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.     

Computer simulation of sustained oscillations in peroxidase-oxidase reaction

A system of differential equations of second order exhibiting transitional behaviour and sustained oscillations has been obtained for a complete scheme of the peroxidase-oxidase reaction. The concentrations of hydrogen peroxide and of hydrogen donor radicals are slow variables of the system. The most essential reactions responsible for oscillations have been selected. Analysis of the system in phase plane and in parameter space has been carried out. The dependence of oscillation period and amplitude on the parameter values has been investigated.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Modeling of hole transfer dynamics in tetramer GAGG

The hole transfer in the nucleotide sequence GAGG, where guanine G is a donor and the guanine doublet GG is an acceptor, was considered. It was shown that the relaxation of the hole on the acceptor is accompanied by rapid oscillations of the hole between the donor and the acceptor with an oscillation period of a few picoseconds. The calculated slow relaxation of the hole on the acceptor over a period of 2 ns was compared with experimental data.     

Slow variable dominance and phase resetting in phantom bursting

Bursting oscillations are common in neurons and endocrine cells. One type of bursting model with two slow variables has been called ‘phantom bursting’ since the burst period is a blend of the time constants of the slow variables. A phantom bursting model can produce bursting with a wide range of periods: fast (short period), medium, and slow (long period). We describe a measure, which we call the ‘dominance factor’, of the relative contributions of the two slow variables to the bursting produced by a simple phantom bursting model. Using this tool, we demonstrate how the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. We then show that the dominance curves obtained as a parameter is varied can be useful in making predictions about the resetting properties of the model cells. Finally, we demonstrate two mechanisms by which phase-independent resetting of a burst can be achieved, as has been shown to occur in the electrical activity of pancreatic islets.     

Correlated oscillations in glucose consumption, oxygen consumption, and intracellular free Ca(2+) in single islets of Langerhans

Micron-sized sensors were used to monitor glucose and oxygen levels in the extracellular space of single islets of Langerhans in real-time. At 10 mM glucose, oscillations in intraislet glucose concentration were readily detected. Changes in glucose level correspond to changes in glucose consumption by glycolysis balanced by mass transport into the islet. Oscillations had a period of 3.1 +/- 0.2 min and amplitude of 0.8 +/- 0.1 mM glucose (n = 21). Superimposed on these oscillations were faster fluctuations in glucose level during the periods of low glucose consumption. Oxygen level oscillations that were out of phase with the glucose oscillations were also detected. Oscillations in both oxygen and glucose consumption were strongly dependent upon extracellular Ca(2+) and sensitive to nifedipine. Simultaneous measurements of glucose with intracellular Ca(2+) ([Ca(2+)](i)) revealed that decreases in [Ca(2+)](i) preceded increases in glucose consumption by 7.4 +/- 2.1 s during an oscillation (n = 9). Conversely, increases in [Ca(2+)](i) preceded increases in oxygen consumption by 1.5 +/- 0.2 s (n = 4). These results suggest that during oscillations, bursts of glycolysis begin after Ca(2+) has stopped entering the cell. Glycolysis stimulates further Ca(2+) entry, which in turn stimulates increases in respiration. The data during oscillation are in contrast to the time course of events during initial exposure to glucose. Under these conditions, a burst of oxygen consumption precedes the initial rise in [Ca(2+)](i). A model to explain these results is described.     

The component composition of the human cortical motor potential during static muscle loading

In summation and averaging of sections of the EEG of sensorimotor cortex of both cerebral hemispheres recorded during human static effort of definite duration, a complex of negative-positive oscillations was observed. These oscillations appear before the beginning of the effort, accompany its execution and finishing and are also recorded after cessation of muscles activity. Before the beginning, the potential of readiness is formed. The execution of the effort is accompanied by a slow negative wave which in some people may be broken by a pronounced positivity. Further a "final" potential appears; its fast positive oscillation is formed before the end of the effort, and a slow negative wave in which it turns, appears only after muscles relaxation.     

Changes in the rabbit brain cortex redox potential accompaning episodes of ECoG-arousal during slow-wave sleep

Local cortex E variations are well expressive indices of rate and peculiarities of energy metabolism. The brain E is determined by the ratio of processes occurring in two energy compartments in glycolysis, in whish glucose is split without oxygen utilization and in oxidative metabolism. In the present investigation, the brain cortex E changes were recorded with implanted platinum electrodes during slow wave sleep. Under such conditions, the E lowering detects acceleration in glycolytic compartment, whereas the E local rising shows acceleration in oxidative metabolism in the tissue surrounding the electrode. Earlier in rats, we have found that E significantly lowered in metabolic active cortical sites during episodes of SWS, and supposed that acceleration of glycolysis increased. Slow oscillations (a 20-40-sec prolongation of the amplitude up to several dozens millivolts) appeared at the same time. We considered these E slow oscillations to reflect changes in the rate in compartment of glycolysis. In this research, we have found the E slow oscillations to be created by regular episodes of ECoG-arousal which were accompanied by E decreases, i. e. by acceleration in glycolysis. We think the data presented show existence of functional system supporting a low level of arousal. As in any complex system with feed back connections, this system works in oscillatory regime.     

Adenine nucleotide regulation in pancreatic beta-cells: modeling of ATP/ADP-Ca2+ interactions

Glucose metabolism stimulates insulin secretion in pancreatic beta-cells. A consequence of metabolism is an increase in the ratio of ATP to ADP ([ATP]/[ADP]) that contributes to depolarization of the plasma membrane via inhibition of ATP-sensitive K+ (K(ATP)) channels. The subsequent activation of calcium channels and increased intracellular calcium leads to insulin exocytosis. Here we evaluate new data and review the literature on nucleotide pool regulation to determine the utility and predictive value of a new mathematical model of ion and metabolic flux regulation in beta-cells. The model relates glucose consumption, nucleotide pool concentration, respiration, Ca2+ flux, and K(ATP) channel activity. The results support the hypothesis that beta-cells maintain a relatively high [ATP]/[ADP] value even in low glucose and that dramatically decreased free ADP with only modestly increased ATP follows from glucose metabolism. We suggest that the mechanism in beta-cells that leads to this result can simply involve keeping the total adenine nucleotide concentration unchanged during a glucose elevation if a high [ATP]/[ADP] ratio exits even at low glucose levels. Furthermore, modeling shows that independent glucose-induced oscillations of intracellular calcium can lead to slow oscillations in nucleotide concentrations, further predicting an influence of calcium flux on other metabolic oscillations. The results demonstrate the utility of comprehensive mathematical modeling in understanding the ramifications of potential defects in beta-cell function in diabetes.     

Oscillations and efficiency in glycolysis

We suggest that temporal oscillations of concentrations of intermediates in biochemical reaction systems may enhance the efficiency of free energy conversion (reduce dissipation) in those reactions. Experiments on glycolysis are used to estimate the Gibbs free energy changes along the glycolysis mechanism, and to postulate a construct for the glycolysis "machine" which involves: the PFK reaction as the primary oscillophor; the GAPDH reaction as a phase-shifting device; and the PK reaction with the property of intrinsic oscillatory response at resonance with the driving frequency. Analysis of a simple reaction mechanism with these postulated properties shows that the conversion of free energy from reactants to products is more efficient in an oscillatory than a steady state operation. The efficiency of free energy conversion in glycolysis from glucose + ADP to products + ATP is estimated to be increased by 5--10% due to oscillations. This may have been relevant for the evolutionary development of oscillations such as in glycolysis, especially in anaerobic cells.     

Landscape and global stability of nonadiabatic and adiabatic oscillations in a gene network

We quantify the potential landscape to determine the global stability and coherence of biological oscillations. We explore a gene network motif in our experimental synthetic biology studies of two genes that mutually repress and activate each other with self-activation and self-repression. We find that in addition to intrinsic molecular number fluctuations, there is another type of fluctuation crucial for biological function: the fluctuation due to the slow binding/unbinding of protein regulators to gene promoters. We find that coherent limit cycle oscillations emerge in two regimes: an adiabatic regime with fast binding/unbinding and a nonadiabatic regime with slow binding/unbinding relative to protein synthesis/degradation. This leads to two mechanisms of producing the stable oscillations: the effective interactions from averaging the gene states in the adiabatic regime; and the time delays due to slow binding/unbinding to promoters in the nonadiabatic regime, which can be tested by forthcoming experiments. In both regimes, the landscape has a topological shape of the Mexican hat in protein concentrations that quantitatively determines the global stability of limit cycle dynamics. The oscillation coherence is shown to be correlated with the shape of the Mexican hat characterized by the height from the oscillation ring to the central top. The oscillation period can be tuned in a wide range by changing the binding/unbinding rate without changing the amplitude much, which is important for the functionality of a biological clock. A negative feedback loop with time delays due to slow binding/unbinding can also generate oscillations. Although positive feedback is not necessary for generating oscillations, it can make the oscillations more robust.     

Spatio-temporal dynamics of glycolysis in cell layers. A mathematical model

Glycolytic oscillations occur in many cell types and have been intensively studied in yeast. Recent experimental and theoretical research has been focussed on the oscillatory dynamics and the synchronisation mechanism in stirred yeast cell suspensions. Here we are interested in the spatio-temporal organisation of glycolysis in cell layers. To this end we study a grid of a few thousand compartments each containing a cell. The intracellular dynamics is described by a core model of glycolysis. The compartments can exchange metabolites via diffusion. The conditions for oscillatory dynamics in a single compartment are investigated by bifurcation analysis. The spatio-temporal behaviour of the cell layer is studied by simulations. The model predicts the propagation of repetitive wave fronts induced by a substrate gradient. The formation of these waves crucially depends on the diffusive exchange of the reaction product between cells. Depending on the kinetic parameters complex spatio-temporal behaviour such as periodic termination of waves can arise. In these cases the cellular oscillation characteristics depend on the location of the cell in the array.     

Thermodynamic and kinetic studies of a stoichiometric model of energetic metabolism under starvation conditions

Abstract A stoichiometric model of anaerobic glycolysis is presented and the influence on its dynamics by the ATP-consuming membrane transport processes and substrate input rate are studied. The model is represented by a system of four ODE (ordinary differential equations), mass conservation equations and functions of state variables, such as thermodynamic efficiency. A low substrate input rate provokes damped oscillations while a high enrgy load determines sustained oscillations in all the metabolites and in thermodynamic efficiency. Due to the lack of linearity between fluxes and forces in the oscillatory region it may be stated that oscillations appear when the system is kinetically controlled.     

Mixed mode oscillations as a mechanism for pseudo-plateau bursting

We combine bifurcation analysis with the theory of canard-induced mixed mode oscillations to investigate the dynamics of a novel form of bursting. This bursting oscillation, which arises from a model of the electrical activity of a pituitary cell, is characterized by small impulses or spikes riding on top of an elevated voltage plateau. Oscillations with these characteristics have been called “pseudo-plateau bursting”. Unlike standard bursting, the subsystem of fast variables does not possess a stable branch of periodic spiking solutions, and in the case studied here the standard fast/slow analysis provides little information about the underlying dynamics. We demonstrate that the bursting is actually a canard-induced mixed mode oscillation, and use canard theory to characterize the dynamics of the oscillation. We also use bifurcation analysis of the full system of equations to extend the results of the singular analysis to the physiological regime. This demonstrates that the combination of these two analysis techniques can be a powerful tool for understanding the pseudo-plateau bursting oscillations that arise in electrically excitable pituitary cells and isolated pancreatic β-cells.     

Regulation of nicotinamide adenine dinucleotide phosphate levels in yeast

The steady-state levels and redox states of pyridine nucleotide pools have been studied in yeast as a function of external growth conditions. Yeast grown aerobically on 0.8% glucose show two distinct phases of logarithmic growth, a first phase utilizing glucose with ethanol accumulation, and a second phase utilizing ethanol. During growth on glucose, the size of the NADP pool (NADP⁺ + NADPH) is maintained at approximately 12% the size of the NAD pool (NAD⁺ + NADH). Upon exhaustion of glucose, the mechanism(s) that maintain the levels of NADP relative to NAD are altered, resulting in a rapid 2- to 2.5-fold decrease in the size of the NADP pool relative to the size of the NAD pool. The lower levels of NADP are maintained during growth on ethanol. The NAD pool is approximately 50% NADH during both the glucose and ethanol phases of growth, while the NADP pool is approximately 67 and 48% NADPH during the glucose and ethanol phases of growth, respectively. Rapid media transfer experiments show that the decrease in NADP is reversible, that it does not require the net synthesis of pyridine nucleotide or protein, and that changes in the size of the NADP pool relative to the total pyridine nucleotide pool are correlated with changes in the redox state of the NADP pool.     

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.     

Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.     

Effect of intracellular delivery of energy metabolites on intracellular Ca2+ in mouse islets of Langerhans

Regulation of glucose-induced oscillations in intracellular Ca2+ concentration ([Ca2+]i) was investigated by using a novel technique, electroporation from an electrolyte-filled capillary, to deliver energy metabolites to the intracellular compartment of mouse islets. Intracellular application of ATP resulted in a nifedipine-sensitive increase in [Ca2+]i, consistent with a KATP-channel dependent mechanism of Ca2+ influx. [Ca2+]i in islets exposed to 10 mM glucose oscillated with a period of approximately 3 min, often superimposed with faster oscillations. Electroporation of ATP blocked all types of oscillations and elevated [Ca2+]i while delivery of ADP had no effect on oscillations. Intracellular delivery of glucose-6-phosphate or fructose-1,6-bisphosphate tended to transform slow oscillations to fast oscillations. These results demonstrate that modulation of ATP concentrations and glycolytic flux are important in development of slow oscillations.