A Conserved Bicycle Model for Circadian Clock Control of Membrane Excitability.

Circadian clocks regulate membrane excitability in master pacemaker neurons to control daily rhythms of sleep and wake. Here, we find that two distinctly timed electrical drives collaborate to impose rhythmicity on Drosophila clock neurons. In the morning, a voltage-independent sodium conductance via the NA/NALCN ion channel depolarizes these neurons. This current is driven by the rhythmic expression of NCA localization factor-1, linking the molecular clock to ion channel function. In the evening, basal potassium currents peak to silence clock neurons. Remarkably, daily antiphase cycles of sodium and potassium currents also drive mouse clock neuron rhythms. Thus, we reveal an evolutionarily ancient strategy for the neural mechanisms that govern daily sleep and wake.

COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator.

Silent hypoxemia, or "happy hypoxia," is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation ( SaO 2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model of the respiratory neural network (Diekman et al. in J Neurophysiol 118(4):2194-2215, 2017) can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer's Disease Using Biophysical Modeling and Deep Learning.

Alzheimer's disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer's mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.

The E3 ubiquitin ligase adaptor Tango10 links the core circadian clock to neuropeptide and behavioral rhythms.

Circadian transcriptional timekeepers in pacemaker neurons drive profound daily rhythms in sleep and wake. Here we reveal a molecular pathway that links core transcriptional oscillators to neuronal and behavioral rhythms. Using two independent genetic screens, we identified mutants of Transport and Golgi organization 10 (Tango10) with poor behavioral rhythmicity. Tango10 expression in pacemaker neurons expressing the neuropeptide PIGMENT-DISPERSING FACTOR (PDF) is required for robust rhythms. Loss of Tango10 results in elevated PDF accumulation in nerve terminals even in mutants lacking a functional core clock. TANGO10 protein itself is rhythmically expressed in PDF terminals. Mass spectrometry of TANGO10 complexes reveals interactions with the E3 ubiquitin ligase CULLIN 3 (CUL3). CUL3 depletion phenocopies Tango10 mutant effects on PDF even in the absence of the core clock gene timeless Patch clamp electrophysiology in Tango10 mutant neurons demonstrates elevated spontaneous firing potentially due to reduced voltage-gated Shaker-like potassium currents. We propose that Tango10/Cul3 transduces molecular oscillations from the core clock to neuropeptide release important for behavioral rhythms.

Beyond the limits of circadian entrainment: Non-24-h sleep-wake disorder, shift work, and social jet lag.

While the vast majority of humans are able to entrain their circadian rhythm to the 24-h light-dark cycle, there are numerous individuals who are not able to do so due to disease or societal reasons. We use computational and mathematical methods to analyze a well-established model of human circadian rhythms to address cases where individuals do not entrain to the 24-h light-dark cycle, leading to misalignment of their circadian phase. For each case, we provide a mathematically justified strategy for how to minimize circadian misalignment. In the case of non-24-h sleep-wake disorder, we show why appropriately timed bright light therapy induces entrainment. With regard to shift work, we explain why reentrainment times following transitions between day and night shifts are asymmetric, and how higher light intensity enables unusually rapid reentrainment after certain transitions. Finally, with regard to teenagers who engage in compensatory catch-up sleep on weekends, we propose a rule of thumb for sleep and wake onset times that minimizes circadian misalignment due to this type of social jet lag. In all cases, the primary mathematical approach involves understanding the dynamics of entrainment maps that measure the phase of the entrained rhythm with respect to the daily onset of lights.

The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems.

Several distinct entrainment patterns can occur in the FitzHugh-Nagumo (FHN) model under external periodic forcing. Investigating the FHN model under different types of periodic forcing reveals the existence of multiple disconnected 1:1 entrainment segments for constant, low enough values of the input amplitude when the unforced system is in the vicinity of a Hopf bifurcation. This entrainment structure is termed polyglot to distinguish it from the single 1:1 entrainment region (monoglot) structure typically observed in Arnold tongue diagrams. The emergence of polyglot entrainment is then explained using phase-plane analysis and other dynamical system tools. Entrainment results are investigated for other slow-fast systems of neuronal, circadian, and glycolytic oscillations. Exploring these models, we found that polyglot entrainment structure (multiple 1:1 regions) is observed when the unforced system is in the vicinity of a Hopf bifurcation and the Hopf point is located near a knee of a cubic-like nullcline.

Circadian Rhythms of Early Afterdepolarizations and Ventricular Arrhythmias in a Cardiomyocyte Model.

Sudden cardiac arrest is a malfunction of the heart's electrical system, typically caused by ventricular arrhythmias, that can lead to sudden cardiac death (SCD) within minutes. Epidemiological studies have shown that SCD and ventricular arrhythmias are more likely to occur in the morning than in the evening, and laboratory studies indicate that these daily rhythms in adverse cardiovascular events are at least partially under the control of the endogenous circadian timekeeping system. However, the biophysical mechanisms linking molecular circadian clocks to cardiac arrhythmogenesis are not fully understood. Recent experiments have shown that L-type calcium channels exhibit circadian rhythms in both expression and function in guinea pig ventricular cardiomyocytes. We developed an electrophysiological model of these cells to simulate the effect of circadian variation in L-type calcium conductance. In our simulations, we found that there is a circadian pattern in the occurrence of early afterdepolarizations (EADs), which are abnormal depolarizations during the repolarization phase of a cardiac action potential that can trigger fatal ventricular arrhythmias. Specifically, the model produces EADs in the morning, but not at other times of day. We show that the model exhibits a codimension-2 Takens-Bogdanov bifurcation that serves as an organizing center for different types of EAD dynamics. We also simulated a two-dimensional spatial version of this model across a circadian cycle. We found that there is a circadian pattern in the breakup of spiral waves, which represents ventricular fibrillation in cardiac tissue. Specifically, the model produces spiral wave breakup in the morning, but not in the evening. Our computational study is the first, to our knowledge, to propose a link between circadian rhythms and EAD formation and suggests that the efficacy of drugs targeting EAD-mediated arrhythmias may depend on the time of day that they are administered.

Delayed Cryptochrome Degradation Asymmetrically Alters the Daily Rhythm in Suprachiasmatic Clock Neuron Excitability.

Suprachiasmatic nuclei (SCN) neurons contain an intracellular molecular circadian clock and the Cryptochromes (CRY1/2), key transcriptional repressors of this molecular apparatus, are subject to post-translational modification through ubiquitination and targeting for proteosomal degradation by the ubiquitin E3 ligase complex. Loss-of-function point mutations in a component of this ligase complex, Fbxl3, delay CRY1/2 degradation, reduce circadian rhythm strength, and lengthen the circadian period by ∼2.5 h. The molecular clock drives circadian changes in the membrane properties of SCN neurons, but it is unclear how alterations in CRY1/2 stability affect SCN neurophysiology. Here we use male and female Afterhours mice which carry the circadian period lengthening loss-of-function Fbxl3Afh mutation and perform patch-clamp recordings from SCN brain slices across the projected day/night cycle. We find that the daily rhythm in membrane excitability in the ventral SCN (vSCN) was enhanced in amplitude and delayed in timing in Fbxl3Afh/Afh mice. At night, vSCN cells from Fbxl3Afh/Afh mice were more hyperpolarized, receiving more GABAergic input than their Fbxl3+/+ counterparts. Unexpectedly, the progression to daytime hyperexcited states was slowed by Afh mutation, whereas the decline to hypoexcited states was accelerated. In long-term bioluminescence recordings, GABAA receptor blockade desynchronized the Fbxl3+/+ but not the Fbxl3Afh/Afh vSCN neuronal network. Further, a neurochemical mimic of the light input pathway evoked larger shifts in molecular clock rhythms in Fbxl3Afh/Afh compared with Fbxl3+/+ SCN slices. These results reveal unanticipated consequences of delaying CRY degradation, indicating that the Afh mutation prolongs nighttime hyperpolarized states of vSCN cells through increased GABAergic synaptic transmission.SIGNIFICANCE STATEMENT The intracellular molecular clock drives changes in SCN neuronal excitability, but it is unclear how mutations affecting post-translational modification of molecular clock proteins influence the temporal expression of SCN neuronal state or intercellular communication within the SCN network. Here we show for the first time, that a mutation that prolongs the stability of key components of the intracellular clock, the cryptochrome proteins, unexpectedly increases in the expression of hypoexcited neuronal state in the ventral SCN at night and enhances hyperpolarization of ventral SCN neurons at this time. This is accompanied by increased GABAergic signaling and by enhanced responsiveness to a neurochemical mimic of the light input pathway to the SCN. Therefore, post-translational modification shapes SCN neuronal state and network properties.

Neuronal oscillations on an ultra-slow timescale: daily rhythms in electrical activity and gene expression in the mammalian master circadian clockwork.

Neuronal oscillations of the brain, such as those observed in the cortices and hippocampi of behaving animals and humans, span across wide frequency bands, from slow delta waves (0.1 Hz) to ultra-fast ripples (600 Hz). Here, we focus on ultra-slow neuronal oscillators in the hypothalamic suprachiasmatic nuclei (SCN), the master daily clock that operates on interlocking transcription-translation feedback loops to produce circadian rhythms in clock gene expression with a period of near 24 h (< 0.001 Hz). This intracellular molecular clock interacts with the cell's membrane through poorly understood mechanisms to drive the daily pattern in the electrical excitability of SCN neurons, exhibiting an up-state during the day and a down-state at night. In turn, the membrane activity feeds back to regulate the oscillatory activity of clock gene programs. In this review, we emphasise the circadian processes that drive daily electrical oscillations in SCN neurons, and highlight how mathematical modelling contributes to our increasing understanding of circadian rhythm generation, synchronisation and communication within this hypothalamic region and across other brain circuits.

Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel.

The normal alignment of circadian rhythms with the 24-h light-dark cycle is disrupted after rapid travel between home and destination time zones, leading to sleep problems, indigestion, and other symptoms collectively known as jet lag. Using mathematical and computational analysis, we study the process of reentrainment to the light-dark cycle of the destination time zone in a model of the human circadian pacemaker. We calculate the reentrainment time for travel between any two points on the globe at any time of the day and year. We construct one-dimensional entrainment maps to explain several properties of jet lag, such as why most people experience worse jet lag after traveling east than west. We show that this east-west asymmetry depends on the endogenous period of the traveler's circadian clock as well as daylength. Thus the critical factor is not simply whether the endogenous period is greater than or less than 24 h as is commonly assumed. We show that the unstable fixed point of an entrainment map determines whether a traveler reentrains through phase advances or phase delays, providing an understanding of the threshold that separates orthodromic and antidromic modes of reentrainment. Contrary to the conventional wisdom that jet lag only occurs after east-west travel across multiple time zones, we predict that the change in daylength encountered during north-south travel can cause jet lag even when no time zones are crossed. Our techniques could be used to provide advice to travelers on how to minimize jet lag on trips involving multiple destinations and a combination of transmeridian and translatitudinal travel.

Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model.

How sensory information influences the dynamics of rhythm generation varies across systems, and general principles for understanding this aspect of motor control are lacking. Determining the origin of respiratory rhythm generation is challenging because the mechanisms in a central circuit considered in isolation may be different from those in the intact organism. We analyze a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. We show that 1) embedding the BRS model neuron in a control loop creates a bistable system; 2) although closed-loop and open-loop (isolated) CPG systems both support eupnea-like bursting activity, they do so via distinct mechanisms; 3) chemosensory feedback in the closed loop improves robustness to variable metabolic demand; 4) the BRS model conductances provide an autoresuscitation mechanism for recovery from transient interruption of chemosensory feedback; and 5) the in vitro brain stem CPG slice responds to hypoxia with transient bursting that is qualitatively similar to in silico autoresuscitation. Bistability of bursting and tonic spiking in the closed-loop system corresponds to coexistence of eupnea-like breathing, with normal minute ventilation and blood oxygen level and a tachypnea-like state, with pathologically reduced minute ventilation and critically low blood oxygen. Disruption of the normal breathing rhythm, through either imposition of hypoxia or interruption of chemosensory feedback, can push the system from the eupneic state into the tachypneic state. We use geometric singular perturbation theory to analyze the system dynamics at the boundary separating eupnea-like and tachypnea-like outcomes.NEW & NOTEWORTHY A common challenge facing rhythmic biological processes is the adaptive regulation of central pattern generator (CPG) activity in response to sensory feedback. We apply dynamical systems tools to understand several properties of a closed-loop respiratory control model, including the coexistence of normal and pathological breathing, robustness to changes in metabolic demand, spontaneous autoresuscitation in response to hypoxia, and the distinct mechanisms that underlie rhythmogenesis in the intact control circuit vs. the isolated, open-loop CPG.

Discovering functional neuronal connectivity from serial patterns in spike train data.

Repeating patterns of precisely timed activity across a group of neurons (called frequent episodes) are indicative of networks in the underlying neural tissue. This letter develops statistical methods to determine functional connectivity among neurons based on nonoverlapping occurrences of episodes. We study the distribution of episode counts and develop a two-phase strategy for identifying functional connections. For the first phase, we develop statistical procedures that are used to screen all two-node episodes and identify possible functional connections (edges). For the second phase, we develop additional statistical procedures to prune the two-node episodes and remove false edges that can be attributed to chains or fan-out structures. The restriction to nonoverlapping occurrences makes the counting of all two-node episodes in phase 1 computationally efficient. The second (pruning) phase is critical since phase 1 can yield a large number of false connections. The scalability of the two-phase approach is examined through simulation. The method is then used to reconstruct the graph structure of observed neuronal networks, first from simulated data and then from recordings of cultured cortical neurons.

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.

Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke.

A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.

COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator.

Silent hypoxemia, or 'happy hypoxia', is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation (SaO2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model (Diekman et al., 2017, J. Neurophysiol) of the respiratory neural network can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

Daily electrical activity in the master circadian clock of a diurnal mammal.

Circadian rhythms in mammals are orchestrated by a central clock within the suprachiasmatic nuclei (SCN). Our understanding of the electrophysiological basis of SCN activity comes overwhelmingly from a small number of nocturnal rodent species, and the extent to which these are retained in day-active animals remains unclear. Here, we recorded the spontaneous and evoked electrical activity of single SCN neurons in the diurnal rodent Rhabdomys pumilio, and developed cutting-edge data assimilation and mathematical modeling approaches to uncover the underlying ionic mechanisms. As in nocturnal rodents, R. pumilio SCN neurons were more excited during daytime hours. By contrast, the evoked activity of R. pumilio neurons included a prominent suppressive response that is not present in the SCN of nocturnal rodents. Our modeling revealed and subsequent experiments confirmed transient subthreshold A-type potassium channels as the primary determinant of this response, and suggest a key role for this ionic mechanism in optimizing SCN function to accommodate R. pumilio's diurnal niche.

Clustering predicted by an electrophysiological model of the suprachiasmatic nucleus.

Despite the wealth of experimental data on the electrophysiology of individual neurons in the suprachiasmatic nuclei (SCN), the neural code of the SCN remains largely unknown. To predict the electrical activity of the SCN, the authors simulated networks of 10,000 GABAergic SCN neurons using a detailed model of the ionic currents within SCN neurons. Their goal was to understand how neuronal firing, which occurs on a time scale faster than a second, can encode a set phase of the circadian (24-h) cycle. The authors studied the effects of key network properties including: 1) the synaptic density within the SCN, 2) the magnitude of postsynaptic currents, 3) the heterogeneity of circadian phase in the neuronal population, 4) the degree of synaptic noise, and 5) the balance between excitation and inhibition. Their main result was that under a wide variety of conditions, the SCN network spontaneously organized into (typically 3) groups of synchronously firing neurons. They showed that this type of clustering can lead to the silencing of neurons whose intracellular clocks are out of circadian phase with the rest of the population. Their results provide clues to how the SCN may generate a coherent electrical output signal at the tissue level to time rhythms throughout the body.

CikA, an Input Pathway Component, Senses the Oxidized Quinone Signal to Generate Phase Delays in the Cyanobacterial Circadian Clock.

The circadian clock is a timekeeping system in most organisms that keeps track of the time of day. The rhythm generated by the circadian oscillator must be constantly synchronized with the environmental day/night cycle to make the timekeeping system truly advantageous. In the cyanobacterial circadian clock, quinone is a biological signaling molecule used for entraining and fine-tuning the oscillator, a process in which the external signals are transduced into biological metabolites that adjust the phase of the circadian oscillation. Among the clock proteins, the pseudo-receiver domain of KaiA and CikA can sense external cues by detecting the oxidation state of quinone, a metabolite that reflects the light/dark cycle, although the molecular mechanism is not fully understood. Here, we show the antagonistic phase shifts produced by the quinone sensing of KaiA and CikA. We introduced a new cyanobacterial circadian clock mixture that includes an input component in vitro. KaiA and CikA cause phase advances and delays, respectively, in this circadian clock mixture in response to the quinone signal. In the entrainment process, oxidized quinone modulates the functions of KaiA and CikA, which dominate alternatively at day and night in the cell. This in turn changes the phosphorylation state of KaiC-the central oscillator in cyanobacteria-ensuring full synchronization of the circadian clock. Moreover, we reemphasize the mechanistic input functionality of CikA, contrary to other reports that focus only on its output action.

CikA Modulates the Effect of KaiA on the Period of the Circadian Oscillation in KaiC Phosphorylation.

Cyanobacteria contain a circadian oscillator that can be reconstituted in vitro. In the reconstituted circadian oscillator, the phosphorylation state of KaiC oscillates with a circadian period, spending about 12 h in the phosphorylation phase and another 12 h in the dephosphorylation phase. Although some entrainment studies have been performed using the reconstituted oscillator, they were insufficient to fully explain entrainment mechanisms of the cyanobacterial circadian clock due to the lack of input pathway components in the in vitro oscillator reaction mixture. Here, we investigate how an input pathway component, CikA, affects the phosphorylation state of KaiC in vitro. In general, CikA affects the amplitude and period of the circadian oscillation of KaiC phosphorylation by competing with KaiA for the same binding site on KaiB. In the presence of CikA, KaiC switches from its dephosphorylation phase to its phosphorylation phase prematurely, due to an early release of KaiA from KaiB as a result of competitive binding between CikA and KaiA. This causes hyperphosphorylation of KaiC and lowers the amplitude of the circadian oscillation. The period of the KaiC phosphorylation oscillation is shortened by adding increased amounts of CikA. A constant period can be maintained as CikA is increased by proportionally decreasing the amount of KaiA. Our findings give insight into how to reconstitute the cyanobacterial circadian clock in vitro by the addition of an input pathway component, and explain how this affects circadian oscillations by directly interacting with the oscillator components.

Magnesium Regulates the Circadian Oscillator in Cyanobacteria.

The circadian clock controls 24-h biological rhythms in our body, influencing many time-related activities such as sleep and wake. The simplest circadian clock is found in cyanobacteria, with the proteins KaiA, KaiB, and KaiC generating a self-sustained circadian oscillation of KaiC phosphorylation and dephosphorylation. KaiA activates KaiC phosphorylation by binding the A-loop of KaiC, while KaiB attenuates the phosphorylation by sequestering KaiA from the A-loop. Structural analysis revealed that magnesium regulates the phosphorylation and dephosphorylation of KaiC by dissociating from and associating with catalytic Glu residues that activate phosphorylation and dephosphorylation, respectively. High magnesium causes KaiC to dephosphorylate, whereas low magnesium causes KaiC to phosphorylate. KaiC alone behaves as an hourglass timekeeper when the magnesium concentration is alternated between low and high levels in vitro. We suggest that a magnesium-based hourglass timekeeping system may have been used by ancient cyanobacteria before magnesium homeostasis was established.