Resynchronization Dynamics Reveal that the Ventral Entrains the Dorsal Suprachiasmatic Nucleus

Are circadian amplitudes and periods correlated? A new twist in the story

Three parameters are important to characterize a circadian and in general any biological clock: period, phase and amplitude. While circadian periods have been shown to correlate with entrainment phases, and clock amplitude influences the phase response of an oscillator to pulse-like zeitgeber signals, the co-modulations of amplitude and periods, which we term twist, have not been studied in detail. In this paper we define two concepts: parametric twist refers to amplitude-period correlations arising in ensembles of self-sustained, limit cycle clocks in the absence of external inputs, and phase space twist refers to the co-modulation of an individual clock's amplitude and period in response to external zeitgebers. Our findings show that twist influences the interaction of oscillators with the environment, facilitating entrainment, speeding upfastening recovery to pulse-like perturbations or modifying the response of an individual clock to coupling. This theoretical framework might be applied to understand the emerging properties of other oscillating systems.

Reduced Plasticity in Coupling Strength in the Aging SCN Clock as Revealed by Kuramoto Modeling

The mammalian circadian clock is located in the suprachiasmatic nucleus (SCN) and consists of a network of coupled neurons, which are entrained to the environmental light-dark cycle. The phase coherence of the neurons is plastic and driven by the duration of daylight. With aging, the capacity to behaviorally adapt to seasonal changes in photoperiod reduces. The mechanisms underlying photoperiodic adaptation are largely unknown, but are important to unravel for the development of novel interventions to improve the quality of life of the elderly. We analyzed the phase coherence of single-cell PERIOD2::LUCIFERASE (PER2::LUC) expression rhythms in the SCN of young and old mice entrained to either long or short photoperiod. The phase coherence was used as input to a 2-community noisy Kuramoto model to estimate the coupling strength between and within neuronal subpopulations. The model revealed a correlation between coupling strength and photoperiod-induced changes in the phase relationship among neurons, suggesting a functional link. We found that the SCN of young mice adapts in coupling strength over a large range, with weak coupling in long photoperiod (LP) and strong coupling in short photoperiod (SP). In aged mice, we also found weak coupling in LP, but a reduced capacity to reach strong coupling in SP. The inability to respond with an increase in coupling strength suggests that manipulation of photoperiod is not a suitable strategy to enhance clock function with aging. We conclude that the inability of aged mice to reach strong coupling contributes to deficits in behavioral adaptation to seasonal changes in photoperiod.

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.

A synthetic population-level oscillator in non-microfluidic environments

Synthetic oscillators have become a research hotspot because of their complexity and importance. The construction and stable operation of oscillators in large-scale environments are important and challenging. Here, we introduce a synthetic population-level oscillator in Escherichia coli that operates stably during continuous culture in non-microfluidic environments without the addition of inducers or frequent dilution. Specifically, quorum-sensing components and protease regulating elements are employed, which form delayed negative feedback to trigger oscillation and accomplish the reset of signals through transcriptional and post-translational regulation. We test the circuit in devices with 1 mL, 50 mL, 400 mL of medium, and demonstrate that the circuit could maintain stable population-level oscillations. Finally, we explore potential applications of the circuit in regulating cellular morphology and metabolism. Our work contributes to the design and testing of synthetic biological clocks that function in large populations.

Limits of entrainment of circadian neuronal networks

Circadian rhythmicity lies at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes, and more. Misalignment of intrinsic neuronal oscillations with the external day-night cycle can disrupt such processes and lead to numerous disorders. In this work, we computationally determine the limits of circadian synchronization to external light signals of different frequency, duty cycle, and simulated amplitude. Instead of modeling circadian dynamics with generic oscillator models (e.g., Kuramoto-type), we use a detailed computational neuroscience model, which integrates biomolecular dynamics, neuronal electrophysiology, and network effects. This allows us to investigate the effect of small drug molecules, such as Longdaysin, and connect our results with experimental findings. To combat the high dimensionality of such a detailed model, we employ a matrix-free approach, while our entire algorithmic pipeline enables numerical continuation and construction of bifurcation diagrams using only direct simulation. We, thus, computationally explore the effect of heterogeneity in the circadian neuronal network, as well as the effect of the corrective therapeutic intervention of Longdaysin. Last, we employ unsupervised learning to construct a data-driven embedding space for representing neuronal heterogeneity.

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

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

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.

A spatio-temporal model to reveal oscillator phenotypes in molecular clocks: Parameter estimation elucidates circadian gene transcription dynamics in single-cells

We propose a stochastic distributed delay model together with a Markov random field prior and a measurement model for bioluminescence-reporting to analyse spatio-temporal gene expression in intact networks of cells. The model describes the oscillating time evolution of molecular mRNA counts through a negative transcriptional-translational feedback loop encoded in a chemical Langevin equation with a probabilistic delay distribution. The model is extended spatially by means of a multiplicative random effects model with a first order Markov random field prior distribution. Our methodology effectively separates intrinsic molecular noise, measurement noise, and extrinsic noise and phenotypic variation driving cell heterogeneity, while being amenable to parameter identification and inference. Based on the single-cell model we propose a novel computational stability analysis that allows us to infer two key characteristics, namely the robustness of the oscillations, i.e. whether the reaction network exhibits sustained or damped oscillations, and the profile of the regulation, i.e. whether the inhibition occurs over time in a more distributed versus a more direct manner, which affects the cells' ability to phase-shift to new schedules. We show how insight into the spatio-temporal characteristics of the circadian feedback loop in the suprachiasmatic nucleus (SCN) can be gained by applying the methodology to bioluminescence-reported expression of the circadian core clock gene Cry1 across mouse SCN tissue. We find that while (almost) all SCN neurons exhibit robust cell-autonomous oscillations, the parameters that are associated with the regulatory transcription profile give rise to a spatial division of the tissue between the central region whose oscillations are resilient to perturbation in the sense that they maintain a high degree of synchronicity, and the dorsal region which appears to phase shift in a more diversified way as a response to large perturbations and thus could be more amenable to entrainment.

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.

Impact of field heterogeneity on the dynamics of the forced Kuramoto model

We studied the impact of field heterogeneity on entrainment in a system of uniformly interacting phase oscillators. Field heterogeneity is shown to induce dynamical heterogeneity in the system. In effect, the heterogeneous field partitions the system into interacting groups of oscillators that feel the same local field strength and phase. Based on numerical and analytical analysis of the explicit dynamical equations derived from the periodically forced Kuramoto model, we found that the heterogeneous field can disrupt entrainment at different field frequencies when compared to the homogeneous field. This transition occurs when the phase- and frequency-locked synchronization between groups of oscillators is broken at a critical field frequency, causing each group to enter a new dynamical state (disrupted state). Strikingly, it is shown that disrupted dynamics can differ between groups.

The Excitatory Effects of GABA within the Suprachiasmatic Nucleus: Regulation of Na-K-2Cl Cotransporters (NKCCs) by Environmental Lighting Conditions

The suprachiasmatic nucleus (SCN) contains a pacemaker that generates circadian rhythms and entrains them with the 24-h light-dark cycle (LD). The SCN is composed of 16,000 to 20,000 heterogeneous neurons in bilaterally paired nuclei. γ-amino butyric acid (GABA) is the primary neurochemical signal within the SCN and plays a key role in regulating circadian function. While GABA is the primary inhibitory neurotransmitter in the brain, there is now evidence that GABA can also exert excitatory effects in the adult brain. Cation chloride cotransporters determine the effects of GABA on chloride equilibrium, thereby determining whether GABA produces hyperpolarizing or depolarizing actions following activation of GABA_A receptors. The activity of Na-K-2Cl cotransporter1 (NKCC1), the most prevalent chloride influx cotransporter isoform in the brain, plays a critical role in determining whether GABA has depolarizing effects. In the present study, we tested the hypothesis that NKCC1 protein expression in the SCN is regulated by environmental lighting and displays daily and circadian changes in the intact circadian system of the Syrian hamster. In hamsters housed in constant light (LL), the overall NKCC1 immunoreactivity (NKCC1-ir) in the SCN was significantly greater than in hamsters housed in LD or constant darkness (DD), although NKCC1 protein levels in the SCN were not different between hamsters housed in LD and DD. In hamsters housed in LD cycles, no differences in NKCC1-ir within the SCN were observed over the 24-h cycle. NKCC1 protein in the SCN was found to vary significantly over the circadian cycle in hamsters housed in free-running conditions. Overall, NKCC1 protein was greater in the ventral SCN than in the dorsal SCN, although no significant differences were observed across lighting conditions or time of day in either subregion. These data support the hypothesis that NKCC1 protein expression can be regulated by environmental lighting and circadian mechanisms within the SCN.

Quantitative Study of Dual Circadian Oscillator Models under Different Skeleton Photoperiods

The daily proportion of light and dark hours (photoperiod) changes annually and plays an important role in the synchronization of seasonal biological phenomena, such as reproduction, hibernation, and migration. In mammals, the first step of photoperiod transduction occurs in the suprachiasmatic nuclei (SCN), the circadian pacemaker that also coordinates 24-h activity rhythms. Thus, in parallel with its role in annual synchronization, photoperiod variation acutely shapes day/night activity patterns, which vary throughout the year. Systematic studies of this behavioral modulation help understand the mechanisms behind its transduction at the SCN level. To explain how entrainment mechanisms could account for daily activity patterns under different photoperiods, Colin Pittendrigh and Serge Daan proposed a conceptual model in which the pacemaker would be composed of 2 coupled, evening (E) and morning (M), oscillators. Although the E-M model has existed for more than 40 years now, its physiological bases are still not fully resolved, and it has not been tested quantitatively under different photoperiods. To better explore the implications of the E-M model, we performed computer simulations of 2 coupled limit-cycle oscillators. Four model configurations were exposed to systematic variation of skeleton photoperiods, and the resulting daily activity patterns were assessed. The criterion for evaluating different model configurations was the successful reproduction of 2 key behavioral phenomena observed experimentally: activity psi-jumps and photoperiod-induced changes in activity phase duration. We compared configurations with either separate light inputs to E and M or the same light inputs to both oscillators. The former replicated experimental results closely, indicating that the configuration with separate E and M light inputs is the mechanism that best reproduces the effects of different skeleton photoperiods on day/night activity patterns. We hope this model can contribute to the search for E and M and their light input organization in the SCN.

Suprachiasmatic function in a circadian period mutant: Duper alters light-induced activation of vasoactive intestinal peptide cells and PERIOD1 immunostaining

Mammalian circadian rhythms are entrained by photic stimuli that are relayed by retinal projections to the core of the suprachiasmatic nucleus (SCN). Neuronal activation, as demonstrated by expression of the immediate early gene c-fos, leads to transcription of the core clock gene per1. The duper mutation in hamsters shortens circadian period and amplifies light-induced phase shifts. We performed two experiments to compare the number of c-FOS immunoreactive (ir) and PER1-ir cells, and the intensity of staining, in the SCN of wild-type (WT) and duper hamsters at various intervals after presentation of a 15-min light pulse in the early subjective night. Light-induced c-FOS-ir within 1 hr in the dorsocaudal SCN of duper, but not WT hamsters. In cells that express vasoactive intestinal peptide (VIP), which plays a critical role in synchronization of SCN cellular oscillators, light-induced c-FOS-ir was greater in duper than WT hamsters. After the light pulse, PER1-ir cells were found in more medial portions of the SCN than FOS-ir, and appeared with a longer latency and over a longer time course, in VIP cells of duper than wild-type hamsters. Our results indicate that the duper allele alters SCN function in ways that may contribute to changes in free running period and phase resetting.

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.

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.

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.

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.

Quantitative analysis of circadian single cell oscillations in response to temperature

Body temperature rhythms synchronize circadian oscillations in different tissues, depending on the degree of cellular coupling: the responsiveness to temperature is higher when single circadian oscillators are uncoupled. So far, the role of coupling in temperature responsiveness has only been studied in organotypic tissue slices of the central circadian pacemaker, because it has been assumed that peripheral target organs behave like uncoupled multicellular oscillators. Since recent studies indicate that some peripheral tissues may exhibit cellular coupling as well, we asked whether peripheral network dynamics also influence temperature responsiveness. Using a novel technique for long-term, high-resolution bioluminescence imaging of primary cultured cells, exposed to repeated temperature cycles, we were able to quantitatively measure period, phase, and amplitude of central (suprachiasmatic nuclei neuron dispersals) and peripheral (mouse ear fibroblasts) single cell oscillations in response to temperature. Employing temperature cycles of different lengths, and different cell densities, we found that some circadian characteristics appear cell-autonomous, e.g. period responses, while others seem to depend on the quality/degree of cellular communication, e.g. phase relationships, robustness of the oscillation, and amplitude. Overall, our findings indicate a strong dependence on the cell's ability for intercellular communication, which is not only true for neuronal pacemakers, but, importantly, also for cells in peripheral tissues. Hence, they stress the importance of comparative studies that evaluate the degree of coupling in a given tissue, before it may be used effectively as a target for meaningful circadian manipulation.

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.