correlation-dependent balance estimation of diffusion entropy (cBEDE), we found that scale-invariance also exists in the individual neurons of the SCN, and the scale invariance properties are significantly increased when the neurons are coupled in a network of neurons. Improved scale invariance in the single neurons is, therefore, imposed by the emergent network properties of the SCN network. Our findings show that the scale-invariance of the SCN can already be found at the level of the individual neurons and that the application of a scale invariance measure, such as cBEDE, can help in determining the network status of the SCN.

Synaptic Specializations of Melanopsin-Retinal Ganglion Cells in Multiple Brain Regions Revealed by Genetic Label for Light and Electron Microscopy

The form and synaptic fine structure of melanopsin-expressing retinal ganglion cells, also called intrinsically photosensitive retinal ganglion cells (ipRGCs), were determined using a new membrane-targeted version of a genetic probe for correlated light and electron microscopy (CLEM). ipRGCs project to multiple brain regions, and because the method labels the entire neuron, it was possible to analyze nerve terminals in multiple retinorecipient brain regions, including the suprachiasmatic nucleus (SCN), olivary pretectal nucleus (OPN), and subregions of the lateral geniculate. Although ipRGCs provide the only direct retinal input to the OPN and SCN, ipRGC terminal arbors and boutons were found to be remarkably different in each target region. A network of dendro-dendritic chemical synapses (DDCSs) was also revealed in the SCN, with ipRGC axon terminals preferentially synapsing on the DDCS-linked cells. The methods developed to enable this analysis should propel other CLEM studies of long-distance brain circuits at high resolution.

Long-range temporal coordination of gene expression in synthetic microbial consortia

Synthetic microbial consortia have an advantage over isogenic synthetic microbes because they can apportion biochemical and regulatory tasks among the strains. However, it is difficult to coordinate gene expression in spatially extended consortia because the range of signaling molecules is limited by diffusion. Here, we show that spatio-temporal coordination of gene expression can be achieved even when the spatial extent of the consortium is much greater than the diffusion distance of the signaling molecules. To do this, we examined the dynamics of a two-strain synthetic microbial consortium that generates coherent oscillations in small colonies. In large colonies, we find that temporally coordinated oscillations across the population depend on the presence of an intrinsic positive feedback loop that amplifies and propagates intercellular signals. These results demonstrate that synthetic multicellular systems can be engineered to exhibit coordinated gene expression using only transient, short-range coupling among constituent cells.

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.

Generation of circadian rhythms in the suprachiasmatic nucleus

The suprachiasmatic nucleus (SCN) of the hypothalamus is remarkable. Despite numbering only about 10,000 neurons on each side of the third ventricle, the SCN is our principal circadian clock, directing the daily cycles of behaviour and physiology that set the tempo of our lives. When this nucleus is isolated in organotypic culture, its autonomous timing mechanism can persist indefinitely, with precision and robustness. The discovery of the cell-autonomous transcriptional and post-translational feedback loops that drive circadian activity in the SCN provided a powerful exemplar of the genetic specification of complex mammalian behaviours. However, the analysis of circadian time-keeping is moving beyond single cells. Technical and conceptual advances, including intersectional genetics, multidimensional imaging and network theory, are beginning to uncover the circuit-level mechanisms and emergent properties that make the SCN a uniquely precise and robust clock. However, much remains unknown about the SCN, not least the intrinsic properties of SCN neurons, its circuit topology and the neuronal computations that these circuits support. Moreover, the convention that the SCN is a neuronal clock has been overturned by the discovery that astrocytes are an integral part of the timepiece. As a test bed for examining the relationships between genes, cells and circuits in sculpting complex behaviours, the SCN continues to offer powerful lessons and opportunities for contemporary neuroscience.

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.

Uncovering functional signature in neural systems via random matrix theory

Neural systems are organized in a modular way, serving multiple functionalities. This multiplicity requires that both positive (e.g. excitatory, phase-coherent) and negative (e.g. inhibitory, phase-opposing) interactions take place across brain modules. Unfortunately, most methods to detect modules from time series either neglect or convert to positive, any measured negative correlation. This may leave a significant part of the sign-dependent functional structure undetected. Here we present a novel method, based on random matrix theory, for the identification of sign-dependent modules in the brain. Our method filters out both local (unit-specific) noise and global (system-wide) dependencies that typically obfuscate the presence of such structure. The method is guaranteed to identify an optimally contrasted functional 'signature', i.e. a partition into modules that are positively correlated internally and negatively correlated across. The method is purely data-driven, does not use any arbitrary threshold or network projection, and outputs only statistically significant structure. In measurements of neuronal gene expression in the biological clock of mice, the method systematically uncovers two otherwise undetectable, negatively correlated modules whose relative size and mutual interaction strength are found to depend on photoperiod.

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.

The organization of the basal ganglia functional connectivity network is non-linear in Parkinson's disease

The motor symptoms in Parkinson's disease (PD) have been linked to changes in the excitatory/inhibitory interactions of centers involved in the cortical-subcortical closed-loop circuits which connect basal ganglia (BG) and the brain cortex. This approach may explain some motor symptoms of PD but not others, which has driven the study of BG from new perspectives. Besides their cortical-subcortical linear circuits, BG have a number of subcortical circuits which directly or indirectly connect each BG with all the others. This suggests that BG may work as a complex network whose output is the result of massive functional interactions between all of their nuclei (decentralized network; DCN), more than the result of the linear excitatory/inhibitory interactions of the cortical-subcortical closed-loops. The aim of this work was to study BG as a DCN, and to test whether the DCN behavior of BG changes in PD. BG activity was recorded with MRI methods and their complex interactions were studied with a procedure based on multiple correspondence analysis, a data-driven multifactorial method which can work with non-linear multiple interactions. The functional connectivity of twenty parkinsonian patients and eighteen age-matched controls were studied during resting and when they were performing sequential hand movements. Seven functional configurations were identified in the control subjects during resting, and some of these interactions changed with motor activity. Five of the seven interactions found in control subjects changed in Parkinson's disease. The BG response to the motor task was also different in PD patients and controls. These data show the basal ganglia as a decentralized network where each region can perform multiple functions and each function is performed by multiple regions. This framework of BG interactions may provide new explanations concerning motor symptoms of PD which are not explained by current BG models.

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The classical basal ganglia model is based on linear excitatory/inhibitory interactions.

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The classical model only explains part of the motor disorders of Parkinson's disease.

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fcMRI images were studied with Multiple Correspondence Analysis (MCA).

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MCA showed multiple non-linear interactions between basal ganglia.

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Parkinson's disease induced marked changes of non-linear basal ganglia interactions.

Inferring dynamic topology for decoding spatiotemporal structures in complex heterogeneous networks

Inferring connections forms a critical step toward understanding large and diverse complex networks. To date, reliable and efficient methods for the reconstruction of network topology from measurement data remain a challenge due to the high complexity and nonlinearity of the system dynamics. These obstacles also form a bottleneck for analyzing and controlling the dynamic structures (e.g., synchrony) and collective behavior in such complex networks. The novel contribution of this work is to develop a unified data-driven approach to reliably and efficiently reveal the dynamic topology of complex networks in different scales—from cells to societies. The developed technique provides guidelines for the refinement of experimental designs toward a comprehensive understanding of complex heterogeneous networks.

Extracting complex interactions (i.e., dynamic topologies) has been an essential, but difficult, step toward understanding large, complex, and diverse systems including biological, financial, and electrical networks. However, reliable and efficient methods for the recovery or estimation of network topology remain a challenge due to the tremendous scale of emerging systems (e.g., brain and social networks) and the inherent nonlinearity within and between individual units. We develop a unified, data-driven approach to efficiently infer connections of networks (ICON). We apply ICON to determine topology of networks of oscillators with different periodicities, degree nodes, coupling functions, and time scales, arising in silico, and in electrochemistry, neuronal networks, and groups of mice. This method enables the formulation of these large-scale, nonlinear estimation problems as a linear inverse problem that can be solved using parallel computing. Working with data from networks, ICON is robust and versatile enough to reliably reveal full and partial resonance among fast chemical oscillators, coherent circadian rhythms among hundreds of cells, and functional connectivity mediating social synchronization of circadian rhythmicity among mice over weeks.

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.

Macroscopic models for networks of coupled biological oscillators

The study of synchronization of coupled biological oscillators is fundamental to many areas of biology including neuroscience, cardiac dynamics, and circadian rhythms. Mathematical models of these systems may involve hundreds of variables in thousands of individual cells resulting in an extremely high-dimensional description of the system. This often contrasts with the low-dimensional dynamics exhibited on the collective or macroscopic scale for these systems. We introduce a macroscopic reduction for networks of coupled oscillators motivated by an elegant structure we find in experimental measurements of circadian protein expression and several mathematical models for coupled biological oscillators. The observed structure in the collective amplitude of the oscillator population differs from the well-known Ott-Antonsen ansatz, but its emergence can be characterized through a simple argument depending only on general phase-locking behavior in coupled oscillator systems. We further demonstrate its emergence in networks of noisy heterogeneous oscillators with complex network connectivity. Applying this structure, we derive low-dimensional macroscopic models for oscillator population activity. This approach allows for the incorporation of cellular-level experimental data into the macroscopic model whose parameters and variables can then be directly associated with tissue- or organism-level properties, thereby elucidating the core properties driving the collective behavior of the system.

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.

Moran's I quantifies spatio-temporal pattern formation in neural imaging data

Motivation

Neural activities of the brain occur through the formation of spatio-temporal patterns. In recent years, macroscopic neural imaging techniques have produced a large body of data on these patterned activities, yet a numerical measure of spatio-temporal coherence has often been reduced to the global order parameter, which does not uncover the degree of spatial correlation. Here, we propose to use the spatial autocorrelation measure Moran’s I, which can be applied to capture dynamic signatures of spatial organization. We demonstrate the application of this technique to collective cellular circadian clock activities measured in the small network of the suprachiasmatic nucleus (SCN) in the hypothalamus.

Results

We found that Moran’s I is a practical quantitative measure of the degree of spatial coherence in neural imaging data. Initially developed with a geographical context in mind, Moran’s I accounts for the spatial organization of any interacting units. Moran’s I can be modified in accordance with the characteristic length scale of a neural activity pattern. It allows a quantification of statistical significance levels for the observed patterns. We describe the technique applied to synthetic datasets and various experimental imaging time-series from cultured SCN explants. It is demonstrated that major characteristics of the collective state can be described by Moran’s I and the traditional Kuramoto order parameter R in a complementary fashion.

Availability and implementation

Python 2.7 code of illustrative examples can be found in the Supplementary Material.

Supplementary information

Supplementary data are available at Bioinformatics online.

CLOCKΔ19 mutation modifies the manner of synchrony among oscillation neurons in the suprachiasmatic nucleus

In mammals, the principal circadian oscillator exists in the hypothalamic suprachiasmatic nucleus (SCN). In the SCN, CLOCK works as an essential component of molecular circadian oscillation, and ClockΔ19 mutant mice show unique characteristics of circadian rhythms such as extended free running periods, amplitude attenuation, and high-magnitude phase-resetting responses. Here we investigated what modifications occur in the spatiotemporal organization of clock gene expression in the SCN of ClockΔ19 mutants. The cultured SCN, sampled from neonatal homozygous ClockΔ19 mice on an ICR strain comprising PERIOD2::LUCIFERASE, demonstrated that the Clock gene mutation not only extends the circadian period, but also affects the spatial phase and period distribution of circadian oscillations in the SCN. In addition, disruption of the synchronization among neurons markedly attenuated the amplitude of the circadian rhythm of individual oscillating neurons in the mutant SCN. Further, with numerical simulations based on the present studies, the findings suggested that, in the SCN of the ClockΔ19 mutant mice, stable oscillation was preserved by the interaction among oscillating neurons, and that the orderly phase and period distribution that makes a phase wave are dependent on the functionality of CLOCK.

Measuring Relative Coupling Strength in Circadian Systems

Modern imaging techniques allow the monitoring of circadian rhythms of single cells. Coupling between these single cellular circadian oscillators can generate coherent periodic signals on the tissue level that subsequently orchestrate physiological outputs. The strength of coupling in such systems of oscillators is often unclear. In particular, effects on coupling strength by varying cell densities, by knockouts, and by inhibitor applications are debated. In this study, we suggest to quantify the relative coupling strength via analyzing period, phase, and amplitude distributions in ensembles of individual circadian oscillators. Simulations of different oscillator networks show that period and phase distributions become narrower with increasing coupling strength. Moreover, amplitudes can increase due to resonance effects. Variances of periods and phases decay monotonically with coupling strength, and can serve therefore as measures of relative coupling strength. Our theoretical predictions are confirmed by studying recently published experimental data from PERIOD2 expression in slices of the suprachiasmatic nucleus during and after the application of tetrodotoxin (TTX). On analyzing the corresponding period, phase, and amplitude distributions, we can show that treatment with TTX can be associated with a reduced coupling strength in the system of coupled oscillators. Analysis of an oscillator network derived directly from the data confirms our conclusions. We suggest that our approach is also applicable to quantify coupling in fibroblast cultures and hepatocyte networks, and for social synchronization of circadian rhythmicity in rodents, flies, and bees.

Ontogeny of Circadian Rhythms and Synchrony in the Suprachiasmatic Nucleus

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus coordinates daily rhythms including sleep-wake, hormone release, and gene expression. The cells of the SCN must synchronize to each other to drive these circadian rhythms in the rest of the body. The ontogeny of circadian cycling and intercellular coupling in the SCN remains poorly understood. Recent in vitro studies have recorded circadian rhythms from the whole embryonic SCN. Here, we tracked the onset and precision of rhythms in PERIOD2 (PER2), a clock protein, within the SCN isolated from embryonic and postnatal mice of undetermined sex. We found that a few SCN cells developed circadian periodicity in PER2 by 14.5 d after mating (E14.5) with no evidence for daily cycling on E13.5. On E15.5, the fraction of competent oscillators increased dramatically corresponding with stabilization of their circadian periods. The cells of the SCN harvested at E15.5 expressed sustained, synchronous daily rhythms. By postnatal day 2 (P2), SCN oscillators displayed the daily, dorsal-ventral phase wave in clock gene expression typical of the adult SCN. Strikingly, vasoactive intestinal polypeptide (VIP), a neuropeptide critical for synchrony in the adult SCN, and its receptor, VPAC2R, reached detectable levels after birth and after the onset of circadian synchrony. Antagonists of GABA or VIP signaling or action potentials did not disrupt circadian synchrony in the E15.5 SCN. We conclude that endogenous daily rhythms in the fetal SCN begin with few noisy oscillators on E14.5, followed by widespread oscillations that rapidly synchronize on E15.5 by an unknown mechanism.SIGNIFICANCE STATEMENT We recorded the onset of PER2 circadian oscillations during embryonic development in the mouse SCN. When isolated at E13.5, the anlagen of the SCN expresses high, arrhythmic PER2. In contrast, a few cells show noisy circadian rhythms in the isolated E14.5 SCN and most show reliable, self-sustained, synchronized rhythms in the E15.5 SCN. Strikingly, this synchrony at E15.5 appears before expression of VIP or its receptor and persists in the presence of blockers of VIP, GABA or neuronal firing. Finally, the dorsal-ventral phase wave of PER2 typical of the adult SCN appears ∼P2, indicating that multiple signals may mediate circadian synchrony during the ontogeny of the SCN.

Regulating the Suprachiasmatic Nucleus (SCN) Circadian Clockwork: Interplay between Cell-Autonomous and Circuit-Level Mechanisms

The suprachiasmatic nucleus (SCN) is the principal circadian clock of the brain, directing daily cycles of behavior and physiology. SCN neurons contain a cell-autonomous transcription-based clockwork but, in turn, circuit-level interactions synchronize the 20,000 or so SCN neurons into a robust and coherent daily timer. Synchronization requires neuropeptide signaling, regulated by a reciprocal interdependence between the molecular clockwork and rhythmic electrical activity, which in turn depends on a daytime Na⁺ drive and nighttime K⁺ drag. Recent studies exploiting intersectional genetics have started to identify the pacemaking roles of particular neuronal groups in the SCN. They support the idea that timekeeping involves nonlinear and hierarchical computations that create and incorporate timing information through the interactions between key groups of neurons within the SCN circuit. The field is now poised to elucidate these computations, their underlying cellular mechanisms, and how the SCN clock interacts with subordinate circadian clocks across the brain to determine the timing and efficiency of the sleep-wake cycle, and how perturbations of this coherence contribute to neurological and psychiatric illness.

Evidence for Weakened Intercellular Coupling in the Mammalian Circadian Clock under Long Photoperiod

For animals living in temperate latitudes, seasonal changes in day length are an important cue for adaptations of their physiology and behavior to the altered environmental conditions. The suprachiasmatic nucleus (SCN) is known as the central circadian clock in mammals, but may also play an important role in adaptations to different photoperiods. The SCN receives direct light input from the retina and is able to encode day-length by approximating the waveform of the electrical activity rhythm to the duration of daylight. Changing the overall waveform requires a reorganization of the neuronal network within the SCN with a change in the degree of synchrony between the neurons; however, the underlying mechanisms are yet unknown. In the present study we used PER2::LUC bioluminescence imaging in cultured SCN slices to characterize network dynamics on the single-cell level and we aimed to provide evidence for a role of modulations in coupling strength in the photoperiodic-induced phase dispersal. Exposure to long photoperiod (LP) induced a larger distribution of peak times of the single-cell PER2::LUC rhythms in the anterior SCN, compared to short photoperiod. Interestingly, the cycle-to-cycle variability in single-cell period of PER2::LUC rhythms is also higher in the anterior SCN in LP, and is positively correlated with peak time dispersal. Applying a new, impartial community detection method on the time series data of the PER2::LUC rhythm revealed two clusters of cells with a specific spatial distribution, which we define as dorsolateral and ventromedial SCN. Post hoc analysis of rhythm characteristics of these clusters showed larger cycle-to-cycle single-cell period variability in the dorsolateral compared to the ventromedial cluster in the anterior SCN. We conclude that a change in coupling strength within the SCN network is a plausible explanation to the observed changes in single-cell period variability, which can contribute to the photoperiod-induced phase distribution.

A systems theoretic approach to analysis and control of mammalian circadian dynamics

The mammalian circadian clock is a complex multi-scale, multivariable biological control system. In the past two decades, methods from systems engineering have led to numerous insights into the architecture and functionality of this system. In this review, we examine the mammalian circadian system through a process systems lens. We present a mathematical framework for examining the cellular circadian oscillator, and show recent extensions for understanding population-scale dynamics. We provide an overview of the routes by which the circadian system can be systemically manipulated, and present in silico proof of concept results for phase resetting of the clock via model predictive control.

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.