Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

Living systems exhibit an unmatched complexity, due to countless and entangled interactions across scales. Here we aim to understand and gain control of a complex system, such as the segmentation timing of a developing mouse embryo, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach in which theory guides the experimental identification of the system-level responses to entrainment, in the context of a network of coupled cellular oscillators that constitute the embryonic somite segmentation clock. We demonstrate period- and phase-locking of the embryonic system across a wide range of entrainment parameters, including higher-order coupling. These experimental quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the system, revealing the essential dynamical properties of the embryonic segmentation clock. Our results indicate that at the macro-scale, the somite segmentation clock has characteristics of a highly non-linear oscillator close to a saddle-node on invariant cycle (SNIC) bifurcation and suggests the presence of long-term feedbacks. Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system and hereby provides precise experimental control over the pace and rhythm of the somite segmentation clock.

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

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

Using phase dynamics to study partial synchrony: three examples

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

635 Evening Sunglasses Plus Stable Wake Times: Can This Intervention Help Adolescents with Delayed Sleep-wake Phase Disorder?

Introduction Evening light can increase alertness and shift the circadian clock later (delay) and, in turn, delay sleep onset timing. We are examining whether reducing evening light exposure (by wearing sunglasses) paired with stable wake times can shift circadian and sleep onset times earlier in adolescents with Delayed Sleep-Wake Phase Disorder (DSWPD). Methods Fifteen adolescents (14.7–18.1 years; 4 male) diagnosed with DSWPD are included in this interim analysis. Participants sleep without restriction at home for a baseline week, and then complete a 2-week intervention. One group (Amber; n=7) wears glasses with amber lenses (Cocoons®, Live Eyewear) beginning 7 hours before their baseline mid-sleep time until self-selected bedtime or for 7 hours (corresponds to the phase delay region of the adolescent phase response curve to light). The amber lens transmits 14% of light to the eye and absorbs most short wavelength light. The frame blocks light from all angles. Amber participants are also instructed to wake at their average baseline school-morning wake-up time (±30 mins). Another group (Clear; n=8) wears identical glasses with clear lenses at the same time and wake time is unrestricted. Glasses wear time is monitored with an iButton placed at the temple tip. Dim Light Melatonin Onset (DLMO) is measured after the baseline week and after the 2-week intervention; 2 participants (one from each group) do not have melatonin data due to technical error. Sleep is measured with wrist actigraphy and sleep diaries throughout the study. DLMO and sleep onset changes (baseline-intervention) are compared between groups with t-tests. Results Amber DLMOs shifted 1.0±2.0h earlier (min-max: 0.4-h delay-5.0-h advance) and Clear DLMOs shifted 0.4±1.1h later (min-max: 2.0-h delay-0.6-h advance) [t(11)=1.60,p=0.14]. Average school-night sleep onset shifted earlier in both groups (Amber:0.4±1.3h; Clear:0.6±1.0h; t(13)=0.2,p=0.8]. Average non-school-night sleep onset shifted 1.1±1.0h earlier in Amber (min-max:0.6-h delay-2.2-h advance) and remained stable (0.03±1.0h) in Clear (min-max: 1.8-h delay-1.7-h advance) [t(13)=1.92,p=.08]. Conclusion Trends from this ongoing study suggest that amber-lensed glasses to block evening light plus stable wake-up times may shift circadian rhythms earlier. This strategy appears to help adolescents with DSWPD fall asleep earlier predominantly on non-school nights. Support (if any) AASMF Strategic Research Award (184-SR-17) to RRA

Transmission delays and frequency detuning can regulate information flow between brain regions

Brain networks exhibit very variable and dynamical functional connectivity and flexible configurations of information exchange despite their overall fixed structure. Brain oscillations are hypothesized to underlie time-dependent functional connectivity by periodically changing the excitability of neural populations. In this paper, we investigate the role of the connection delay and the detuning between the natural frequencies of neural populations in the transmission of signals. Based on numerical simulations and analytical arguments, we show that the amount of information transfer between two oscillating neural populations could be determined by their connection delay and the mismatch in their oscillation frequencies. Our results highlight the role of the collective phase response curve of the oscillating neural populations for the efficacy of signal transmission and the quality of the information transfer in brain networks.

The Circadian Phase Response Curve to Light: Conservation across Seasons and Anchorage to Sunset

Predictions about circadian light responses are largely based on photic phase-response curves (PRCs) generated from animals housed under seasonally agnostic equatorial photoperiods with alternating 12-hour segments of light and darkness. Most of the human population, however, lives at northerly latitudes where seasonal variations in the light-dark schedule are pronounced. Here, we address this disconnect by constructing the first high-resolution seasonal atlas for light-induced circadian phase-resetting. Testing the light responses of nearly 4,000 Drosophila at 120 timepoints across 5 seasonally relevant photoperiods, we determined that many aspects of the circadian PRC waveform are conserved with increasing daylength. Surprisingly though, irrespective of LD schedule, the start of the PRCs always remained anchored to the timing of subjective sunset, creating a differential overlap of the advance zone with the morning hours after subjective sunrise that was maximized under summer photoperiods and minimized under winter photoperiods. These data suggest that circadian photosensitivity is effectively extinguished by the early winter morning and out of optimal phase alignment with the wake schedules of many individuals. They raise the possibility that phototherapy protocols for conditions such as seasonal depression might be improved with programmed light exposure during the final hours of sleep.

Divergent Importance of Chronobiological Considerations in High- and Low-dose Melatonin Therapies

Melatonin has been used preclinically and clinically for different purposes. Some applications are related to readjustment of circadian oscillators, others use doses that exceed the saturation of melatonin receptors MT1 and MT2 and are unsuitable for chronobiological purposes. Conditions are outlined for appropriately applying melatonin as a chronobiotic or for protective actions at elevated levels. Circadian readjustments require doses in the lower mg range, according to receptor affinities. However, this needs consideration of the phase response curve, which contains a silent zone, a delay part, a transition point and an advance part. Notably, the dim light melatonin onset (DLMO) is found in the silent zone. In this specific phase, melatonin can induce sleep onset, but does not shift the circadian master clock. Although sleep onset is also under circadian control, sleep and circadian susceptibility are dissociated at this point. Other limits of soporific effects concern dose, duration of action and poor individual responses. The use of high melatonin doses, up to several hundred mg, for purposes of antioxidative and anti-inflammatory protection, especially in sepsis and viral diseases, have to be seen in the context of melatonin’s tissue levels, its formation in mitochondria, and detoxification of free radicals.

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.