Mathematical simulation of membrane processes and metabolic fluxes of the pancreatic beta-cell

Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca²⁺ initiated by bursts of electrical activity. In parallel with these electrical and Ca²⁺ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca²⁺, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this article, we discuss a recent mathematical model, the Integrated Oscillator Model (IOM), that was the product of many years of development. We use the model to demonstrate that the relationship between calcium and metabolism in beta cells is symbiotic: in some contexts, the electrical oscillations drive the metabolic oscillations, while in other contexts it is the opposite. We provide new insights regarding these results and illustrate that what might at first appear to be contradictory data are actually compatible when viewed holistically with the IOM.

Transitions between bursting modes in the integrated oscillator model for pancreatic β-cells

Insulin-secreting β-cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca²⁺ oscillations and pulsatile insulin secretion. The mechanism for this bursting activity has been the focus of mathematical modeling for more than three decades, and as new data are acquired old models are modified and new models are developed. Comprehensive models must now account for the various modes of bursting observed in islet β-cells, which include fast bursting, slow bursting, and compound bursting. One such model is the Integrated Oscillator Model (IOM), in which β-cell electrical activity, intracellular Ca²⁺, and glucose metabolism interact via numerous feedforward and feedback pathways. These interactions can produce metabolic oscillations with a sawtooth time course or a pulsatile time course, reflecting very different oscillation mechanisms. In this report, we determine conditions favorable to one form of oscillations or the other, and examine the transitions between modes of bursting and the relationship of the transitions to the patterns of metabolic oscillations. Importantly, this work clarifies what can be expected in experimental measurements of β-cell oscillatory activity, and suggests pathways through which oscillations of one type can be converted to oscillations of another type.

Closing in on the Mechanisms of Pulsatile Insulin Secretion

Insulin secretion from pancreatic islet β-cells occurs in a pulsatile fashion, with a typical period of ∼5 min. The basis of this pulsatility in mouse islets has been investigated for more than four decades, and the various theories have been described as either qualitative or mathematical models. In many cases the models differ in their mechanisms for rhythmogenesis, as well as other less important details. In this Perspective, we describe two main classes of models: those in which oscillations in the intracellular Ca²⁺ concentration drive oscillations in metabolism, and those in which intrinsic metabolic oscillations drive oscillations in Ca²⁺ concentration and electrical activity. We then discuss nine canonical experimental findings that provide key insights into the mechanism of islet oscillations and list the models that can account for each finding. Finally, we describe a new model that integrates features from multiple earlier models and is thus called the Integrated Oscillator Model. In this model, intracellular Ca²⁺ acts on the glycolytic pathway in the generation of oscillations, and it is thus a hybrid of the two main classes of models. It alone among models proposed to date can explain all nine key experimental findings, and it serves as a good starting point for future studies of pulsatile insulin secretion from human islets.

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 Ca(2+) 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 Ca(2+) 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 Ca(2+) 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.

Modeling K,ATP--dependent excitability in pancreatic islets

In pancreatic ?-cells, K,ATP channels respond to changes in glucose to regulate cell excitability and insulin release. Confirming a high sensitivity of electrical activity to K,ATP activity, mutations that cause gain of K,ATP function cause neonatal diabetes. Our aim was to quantitatively assess the contribution of K,ATP current to the regulation of glucose-dependent bursting by reproducing experimentally observed changes in excitability when K,ATP conductance is altered by genetic manipulation. A recent detailed computational model of single cell pancreatic ?-cell excitability reproduces the ?-cell response to varying glucose concentrations. However, initial simulations showed that the model underrepresents the significance of K,ATP activity and was unable to reproduce K,ATP conductance-dependent changes in excitability. By altering the ATP and glucose dependence of the L-type Ca(2+) channel and the Na-K ATPase to better fit experiment, appropriate dependence of excitability on K,ATP conductance was reproduced. Because experiments were conducted in islets, which contain cell-to-cell variability, we extended the model from a single cell to a three-dimensional model (10×10×10 cell) islet with 1000 cells. For each cell, the conductance of the major currents was allowed to vary as was the gap junction conductance between cells. This showed that single cell glucose-dependent behavior was then highly variable, but was uniform in coupled islets. The study highlights the importance of parameterization of detailed models of ?-cell excitability and suggests future experiments that will lead to improved characterization of ?-cell excitability and the control of insulin secretion.

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.

Mathematical models of electrical activity of the pancreatic β-cell: a physiological review

Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

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.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Mathematical modeling demonstrates how multiple slow processes can provide adjustable control of islet bursting

Pancreatic islets exhibit bursting oscillations that give rise to oscillatory Ca (2+) entry and insulin secretion from β-cells. These oscillations are driven by a slowly activating K (+) current, Kslow, which is composed of two components: an ATP-sensitive K (+) current and a Ca (2+) -activated K (+) current through SK4 channels. Using a mathematical model of pancreatic β-cells, we analyze how the factors that comprise Kslow can contribute to bursting. We employ the dominance factor technique developed recently to do this and demonstrate that the contributions the slow processes make to bursting are non-obvious and often counterintuitive, and that their contributions vary with parameter values and are thus adjustable.

Ionic mechanisms and Ca2+ dynamics underlying the glucose response of pancreatic β cells: a simulation study

To clarify the mechanisms underlying the pancreatic β-cell response to varying glucose concentrations ([G]), electrophysiological findings were integrated into a mathematical cell model. The Ca²⁺ dynamics of the endoplasmic reticulum (ER) were also improved. The model was validated by demonstrating quiescent potential, burst–interburst electrical events accompanied by Ca²⁺ transients, and continuous firing of action potentials over [G] ranges of 0–6, 7–18, and >19 mM, respectively. These responses to glucose were completely reversible. The action potential, input impedance, and Ca²⁺ transients were in good agreement with experimental measurements. The ionic mechanisms underlying the burst–interburst rhythm were investigated by lead potential analysis, which quantified the contributions of individual current components. This analysis demonstrated that slow potential changes during the interburst period were attributable to modifications of ion channels or transporters by intracellular ions and/or metabolites to different degrees depending on [G]. The predominant role of adenosine triphosphate–sensitive K⁺ current in switching on and off the repetitive firing of action potentials at 8 mM [G] was taken over at a higher [G] by Ca²⁺- or Na⁺-dependent currents, which were generated by the plasma membrane Ca²⁺ pump, Na⁺/K⁺ pump, Na⁺/Ca²⁺ exchanger, and TRPM channel. Accumulation and release of Ca²⁺ by the ER also had a strong influence on the slow electrical rhythm. We conclude that the present mathematical model is useful for quantifying the role of individual functional components in the whole cell responses based on experimental findings.

Analyzing electrical activities of pancreatic β cells using mathematical models

Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.

Metabolic oscillations in pancreatic islets depend on the intracellular Ca2+ level but not Ca2+ oscillations

Plasma insulin is pulsatile and reflects oscillatory insulin secretion from pancreatic islets. Although both islet Ca(2+) and metabolism oscillate, there is disagreement over their interrelationship, and whether they can be dissociated. In some models of islet oscillations, Ca(2+) must oscillate for metabolic oscillations to occur, whereas in others metabolic oscillations can occur without Ca(2+) oscillations. We used NAD(P)H fluorescence to assay oscillatory metabolism in mouse islets stimulated by 11.1 mM glucose. After abolishing Ca(2+) oscillations with 200 microM diazoxide, we observed that oscillations in NAD(P)H persisted in 34% of islets (n = 101). In the remainder of the islets (66%) both Ca(2+) and NAD(P)H oscillations were eliminated by diazoxide. However, in most of these islets NAD(P)H oscillations could be restored and amplified by raising extracellular KCl, which elevated the intracellular Ca(2+) level but did not restore Ca(2+) oscillations. Comparatively, we examined islets from ATP-sensitive K(+) (K(ATP)) channel-deficient SUR1(-/-) mice. Again NAD(P)H oscillations were evident even though Ca(2+) and membrane potential oscillations were abolished. These observations are predicted by the dual oscillator model, in which intrinsic metabolic oscillations and Ca(2+) feedback both contribute to the oscillatory islet behavior, but argue against other models that depend on Ca(2+) oscillations for metabolic oscillations to occur.

Bursting and calcium oscillations in pancreatic beta-cells: specific pacemakers for specific mechanisms

Oscillatory phenomenon in electrical activity and cytoplasmic calcium concentration in response to glucose are intimately connected to multiple key aspects of pancreatic β-cell physiology. However, there is no single model for oscillatory mechanisms in these cells. We set out to identify possible pacemaker candidates for burst activity and cytoplasmic Ca(2+) oscillations in these cells by analyzing published hypotheses, their corresponding mathematical models, and relevant experimental data. We found that although no single pacemaker can account for the variety of oscillatory phenomena in β-cells, at least several separate mechanisms can underlie specific kinds of oscillations. According to our analysis, slowly activating Ca(2+)-sensitive K(+) channels can be responsible for very fast Ca(2+) oscillations; changes in the ATP/ADP ratio and in the endoplasmic reticulum calcium concentration can be pacemakers for both fast bursts and cytoplasmic calcium oscillations, and cyclical cytoplasmic Na(+) changes may underlie patterning of slow calcium oscillations. However, these mechanisms still lack direct confirmation, and their potential interactions raises new issues. Further studies supported by improved mathematical models are necessary to understand oscillatory phenomena in β-cell physiology.

Energetics of glucose metabolism: a phenomenological approach to metabolic network modeling

A new formalism to describe metabolic fluxes as well as membrane transport processes was developed. The new flux equations are comparable to other phenomenological laws. Michaelis-Menten like expressions, as well as flux equations of nonequilibrium thermodynamics, can be regarded as special cases of these new equations. For metabolic network modeling, variable conductances and driving forces are required to enable pathway control and to allow a rapid response to perturbations. When applied to oxidative phosphorylation, results of simulations show that whole oxidative phosphorylation cannot be described as a two-flux-system according to nonequilibrium thermodynamics, although all coupled reactions per se fulfill the equations of this theory. Simulations show that activation of ATP-coupled load reactions plus glucose oxidation is brought about by an increase of only two different conductances: a [Ca²⁺] dependent increase of cytosolic load conductances, and an increase of phosphofructokinase conductance by [AMP], which in turn becomes increased through [ADP] generation by those load reactions. In ventricular myocytes, this feedback mechanism is sufficient to increase cellular power output and O₂ consumption several fold, without any appreciable impairment of energetic parameters. Glucose oxidation proceeds near maximal power output, since transformed input and output conductances are nearly equal, yielding an efficiency of about 0.5. This conductance matching is fulfilled also by glucose oxidation of β-cells. But, as a price for the metabolic mechanism of glucose recognition, β-cells have only a limited capability to increase their power output.

Electrical bursting, calcium oscillations, and synchronization of pancreatic islets

Oscillations are an integral part of insulin secretion and are ultimately due to oscillations in the electrical activity of pancreatic beta-cells, called bursting. In this chapter we discuss islet bursting oscillations and a unified biophysical model for this multi-scale behavior. We describe how electrical bursting is related to oscillations in the intracellular Ca(2+) concentration within beta-cells and the role played by metabolic oscillations. Finally, we discuss two potential mechanisms for the synchronization of islets within the pancreas. Some degree of synchronization must occur, since distinct oscillations in insulin levels have been observed in hepatic portal blood and in peripheral blood sampling of rats, dogs, and humans. Our central hypothesis, supported by several lines of evidence, is that insulin oscillations are crucial to normal glucose homeostasis. Disturbance of oscillations, either at the level of the individual islet or at the level of islet synchronization, is detrimental and can play a major role in type 2 diabetes.

Lessons from models of pancreatic beta cells for engineering glucose-sensing cells

Mathematical models of pancreatic beta cells suggest design principles that can be applied to engineering cells to sense glucose and secrete insulin. Engineering cells can potentially both contribute to future diabetes therapies and generate new insights into beta-cell function. The focus is on ion channels, Ca(2+)handling, and elements of metabolism that combine to produce the varied oscillatory patterns exhibited by beta cells.

Pancreatic islet cells: a model for calcium-dependent peptide release

In mammals the concentration of blood glucose is kept close to 5 mmol∕l. Different cell types in the islet of Langerhans participate in the control of glucose homeostasis. β-cells, the most frequent type in pancreatic islets, are responsible for the synthesis, storage, and release of insulin. Insulin, released with increases in blood glucose promotes glucose uptake into the cells. In response to glucose changes, pancreatic α-, β-, and δ-cells regulate their electrical activity and Ca(2+) signals to release glucagon, insulin, and somatostatin, respectively. While all these signaling steps are stimulated in hypoglycemic conditions in α-cells, the activation of these events require higher glucose concentrations in β and also in δ-cells. The stimulus-secretion coupling process and intracellular Ca(2+) ([Ca(2+)](i)) dynamics that allow β-cells to secrete is well-accepted. Conversely, the mechanisms that regulate α- and δ-cell secretion are still under study. Here, we will consider the glucose-induced signaling mechanisms in each cell type and the mathematical models that explain Ca(2+) dynamics.

Accounting for near-normal glucose sensitivity in Kir6.2[AAA] transgenic mice

K(ir)6.2[AAA] transgenic mouse islets exhibit mosaicism such that approximately 70% of the beta-cells have nonfunctional ATP-sensitive potassium (K(ATP)) channels, whereas the remainder have normal K(ATP) function. Despite this drastic reduction, the glucose dose-response curve is only shifted by approximately 2 mM. We use a previously published mathematical model, in which K(ATP) conductance is increased by rises in cytosolic calcium through indirect effects on metabolism, to investigate how cells could compensate for the loss of K(ATP) conductance. Compensation is favored by the assumption that only a small fraction of K(ATP) channels are open during oscillations, which renders it easy to upregulate the open fraction via a modest elevation of calcium. We show further that strong gap-junctional coupling of both membrane potential and calcium is needed to overcome the stark heterogeneity of cell properties in these mosaic islets.

Glucose-dependent and -independent electrical activity in islets of Langerhans of Psammomys obesus, an animal model of nutritionally induced obesity and diabetes

Glucose-induced insulin secretion from pancreatic beta-cells involves metabolism-induced membrane depolarization and voltage-dependent Ca(2+) influx. The electrical events in beta-cell glucose sensing have been studied intensely using mouse islets of Langerhans, but data from other species, including models of type 2 diabetes mellitus (T2DM), are lacking. In this work, we made intracellular recordings of electrical activity from cells within islets of the gerbil Psammomys obesus (fat sand rat), a model of dietary-induced T2DM. Most islet cells from lean, non-diabetic sand rats displayed glucose-induced, K(ATP) channel-dependent, oscillatory electrical activity that was similar to the classic "bursting" pattern of mouse beta-cells. However, the oscillations were slower in sand rat islets, and the dose-response curve of electrical activity versus glucose concentration was left-shifted. Of the non-bursting cells, some produced action potentials continuously, while others displayed electrical activity that was largely independent of glucose. The latter activity consisted of continuous or intermittent action potential firing, and persisted for long periods in the absence of glucose. The glucose-insensitive activity was suppressed by diazoxide, indicating that the cells expressed K(ATP) channels. Sand rat islets produced intracellular Ca(2+) oscillations reminiscent of the oscillatory electrical pattern observed in most cells, albeit with a longer period. Finally, we found that the glucose dependence of insulin secretion from sand rat islets closely paralleled that of the bursting electrical activity. We conclude that while subpopulations of K(ATP)-expressing cells in sand rat islets display heterogeneous electrical responses to glucose, insulin secretion most closely follows the oscillatory activity. The ease of recording membrane potential from sand rat islets makes this a useful model for studies of beta-cell electrical signaling during the development of T2DM.

The hyperbolic effect of density and strength of inter beta-cell coupling on islet bursting: a theoretical investigation

BACKGROUND

Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP) model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each beta-cell is coupled to, nc, and the coupling strength, gc.

RESULTS

BETA-cell clusters of different sizes with number of beta-cells nbeta ranging from 1-343, nc from 0-12, and gc from 0-1000 pS, were simulated. Three functional measures of islet bursting characteristics--fraction of bursting beta-cells fb, synchronization index lambda, and bursting period Tb, were quantified. The results revealed a hyperbolic dependence on the combined effect of nc and gc. From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures fb, lambda and Tb increasing monotonically with CCI when it is small, and plateau around CCI = 1.

CONCLUSION

CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet beta-cell mass and function.

Dynamic simulation of mitochondrial respiration and oxidative phosphorylation: comparison with experimental results

Hypoxia hampers ATP production and threatens cell survival. Since cellular energetics tightly controls cell responses and fate, ATP levels and dynamics are of utmost importance. An integrated mathematical model of ATP synthesis by the mitochondrial oxidative phosphorylation/electron transfer chain system has been recently published (Beard, PLoS Comput Biol 1(4):e36, 2005). This model was validated under static conditions. To evaluate its performance under dynamical situations, we implemented and simulated it (Simulink), The Mathworks). Inner membrane potential (DeltaPsi) and [NADH] (feeding the electron transfer chain) were used as indicators of mitochondrial function. Root mean squared error (rmse) was used to compare simulations and experiments (isolated cardiac mitochondria, Bose et al. J Biol Chem 278(40):39155-39165, 2003). Steady-state experimental data were reproduced within 2-6%. Model dynamics were evaluated under: (i) baseline, (ii) activation of NADH production, (iii) addition of ADP, (iv) addition of inorganic phosphate, (v) oxygen exhaustion. In all phases, except the last one, DeltaPsi and [NADH] as well as oxygen consumption, were reproduced (within 10, 7 and 12%, respectively). Under anoxia, simulated DeltaPsi markedly depolarized (no change in experiments). In conclusion, the model reproduces dynamic data as long as oxygen is present. Anticipated improvement by the inclusion of ATP consumption and explicit Krebs cycle are under evaluation.

Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion

Impairment of insulin secretion from the beta-cells of the pancreatic islets of Langerhans is central to the development of type 2 diabetes mellitus and has therefore been the subject of much investigation. Great advances have been made in this area, but the mechanisms underlying the pulsatility of insulin secretion remain controversial. The period of these pulses is 4-6 min and reflects oscillations in islet membrane potential and intracellular free Ca(2+). Pulsatile blood insulin levels appear to play an important physiological role in insulin action and are lost in patients with type 2 diabetes and their near relatives. We present evidence for a recently developed beta-cell model, the "dual oscillator model," in which oscillations in activity are due to both electrical and metabolic mechanisms. This model is capable of explaining much of the available data on islet activity and offers possible resolutions of a number of longstanding issues. The model, however, still lacks direct confirmation and raises new issues. In this article, we highlight both the successes of the model and the challenges that it poses for the field.