Keeping the beat in the rising heat.

Circadian clocks use temperature compensation to keep accurate time over a range of temperatures, thus allowing reliable timekeeping under diverse environmental conditions. Mehra et al. (2009) and Baker et al. (2009) now show that phosphorylation-regulated protein degradation plays a key role in circadian temperature compensation.

A Period2 Phosphoswitch Regulates and Temperature Compensates Circadian Period.

Period (PER) protein phosphorylation is a critical regulator of circadian period, yet an integrated understanding of the role and interaction between phosphorylation sites that can both increase and decrease PER2 stability remains elusive. Here, we propose a phosphoswitch model, where two competing phosphorylation sites determine whether PER2 has a fast or slow degradation rate. This mathematical model accurately reproduces the three-stage degradation kinetics of endogenous PER2. We predict and demonstrate that the phosphoswitch is intrinsically temperature sensitive, slowing down PER2 degradation as a result of faster reactions at higher temperatures. The phosphoswitch provides a biochemical mechanism for circadian temperature compensation of circadian period. This phosphoswitch additionally explains the phenotype of Familial Advanced Sleep Phase (FASP) and CK1ε(tau) genetic circadian rhythm disorders, metabolic control of PER2 stability, and how drugs that inhibit CK1 alter period. The phosphoswitch provides a general mechanism to integrate diverse stimuli to regulate circadian period.

Optimal adjustment of the human circadian clock in the real world.

Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body's internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock's primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain. We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings.

CK1δ/ε protein kinase primes the PER2 circadian phosphoswitch.

Multisite phosphorylation of the PERIOD 2 (PER2) protein is the key step that determines the period of the mammalian circadian clock. Previous studies concluded that an unidentified kinase is required to prime PER2 for subsequent phosphorylation by casein kinase 1 (CK1), an essential clock component that is conserved from algae to humans. These subsequent phosphorylations stabilize PER2, delay its degradation, and lengthen the period of the circadian clock. Here, we perform a comprehensive biochemical and biophysical analysis of mouse PER2 (mPER2) priming phosphorylation and demonstrate, surprisingly, that CK1δ/ε is indeed the priming kinase. We find that both CK1ε and a recently characterized CK1δ2 splice variant more efficiently prime mPER2 for downstream phosphorylation in cells than the well-studied splice variant CK1δ1. While CK1 phosphorylation of PER2 was previously shown to be robust to changes in the cellular environment, our phosphoswitch mathematical model of circadian rhythms shows that the CK1 carboxyl-terminal tail can allow the period of the clock to be sensitive to cellular signaling. These studies implicate the extreme carboxyl terminus of CK1 as a key regulator of circadian timing.

GABA-mediated repulsive coupling between circadian clock neurons in the SCN encodes seasonal time.

The mammalian suprachiasmatic nucleus (SCN) forms not only the master circadian clock but also a seasonal clock. This neural network of ∼10,000 circadian oscillators encodes season-dependent day-length changes through a largely unknown mechanism. We show that region-intrinsic changes in the SCN fine-tune the degree of network synchrony and reorganize the phase relationship among circadian oscillators to represent day length. We measure oscillations of the clock gene Bmal1, at single-cell and regional levels in cultured SCN explanted from animals raised under short or long days. Coupling estimation using the Kuramoto framework reveals that the network has couplings that can be both phase-attractive (synchronizing) and -repulsive (desynchronizing). The phase gap between the dorsal and ventral regions increases and the overall period of the SCN shortens with longer day length. We find that one of the underlying physiological mechanisms is the modulation of the intracellular chloride concentration, which can adjust the strength and polarity of the ionotropic GABAA-mediated synaptic input. We show that increasing day-length changes the pattern of chloride transporter expression, yielding more excitatory GABA synaptic input, and that blocking GABAA signaling or the chloride transporter disrupts the unique phase and period organization induced by the day length. We test the consequences of this tunable GABA coupling in the context of excitation-inhibition balance through detailed realistic modeling. These results indicate that the network encoding of seasonal time is controlled by modulation of intracellular chloride, which determines the phase relationship among and period difference between the dorsal and ventral SCN.

Distinct roles for GABA across multiple timescales in mammalian circadian timekeeping.

The suprachiasmatic nuclei (SCN), the central circadian pacemakers in mammals, comprise a multiscale neuronal system that times daily events. We use recent advances in graphics processing unit computing to generate a multiscale model for the SCN that resolves cellular electrical activity down to the timescale of individual action potentials and the intracellular molecular events that generate circadian rhythms. We use the model to study the role of the neurotransmitter GABA in synchronizing circadian rhythms among individual SCN neurons, a topic of much debate in the circadian community. The model predicts that GABA signaling has two components: phasic (fast) and tonic (slow). Phasic GABA postsynaptic currents are released after action potentials, and can both increase or decrease firing rate, depending on their timing in the interspike interval, a modeling hypothesis we experimentally validate; this allows flexibility in the timing of circadian output signals. Phasic GABA, however, does not significantly affect molecular timekeeping. The tonic GABA signal is released when cells become very excited and depolarized; it changes the excitability of neurons in the network, can shift molecular rhythms, and affects SCN synchrony. We measure which neurons are excited or inhibited by GABA across the day and find GABA-excited neurons are synchronized by-and GABA-inhibited neurons repelled from-this tonic GABA signal, which modulates the synchrony in the SCN provided by other signaling molecules. Our mathematical model also provides an important tool for circadian research, and a model computational system for the many multiscale projects currently studying brain function.

Characterizing and modeling the intrinsic light response of rat ganglion-cell photoreceptors.

Intrinsically photosensitive retinal ganglion cells (ipRGCs) mediate both image-forming vision and non-image-forming visual responses such as pupillary constriction and circadian photoentrainment. Five types of ipRGCs, named M1-M5, have been discovered in rodents. To further investigate their photoresponse properties, we made multielectrode array spike recordings from rat ipRGCs, classified them into M1, M2/M4, and M3/M5 clusters, and measured their intrinsic, melanopsin-based responses to single and flickering light pulses. Results showed that ipRGC spiking can track flickers up to ∼0.2 Hz in frequency and that flicker intervals between 5 and 14 s evoke the most spikes. We also learned that melanopsin's integration time is intensity and cluster dependent. Using these data, we constructed a mathematical model for each cluster's intrinsic photoresponse. We found that the data for the M1 cluster are best fit by a model that assumes a large photoresponse, causing the cell to enter depolarization block. Our models also led us to hypothesize that the M2/M4 and M3/M5 clusters experience comparable photoexcitation but that the M3/M5 cascade decays significantly faster than the M2/M4 cascade, resulting in different response waveforms between these clusters. These mathematical models will help predict how each ipRGC cluster might respond to stimuli of any waveform and could inform the invention of lighting technologies that promote health through melanopsin stimulation.

Characterizing spiking in noisy type II neurons.

Understanding the dynamics of noisy neurons remains an important challenge in neuroscience. Here, we describe a simple probabilistic model that accurately describes the firing behavior in a large class (type II) of neurons. To demonstrate the usefulness of this model, we show how it accurately predicts the interspike interval (ISI) distributions, bursting patterns and mean firing rates found by: (1) simulations of the classic Hodgkin-Huxley model with channel noise, (2) experimental data from squid giant axon with a noisy input current and (3) experimental data on noisy firing from a neuron within the suprachiasmatic nucleus (SCN). This simple model has 6 parameters, however, in some cases, two of these parameters are coupled and only 5 parameters account for much of the known behavior. From these parameters, many properties of spiking can be found through simple calculation. Thus, we show how the complex effects of noise can be understood through a simple and general probabilistic model.

Optimal schedules of light exposure for rapidly correcting circadian misalignment.

Jet lag arises from a misalignment of circadian biological timing with the timing of human activity, and is caused by rapid transmeridian travel. Jet lag's symptoms, such as depressed cognitive alertness, also arise from work and social schedules misaligned with the timing of the circadian clock. Using experimentally validated mathematical models, we develop a new methodology to find mathematically optimal schedules of light exposure and avoidance for rapidly re-entraining the human circadian system. In simulations, our schedules are found to significantly outperform other recently proposed schedules. Moreover, our schedules appear to be significantly more robust to both noise in light and to inter-individual variations in endogenous circadian period than other proposed schedules. By comparing the optimal schedules for thousands of different situations, and by using general mathematical arguments, we are also able to translate our findings into general principles of optimal circadian re-entrainment. These principles include: 1) a class of schedules where circadian amplitude is only slightly perturbed, optimal for dim light and for small shifts 2) another class of schedules where shifting occurs along the shortest path in phase-space, optimal for bright light and for large shifts 3) the determination that short light pulses are less effective than sustained light if the goal is to re-entrain quickly, and 4) the determination that length of daytime should be significantly shorter when delaying the clock than when advancing it.

Causes and consequences of hyperexcitation in central clock neurons.

Hyperexcited states, including depolarization block and depolarized low amplitude membrane oscillations (DLAMOs), have been observed in neurons of the suprachiasmatic nuclei (SCN), the site of the central mammalian circadian (~24-hour) clock. The causes and consequences of this hyperexcitation have not yet been determined. Here, we explore how individual ionic currents contribute to these hyperexcited states, and how hyperexcitation can then influence molecular circadian timekeeping within SCN neurons. We developed a mathematical model of the electrical activity of SCN neurons, and experimentally verified its prediction that DLAMOs depend on post-synaptic L-type calcium current. The model predicts that hyperexcited states cause high intracellular calcium concentrations, which could trigger transcription of clock genes. The model also predicts that circadian control of certain ionic currents can induce hyperexcited states. Putting it all together into an integrative model, we show how membrane potential and calcium concentration provide a fast feedback that can enhance rhythmicity of the intracellular circadian clock. This work puts forward a novel role for electrical activity in circadian timekeeping, and suggests that hyperexcited states provide a general mechanism for linking membrane electrical dynamics to transcription activation in the nucleus.

Signal processing in cellular clocks.

Many biochemical events within a cell need to be timed properly to occur at specific times of day, after other events have happened within the cell or in response to environmental signals. The cellular biochemical feedback loops that time these events have already received much recent attention in the experimental and modeling communities. Here, we show how ideas from signal processing can be applied to understand the function of these clocks. Consider two signals from the network s(t) and r(t), either two variables of a model or two experimentally measured time courses. We show how s(t) can be decomposed into two parts, the first being a function of r(t), and the second the derivative of a function of r(t). Geometric principles are then derived that can be used to understand when oscillations appear in biochemical feedback loops, the period of these oscillations, and their time course. Specific examples of this theory are provided that show how certain networks are prone or not prone to oscillate, how individual biochemical processes affect the period, and how oscillations in one chemical species can be deduced from oscillations in other parts of the network.

A mechanism for robust circadian timekeeping via stoichiometric balance.

Circadian (∼24 h) timekeeping is essential for the lives of many organisms. To understand the biochemical mechanisms of this timekeeping, we have developed a detailed mathematical model of the mammalian circadian clock. Our model can accurately predict diverse experimental data including the phenotypes of mutations or knockdown of clock genes as well as the time courses and relative expression of clock transcripts and proteins. Using this model, we show how a universal motif of circadian timekeeping, where repressors tightly bind activators rather than directly binding to DNA, can generate oscillations when activators and repressors are in stoichiometric balance. Furthermore, we find that an additional slow negative feedback loop preserves this stoichiometric balance and maintains timekeeping with a fixed period. The role of this mechanism in generating robust rhythms is validated by analysis of a simple and general model and a previous model of the Drosophila circadian clock. We propose a double-negative feedback loop design for biological clocks whose period needs to be tightly regulated even with large changes in gene dosage.

Emergence of noise-induced oscillations in the central circadian pacemaker.

Bmal1 is an essential transcriptional activator within the mammalian circadian clock. We report here that the suprachiasmatic nucleus (SCN) of Bmal1-null mutant mice, unexpectedly, generates stochastic oscillations with periods that overlap the circadian range. Dissociated SCN neurons expressed fluctuating levels of PER2 detected by bioluminescence imaging but could not generate circadian oscillations intrinsically. Inhibition of intercellular communication or cyclic-AMP signaling in SCN slices, which provide a positive feed-forward signal to drive the intracellular negative feedback loop, abolished the stochastic oscillations. Propagation of this feed-forward signal between SCN neurons then promotes quasi-circadian oscillations that arise as an emergent property of the SCN network. Experimental analysis and mathematical modeling argue that both intercellular coupling and molecular noise are required for the stochastic rhythms, providing a novel biological example of noise-induced oscillations. The emergence of stochastic circadian oscillations from the SCN network in the absence of cell-autonomous circadian oscillatory function highlights a previously unrecognized level of circadian organization.

Impact of Light Schedules and Model Parameters on the Circadian Outcomes of Individuals.

Key differences exist between individuals in terms of certain circadian-related parameters, such as intrinsic period and sensitivity to light. These variations can differentially impact circadian timing, leading to challenges in accurately implementing time-sensitive interventions. In this work, we parse out these effects by investigating the impact of parameters from a macroscopic model of human circadian rhythms on phase and amplitude outputs. Using in silico light data designed to mimic commonly studied schedules, we assess the impact of parameter variations on model outputs to gain insight into the different effects of these schedules. We show that parameter sensitivity is heavily modulated by the lighting routine that a person follows, with darkness and shift work schedules being the most sensitive. We develop a framework to measure overall sensitivity levels of the given light schedule and furthermore decompose the overall sensitivity into individual parameter contributions. Finally, we measure the ability of the model to extract parameters given light schedules with noise and show that key parameters like the circadian period can typically be recovered given known light history. This can inform future work on determining the key parameters to consider when personalizing a model and the lighting protocols to use when assessing interindividual variability.

Efficient assessment of real-world dynamics of circadian rhythms in heart rate and body temperature from wearable data.

Laboratory studies have made unprecedented progress in understanding circadian physiology. Quantifying circadian rhythms outside of laboratory settings is necessary to translate these findings into real-world clinical practice. Wearables have been considered promising way to measure these rhythms. However, their limited validation remains an open problem. One major barrier to implementing large-scale validation studies is the lack of reliable and efficient methods for circadian assessment from wearable data. Here, we propose an approximation-based least-squares method to extract underlying circadian rhythms from wearable measurements. Its computational cost is ∼ 300-fold lower than that of previous work, enabling its implementation in smartphones with low computing power. We test it on two large-scale real-world wearable datasets: [Formula: see text] of body temperature data from cancer patients and ∼ 184 000 days of heart rate and activity data collected from the 'Social Rhythms' mobile application. This shows successful extraction of real-world dynamics of circadian rhythms. We also identify a reasonable harmonic model to analyse wearable data. Lastly, we show our method has broad applicability in circadian studies by embedding it into a Kalman filter that infers the state space of the molecular clocks in tissues. Our approach facilitates the translation of scientific advances in circadian fields into actual improvements in health.

Optimal stimulus shapes for neuronal excitation.

An important problem in neuronal computation is to discern how features of stimuli control the timing of action potentials. One aspect of this problem is to determine how an action potential, or spike, can be elicited with the least energy cost, e.g., a minimal amount of applied current. Here we show in the Hodgkin & Huxley model of the action potential and in experiments on squid giant axons that: 1) spike generation in a neuron can be highly discriminatory for stimulus shape and 2) the optimal stimulus shape is dependent upon inputs to the neuron. We show how polarity and time course of post-synaptic currents determine which of these optimal stimulus shapes best excites the neuron. These results are obtained mathematically using the calculus of variations and experimentally using a stochastic search methodology. Our findings reveal a surprising complexity of computation at the single cell level that may be relevant for understanding optimization of signaling in neurons and neuronal networks.

Reducing chronic disease may just be a walk in the park.

Wearable technology allows the collection of real-world granular data at scales that would be impossible using traditional collection methods. Master et al. demonstrate the power of this technology to estimate the risk of disease based on daily step counts.1.

Evolution of the repression mechanisms in circadian clocks.

BACKGROUND: Circadian (daily) timekeeping is essential to the survival of many organisms. An integral part of all circadian timekeeping systems is negative feedback between an activator and repressor. However, the role of this feedback varies widely between lower and higher organisms. RESULTS: Here, we study repression mechanisms in the cyanobacterial and eukaryotic clocks through mathematical modeling and systems analysis. We find a common mathematical model that describes the mechanism by which organisms generate rhythms; however, transcription's role in this has diverged. In cyanobacteria, protein sequestration and phosphorylation generate and regulate rhythms while transcription regulation keeps proteins in proper stoichiometric balance. Based on recent experimental work, we propose a repressor phospholock mechanism that models the negative feedback through transcription in clocks of higher organisms. Interestingly, this model, when coupled with activator phosphorylation, allows for oscillations over a wide range of protein stoichiometries, thereby reconciling the negative feedback mechanism in Neurospora with that in mammals and cyanobacteria. CONCLUSIONS: Taken together, these results paint a picture of how circadian timekeeping may have evolved.

Consumer-grade wearables identify changes in multiple physiological systems during COVID-19 disease progression.

Consumer-grade wearables are needed to track disease, especially in the ongoing pandemic, as they can monitor patients in real time. We show that decomposing heart rate from low-cost wearable technologies into signals from different systems can give a multidimensional description of physiological changes due to COVID-19 infection. We find that the separate physiological features of basal heart rate, heart rate response to physical activity, circadian variation in heart rate, and autocorrelation of heart rate are significantly altered and can classify symptomatic versus healthy periods. Increased heart rate and autocorrelation begin at symptom onset, while the heart rate response to activity increases soon after symptom onset and increases more in individuals exhibiting cough. Symptom onset is associated with a blunting of circadian variation in heart rate, as measured by the uncertainty in the phase estimate. This work establishes an innovative data analytic approach to monitor disease progression remotely using consumer-grade wearables.

Day-to-day variability in sleep parameters and depression risk: a prospective cohort study of training physicians.

While 24-h total sleep time (TST) is established as a critical driver of major depression, the relationships between sleep timing and regularity and mental health remain poorly characterized because most studies have relied on either self-report assessments or traditional objective sleep measurements restricted to cross-sectional time frames and small cohorts. To address this gap, we assessed sleep with a wearable device, daily mood with a smartphone application and depression through the 9-item Patient Health Questionnaire (PHQ-9) over the demanding first year of physician training (internship). In 2115 interns, reduced TST (b = -0.11, p < 0.001), later bedtime (b = 0.068, p = 0.015), along with increased variability in TST (b = 0.4, p = 0.0012) and in wake time (b = 0.081, p = 0.005) were associated with more depressive symptoms. Overall, the aggregated impact of sleep variability parameters and of mean sleep parameters on PHQ-9 were similar in magnitude (both r2 = 0.01). Within individuals, increased TST (b = 0.06, p < 0.001), later wake time (b = 0.09, p < 0.001), earlier bedtime (b = - 0.07, p < 0.001), as well as lower day-to-day shifts in TST (b = -0.011, p < 0.001) and in wake time (b = -0.004, p < 0.001) were associated with improved next-day mood. Variability in sleep parameters substantially impacted mood and depression, similar in magnitude to the mean levels of sleep parameters. Interventions that target sleep consistency, along with sleep duration, hold promise to improve mental health.