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

Astrocytes actively support long-range molecular clock synchronization of segregated neuronal populations

In mammals, the suprachiasmatic nucleus of the hypothalamus is the master circadian pacemaker that synchronizes the clocks in the central nervous system and periphery, thus orchestrating rhythms throughout the body. However, little is known about how so many cellular clocks within and across brain circuits can be effectively synchronized. In this work, we investigated the implication of two possible pathways: (i) astrocytes-mediated synchronization and (ii) neuronal paracrine factors-mediated synchronization. By taking advantage of a lab-on-a-chip microfluidic device developed in our laboratory, here we report that both pathways are involved. We found the paracrine factors-mediated synchronization of molecular clocks is diffusion-limited and, in our device, effective only in case of a short distance between neuronal populations. Interestingly, interconnecting astrocytes define an active signaling channel that can synchronize molecular clocks of neuronal populations also at longer distances. At mechanism level, we found that astrocytes-mediated synchronization involves both GABA and glutamate, while neuronal paracrine factors-mediated synchronization occurs through GABA signaling. These findings identify a previously unknown role of astrocytes as active cells that might distribute long-range signals to synchronize the brain clocks, thus further strengthening the importance of reciprocal interactions between glial and neuronal cells in the context of circadian circuitry.

Time-keeping and decision-making in living cells: Part I

To survive and reproduce, a cell must process information from its environment and its own internal state and respond accordingly, in terms of metabolic activity, gene expression, movement, growth, division and differentiation. These signal–response decisions are made by complex networks of interacting genes and proteins, which function as biochemical switches and clocks, and other recognizable information-processing circuitry. This theme issue of Interface Focus (in two parts) brings together articles on time-keeping and decision-making in living cells—work that uses precise mathematical modelling of underlying molecular regulatory networks to understand important features of cell physiology. Part I focuses on time-keeping: mechanisms and dynamics of biological oscillators and modes of synchronization and entrainment of oscillators, with special attention to circadian clocks.

UBR4/POE facilitates secretory trafficking to maintain circadian clock synchrony

Ubiquitin ligases control the degradation of core clock proteins to govern the speed and resetting properties of the circadian pacemaker. However, few studies have addressed their potential to regulate other cellular events within clock neurons beyond clock protein turnover. Here, we report that the ubiquitin ligase, UBR4/POE, strengthens the central pacemaker by facilitating neuropeptide trafficking in clock neurons and promoting network synchrony. Ubr4-deficient mice are resistant to jetlag, whereas poe knockdown flies are prone to arrhythmicity, behaviors reflective of the reduced axonal trafficking of circadian neuropeptides. At the cellular level, Ubr4 ablation impairs the export of secreted proteins from the Golgi apparatus by reducing the expression of Coronin 7, which is required for budding of Golgi-derived transport vesicles. In summary, UBR4/POE fulfills a conserved and unexpected role in the vesicular trafficking of neuropeptides, a function that has important implications for circadian clock synchrony and circuit-level signal processing.

Although ubiquitin ligases are known to control clock protein degradation, their other roles in clock neurons are unclear. Here the authors report that UBR4 promotes export of neuropeptides from the Golgi for axonal trafficking, which is important for circadian clock synchrony in mice and flies.

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.

Complementary phase responses via functional differentiation of dual negative feedback loops

Multiple feedback loops are often found in gene regulations for various cellular functions. In mammalian circadian clocks, oscillations of Period1 (Per1) and Period2 (Per2) expression are caused by interacting negative feedback loops (NFLs) whose protein products with similar molecular functions repress each other. However, Per1 expression peaks earlier than Per2 in the pacemaker tissue, raising the question of whether the peak time difference reflects their different dynamical functions. Here, we address this question by analyzing phase responses of the circadian clock caused by light-induced transcription of both Per1 and Per2 mRNAs. Through mathematical analyses of dual NFLs, we show that phase advance is mainly driven by light inputs to the repressor with an earlier expression peak as Per1, whereas phase delay is driven by the other repressor with a later peak as Per2. Due to the complementary contributions to phase responses, the ratio of light-induced transcription rates between Per1 and Per2 determines the magnitude and direction of phase shifts at each time of day. Specifically, stronger Per1 light induction than Per2 results in a phase response curve (PRC) with a larger phase advance zone than delay zone as observed in rats and hamsters, whereas stronger Per2 induction causes a larger delay zone as observed in mice. Furthermore, the ratio of light-induced transcription rates required for entrainment is determined by the relation between the circadian and light-dark periods. Namely, if the autonomous period of a circadian clock is longer than the light-dark period, a larger light-induced transcription rate of Per1 than Per2 is required for entrainment, and vice versa. In short, the time difference between Per1 and Per2 expression peaks can differentiate their dynamical functions. The resultant complementary contributions to phase responses can determine entrainability of the circadian clock to the light-dark cycle.

Cancer stem cell generation during epithelial-mesenchymal transition is temporally gated by intrinsic circadian clocks

Epithelial-mesenchymal transition (EMT) is a key event preceding tumor cell metastasis that increases cell invasiveness and cancer stem cell (CSC) populations. Studies suggest that genes used in generating circadian rhythms also serve in regulating EMT. To test the role of circadian clocks in cellular EMT events two cancer cell lines were compared, one that has a well-established circadian clock, C6 from rat glioma, and one that does not, MCF-7 from human breast tumor. MCF-7 tumorsphere cultures were tested for evidence of circadian rhythms because of previously reported circadian rhythm enhancement in C6 tumorspheres shown by elevated rhythm amplitude and increased expression of circadian clock gene Per2. Bioluminescence imaging of Per2 gene expression in MCF-7 tumorspheres revealed a previously unconfirmed circadian clock in this important cancer research model. Inducing CSC generation through EMT in C6 and MCF-7 monolayer cultures revealed circadian oscillations in the size of the post-EMT CSC population, confirming that circadian rhythms are additional processes controlling this stage of cancer progression. EMT was verified by distinct cellular morphological changes and expression of stem cell proteins OCT4, nestin, MSI1, and CD133 along with EMT-related proteins ZEB1, vimentin, and TWIST. Quantifying single-cell events and behaviors through time-lapse imaging indicated the post-EMT population size was determined largely by circadian rhythms in epithelial-like cancer cells undergoing EMT. We then identified a specific phase of the circadian rhythm in Per2 gene activation as a potential target for therapeutic treatments that may suppress EMT, minimize CSCs, and limit metastasis.

Reduced VIP Expression Affects Circadian Clock Function in VIP-IRES-CRE Mice (JAX 010908)

Circadian rhythms are programmed by the suprachiasmatic nucleus (SCN), which relies on neuropeptide signaling to maintain daily timekeeping. Vasoactive intestinal polypeptide (VIP) is critical for SCN function, but the precise role of VIP neurons in SCN circuits is not fully established. To interrogate their contribution to SCN circuits, VIP neurons can be manipulated specifically using the DNA-editing enzyme Cre recombinase. Although the Cre transgene is assumed to be inert by itself, we find that VIP expression is reduced in both heterozygous and homozygous adult VIP-IRES-Cre mice (JAX 010908). Compared with wild-type mice, homozygous VIP-Cre mice display faster reentrainment and shorter free-running period but do not become arrhythmic in constant darkness. Consistent with this phenotype, homozygous VIP-Cre mice display intact SCN PER2::LUC rhythms, albeit with altered period and network organization. We present evidence that the ability to sustain molecular rhythms in the VIP-Cre SCN is not due to residual VIP signaling; rather, arginine vasopressin signaling helps to sustain SCN function at both intracellular and intercellular levels in this model. This work establishes that the VIP-IRES-Cre transgene interferes with VIP expression but that loss of VIP can be mitigated by other neuropeptide signals to help sustain SCN function. Our findings have implications for studies employing this transgenic model and provide novel insight into neuropeptide signals that sustain daily timekeeping in the master clock.

A microfluidic approach for experimentally modelling the intercellular coupling system of a mammalian circadian clock at single-cell level

In mammals, it is believed that the intercellular coupling mechanism between neurons in the suprachiasmatic nucleus (SCN) confers robustness and distinguishes the central clock from peripheral circadian oscillators. Current in vitro culturing methods used in Petri dishes to study intercellular coupling by exogenous factors invariably cause perturbations, such as simple media changes. Here, we design a microfluidic device to quantitatively study the intercellular coupling mechanism of circadian clock at the single cell level, and demonstrate that vasoactive intestinal peptide (VIP) induced coupling in clock mutant Cry1-/- mouse adult fibroblasts engineered to express the VIP receptor, VPAC2, is sufficient to synchronize and maintain robust circadian oscillations. Our study provides a proof-of-concept platform to reconstitute the intercellular coupling system of the central clock using uncoupled, single fibroblast cells in vitro, to mimic SCN slice cultures ex vivo and mouse behavior in vivo phenotypically. Such a versatile microfluidic platform may greatly facilitate the studies of intercellular regulation networks, and provide new insights into the coupling mechanisms of the circadian clock.

Filtering and inference for stochastic oscillators with distributed delays

Motivation

The time evolution of molecular species involved in biochemical reaction networks often arises from complex stochastic processes involving many species and reaction events. Inference for such systems is profoundly challenged by the relative sparseness of experimental data, as measurements are often limited to a small subset of the participating species measured at discrete time points. The need for model reduction can be realistically achieved for oscillatory dynamics resulting from negative translational and transcriptional feedback loops by the introduction of probabilistic time-delays. Although this approach yields a simplified model, inference is challenging and subject to ongoing research. The linear noise approximation (LNA) has recently been proposed to address such systems in stochastic form and will be exploited here.

Results

We develop a novel filtering approach for the LNA in stochastic systems with distributed delays, which allows the parameter values and unobserved states of a stochastic negative feedback model to be inferred from univariate time-series data. The performance of the methods is tested for simulated data. Results are obtained for real data when the model is fitted to imaging data on Cry1, a key gene involved in the mammalian central circadian clock, observed via a luciferase reporter construct in a mouse suprachiasmatic nucleus.

Availability and implementation

Programmes are written in MATLAB and Statistics Toolbox Release 2016 b, The MathWorks, Inc., Natick, Massachusetts, USA. Sample code and Cry1 data are available on GitHub https://github.com/scalderazzo/FLNADD.

Supplementary information

Supplementary data are available at Bioinformatics online.

Amplitude Effects Allow Short Jet Lags and Large Seasonal Phase Shifts in Minimal Clock Models

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jet lag, and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of models satisfying certain constraints; here, a 1h-pulse PRC with a range of 3h and clock periods between 22h and 26h is designed. Surprisingly, almost all these randomly parameterized models showed a 4h change in phase of entrainment between long and short days and jet lag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jet lag duration and entrainment amplitude and phase. Fast jet lag was realized in this model by means of an interesting amplitude effect: the association between clock amplitude and clock period termed "twist." This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of positive feedback to the model. In summary, the known design principles of rhythm generation - negative feedback, long delay, and switch-like inhibition (we review these in detail) - are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.

A Symphony of Signals: Intercellular and Intracellular Signaling Mechanisms Underlying Circadian Timekeeping in Mice and Flies

The central pacemakers of circadian timekeeping systems are highly robust yet adaptable, providing the temporal coordination of rhythms in behavior and physiological processes in accordance with the demands imposed by environmental cycles. These features of the central pacemaker are achieved by a multi-oscillator network in which individual cellular oscillators are tightly coupled to the environmental day-night cycle, and to one another via intercellular coupling. In this review, we will summarize the roles of various neurotransmitters and neuropeptides in the regulation of circadian entrainment and synchrony within the mammalian and Drosophila central pacemakers. We will also describe the diverse functions of protein kinases in the relay of input signals to the core oscillator or the direct regulation of the molecular clock machinery.

Reducing the complexity of mathematical models for the plant circadian clock by distributed delays

A major bottleneck in the modelling of biological networks is the parameter explosion problem - the exponential increase in the number of parameters that need to be optimised to data as the size of the model increases. Here, we address this problem in the context of the plant circadian clock by applying the method of distributed delays. We show that using this approach, the system architecture can be simplified efficiently - reducing the number of parameters - whilst still preserving the core mechanistic dynamics of the gene regulatory network. Compared to models with discrete time-delays, which are governed by functional differential equations, the distributed delay models can be converted into sets of equivalent ordinary differential equations, enabling the use of standard methods for numerical integration, and for stability and bifurcation analyses. We demonstrate the efficiency of our modelling approach by applying it to three exemplar mathematical models of the Arabidopsis circadian clock of varying complexity, obtaining significant reductions in complexity in each case. Moreover, we revise one of the most up-to-date Arabidopsis models, updating the regulation of the PRR9 and PRR7 genes by LHY in accordance with recent experimental data. The revised model more accurately reproduces the LHY-induction experiments of core clock genes, compared with the original model. Our work thus shows that the method of distributed delays facilitates the optimisation and reformulation of genetic network models.

Coherency of circadian rhythms in the SCN is governed by the interplay of two coupling factors

Circadian clocks are autonomous oscillators driving daily rhythms in physiology and behavior. In mammals, a network of coupled neurons in the suprachiasmatic nucleus (SCN) is entrained to environmental light-dark cycles and orchestrates the timing of peripheral organs. In each neuron, transcriptional feedbacks generate noisy oscillations. Coupling mediated by neuropeptides such as VIP and AVP lends precision and robustness to circadian rhythms. The detailed coupling mechanisms between SCN neurons are debated. We analyze organotypic SCN slices from neonatal and adult mice in wild-type and multiple knockout conditions. Different degrees of rhythmicity are quantified by pixel-level analysis of bioluminescence data. We use empirical orthogonal functions (EOFs) to characterize spatio-temporal patterns. Simulations of coupled stochastic single cell oscillators can reproduce the diversity of observed patterns. Our combination of data analysis and modeling provides deeper insight into the enormous complexity of the data: (1) Neonatal slices are typically stronger oscillators than adult slices pointing to developmental changes of coupling. (2) Wild-type slices are completely synchronized and exhibit specific spatio-temporal patterns of phases. (3) Some slices of Cry double knockouts obey impaired synchrony that can lead to co–existing rhythms (“splitting”). (4) The loss of VIP-coupling leads to desynchronized rhythms with few residual local clusters. Additional information was extracted from co–culturing slices with rhythmic neonatal wild-type SCNs. These co–culturing experiments were simulated using external forcing terms representing VIP and AVP signaling. The rescue of rhythmicity via co–culturing lead to surprising results, since a cocktail of AVP-antagonists improved synchrony. Our modeling suggests that these counter-intuitive observations are pointing to an antagonistic action of VIP and AVP coupling. Our systematic theoretical and experimental study shows that dual coupling mechanisms can explain the astonishing complexity of spatio-temporal patterns in SCN slices.

The mammalian circadian clock is orchestrated by a network of coupled neurons. Brain slice preparations allow the analysis of coupling mechanisms mediated by neuropeptides. From bioluminescence recordings, we extract single cell characteristics such as period, amplitude and damping rate. Our data-based stochastic network model involves local coupling between cells and additional external forcing. Available experimental data guide our simulations with two distinct coupling and forcing mechanisms representing the neuropeptides VIP and AVP. We compare our simulations with experiments from neonatal and adult wild-type brain slices and multiple knockouts. Furthermore, we study co–culturing of slices with synchronized neonatal wild-type slices. The extreme complexity of the spatio-temporal patterns is quantified using empirical orthogonal functions (EOFs). The experimental reduction of AVP coupling leads to surprising observations. In double knockouts, inhibition of AVP signaling can improve synchrony, whereas, in triple knockouts, coherency is reduced. Our network modeling shows that these counter-intuitive observations can be explained by an antagonistic action of VIP and AVP signaling. The agreement of experiments and simulations suggests that quite complex spatio-temporal patterns can appear as emergent properties of oscillator networks with dual coupling mechanisms.

Recurring circadian disruption alters circadian clock sensitivity to resetting

A single phase advance of the light:dark (LD) cycle can temporarily disrupt synchrony of neural circadian rhythms within the suprachiasmatic nucleus (SCN) and between the SCN and peripheral tissues. Compounding this, modern life can involve repeated disruptive light conditions. To model chronic disruption to the circadian system, we exposed male mice to more than a month of a 20-hr light cycle (LD10:10), which mice typically cannot entrain to. Control animals were housed under LD12:12. We measured locomotor activity and body temperature rhythms in vivo, and rhythms of PER2::LUC bioluminescence in SCN and peripheral tissues ex vivo. Unexpectedly, we discovered strong effects of the time of dissection on circadian phase of PER2::LUC bioluminescent rhythms, which varied across tissues. White adipose tissue was strongly reset by dissection, while thymus phase appeared independent of dissection timing. Prior light exposure impacted the SCN, resulting in strong resetting of SCN phase by dissection for mice housed under LD10:10, and weak phase shifts by time of dissection in SCN from control LD12:12 mice. These findings suggest that exposure to circadian disruption may desynchronize SCN neurons, increasing network sensitivity to perturbations. We propose that tissues with a weakened circadian network, such as the SCN under disruptive light conditions, or with little to no coupling, for example, some peripheral tissues, will show increased resetting effects. In particular, exposure to light at inconsistent circadian times on a recurring weekly basis disrupts circadian rhythms and alters sensitivity of the SCN neural pacemaker to dissection time.

Chemical event chain model of coupled genetic oscillators

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Stability of Wake-Sleep Cycles Requires Robust Degradation of the PERIOD Protein

Robustness in biology is the stability of phenotype under diverse genetic and/or environmental perturbations. The circadian clock has remarkable stability of period and phase that-unlike other biological oscillators-is maintained over a wide range of conditions. Here, we show that the high fidelity of the circadian system stems from robust degradation of the clock protein PERIOD. We show that PERIOD degradation is regulated by a balance between ubiquitination and deubiquitination, and that disruption of this balance can destabilize the clock. In mice with a loss-of-function mutation of the E3 ligase gene β-Trcp2, the balance of PERIOD degradation is perturbed and the clock becomes dramatically unstable, presenting a unique behavioral phenotype unlike other circadian mutant animal models. We believe that our data provide a molecular explanation for how circadian phases, such as wake-sleep onset times, can become unstable in humans, and we present a unique mouse model to study human circadian disorders with unstable circadian rhythm phases.

Fluorescence circadian imaging reveals a PDF-dependent transcriptional regulation of the Drosophila molecular clock

Circadian locomotor behaviour is controlled by a pacemaker circuit composed of clock-containing neurons. To interrogate the mechanistic relationship between the molecular clockwork and network communication critical to the operation of the Drosophila circadian pacemaker circuit, we established new fluorescent circadian reporters that permit single-cell recording of transcriptional and post-transcriptional rhythms in brain explants and cultured neurons. Live-imaging experiments combined with pharmacological and genetic manipulations demonstrate that the neuropeptide pigment-dispersing factor (PDF) amplifies the molecular rhythms via time-of-day- and activity-dependent upregulation of transcription from E-box-containing clock gene promoters within key pacemaker neurons. The effect of PDF on clock gene transcription and the known role of PDF in enhancing PER/TIM stability occur via independent pathways downstream of the PDF receptor, the former through a cAMP-independent mechanism and the latter through a cAMP-PKA dependent mechanism. These results confirm and extend the mechanistic understanding of the role of PDF in controlling the synchrony of the pacemaker neurons. More broadly, our results establish the utility of the new live-imaging tools for the study of molecular-neural interactions important for the operation of the circadian pacemaker circuit.

An LHX1-Regulated Transcriptional Network Controls Sleep/Wake Coupling and Thermal Resistance of the Central Circadian Clockworks

The suprachiasmatic nucleus (SCN) is the central circadian clock in mammals. It is entrained by light but resistant to temperature shifts that entrain peripheral clocks [1-5]. The SCN expresses many functionally important neuropeptides, including vasoactive intestinal peptide (VIP), which drives light entrainment, synchrony, and amplitude of SCN cellular clocks and organizes circadian behavior [5-16]. The transcription factor LHX1 drives SCN Vip expression, and cellular desynchrony in Lhx1-deficient SCN largely results from Vip loss [17, 18]. LHX1 regulates many genes other than Vip, yet activity rhythms in Lhx1-deficient mice are similar to Vip^-/- mice under light-dark cycles and only somewhat worse in constant conditions. We suspected that LHX1 targets other than Vip have circadian functions overlooked in previous studies. In this study, we compared circadian sleep and temperature rhythms of Lhx1- and Vip-deficient mice and found loss of acute light control of sleep in Lhx1 but not Vip mutants. We also found loss of circadian resistance to fever in Lhx1 but not Vip mice, which was partially recapitulated by heat application to cultured Lhx1-deficient SCN. Having identified VIP-independent functions of LHX1, we mapped the VIP-independent transcriptional network downstream of LHX1 and a largely separable VIP-dependent transcriptional network. The VIP-independent network does not affect core clock amplitude and synchrony, unlike the VIP-dependent network. These studies identify Lhx1 as the first gene required for temperature resistance of the SCN clockworks and demonstrate that acute light control of sleep is routed through the SCN and its immediate output regions.

Design Principles of Biological Oscillators through Optimization: Forward and Reverse Analysis

From cyanobacteria to human, sustained oscillations coordinate important biological functions. Although much has been learned concerning the sophisticated molecular mechanisms underlying biological oscillators, design principles linking structure and functional behavior are not yet fully understood. Here we explore design principles of biological oscillators from a multiobjective optimization perspective, taking into account the trade-offs between conflicting performance goals or demands. We develop a comprehensive tool for automated design of oscillators, based on multicriteria global optimization that allows two modes: (i) the automatic design (forward problem) and (ii) the inference of design principles (reverse analysis problem). From the perspective of synthetic biology, the forward mode allows the solution of design problems that mimic some of the desirable properties appearing in natural oscillators. The reverse analysis mode facilitates a systematic exploration of the design space based on Pareto optimality concepts. The method is illustrated with two case studies: the automatic design of synthetic oscillators from a library of biological parts, and the exploration of design principles in 3-gene oscillatory systems.

Entrainment Maps

Circadian oscillators found across a variety of species are subject to periodic external light-dark forcing. Entrainment to light-dark cycles enables the circadian system to align biological functions with appropriate times of day or night. Phase response curves (PRCs) have been used for decades to gain valuable insights into entrainment; however, PRCs may not accurately describe entrainment to photoperiods with substantial amounts of both light and dark due to their reliance on a single limit cycle attractor. We have developed a new tool, called an entrainment map, that overcomes this limitation of PRCs and can assess whether, and at what phase, a circadian oscillator entrains to external forcing with any photoperiod. This is a 1-dimensional map that we construct for 3 different mathematical models of circadian clocks. Using the map, we are able to determine conditions for existence and stability of phase-locked solutions. In addition, we consider the dependence on various parameters such as the photoperiod and intensity of the external light as well as the mismatch in intrinsic oscillator frequency with the light-dark cycle. We show that the entrainment map yields more accurate predictions for phase locking than methods based on the PRC. The map is also ideally suited to calculate the amount of time required to achieve entrainment as a function of initial conditions and the bifurcations of stable and unstable periodic solutions that lead to loss of entrainment.

Coupling Controls the Synchrony of Clock Cells in Development and Knockouts

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

Differential roles of AVP and VIP signaling in the postnatal changes of neural networks for coherent circadian rhythms in the SCN

The suprachiasmatic nucleus (SCN) is the site of the master circadian clock in mammals. The SCN neural network plays a critical role in expressing the tissue-level circadian rhythm. Previously, we demonstrated postnatal changes in the SCN network in mice, in which the clock gene products CRYPTOCHROMES (CRYs) are involved. Here, we show that vasoactive intestinal polypeptide (VIP) signaling is essential for the tissue-level circadian PER2::LUC rhythm in the neonatal SCN of CRY double-deficient mice (Cry1,2 (-/-) ). VIP and arginine vasopressin (AVP) signaling showed redundancy in expressing the tissue-level circadian rhythm in the SCN. AVP synthesis was significantly attenuated in the Cry1,2 (-/-) SCN, which contributes to aperiodicity in the adult mice together with an attenuation of VIP signaling as a natural process of ontogeny. The SCN network consists of multiple clusters of cellular circadian rhythms that are differentially integrated by AVP and VIP signaling, depending on the postnatal period.

Collective timekeeping among cells of the master circadian clock

The suprachiasmatic nucleus (SCN) of the anterior hypothalamus is the master circadian clock that coordinates daily rhythms in behavior and physiology in mammals. Like other hypothalamic nuclei, the SCN displays an impressive array of distinct cell types characterized by differences in neurotransmitter and neuropeptide expression. Individual SCN neurons and glia are able to display self-sustained circadian rhythms in cellular function that are regulated at the molecular level by a 24h transcriptional-translational feedback loop. Remarkably, SCN cells are able to harmonize with one another to sustain coherent rhythms at the tissue level. Mechanisms of cellular communication in the SCN network are not completely understood, but recent progress has provided insight into the functional roles of several SCN signaling factors. This review discusses SCN organization, how intercellular communication is critical for maintaining network function, and the signaling mechanisms that play a role in this process. Despite recent progress, our understanding of SCN circuitry and coupling is far from complete. Further work is needed to map SCN circuitry fully and define the signaling mechanisms that allow for collective timekeeping in the SCN network.

Functional Contributions of Strong and Weak Cellular Oscillators to Synchrony and Light-shifted Phase Dynamics

Light is the primary signal that calibrates circadian neural circuits and thus coordinates daily physiological and behavioral rhythms with solar entrainment cues. Drosophila and mammalian circadian circuits consist of diverse populations of cellular oscillators that exhibit a wide range of dynamic light responses, periods, phases, and degrees of synchrony. How heterogeneous circadian circuits can generate robust physiological rhythms while remaining flexible enough to respond to synchronizing stimuli has long remained enigmatic. Cryptochrome is a short-wavelength photoreceptor that is endogenously expressed in approximately half of Drosophila circadian neurons. In a previous study, physiological light response was measured using real-time bioluminescence recordings in Drosophila whole-brain explants, which remain intrinsically light-sensitive. Here we apply analysis of real-time bioluminescence experimental data to show detailed dynamic ensemble representations of whole circadian circuit light entrainment at single neuron resolution. Organotypic whole-brain explants were either maintained in constant darkness (DD) for 6 days or exposed to a phase-advancing light pulse on the second day. We find that stronger circadian oscillators support robust overall circuit rhythmicity in DD, whereas weaker oscillators can be pushed toward transient desynchrony and damped amplitude to facilitate a new state of phase-shifted network synchrony. Additionally, we use mathematical modeling to examine how a network composed of distinct oscillator types can give rise to complex dynamic signatures in DD conditions and in response to simulated light pulses. Simulations suggest that complementary coupling mechanisms and a combination of strong and weak oscillators may enable a robust yet flexible circadian network that promotes both synchrony and entrainment. A more complete understanding of how the properties of oscillators and their signaling mechanisms facilitate their distinct roles in light entrainment may allow us to direct and augment the circadian system to speed recovery from jet lag, shift work, and seasonal affective disorder.

Deconstructing Circadian Rhythmicity with Models and Manipulations

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

Functional network inference of the suprachiasmatic nucleus

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

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

Astounding properties of biological sensors can often be mapped onto a dynamical system below the occurrence of a bifurcation. For mammalian hearing, a Hopf bifurcation description has been shown to work across a whole range of scales, from individual hair bundles to whole regions of the cochlea. We reveal here the origin of this scale invariance, from a general level, applicable to all dynamics in the vicinity of a Hopf bifurcation (embracing, e.g., neuronal Hodgkin-Huxley equations). When subject to natural "signal coupling," ensembles of Hopf systems below the bifurcation threshold exhibit a collective Hopf bifurcation. This collective Hopf bifurcation occurs at parameter values substantially below where the average of the individual systems would bifurcate, with a frequency profile that is sharpened if compared to the individual systems.

Inhibitory and excitatory networks balance cell coupling in the suprachiasmatic nucleus: A modeling approach

Neuronal coupling contributes to circadian rhythms formation in the suprachiasmatic nucleus (SCN). While the neurotransmitter vasoactive intestinal polypeptide (VIP) is considered essential for synchronizing the oscillations of individual neurons, γ-aminobutyric acid (GABA) does not have a clear functional role despite being highly concentrated in the SCN. While most studies have examined the role of either GABA or VIP, our mathematical modeling approach explored their interplay on networks of SCN neurons. Tuning the parameters that control the release of GABA and VIP enabled us to optimize network synchrony, which was achieved at a peak firing rate during the subjective day of about 7Hz. Furthermore, VIP and GABA modulation could adjust network rhythm amplitude and period without sacrificing synchrony. We also performed simulations of SCN networks to phase shifts during 12h:12h light-dark cycles and showed that GABA networks reduced the average time for the SCN model to re-synchronize. We hypothesized that VIP and GABA balance cell coupling in the SCN to promote synchronization of heterogeneous oscillators while allowing flexibility for adjustment to environmental changes.

In synch but not in step: Circadian clock circuits regulating plasticity in daily rhythms

The suprachiasmatic nucleus (SCN) is a network of neural oscillators that program daily rhythms in mammalian behavior and physiology. Over the last decade much has been learned about how SCN clock neurons coordinate together in time and space to form a cohesive population. Despite this insight, much remains unknown about how SCN neurons communicate with one another to produce emergent properties of the network. Here we review the current understanding of communication among SCN clock cells and highlight a collection of formal assays where changes in SCN interactions provide for plasticity in the waveform of circadian rhythms in behavior. Future studies that pair analytical behavioral assays with modern neuroscience techniques have the potential to provide deeper insight into SCN circuit mechanisms.

A mathematical model of communication between groups of circadian neurons in Drosophila melanogaster

In the fruit fly, circadian behavior is controlled by a small number of specialized neurons, whose molecular clocks are relatively well known. However, much less is known about how these neurons communicate among themselves. In particular, only 1 circadian neuropeptide, pigment-dispersing factor (PDF), has been identified, and most aspects of its interaction with the molecular clock remain to be elucidated. Furthermore, it is speculated that many other peptides should contribute to circadian communication. We have developed a relatively detailed model of the 2 main groups of circadian pacemaker neurons (sLNvs and LNds) to investigate these issues. We have proposed many possible mechanisms for the interaction between the synchronization factors and the molecular clock, and we have compared the outputs with the experimental results reported in the literature both for the wild-type and PDF-null mutant. We have studied how different the properties of each neuron should be to account for the observations reported for the sLNvs in the mutant. We have found that only a few mechanisms, mostly related to the slowing down of nuclear entry of a circadian protein, can synchronize neurons that present these differences. Detailed immunofluorescent recordings have suggested that, whereas in the mutant, LNd neurons are synchronized, in the wild-type, a subset of the LNds oscillate faster than the rest. With our model, we find that a more likely explanation for the same observations is that this subset is being driven outside its synchronization range and displays therefore a complex pattern of oscillation.

Rhythmic control of activity and sleep by class B1 GPCRs

Members of the class B1 family of G-protein coupled receptors (GPCRs) whose ligands are neuropeptides have been implicated in regulation of circadian rhythms and sleep in diverse metazoan clades. This review discusses the cellular and molecular mechanisms by which class B1 GPCRs, especially the mammalian VPAC2 receptor and its functional homologue PDFR in Drosophila and C. elegans, regulate arousal and daily rhythms of sleep and wake. There are remarkable parallels in the cellular and molecular roles played by class B1 intercellular signaling pathways in coordinating arousal and circadian timekeeping across multiple cells and tissues in these very different genetic model organisms.

Brain clock driven by neuropeptides and second messengers

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