Internal noise-driven circadian oscillator in Drosophila

An internal noise-driven oscillator was studied in a two-variable Drosophila model, where both positive feedback and negative feedback are crucial to the circadian oscillations. It is shown that internal noise could sustain reliable oscillations for the parameter which produces a stable steady state in the deterministic system. The noise-sustained oscillations are interpreted by using phase plane analysis. The period of such oscillations fluctuates slightly around the period of deterministic oscillations and the coherence of oscillations becomes the best at an optimal internal noise intensity, indicating the occurrence of intrinsic coherence resonance. In addition, in the oscillatory region, the coherence of noisy circadian oscillations is suppressed by the internal noise, but the period is hardly affected, demonstrating the robustness of the Drosophila model for circadian rhythms to the intrinsic noise.     

视觉注意与神经振荡

人脑每时每刻都要接收大量视觉信息，由于人脑加工信息的能力有限，所以在较大视野内将注意分配给相关信息，同时抑制引起注意分散的不相关信息，对执行目标导向的行为至关重要。这种对视觉信息的选择性和主动性加工以适应当前目标的过程被称作视觉注意（visual attention），且视觉注意可分为自上而下的注意与自下而上的注意两种不同功能。由于来自大脑电信号的神经振荡活动在认知加工中发挥重要作用，已有研究综述了视觉注意与神经振荡（neural oscillation）的密切关系，但并未涉及不同的注意功能与神经振荡的关系。本文系统性调查了不同注意功能与神经振荡的关系，发现额-顶区域的theta频带振荡活动反映了自上而下的认知控制，而后部脑区的theta振荡与自下而上的注意相关。顶-枕区域alpha振荡的偏侧化有助于注意分配，而alpha频带的大规模同步促成了注意对视皮层自上而下的影响。Beta振荡介导了自上而下的信息与自下而上的信息之间的互动，作为信息载体促进了视觉信息处理。Gamma振荡则可能与自上而下和自下而上的注意间整合相关。本文就视觉注意功能与神经振荡关系的研究现状展开综述，旨在揭示不同的神经振荡活动在特定的视觉注意功能中的作用。     

Calcium oscillations in endothelial cells

Several different types of endothelial cells are now known to respond to agonist stimulation with oscillations of cytosolic free [Ca2+] ([Ca2+]i). The oscillations can be repetitive [Ca2+]i spikes or sinusoidal-like oscillations according to the type of endothelial cell. Several properties of these oscillations are described including the effect of removal of extracellular Ca2+ and of changes in membrane potential, and the spatial heterogeneity of the oscillations. Results obtained with human umbilical vein endothelial cells are assessed in relation to a model for [Ca2+]i oscillations that involves Ca(2+)-induced Ca2+ release. In some preparations the oscillations are synchronized in neighbouring cells, whereas in other preparations they are not. The degree of synchrony may have functional implications and this is discussed with respect to control of blood flow and transmural permeability. A third functional implication of oscillations, their possible effect on desensitization, is also discussed.     

Heterogeneity of glycolytic oscillatory behaviour in individual yeast cells

There are many examples of oscillations in biological systems and one of the most investigated is glycolytic oscillations in yeast. These oscillations have been studied since the 1950s in dense, synchronized populations and in cell-free extracts, but it has for long been unknown whether a high cell density is a requirement for oscillations to be induced, or if individual cells can oscillate also in isolation without synchronization. Here we present an experimental method and a detailed kinetic model for studying glycolytic oscillations in individual, isolated yeast cells and compare them to previously reported studies of single-cell oscillations. The importance of single-cell studies of this phenomenon and relevant future research questions are also discussed.     

On the mechanisms of glycolytic oscillations in yeast

This work concerns the cause of glycolytic oscillations in yeast. We analyse experimental data as well as models in two distinct cases: the relaxation-like oscillations seen in yeast extracts, and the sinusoidal Hopf oscillations seen in intact yeast cells. In the case of yeast extracts, we use flux-change plots and model analyses to establish that the oscillations are driven by on/off switching of phosphofructokinase. In the case of intact yeast cells, we find that the instability leading to the appearance of oscillations is caused by the stoichiometry of the ATP-ADP-AMP system and the allosteric regulation of phosphofructokinase, whereas frequency control is distributed over the reaction network. Notably, the NAD+/NADH ratio modulates the frequency of the oscillations without affecting the instability. This is important for understanding the mutual synchronization of oscillations in the individual yeast cells, as synchronization is believed to occur via acetaldehyde, which in turn affects the frequency of oscillations by changing this ratio.     

Oscillations of Ca++ concentration during the cell differentiation of Dictyostelium discoideum: their relation to oscillations in cyclic AMP and other components

Periodic cyclic-AMP pulses control the cell aggregation and differentiation of Dictyostelium discoideum. Another component required for the aggregation and differentiation of these cells appears to be extracellular Ca+ +. Oscillations in extracellular Ca+ + concentration were investigated in suspensions of differentiating cells. We observed spike-shaped and sinusoidal Ca+ + oscillations. In the course of differentiation, spike-shaped Ca+ + oscillations preceded sinusoidal oscillations, and no phase change occurred at the transition from spike-shaped to sinusoidal Ca+ + oscillations. Spike-shaped and sinusoidal Ca+ + oscillations were related to oscillations in (1) the cyclic-AMP and cyclic-GMP content of cells, (2) the light-scattering properties of cells, and (3) the extracellular pH. Spikeshaped Ca+ + oscillations were observed together with cyclic-AMP oscillations. The minima of the extracellular Ca+ + concentration trailed the maxima of the cyclic-AMP concentration by about 30 s. Sinusoidal Ca+ + oscillations were not accompanied by measurable cyclic-AMP oscillations. The amplitudes of the sinusoidal Ca+ + oscillations were smaller than those of the spike-shaped Ca+ + oscillations. A Ca+ + oscillation of small amplitude (instead of a spike-shaped oscillation) was observed when one cyclic-AMP spike was skipped. Our results provide evidence for the existence of a sinusoidal cyclic-AMP-independent Ca+ + oscillation of small amplitude, and they also suggest that spike-shaped Ca+ + oscillations may be superimposed on such small-amplitude oscillations. When D. discoideum cells produce cyclic-AMP spikes, the uptake of additional Ca+ + is induced, resulting in Ca+ + oscillations of a large amplitude.     

Citrate oscillates in liver and pancreatic beta cell mitochondria and in INS-1 insulinoma cells

Oscillations in citric acid cycle intermediates have never been previously reported in any type of cell. Here we show that adding pyruvate to isolated mitochondria from liver, pancreatic islets, and INS-1 insulinoma cells or adding glucose to intact INS-1 cells causes sustained oscillations in citrate levels. Other citric acid cycle intermediates measured either did not oscillate or possibly oscillated with a low amplitude. In INS-1 mitochondria citrate oscillations are in phase with NAD(P) oscillations, and in intact INS-1 cells citrate oscillations parallel oscillations in ATP, suggesting that these processes are co-regulated. Oscillations have been extensively studied in the pancreatic beta cell where oscillations in glycolysis, NAD(P)/NAD(P)H and ATP/ADP ratios, plasma membrane electrical activity, calcium levels, and insulin secretion have been well documented. Because the mitochondrion is the major site of ATP synthesis and NADH oxidation and the only site of citrate synthesis, mitochondria need to be synchronized for these factors to oscillate. In suspensions of mitochondria from various organs, most of the citrate is exported from the mitochondria. In addition, citrate inhibits its own synthesis. We propose that this enables citrate itself to act as one of the cellular messengers that synchronizes mitochondria. Furthermore, because citrate is a potent inhibitor of the glycolytic enzyme phosphofructokinase, the pacemaker of glycolytic oscillations, citrate may act as a metabolic link between mitochondria and glycolysis. Citrate oscillations may coordinate oscillations in mitochondrial energy production and anaplerosis with glycolytic oscillations, which in the beta cell are known to parallel oscillations in insulin secretion.     

Comparison of glycolytic NADH oscillations in yeasts Saccharomyces cerevisiae and Saccharomyces carlsbergensis

The possible mechanism of synchronization of NADH oscillations in yeasts were studied. It was shown that the synchronization time depends on cell concentration in suspension. Synchronization of oscillations after acetaldehyde addition was found in Saccharomyces carlsbergensis whereas in S. cerevisiae oscillations were synchronized after adding potassium cyanide. It is possible, that synchronization of oscillations in S. cerevisiae requires low concentration of acetaldehyde and the high acetaldehyde concentration synchronizes oscillations in S. carlsbergensis. In addition, a possible mechanism of synchronization by acetaldehyde in proposed.     

Peripheral chemoreceptors in respiratory oscillations

The hypothesis that instability of cardiorespiratory control may depend on the response and sensitivity of carotid body chemoreceptors to arterial blood gases was studied in anesthetized cats under three different experimental conditions. 1) Following administration of the peripheral dopamine receptor blocker [domperidone (0.6-0.8 mg X kg-1, iv)], carotid chemoreceptor activity and its sensitivity to CO2 during hypoxia increased, leading to cardiorespiratory oscillations at low arterial PO2 in four of eight cats. Inhalation of 100% O2 promptly decreased chemoreceptor activity and eliminated the oscillations. Inhalation of CO2 stimulated the chemoreceptor activity and ventilation but did not eliminate the oscillations. Bilateral section of carotid sinus nerves abolished the cardiorespiratory oscillations. The implication is that the dopaminergic system in the carotid body keeps chemoreceptor responses to blood gas stimuli suppressed and hence cardiorespiratory oscillations damped. 2) Hypotension and circulatory delay induced by the partial occlusion of venous return led to cardiorespiratory oscillations at low but not at high arterial PO2. 3) A few cats developed cardiorespiratory oscillations without any particular experimental intervention. These oscillations were independent of arterial PO2 and chemoreceptor activity. Thus it is reasonable to conclude that the peripheral chemoreflex can play a critical role in developing cardiorespiratory oscillations in certain instances.     

Tremor and other oscillations in neuromuscular systems

A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.     

The rhythm of yeast

Although yeast are unicellular and comparatively simple organisms, they have a sense of time which is not related to reproduction cycles. The glycolytic pathway exhibits oscillatory behaviour, i.e. the metabolite concentrations oscillate around phosphofructokinase. The frequency of these oscillations is about 1 min when using intact cells. Also a yeast cell extract can oscillate, though with a lower frequency. With intact cells the macroscopic oscillations can only be observed when most of the cells oscillate in concert. Transient oscillations can be observed upon simultaneous induction; sustained oscillations require an active synchronisation mechanism. Such an active synchronisation mechanism, which involves acetaldehyde as a signalling compound, operates under certain conditions. How common these oscillations are in the absence of a synchronisation mechanism is an open question. Under aerobic conditions an oscillatory metabolism can also be observed, but with a much lower frequency than the glycolytic oscillations. The frequency is between one and several hours. These oscillations are partly related to the reproductive cycle, i.e. the budding index also oscillates; however, under some conditions they are unrelated to the reproductive cycle, i.e. the budding index is constant. These oscillations also have an active synchronisation mechanism, which involves hydrogen sulfide as a synchronising agent. Oscillations with a frequency of days can be observed with yeast colonies on plates. Here the oscillations have a synchronisation mechanism which uses ammonia as a synchronising agent.     

Single cell studies and simulation of cell-cell interactions using oscillating glycolysis in yeast cells

The observation of oscillations in the concentrations of NADH and other intermediates in glycolysis in dense yeast cell suspensions is generally believed to be the result of synchronization of such oscillations between individual cells. The synchrony is believed to be a property of cell density and the question is: does metabolism in each individual yeast cell continue to oscillate, but out of phase, in the absence of synchronization? Here we have used high-sensitivity fluorescence microscopy to measure NADH in single isolated yeast cells under conditions where we observe oscillations of glycolysis in dense cell suspensions. However, we have not been able to detect intracellular oscillations in NADH in these isolated cells, which cannot synchronize their metabolism with other cells. However, addition of acetaldehyde to a single cell as pulses with a frequency similar to the oscillations in dense cell suspensions will induce oscillations in that cell. Ethanol, another product of glycolysis, which has been proposed as a synchronizing agent of glycolysis in cells, was not able to induce oscillations when added as pulses. The experiments support the notion that the intracellular oscillations are associated with the cell density of the yeast cell suspension and mediated by acetaldehyde and perhaps also other substances.     

High frequency spikes in long period blood cell oscillations

Several hematological diseases are characterised by oscillations of various blood cell populations. Two of these are a variant of chronic myelogenous leukemia (CML) and cyclical neutropenia (CN). These oscillations typically have long periods ranging from 20 to 60 days, despite the fact that the stem cell cycling time is thought to be of the order of 2–3 days. Clinical data from humans and laboratory data from the grey collie animal model of CN is suggestive of the idea that these long period oscillations may also contain higher frequency spiky oscillations. We show how such oscillations can be understood in the context of slow periodic stem cell oscillations, by analysing a two component differential-delay equation model of stem cell and neutrophil populations.For Karl Hadeler, on his 70th birthday, leader, teacher, colleague and friend.     

Analysis of chaotic oscillations induced in two coupled Wilson–Cowan models

Although it is known that two coupled Wilson–Cowan models with reciprocal connections induce aperiodic oscillations, little attention has been paid to the dynamical mechanism for such oscillations so far. In this study, we aim to elucidate the fundamental mechanism to induce the aperiodic oscillations in the coupled model. First, aperiodic oscillations observed are investigated for the case when the connections are unidirectional and when the input signal is a periodic oscillation. By the phase portrait analysis, we determine that the aperiodic oscillations are caused by periodically forced state transitions between a stable equilibrium and a stable limit cycle attractors around the saddle-node and saddle separatrix loop bifurcation points. It is revealed that the dynamical mechanism where the state crosses over the saddle-node and saddle separatrix loop bifurcations significantly contributes to the occurrence of chaotic oscillations forced by a periodic input. In addition, this mechanism can also give rise to chaotic oscillations in reciprocally connected Wilson–Cowan models. These results suggest that the dynamic attractor transition underlies chaotic behaviors in two coupled Wilson–Cowan oscillators.     

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.     

Resonance of the Larmor drift with plasma oscillations

Resonance phenomena arising when the Larmor drift velocity is locally equal to the phase velocity of plasma oscillations are analyzed. It is shown that, in a plasma with a nonuniform temperature, the wavelength of the oscillations sharply reduces at the resonant point, so that the oscillations convert into small-scale waves. In a plasma with a uniform temperature, Coulomb collisions cause the oscillations to dissipate at the resonant point. It is noted that a resonance with the Larmor drift can be used to heat the plasma.     

Integration,coincidence detection and resonance in networks of spiking neurons expressing Gamma oscillations and asynchronous states

Gamma oscillations are widely seen in the awake and sleeping cerebral cortex, but the exact role of these oscillations is still debated. Here, we used biophysical models to examine how Gamma oscillations may participate to the processing of afferent stimuli. We constructed conductance-based network models of Gamma oscillations, based on different cell types found in cerebral cortex. The models were adjusted to extracellular unit recordings in humans, where Gamma oscillations always coexist with the asynchronous firing mode. We considered three different mechanisms to generate Gamma, first a mechanism based on the interaction between pyramidal neurons and interneurons (PING), second a mechanism in which Gamma is generated by interneuron networks (ING) and third, a mechanism which relies on Gamma oscillations generated by pacemaker chattering neurons (CHING). We find that all three mechanisms generate features consistent with human recordings, but that the ING mechanism is most consistent with the firing rate change inside Gamma bursts seen in the human data. We next evaluated the responsiveness and resonant properties of these networks, contrasting Gamma oscillations with the asynchronous mode. We find that for both slowly-varying stimuli and precisely-timed stimuli, the responsiveness is generally lower during Gamma compared to asynchronous states, while resonant properties are similar around the Gamma band. We could not find conditions where Gamma oscillations were more responsive. We therefore predict that asynchronous states provide the highest responsiveness to external stimuli, while Gamma oscillations tend to overall diminish responsiveness.     

Substrate effects on oscillations in metabolism, calcium and secretion in single mouse islets of Langerhans

Glucose induces complex patterns of oscillations in intracellular Ca2+ concentration ([Ca2+]i), metabolism and secretion in islets of Langerhans including "slow" and "fast" pulses with period of 2-5 min and 10-20 s respectively. In an effort to elucidate the origin of slow oscillations, individual mouse islets were exposed to different fuels including glyceraldehyde, pyruvate, methyl pyruvate and alpha-ketoisocaproate (KIC), all of which bypass key steps of glycolytic metabolism, while monitoring [Ca2+]i, oxygen consumption and secretion. Glyceraldehyde gave rise to slow oscillations only when substimulatory glucose was also added to the media. Glucosamine, an inhibitor of glucokinase, blocked these slow oscillations. KIC, pyruvate, and methyl pyruvate did not give rise to slow oscillations alone or with glucose present. The addition of glucose to islets bathed in nutrient-rich cell culture media accelerated metabolism and initiated slow oscillations while glyceraldehyde did not. It is concluded that glucose has a special role in accelerating metabolism and generating slow oscillations in isolated islets of Langerhans from mice. Combined with previous observations of Ca2+ dependency for all oscillations in islets, we propose that interactions between Ca2+ influx and glycolysis are responsible for the slow oscillations. In contrast, fast oscillations can occur independent of glycolytic flux.     

The Effect of Loss of Immunity on Noise-Induced Sustained Oscillations in Epidemics

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.