Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e., regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.     

Ca2+ oscillations induced by histamine H1 receptor stimulation in HeLa cells: Fura-2 and patch clamp analysis

The response of HeLa cells to histamine H1 receptor stimulation is characterized by periodic increases in cytosolic free Ca2+ concentration. The mechanisms underlying this oscillatory behaviour are not well understood. Fura-2 and patch clamp experiments carried out on HeLa cells have previously shown: (a) that Ca2+ oscillations are not initially dependent on the presence of external Ca2+, that external Ca2+ is required to maintain the oscillatory activity; (b) that a depolarization of the cell membrane leads to an inhibition of Ca2+ oscillations during the external Ca2+ dependent phase of the process; and (c) that Ca2+ oscillations can be abolished during this latter phase by the exogenous addition of Ca2+ channel blocking agents, such as Co2+ or La3+. The contribution of the inositol phosphate pathway to Ca2+ oscillations was more recently investigated in whole cell experiments performed with patch pipettes containing IP3 or the non-hydrolysable GTP analogue GTP-gamma S. Clear periodic current fluctuations were recorded using both patch pipette solutions. Assuming that the intracellular IP3 level remained constant under these conditions, these findings provide direct evidence that the Ca2+ oscillations in HeLa cells do not arise from a periodic production of IP3. The effect of the internal and external cell pH on the oscillatory process was also investigated in Fura-2 and patch clamp experiments. It was found that an increase in intracellular pH from 7.4 to 7.7 during the external Ca2+ dependent phase of the histamine stimulation abolishes the appearance of Ca2+ spikes whereas, a cellular acidification to pH 7.2 maintains or stimulates the Ca2+ oscillatory activity. The former effect was observed in the absence of Ca2+ in the bathing medium, indicating that the inhibitory action of alkaline pH was not related to a reduced Ca2+ entry. An increase in extracellular pH from 7.3 to 9.0 in contrast elicited an intracellular Ca2+ accumulation which resulted in most cases in an inhibition of the oscillatory process. This effect was dependent on external Ca2+ and was observed in alkaline internal pH conditions (pH 7.7). These observations suggest: (a) that the net Ca2+ influx in HeLa cells is strongly dependent on the cell internal and external pH; and (b) that the magnitude of this Ca2+ influx controls to a large extent the oscillation frequency. Finally, an inhibition of the histamine induced Ca2+ oscillatory activity was observed following the addition of the Ca(2+)-induced Ca(2+)-release (CICR) inhibitor adenine to the external medium.(ABSTRACT TRUNCATED AT 250 WORDS)     

Oscillations in plant membrane transport: model predictions, experimental validation, and physiological implications

Although oscillations in membrane-transport activity are ubiquitous in plants, the ionic mechanisms of ultradian oscillations in plant cells remain largely unknown, despite much phenomenological data. The physiological role of such oscillations is also the subject of much speculation. Over the last decade, much experimental evidence showing oscillations in net ion fluxes across the plasma membrane of plant cells has been accumulated using the non-invasive MIFE technique. In this study, a recently proposed feedback-controlled oscillatory model was used. The model adequately describes the observed ion flux oscillations within the minute range of periods and predicts: (i) strong dependence of the period of oscillations on the rate constants for the H+ pump; (ii) a substantial phase shift between oscillations in net H+ and K+ fluxes; (iii) cessation of oscillations when H+ pump activity is suppressed; (iv) the existence of some 'window' of external temperatures and ionic concentrations, where non-damped oscillations are observed: outside this range, even small changes in external parameters lead to progressive damping and aperiodic behaviour; (v) frequency encoding of environmental information by oscillatory patterns; and (vi) strong dependence of oscillatory characteristics on cell size. All these predictions were successfully confirmed by direct experimental observations, when net ion fluxes were measured from root and leaf tissues of various plant species, or from single cells. Because oscillatory behaviour is inherent in feedback control systems having phase shifts, it is argued from this model that suitable conditions will allow oscillations in any cell or tissue. The possible physiological role of such oscillations is discussed in the context of plant adaptive responses to salinity, temperature, osmotic, hypoxia, and pH stresses.     

Neural control of interlimb oscillations

How do humans and other animals accomplish coordinated movements? How are novel combinations of limb joints rapidly assembled into new behavioral units that move together in in-phase or anti-phase movement patterns during complex movement tasks? A neural central pattern generator (CPG) model simulates data from human bimanual coordination tasks. As in the data, anti-phase oscillations at low frequencies switch to in-phase oscillations at high frequencies, in-phase oscillations occur at both low and high frequencies, phase fluctuations occur at the anti-phase in-phase transition, a “seagull effect” of larger errors occurs at intermediate phases, and oscillations slip toward in-phase and anti-phase when driven at intermediate phases. These oscillations and bifurcations are emergent properties of the CPG model in response to volitional inputs. The CPG model is a version of the Ellias-Grossberg oscillator. Its neurons obey Hodgkin-Huxley type equations whose excitatory signals operate on a faster time scale than their inhibitory signals in a recurrent on-center off-surround anatomy. When an equal command or GO signal activates both model channels, the model CPG can generate both in-phase and anti-phase oscillations at different GO amplitudes. Phase transitions from either in-phase to anti-phase oscillations, or from anti-phase to in-phase oscillations, can occur in different parameter ranges, as the GO signal increases. Received: 22 August 1994 / Accepted in revised form: 13 May 1997     

State selection in coupled identical biochemical systems with coexisting stable states

This work examines state selection for coupled biochemical systems with coexisting stable states. For biochemically identical biochemical systems, different coupled systems are examined for the coexistence of (a) one steady state and one oscillatory state or (b) two oscillatory states. For case (a), it is revealed that state selection is always governed by two key factors: the values of kinetic parameters and the coupling strength. When the coupling strength is small, the coupled systems remain in the basin of attraction of their original states. When it is sufficiently large, all coupled systems are always entrained, independently of their original states. Furthermore, for the entrainment, which of the two coexisting states is selected depends sensitively on the activity of recycling enzyme (one of kinetic parameters). It is shown that this is because changing the activity of recycling enzyme alters the size of basin of attraction of each state. When both systems in the same oscillatory state are coupled, an additional factor, namely phase shift between two oscillations, may also affect state selection, and coupling may cause the systems to select either the original oscillatory state or the coexisting steady state. In addition to the features of case (a), case (b) also supports quasiperiodic oscillations and synchronisation of two periodic oscillations. Implications of the results for understanding state selection during the evolution of coupled biochemical systems with coexisting stable states are discussed.     

Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons.

The oscillatory properties of single thalamocortical neurons were investigated by using a Hodgkin-Huxley-like model that included Ca2+ diffusion, the low-threshold Ca2+ current (lT) and the hyperpolarization-activated inward current (lh). lh was modeled by double activation kinetics regulated by intracellular Ca2+. The model exhibited waxing and waning oscillations consisting of 1-25-s bursts of slow oscillations (3.5-4 Hz) separated by long silent periods (4-20 s). During the oscillatory phase, the entry of Ca2+ progressively shifted the activation function of lh, terminating the oscillations. A similar type of waxing and waning oscillation was also observed, in the absence of Ca2+ regulation of lh, from the combination of lT, lh, and a slow K+ current. Singular approximation showed that for both models, the activation variables of lh controlled the dynamics of thalamocortical cells. Dynamical analysis of the system in a phase plane diagram showed that waxing and waning oscillations arose when lh entrained the system alternately between stationary and oscillating branches.     

Coherency and connectivity in oscillating neural networks: linear partialization analysis

 This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works. Received: 20 October 1995 / Accepted in revised form: 20 May 1996     

Spatio-temporal synchronization of recurrent epidemics

Long-term spatio-temporal datasets of disease incidences have made it clear that many recurring epidemics, especially childhood infections, tend to synchronize in-phase across suburbs. In some special cases, epidemics between suburbs have been found to oscillate in an out-of-phase ('antiphase') relationship for lengthy periods. Here, we use modelling techniques to help explain the presence of in-phase and antiphase synchronization. The nonlinearity of the epidemic dynamics is often such that the intensity of the outbreak influences the phase of the oscillation thereby introducing 'shear', a factor that is found to be important for generating antiphase synchronization. By contrast, the coupling between suburbs via the immigration of infectives tends to enhance in-phase synchronization. The emerging synchronization depends delicately on these opposite factors. We use theoretical results from continuous time models to provide a framework for understanding the relationship between synchronization patterns for different model structures.     

An oscillatory mode for microtubule assembly.

Depending upon the conditions under which polymerization takes place, pure tubulin can assemble into microtubules following either the usual monotonic kinetics or a more complex oscillatory mechanism. When present, these oscillations involve large cyclic changes in the extent of polymer formed before a steady-state is reached. Analysis of the microtubules formed at different times shows that these oscillations involve marked redistribution in both the length and number of microtubules. No significant difference is found between two populations of microtubules corresponding to the same level of assembly, one for which the extent of polymerization will remain stable with time and one for which it will decrease by as much as 90% in the next oscillation. The amplitude of these oscillations is sensitive to changes in the concentrations of protein, nucleotide (GTP, GDP or GMPpNp), magnesium ion or GTP regenerating system. A complete shift from an oscillatory to a monotonic polymerization can be induced by a minor increase in the concentration of free nucleotide, GTP or GDP.     

Ventilation-perfusion matching in long-term microgravity.

We studied the ventilation-perfusion matching pattern in normal gravity (1 G) and short- and long-duration microgravity (microG) using the cardiogenic oscillations in the sulfur hexaflouride (SF(6)) and CO(2) concentration signals during the phase III portion of vital capacity single-breath washout experiments. The signal power of the cardiogenic concentration variations was assessed by spectral analysis, and the phase angle between the oscillations of the two simultaneously expired gases was obtained through cross-correlation. For CO(2), a significant reduction of cardiogenic power was observed in microG, with respect to 1 G, but the reduction was smaller and more variable in the case of SF(6). A shift from an in-phase condition in 1 G to an out-of-phase condition was found for both short- and long-duration microG. We conclude that, although the distribution of ventilation and perfusion becomes more homogeneous in microG, significant inhomogeneities persist and that areas of high perfusion become associated with areas of relatively lower ventilation. In addition, these modifications seem to remain constant during long-term exposure to microG.     

Voltage oscillations in the barnacle giant muscle fiber.

Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.     

Rate theory models for ion transport through rigid pores. II. Time-dependent analysis of the single-file model with special reference to oscillatory behavior

This article deals with the time-dependent evolution of the single-file movement of ions through channels of both biological and artificial membranes. The single-file transport process may exhibit not only the usual relaxation behaviour but also oscillatory behaviour as a steady state is approached after an initial perturbation. A necessary condition for the occurrence of oscillations is that the system acts sufficiently far from equilibrium. The occurrence of oscillations is due to the interactions within the transport system which are taken into account by the single-file model; these are the electrostatic repulsion between the ions being transported, and the competition of the ions for the free binding sites within the pore. Information about the strength of the interactions can be obtained by measuring the damping of the transport observables (e.g. the electric current): The stronger the inter-ionic repulsion, the more apparent the oscillatory behaviour will become. Furthermore, the damping is influenced by the microscopic structure of the transport system (i.e. the energy profile of the pores). With an increasing degree of microscopicity, i.e. with a decreasing number of binding sites and an increasingly irregular pore profile, the oscillations become more damped. However, a considerable oscillatory behaviour can only be predicted for pores with both a sufficiently regular structure and a sufficiently large number of binding sites. For this class of pores, however, the measurement of the damping represents an appropriate method of gaining information which could exceed that obtainable from the usual methods of measuring stationary quantities (e.g. stationary conductance). Moreover, our goal is to explain theoretically how the oscillatory behaviour can be interpreted in terms of the order inherent in the ionic movement, which is determined by both the external and internal forces and the microscopic properties of the system.     

Oscillations in microtubule polymerization: the rate of GTP regeneration on tubulin controls the period.

The essential reactions involved in the oscillatory kinetics of microtubule polymerization have been investigated. The rate of GDP dissociation from tubulin decreased cooperatively upon increasing tubulin concentration above 20 microM, consistent with the formation of GDP oligomers whose dissociation is rate limiting in nucleotide exchange. The apparent rate constant for nucleotide exchange at high tubulin concentration was 0.02 s-1 at 37 degrees C, which is the exact value needed in previous theoretical simulations to obtain oscillations with the real period of 70-80 s. A glass filter assay separating microtubules from oligomers and tubulin allowed nucleotide bound to non-microtubular tubulin during the oscillations to be monitored. In agreement with nucleotide exchange data, tubulin-bound GDP was found to oscillate in antiphase with microtubules. By varying the concentration of an enzymatic GTP-regenerating system, we could demonstrate that the period of the oscillations is directly controlled by the rate at which GTP is regenerated on tubulin, and oscillations can be observed under conditions where the dissociation of oligomers is no longer rate limiting. The possible physiological significance of GTP-regenerating systems in establishing synchrony in a microtubule population is evoked. The present data confirm and extend the model that we previously proposed to account for the oscillations.     

Temporal variability in a system of coupled mitotic timers

 Cell proliferation is considered a periodic process governed by a relaxation timer. The collective behavior of a system composed of three identical relaxation oscillators in numerically studied under the condition that diffusion of the slow mode dominates. We demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and an unsymmetrical, stable steady-state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors; and (4) the emergence of a two-loop limit cycle coexisting with both in-phase oscillations and a stable steady-state. The qualitative reasons for such a diversitiy and its possible role in the generation of cell cycle variability are discussed. Received: 18 March 1992/Accepted in revised form: 16 April 1994     

Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome.     

Sustained neural rhythms reveal endogenous oscillations supporting speech perception

Rhythmic sensory or electrical stimulation will produce rhythmic brain responses. These rhythmic responses are often interpreted as endogenous neural oscillations aligned (or “entrained”) to the stimulus rhythm. However, stimulus-aligned brain responses can also be explained as a sequence of evoked responses, which only appear regular due to the rhythmicity of the stimulus, without necessarily involving underlying neural oscillations. To distinguish evoked responses from true oscillatory activity, we tested whether rhythmic stimulation produces oscillatory responses which continue after the end of the stimulus. Such sustained effects provide evidence for true involvement of neural oscillations. In Experiment 1, we found that rhythmic intelligible, but not unintelligible speech produces oscillatory responses in magnetoencephalography (MEG) which outlast the stimulus at parietal sensors. In Experiment 2, we found that transcranial alternating current stimulation (tACS) leads to rhythmic fluctuations in speech perception outcomes after the end of electrical stimulation. We further report that the phase relation between electroencephalography (EEG) responses and rhythmic intelligible speech can predict the tACS phase that leads to most accurate speech perception. Together, we provide fundamental results for several lines of research—including neural entrainment and tACS—and reveal endogenous neural oscillations as a key underlying principle for speech perception.

Just as a child on a swing continues to move after the pushing stops, this study reveals similar entrained rhythmic echoes in brain activity after hearing speech and electrical brain stimulation; perturbation with tACS shows that these brain oscillations help listeners to understand speech.     

On the phase shift between electric potential and plasma density fluctuations in the edge turbulence

In some cases, the phase shift between fluctuations of the electric potential and plasma density helps to identify the instability that governs the turbulent state. In this paper, the basic experimental and theoretical results that denote the possibility (or impossibility) of such identification are briefly discussed. The experimental data based on measurements of the phase shift between the floating potential and ion saturation current fluctuations in the L-2M stellarator—a system with externally imposed magnetic surfaces—are presented (Shchepetov, Kholnov, Fedyanin, et al., Plasma Phys. Controlled Fusion 50, 045001 (2008)). It is shown that the observed phase shift Ω varies in a wide range from π to 0, gradually decreasing with deepening inside the plasma. A number of arguments are presented suggesting that Ω ≈ π can indicate that the process is nonlocal, i.e., oscillations at a given spatial point are driven and mainly determined by the processes localized outside of the observation point. We note that, within the framework of the magnetohydrodynamic theory, plasma was definitely unstable with respect to resistive interchange modes in all cases under study. It is demonstrated experimentally that the widespread notion that the phase shift Ω ≈ π/2 is characteristic of only resistive interchange modes is hardly universal. The experimental results are analyzed on the basis of analytical estimates.     

The Relationship between Membrane Potential and Calcium Dynamics in Glucose-Stimulated Beta Cell Syncytium in Acute Mouse Pancreas Tissue Slices

Oscillatory electrical activity is regarded as a hallmark of the pancreatic beta cell glucose-dependent excitability pattern. Electrophysiologically recorded membrane potential oscillations in beta cells are associated with in-phase oscillatory cytosolic calcium activity ([Ca²⁺]_i) measured with fluorescent probes. Recent high spatial and temporal resolution confocal imaging revealed that glucose stimulation of beta cells in intact islets within acute tissue slices produces a [Ca²⁺]_i change with initial transient phase followed by a plateau phase with highly synchronized [Ca²⁺]_i oscillations. Here, we aimed to correlate the plateau [Ca²⁺]_i oscillations with the oscillations of membrane potential using patch-clamp and for the first time high resolution voltage-sensitive dye based confocal imaging. Our results demonstrated that the glucose-evoked membrane potential oscillations spread over the islet in a wave-like manner, their durations and wave velocities being comparable to the ones for [Ca²⁺]_i oscillations and waves. High temporal resolution simultaneous records of membrane potential and [Ca²⁺]_i confirmed tight but nevertheless limited coupling of the two processes, with membrane depolarization preceding the [Ca²⁺]_i increase. The potassium channel blocker tetraethylammonium increased the velocity at which oscillations advanced over the islet by several-fold while, at the same time, emphasized differences in kinetics of the membrane potential and the [Ca²⁺]_i. The combination of both imaging techniques provides a powerful tool that will help us attain deeper knowledge of the beta cell network.     

Oscillatory isozymes as the simplest model for coupled biochemical oscillators

We analyze a simple model for two autocatalytic reactions catalyzed by two distinct isozymes transforming, with different kinetic properties, a given substrate into the same product. This two-variable system can be viewed as the simplest model of chemically coupled biochemical oscillators. Phase-plane analysis indicates how the kinetic differences between the two enzymes give rise to complex oscillatory phenomena such as the coexistence of a stable steady state and a stable limit cycle, or the co-existence of two simultaneously stable oscillatory regimes (birhythmicity). The model allows one to verify a previously proposed conjecture for the origin of birhythmicity. In other conditions, the system admits multiple oscillatory domains as a function of a control parameter whose variation gives rise to markedly different types of oscillations. The latter behavior provides an explanation for the occurrence of multiple modes of oscillations in thalamic neurons.     

Theta oscillations decrease spike synchrony in the hippocampus and entorhinal cortex

Oscillations and synchrony are often used synonymously. However, oscillatory mechanisms involving both excitation and inhibition can generate non-synchronous yet coordinated firing patterns. Using simultaneous recordings from multiple layers of the entorhinal–hippocampal loop, we found that coactivation of principal cell pairs (synchrony) was lowest during exploration and rapid-eye-movement (REM) sleep, associated with theta oscillations, and highest in slow wave sleep. Individual principal neurons had a wide range of theta phase preference. Thus, while theta oscillations reduce population synchrony, they nevertheless coordinate the phase (temporal) distribution of neurons. As a result, multiple cell assemblies can nest within the period of the theta cycle.