Dual Oscillator Model Research Articles

Two oscillatory components detected by forced splitting of the sleep-wake cycle in humans.

The sleep-wake cycle of human subjects was artificially split into two episodes by imposing an 8-h light and 4-h dark cycle (LD 8:4) twice a day for 7 days, which was followed by a 3-day free-running session. Sleep was permitted only in the dark period. The subjects in the ordinary group were exposed to ordinary light (ca. 500 lx) in the 8-h light period, and those in the bright light group to bright (ca. 5,000 lx) and ordinary light alternatively with bright light after the first dark period (2400-400). Split sleeps persisted in the free-running session with the major episode around the first dark period and the minor episode around the second dark period. By contrast, circadian melatonin rhythm in the free-running session significantly phase delayed in the ordinary light group, but phase advanced in the bright light group, keeping the melatonin rhythm unsplit. The length of nocturnal melatonin secretion (NMS) was significantly shortened in the bright light group. Interestingly, the falling phase of NMS advanced significantly further than the rising phase. Such a difference was not detected in the ordinary light group. Similar differences were observed in the body temperature rhythm. These findings indicated oscillatory mechanisms underlying split sleeps distinct from the circadian pacemaker and suggested an involvement of different circadian oscillators in the rising and falling phases of NMS, which is consistent with the dual oscillator model proposed for the circadian system of nocturnal rodents.NEW & NOTEWORTHY The present study demonstrated that human sleep was separated into two essentially identical components, which persisted under constant conditions, suggesting circadian oscillator underlying split-sleep episodes. The study also indicated differential light sensitivities in the rising and falling phases of circadian melatonin rhythm, indicating the involvement of two different oscillators. These results consisted of the evening and morning dual-oscillator hypothesis for the circadian pacemaker and the hierarchical model for the pacemaker and sleep-wake cycle.

On the origin and evolution of the dual oscillator model underlying the photoperiodic clockwork in the suprachiasmatic nucleus.

Decades have now passed since Colin Pittendrigh first proposed a model of a circadian clock composed of two coupled oscillators, individually responsive to the rising and setting sun, as a flexible solution to the challenge of behavioral and physiological adaptation to the changing seasons. The elegance and predictive power of this postulation has stimulated laboratories around the world in searches to identify and localize such hypothesized evening and morning oscillators, or sets of oscillators, in insects, rodents, and humans, with experimental designs and approaches keeping pace over the years with technological advances in biology and neuroscience. Here, we recount the conceptual origin and highlight the subsequent evolution of this dual oscillator model for the circadian clock in the mammalian suprachiasmatic nucleus; and how, despite our increasingly sophisticated view of this multicellular pacemaker, Pittendrigh's binary conception has remained influential in our clock models and metaphors.

Lattice induced transparency-like in symmetric metasurfaces tuned with incident angles in mid-infrared region

It is very meaningful to implement a tunable transparency window device with a simple metasurface structure in the mid-infrared band. In this paper, we propose a symmetric metasurface structure that consists of thin layers of graphene and a split anti-ring (SAR). This structure can achieve a tunable lattice-induced transparency-like (LIT-like) spectral response in the wide frequency range of 20–40 THz. Our simulation results show that the realization of the LIT-like phenomenon is due to the strong coupling between the lattice diffraction resonance mode (LDRM) and the wide plasmon resonance mode produced by SAR. The LIT-like response can be dynamically shifted by adjusting the incident pitch angle, the single and double LIT-like can also be switched by adjusting the azimuth angle, which provides convenient post-fabrication tunability. The coupling mechanism of the single LIT-like phenomenon is explained via a dual-oscillator model, which agrees well with the simulation results. In addition, the effects of spacer layer thickness, spacer layer refractive index, ambient refractive index on the position and size of the transparency window are analyzed. Lastly, a tunable delay bandwidth product between 0.46 and 0.86 will be produced due to the addition of graphene. Our finding manifests a novel design of the mid-infrared dynamically tuned slow-light device. • The symmetric metasurface can realized the LIT-like effect, which is produced by the strong coupling of plasmonic mode and LDRM. • The LIT-like effect can be tuned in mid-infrared regime by changing the incident pitch angle. • Single and double transparency windows can be switched when the incident azimuth angle is 0° and 90°. • The delay bandwidth product can be dynamically controlled by Fermi energy and incident pitch angle.

Optical access to folded transverse acoustic phonon doublet in 6H-SiC

We report on the study of far-infrared transmission in silicon carbide of 6H polytype in the region of IR active folded transverse acoustic (FTA) phonon doublet. Joint analysis of the transmittance spectra obtained at low and high resolutions is performed to determine spectral dependences of the refractive index and absorption coefficient. A dual Lorentz oscillator model is used to simulate the FTA phonon contributions to the dielectric function. The oscillator strengths and phonon lifetimes for both the components of the FTA phonon doublet in 6H-SiC are determined. At temperature decrease from 300 to 5 K, the FTA phonon lifetimes increase more than six times, while the oscillator strengths remain the same.

Uncovering the Roles of Clocks and Neural Transmission in the Resilience of Drosophila Circadian Network.

Studies of circadian locomotor rhythms in Drosophila melanogaster gave evidence to the preceding theoretical predictions on circadian rhythms. The molecular oscillator in flies, as in virtually all organisms, operates using transcriptional-translational feedback loops together with intricate post-transcriptional processes. Approximately150 pacemaker neurons, each equipped with a molecular oscillator, form a circuit that functions as the central pacemaker for locomotor rhythms. Input and output pathways to and from the pacemaker circuit are dissected to the level of individual neurons. Pacemaker neurons consist of functionally diverse subclasses, including those designated as the Morning/Master (M)-oscillator essential for driving free-running locomotor rhythms in constant darkness and the Evening (E)-oscillator that drives evening activity. However, accumulating evidence challenges this dual-oscillator model for the circadian circuit organization and propose the view that multiple oscillators are coordinated through network interactions. Here we attempt to provide further evidence to the revised model of the circadian network. We demonstrate that the disruption of molecular clocks or neural output of the M-oscillator during adulthood dampens free-running behavior surprisingly slowly, whereas the disruption of both functions results in an immediate arrhythmia. Therefore, clocks and neural communication of the M-oscillator act additively to sustain rhythmic locomotor output. This phenomenon also suggests that M-oscillator can be a pacemaker or a downstream path that passively receives rhythmic inputs from another pacemaker and convey output signals. Our results support the distributed network model and highlight the remarkable resilience of the Drosophila circadian pacemaker circuit, which can alter its topology to maintain locomotor rhythms.

Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to explain the morning and evening oscillators. The proposed dual oscillator model based on Daan's hypothesis supports per1 and per2 playing the role of morning and evening oscillators respectively and this may be the first step towards the understanding of the core molecular mechanism responsible for encoding the day length.

The Interaction of Calcium and Metabolic Oscillations in Pancreatic Beta-cells

Diabetes is a disease characterized by an excessive level of glucose in the bloodstream, which may be a result of improper insulin secretion. Insulin is secreted in a bursting behavior of pancreatic $\beta$-cells in islets, which is affected by oscillations of cytosolic calcium concentration. We used the Dual Oscillator Model to explore the role of calcium in calcium oscillation independent and calcium oscillation dependent modes and the synchronization of metabolic oscillations in electrically coupled $\beta$-cells. We implemented a synchronization index in order to better measure the synchronization of the $\beta$-cells within an islet and we studied heterogeneous modes of coupled $\beta$-cells. We saw that increasing calcium coupling or voltage coupling in heterogeneous cases increases synchronization; however, in certain cases increasing both voltage and calcium coupling causes desynchronization. To better represent an islet, we altered previous code to allow for a greater number of cells to be simulated.

Glucose Oscillations Can Activate an Endogenous Oscillator in Pancreatic Islets.

Pancreatic islets manage elevations in blood glucose level by secreting insulin into the bloodstream in a pulsatile manner. Pulsatile insulin secretion is governed by islet oscillations such as bursting electrical activity and periodic Ca2+ entry in β-cells. In this report, we demonstrate that although islet oscillations are lost by fixing a glucose stimulus at a high concentration, they may be recovered by subsequently converting the glucose stimulus to a sinusoidal wave. We predict with mathematical modeling that the sinusoidal glucose signal’s ability to recover islet oscillations depends on its amplitude and period, and we confirm our predictions by conducting experiments with islets using a microfluidics platform. Our results suggest a mechanism whereby oscillatory blood glucose levels recruit non-oscillating islets to enhance pulsatile insulin output from the pancreas. Our results also provide support for the main hypothesis of the Dual Oscillator Model, that a glycolytic oscillator endogenous to islet β-cells drives pulsatile insulin secretion.

Circadian and ultradian patterns of epileptiform discharges differ by seizure-onset location during long-term ambulatory intracranial monitoring.

Previous studies reporting circadian patterns of epileptiform activity and seizures are limited by (1) short-term recording in an epilepsy monitoring unit (EMU) with altered antiepileptic drugs (AEDs) and sleep, or (2) subjective seizure diary reports. We studied circadian patterns using long-term ambulatory intracranial recordings captured by the NeuroPace RNS System. Retrospective study of RNS System trial participants with stable detection parameters over a continuous 84-day period. We analyzed all detections and long device-detected epileptiform events (long episodes) and defined a subset of subjects in whom long episodes represented electrographic seizures (LE-SZ). Spectrum resampling determined the dominant frequency periodicity and cosinor analysis identified significant circadian peaks in detected activity. Chi-square analysis was used to compare subjects grouped by region of seizure onset. In the 134 subjects, detections showed a strongly circadian and uniform pattern irrespective of region of onset that peaked during normal sleep hours. In contrast, long episodes and LE-SZ patterns varied by region. Neocortical regions had a monophasic, nocturnally dominant rhythm, whereas limbic regions showed a more complex pattern and diurnal peak. Rhythms in some individual limbic subjects were best fit by a dual oscillator (circadian + ultradian) model. Epileptiform activity has a strong 24h periodicity with peak nocturnal occurrence. Limbic and neocortical epilepsy show divergent circadian influences. These findings confirm that circadian patterns of epileptiform activity vary by seizure-onset zone, with implications for treatment and safety, including SUDEP.

Ca2+ Effects on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet Activity

Pancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca2+ concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of oscillatory metabolism. In the companion article, we use recently developed biosensors to confirm that glycolysis is oscillatory and further elucidate the coordination of metabolic and electrical signals in the insulin secretory pathway. In this report, we modify the DOM by incorporating an established link between metabolism and intracellular Ca2+ to reconcile model predictions with experimental observations from the companion article. With modification, we maintain the distinguishing feature of the DOM, oscillatory glycolysis, but introduce the ability of Ca2+ influx to reshape glycolytic oscillations by promoting glycolytic efflux. We use the modified model to explain measurements from the companion article and from previously published experiments with islets.

Phase Analysis of Metabolic Oscillations and Membrane Potential in Pancreatic Islet β-Cells

Metabolism in islet β-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca2+ that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured simultaneously with membrane potential bursting to determine the phase relationships between the metabolic oscillations and electrical activity. Our experimental findings suggest that Ca2+ entry into β-cells stimulates the rate of mitochondrial metabolism, accounting for the depletion of glycolytic intermediates during each oscillatory burst. We also performed Ca2+ clamp tests in which we clamped membrane potential with the KATP channel-opener diazoxide and KCl to fix Ca2+ at an elevated level. These tests confirm that metabolic oscillations do not require Ca2+ oscillations, but show that Ca2+ plays a larger role in shaping metabolic oscillations than previously suspected. A dynamical picture of the mechanisms of oscillations emerged that requires the restructuring of contemporary mathematical β-cell models, including our own dual oscillator model. In the companion article, we modified our model to account for these new data.

Investigating How Calcium Diffusion Affects Metabolic Oscillations and Synchronization of Pancreatic Beta Cells

Diabetes is a disease characterized by improper concentrations of blood glucose due to irregular insulin production or sensitivity. Coupled in islets of Langerhans within the pancreas, β-cells are responsible for the production and regulation of insulin based on changes in glucose levels. Using the Dual Oscillator Model (DOM), we will examine how calcium handling between individual pancreatic β-cells affects the synchronization of metabolic oscillations within electrically coupled islets. Calcium permeability was implemented into the DOM, and numerical solutions of the system were obtained via MATLAB using a modified ordinary differential equation solver for stiff systems and the Automatic Differentiation for MATLAB software. We developed a synchronization index to quantitatively describe the synchronization of variables between nearest neighboring cells and throughout the islet as a whole. We considered how calcium permeability between heterogeneous cells affects the behavior of metabolic oscillations and their synchronization. In particular, we examined fructose-1, 6-bisphosphate. In our study metabolic oscillations were always maintained. We also showed that, for low to moderate levels of electrical coupling, calcium permeability increased the synchronization index, but increasing calcium permeability had little effect on synchronization when cells were already strongly synchronized with strong electrical coupling. Heterogeneity due to glucose influx or initial state of the cells had similar synchronization results.

Modeling of Glucose-Induced cAMP Oscillations in Pancreatic β Cells: cAMP Rocks when Metabolism Rolls

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.

Drosophila circadian rhythms in seminatural environments: Summer afternoon component is not an artifact and requires TrpA1 channels

Under standard laboratory conditions of rectangular light/dark cycles and constant warm temperature, Drosophila melanogaster show bursts of morning (M) and evening (E) locomotor activity and a "siesta" in the middle of the day. These M and E components have been critical for developing the neuronal dual oscillator model in which clock gene expression in key cells generates the circadian phenotype. However, under natural European summer conditions of cycling temperature and light intensity, an additional prominent afternoon (A) component that replaces the siesta is observed. This component has been described as an "artifact" of the TriKinetics locomotor monitoring system that is used by many circadian laboratories world wide. Using video recordings, we show that the A component is not an artifact, neither in the glass tubes used in TriKinetics monitors nor in open-field arenas. By studying various mutants in the visual and peripheral and internal thermo-sensitive pathways, we reveal that the M component is predominantly dependent on visual input, whereas the A component requires the internal thermo-sensitive channel transient receptor potential A1 (TrpA1). Knockdown of TrpA1 in different neuronal groups reveals that the reported expression of TrpA1 in clock neurons is unlikely to be involved in generating the summer locomotor profile, suggesting that other TrpA1 neurons are responsible for the A component. Studies of circadian rhythms under seminatural conditions therefore provide additional insights into the molecular basis of circadian entrainment that would otherwise be lost under the usual standard laboratory protocols.

Glucose-Induced Cyclic-AMP Oscillations: Modeling Incretin Impact on Pancreatic Beta Cell Secretion

Pancreatic beta cells modulate insulin secretion via incretin-induced amplification pathways of cytosolic calcium (Ca2+)-induced exocytosis, which may be help compensate for reduced insulin sensitivity in Type II Diabetes Mellitus. One modulator is cAMP, which is activated by an incretin-triggered Gs protein cascade and sensitive to glucose levels. Interestingly, cAMP is found to be oscillatory, even in cases where Ca2+ is not, providing a possible mechanism for pulstile insulin secretion in the absence of Ca2+ oscillations. When Ca2+ and cAMP both oscillate, the two may be either in-phase or out-of-phase with one another. To understand the cAMP oscillations and their relationship to Ca2+ oscillations we use mathematical modeling. We model the cAMP production sensitivity to glucose metabolism with AMP sensitive adenylyl cyclases and degradation with Ca2+ sensitive phosphodiesterases. These modest additions to the Dual Oscillator Model for beta cells allow us to capture observed relationships between cAMP and Ca2+. This provides further evidence for metabolic oscillations in beta-cells that are affected by, but that do not require, oscillations in Ca2+.

PDF neuron firing phase-shifts key circadian activity neurons in Drosophila.

Our experiments address two long-standing models for the function of the Drosophila brain circadian network: a dual oscillator model, which emphasizes the primacy of PDF-containing neurons, and a cell-autonomous model for circadian phase adjustment. We identify five different circadian (E) neurons that are a major source of rhythmicity and locomotor activity. Brief firing of PDF cells at different times of day generates a phase response curve (PRC), which mimics a light-mediated PRC and requires PDF receptor expression in the five E neurons. Firing also resembles light by causing TIM degradation in downstream neurons. Unlike light however, firing-mediated phase-shifting is CRY-independent and exploits the E3 ligase component CUL-3 in the early night to degrade TIM. Our results suggest that PDF neurons integrate light information and then modulate the phase of E cell oscillations and behavioral rhythms. The results also explain how fly brain rhythms persist in constant darkness and without CRY.

Calcium and Metabolic Oscillations in Pancreatic Islets: Who's Driving the Bus?*

Pancreatic islets exhibit bursting oscillations in response to elevated blood glucose. These oscillations are accompanied by oscillations in the free cytosolic Ca2+ concentration (Cac ), which drives pulses of insulin secretion. Both islet Ca2+ and metabolism oscillate, but there is some debate about their interrelationship. Recent experimental data show that metabolic oscillations in some cases persist after the addition of diazoxide (Dz), which opens K(ATP) channels, hyperpolarizing β-cells and preventing Ca2+ entry and Ca2+ oscillations. Further, in some islets in which metabolic oscillations were eliminated with Dz, increasing the cytosolic Ca2+ concentration by the addition of KCl could restart the metabolic oscillations. Here we address why metabolic oscillations persist in some islets but not others, and why raising Cac restarts oscillations in some islets but not others. We answer these questions using the dual oscillator model (DOM) for pancreatic islets. The DOM can reproduce the experimental data and shows that the model supports two different mechanisms for slow metabolic oscillations, one that requires calcium oscillations and one that does not.

Slow oscillations of KATP conductance in mouse pancreatic islets provide support for electrical bursting driven by metabolic oscillations

We used the patch clamp technique in situ to test the hypothesis that slow oscillations in metabolism mediate slow electrical oscillations in mouse pancreatic islets by causing oscillations in KATP channel activity. Total conductance was measured over the course of slow bursting oscillations in surface β-cells of islets exposed to 11.1 mM glucose by either switching from current clamp to voltage clamp at different phases of the bursting cycle or by clamping the cells to -60 mV and running two-second voltage ramps from -120 to -50 mV every 20 s. The membrane conductance, calculated from the slopes of the ramp current-voltage curves, oscillated and was larger during the silent phase than during the active phase of the burst. The ramp conductance was sensitive to diazoxide, and the oscillatory component was reduced by sulfonylureas or by lowering extracellular glucose to 2.8 mM, suggesting that the oscillatory total conductance is due to oscillatory KATP channel conductance. We demonstrate that these results are consistent with the Dual Oscillator model, in which glycolytic oscillations drive slow electrical bursting, but not with other models in which metabolic oscillations are secondary to calcium oscillations. The simulations also confirm that oscillations in membrane conductance can be well estimated from measurements of slope conductance and distinguished from gap junction conductance. Furthermore, the oscillatory conductance was blocked by tolbutamide in isolated β-cells. The data, combined with insights from mathematical models, support a mechanism of slow (∼5 min) bursting driven by oscillations in metabolism, rather than by oscillations in the intracellular free calcium concentration.

Large Ventral Lateral Neurons Determine the Phase of Evening Activity Peak across Photoperiods in Drosophila melanogaster

The dual-oscillator model, originally proposed as a mechanism for how vertebrates adapt to seasonal changes, has been invoked to explain circadian entrainment in Drosophila melanogaster. Distinct subsets of neurons have been designated as "morning" and "evening" oscillators that function as regulators of rhythmic activity/rest behavior. Some studies have led to a model in which a subset of 8 "morning" cells (4 bilaterally located small ventral lateral neurons) and another subset of approximately 130 "evening" cells exert different levels of dominance within the circadian circuit in different seasons. However, many studies propose a more integrative neuronal network, with the whole network orchestrating activity/rest rhythms in different seasons, as opposed to hierarchical dominance among neurons. Within the circadian network, our understanding of the role of the large ventral lateral neurons (l-LN(v)) has thus far been limited to conveying light information to the clocks and as light-activated neurons mediating arousal. In support of the framework of a more distributed model, we report an important circadian clock-related role for the l-LN(v) in electrical activity-dependent phasing of the evening peak across a range of photoperiods. Further, we propose a model in which l-LN(v) enable adaptation to seasonal changes by regulating the phase of the evening peak. Additionally, we demonstrate a hitherto unknown role for the small ventral lateral neurons (s-LN(v)) in the arousal circuit, thus showing that neuronal function is flexible such that certain neurons can play more than one role in distinct circuits.

Balance of Activity between LNvs and Glutamatergic Dorsal Clock Neurons Promotes Robust Circadian Rhythms in Drosophila

Circadian rhythms offer an excellent opportunity to dissect the neural circuits underlying innate behavior because the genes and neurons involved are relatively well understood. We first sought to understand how Drosophila clock neurons interact in the simple circuit that generates circadian rhythms in larval light avoidance. We used genetics to manipulate two groups of clock neurons, increasing or reducing excitability, stopping their molecular clocks, and blocking neurotransmitter release and reception. Our results revealed that lateral neurons (LN(v)s) promote and dorsal clock neurons (DN(1)s) inhibit light avoidance, these neurons probably signal at different times of day, and both signals are required for rhythmic behavior. We found that similar principles apply in the more complex adult circadian circuit that generates locomotor rhythms. Thus, the changing balance in activity between clock neurons with opposing behavioral effects generates robust circadian behavior and probably helps organisms transition between discrete behavioral states, such as sleep and wakefulness.