Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

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.

Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke

A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.

Direct measurements of oscillatory glycolysis in pancreatic islet β-cells using novel fluorescence resonance energy transfer (FRET) biosensors for pyruvate kinase M2 activity

Pulses of insulin released from pancreatic β-cells maintain blood glucose in a narrow range, although the source of these pulses is unclear. We and others have proposed that positive feedback mediated by the glycolytic enzyme phosphofructokinase-1 (PFK1) enables β-cells to generate metabolic oscillations via autocatalytic activation by its product fructose 1,6-bisphosphate (FBP). Although much indirect evidence has accumulated in favor of this hypothesis, a direct measurement of oscillating glycolytic intermediates has been lacking. To probe glycolysis directly, we engineered a family of inter- and intramolecular FRET biosensors based on the glycolytic enzyme pyruvate kinase M2 (PKAR; pyruvate kinase activity reporter), which multimerizes and is activated upon binding FBP. When introduced into Min6 β-cells, PKAR FRET efficiency increased rapidly in response to glucose. Importantly, however, metabolites entering downstream of PFK1 (glyceraldehyde, pyruvate, and ketoisocaproate) failed to activate PKAR, consistent with sensor activation by FBP; the dependence of PKAR on FBP was further confirmed using purified sensor in vitro. Using a novel imaging modality for monitoring mitochondrial flavin fluorescence in mouse islets, we show that slow oscillations in mitochondrial redox potential stimulated by 10 mm glucose are in phase with glycolytic efflux through PKM2, measured simultaneously from neighboring islet β-cells expressing PKAR. These results indicate that PKM2 activity in β-cells is oscillatory and are consistent with pulsatile PFK1 being the mediator of slow glycolytic oscillations.

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.

Learning theories reveal loss of pancreatic electrical connectivity in diabetes as an adaptive response

Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secreting the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however, explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.

The impact of mathematical modeling on the understanding of diabetes and related complications

Diabetes is a chronic and complex multifactorial disease caused by persistent hyperglycemia and for which underlying pathogenesis is still not completely understood. The mathematical modeling of glucose homeostasis, diabetic condition, and its associated complications is rapidly growing and provides new insights into the underlying mechanisms involved. Here, we discuss contributions to the diabetes modeling field over the past five decades, highlighting the areas where more focused research is required.

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.

Phosphofructo-2-kinase/fructose-2,6-bisphosphatase modulates oscillations of pancreatic islet metabolism

Pulses of insulin from pancreatic beta-cells help maintain blood glucose in a narrow range, although the source of these pulses is unclear. It has been proposed that a positive feedback circuit exists within the glycolytic pathway, the autocatalytic activation of phosphofructokinase-1 (PFK1), which endows pancreatic beta-cells with the ability to generate oscillations in metabolism. Flux through PFK1 is controlled by the bifunctional enzyme PFK2/FBPase2 (6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase) in two ways: via (1) production/degradation of fructose-2,6-bisphosphate (Fru2,6-BP), a potent allosteric activator of PFK1, as well as (2) direct activation of glucokinase due to a protein-protein interaction. In this study, we used a combination of live-cell imaging and mathematical modeling to examine the effects of inducibly-expressed PFK2/FBPase2 mutants on glucose-induced Ca²⁺ pulsatility in mouse islets. Irrespective of the ability to bind glucokinase, mutants of PFK2/FBPase2 that increased the kinase:phosphatase ratio reduced the period and amplitude of Ca²⁺ oscillations. Mutants which reduced the kinase:phosphatase ratio had the opposite effect. These results indicate that the main effect of the bifunctional enzyme on islet pulsatility is due to Fru2,6-BP alteration of the threshold for autocatalytic activation of PFK1 by Fru1,6-BP. Using computational models based on PFK1-generated islet oscillations, we then illustrated how moderate elevation of Fru-2,6-BP can increase the frequency of glycolytic oscillations while reducing their amplitude, with sufficiently high activation resulting in termination of slow oscillations. The concordance we observed between PFK2/FBPase2-induced modulation of islet oscillations and the models of PFK1-driven oscillations furthermore suggests that metabolic oscillations, like those found in yeast and skeletal muscle, are shaped early in glycolysis.

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 model for glucose regulation in the whole-body system

The human body needs continuous and stable glucose supply for maintaining its biological functions. Stable glucose supply comes from the homeostatic regulation of the blood glucose level, which is controlled by various glucose consuming or producing organs. Therefore, it is important to understand the whole-body glucose regulation mechanism. In this article, we describe various mathematical models proposed for glucose regulation in the human body, and discuss the difficulty and limitation in reproducing real processes of glucose regulation.

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.

A novel fluorescence imaging approach for comparative measurements of pancreatic islet function in vitro

Pancreatic islet dysfunction is a key element in the development of type 2 diabetes. Determining possible early warning signs of dysfunction is thus important to determining the underlying causes of diabetes. We describe an improved fluorescent imaging approach to detect potential islet dysfunction. Using Cell Tracker Red (CTR, a mildly thiol-reactive fluorescent probe) to positively label particular islets, we measured intracellular free calcium with fura-2 AM in both CTR-labeled and unlabeled sets of pancreatic islets simultaneously in vitro. This approach enhances sensitivity by controlling for differences in background fluorescence, temperature, and perifusion dynamics. We confirmed that 200 nM CTR produced no spectral overlap with fura-2 and no significant physiological effects in selective tests of islet function. To demonstrate the utility of dual-labeling, we compared untreated islets with islets pretreated with low-dose pro-inflammatory cytokines (IL-6 + IL-1B) to induce mild dysfunction. We alternated CTR-labeling between control and test islets and identified consistent reductions in the amplitude and trajectory of glucose-stimulated calcium responses (GSCa) among cytokine-treated islets that were independent of labeling. Observations were verified using a MATLAB program specifically designed to identify key features in the GSCa. Our findings thus demonstrate the utility of CTR-labeling in identifying islet dysfunction and propose that this technique can be adapted for other cells and tissues.

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.

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.

Modeling of the gap junction of pancreatic β-cells and the robustness of insulin secretion

Pancreatic β-cells are interconnected by gap junctions, which allow small molecules to pass from cell to cell. In spite of the importance of the gap junctions in cellular communication, modeling studies have been limited by the complexity of the system. Here, we propose a mathematical gap junction model that properly takes into account biological functions, and apply this model to the study of the β-cell cluster. We consider both electrical and metabolic features of the system. Then, we find that when a fraction of the ATP-sensitive K⁺ channels are damaged, robust insulin secretion can only be achieved by gap junctions. Our finding is consistent with recent experiments conducted by Rocheleau et al. Our study also suggests that the free passage of potassium ions through gap junctions plays an important role in achieving metabolic synchronization between β-cells.

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.

A design principle underlying the synchronization of oscillations in cellular systems

Biological oscillations are found ubiquitously in cells and are widely variable, with periods varying from milliseconds to months, and scales involving subcellular components to large groups of organisms. Interestingly, independent oscillators from different cells often show synchronization that is not the consequence of an external regulator. What is the underlying design principle of such synchronized oscillations, and can modeling show that the complex consequences arise from simple molecular or other interactions between oscillators? When biological oscillators are coupled with each other, we found that synchronization is induced when they are connected together through a positive feedback loop. Increasing the coupling strength of two independent oscillators shows a threshold beyond which synchronization occurs within a few cycles, and a second threshold where oscillation stops. The positive feedback loop can be composed of either double-positive (PP) or double-negative (NN) interactions between a node of each of the two oscillating networks. The different coupling structures have contrasting characteristics. In particular, PP coupling is advantageous with respect to stability of period and amplitude, when local oscillators are coupled with a short time delay, whereas NN coupling is advantageous for a long time delay. In addition, PP coupling results in more robust synchronized oscillations with respect to amplitude excursions but not period, with applied noise disturbances compared to NN coupling. However, PP coupling can induce a large fluctuation in the amplitude and period of the resulting synchronized oscillation depending on the coupling strength, whereas NN coupling ensures almost constant amplitude and period irrespective of the coupling strength. Intriguingly, we have also observed that artificial evolution of random digital oscillator circuits also follows this design principle. We conclude that a different coupling strategy might have been selected according to different evolutionary requirements.

Glucose metabolism, islet architecture, and genetic homogeneity in imprinting of [Ca2+](i) and insulin rhythms in mouse islets

We reported previously that islets isolated from individual, outbred Swiss-Webster mice displayed oscillations in intracellular calcium ([Ca²⁺]_i) that varied little between islets of a single mouse but considerably between mice, a phenomenon we termed “islet imprinting.” We have now confirmed and extended these findings in several respects. First, imprinting occurs in both inbred (C57BL/6J) as well as outbred mouse strains (Swiss-Webster; CD1). Second, imprinting was observed in NAD(P)H oscillations, indicating a metabolic component. Further, short-term exposure to a glucose-free solution, which transiently silenced [Ca²⁺]_i oscillations, reset the oscillatory patterns to a higher frequency. This suggests a key role for glucose metabolism in maintaining imprinting, as transiently suppressing the oscillations with diazoxide, a K_ATP-channel opener that blocks [Ca²⁺]_i influx downstream of glucose metabolism, did not change the imprinted patterns. Third, imprinting was not as readily observed at the level of single beta cells, as the [Ca²⁺]_i oscillations of single cells isolated from imprinted islets exhibited highly variable, and typically slower [Ca²⁺]_i oscillations. Lastly, to test whether the imprinted [Ca²⁺]_i patterns were of functional significance, a novel microchip platform was used to monitor insulin release from multiple islets in real time. Insulin release patterns correlated closely with [Ca²⁺]_i oscillations and showed significant mouse-to-mouse differences, indicating imprinting. These results indicate that islet imprinting is a general feature of islets and is likely to be of physiological significance. While islet imprinting did not depend on the genetic background of the mice, glucose metabolism and intact islet architecture may be important for the imprinting phenomenon.

Modeling dynamic changes in type 1 diabetes progression: quantifying beta-cell variation after the appearance of islet-specific autoimmune responses

Type 1 diabetes (T1DM) is a chronic autoimmune disease with a long prodrome, which is characterized by dysfunction and ultimately destruction of pancreatic beta-cells. Because of the limited access to pancreatic tissue and pancreatic lymph nodes during the normoglycemic phase of the disease, little is known about the dynamics involved in the chain of events leading to the clinical onset of the disease in humans. In particular, during T1DM progression there is limited information about temporal fluctuations of immunologic abnormalities and their effect on pancreatic beta-cell function and mass. Therefore, our understanding of the pathoetiology of T1DM relies almost entirely on studies in animal models of this disease. In an effort to elucidate important mechanisms that may play a critical role in the progression to overt disease, we propose a mathematical model that takes into account the dynamics of functional and dysfunctional beta-cells, regulatory T cells, and pathogenic T cells. The model assumes that all individuals carrying susceptible HLA haplotypes will develop variable degrees of T1DM-related immunologic abnormalities. The results provide information about the concentrations and ratios of pathogenic T cells and regulatory T cells, the timing in which beta-cells become dysfunctional, and how certain kinetic parameters affect the progression to T1DM. Our model is able to describe changes in the ratio of pathogenic T cells and regulatory T cells after the appearance of islet antibodies in the pancreas. Finally, we discuss the robustness of the model and its ability to assist experimentalists in designing studies to test complicated theories about the disease.

Modeling of oscillatory bursting activity of pancreatic beta-cells under regulated glucose stimulation

A mathematical model to describe the oscillatory bursting activity of pancreatic beta-cells is combined with a model of glucose regulation system in this work to study the bursting pattern under regulated extracellular glucose stimulation. The bursting electrical activity in beta-cells is crucial for the release of insulin, which acts to regulate the blood glucose level. Different types of bursting pattern have been observed experimentally in glucose-stimulated islets both in vivo and in vitro, and the variations in these patterns have been linked to changes in glucose level. The combined model in this study enables us to have a deeper understanding on the regime change of bursting pattern when glucose level changes due to hormonal regulation, especially in the postprandial state. This is especially important as the oscillatory components of electrical activity play significant physiological roles in insulin secretion and some components have been found to be lost in type 2 diabetic patients.

Synchronization of pancreatic islet oscillations by intrapancreatic ganglia: a modeling study

Plasma insulin measurements from mice, rats, dogs, and humans indicate that insulin levels are oscillatory, reflecting pulsatile insulin secretion from individual islets. An unanswered question, however, is how the activity of a population of islets is coordinated to yield coherent oscillations in plasma insulin. Here, using mathematical modeling, we investigate the feasibility of a potential islet synchronization mechanism, cholinergic signaling. This hypothesis is based on well-established experimental evidence demonstrating intrapancreatic parasympathetic (cholinergic) ganglia and recent in vitro evidence that a brief application of a muscarinic agonist can transiently synchronize islets. We demonstrate using mathematical modeling that periodic pulses of acetylcholine released from cholinergic neurons is indeed able to coordinate the activity of a population of simulated islets, even if only a fraction of these are innervated. The role of islet-to-islet heterogeneity is also considered. The results suggest that the existence of cholinergic input to the pancreas may serve as a regulator of endogenous insulin pulsatility in vivo.

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.

Explicit calcium bursting stochastic resonance

In the present work the influence of internal noise resulting from small cell volume on bursting calcium oscillations is studied. With the internal noise switched on, the center of the main peak in the PSD (power spectrum density) was modified by internal noise. With increasing of the cell volume, the calculated signal-to-noise ratio (SNR) undergoes a maximum, which is referred in the present work as explicit bursting stochastic resonance. In addition, another quantity, the correlation time is used to measure the coherence of bursting oscillations. We demonstrate that the correlation time of the oscillations also exhibits a maximum at a certain cell volume.

Contributions of mathematical modeling of beta cells to the understanding of beta-cell oscillations and insulin secretion

Mathematical modeling of pancreatic beta cells has contributed significantly to the understanding of the mechanisms involved in glucose-stimulated insulin secretion (GSIS). Early models of insulin secretion built in the 1970s were phenomenological with little biological foundation for the proposed mechanisms. In the 1980s, models focused on identifying the regulation of bursting electrical activity known to be important for insulin secretion. The main result was to reject proposed mechanisms as new data emerged, but important results of the role of cell-to-cell coupling were also established. New models have been proposed that provide possible explanations for the occurrence of various patterns of bursting and calcium oscillations. In addition, modeling has played an important role in comparing competing effects of calcium on both NADH and adenosine 3'-5'-cyclic monophosphate levels. Models including modern cell biological results of the regulation of insulin containing granules and cell heterogeneity have appeared, providing updated versions of the early models proposed in the 1970s. These models, when coupled to electrophysiological- and calcium-based ones, have the prospect to aid in understanding the overall picture of GSIS. In addition, they might be useful for estimating in vivo beta-cell functioning. Beta-cell modeling will likely move closer to clinical applications, where it can be expected to play an important role, as it has and will, in understanding the complex oscillatory phenomena observed in beta cells and islets.

Gap junction coupling and calcium waves in the pancreatic islet

The pancreatic islet is a highly coupled, multicellular system that exhibits complex spatiotemporal electrical activity in response to elevated glucose levels. The emergent properties of islets, which differ from those arising in isolated islet cells, are believed to arise in part by gap junctional coupling, but the mechanisms through which this coupling occurs are poorly understood. To uncover these mechanisms, we have used both high-speed imaging and theoretical modeling of the electrical activity in pancreatic islets under a reduction in the gap junction mediated electrical coupling. Utilizing islets from a gap junction protein connexin 36 knockout mouse model together with chemical inhibitors, we can modulate the electrical coupling in the islet in a precise manner and quantify this modulation by electrophysiology measurements. We find that after a reduction in electrical coupling, calcium waves are slowed as well as disrupted, and the number of cells showing synchronous calcium oscillations is reduced. This behavior can be reproduced by computational modeling of a heterogeneous population of beta-cells with heterogeneous levels of electrical coupling. The resulting quantitative agreement between the data and analytical models of islet connectivity, using only a single free parameter, reveals the mechanistic underpinnings of the multicellular behavior of the islet.

Selection of in-phase or out-of-phase synchronization in a model based on global coupling of cells undergoing metabolic oscillations

On the basis of experimental observations, it has been suggested that glycolytic oscillations underlie the pulsatile secretion of insulin by pancreatic beta cells, with a periodicity of about 13 min. If beta cells within an islet are synchronized through gap junctions, the question arises as to how beta cells located in different islets of Langerhans synchronize to produce oscillations in plasma levels of insulin. We address this question by means of a minimal model that incorporates the secretion of insulin by cells undergoing glycolytic oscillations. Global coupling and synchronization result from the inhibition exerted by insulin on the production of glucose, which serves as the substrate for metabolic oscillations. Glycolytic oscillations are described by a simple two-variable model centered on the product-activated reaction catalyzed by the allosteric enzyme phosphofructokinase. We obtain bifurcation diagrams for the cases in which insulin secretion is controlled solely by the product or by the substrate of the metabolic oscillator. Remarkably, we find that the oscillating cells in these conditions synchronize, respectively, in phase or out of phase. Numerical simulations show that in-phase and out-of-phase synchronization can sometimes coexist when insulin release is controlled by both the substrate and the product of the metabolic oscillator. The results provide an example of a system in which the selection of in-phase or out-of-phase synchronization is governed by the nature of the coupling between the intracellular oscillations and the secretion of the biochemical signal through which the oscillating cells are globally coupled.

Long lasting synchronization of calcium oscillations by cholinergic stimulation in isolated pancreatic islets

Individual mouse pancreatic islets exhibit oscillations in [Ca(2+)](i) and insulin secretion in response to glucose in vitro, but how the oscillations of a million islets are coordinated within the human pancreas in vivo is unclear. Islet to islet synchronization is necessary, however, for the pancreas to produce regular pulses of insulin. To determine whether neurohormone release within the pancreas might play a role in coordinating islet activity, [Ca(2+)](i) changes in 4-6 isolated mouse islets were simultaneously monitored before and after a transient pulse of a putative synchronizing agent. The degree of synchronicity was quantified using a novel analytical approach that yields a parameter that we call the "Synchronization Index". Individual islets exhibited [Ca(2+)](i) oscillations with periods of 3-6 min, but were not synchronized under control conditions. However, raising islet [Ca(2+)](i) with a brief application of the cholinergic agonist carbachol (25 microM) or elevated KCl in glucose-containing saline rapidly synchronized islet [Ca(2+)](i) oscillations for >/=30 min, long after the synchronizing agent was removed. In contrast, the adrenergic agonists clonidine or norepinephrine, and the K(ATP) channel inhibitor tolbutamide, failed to synchronize islets. Partial synchronization was observed, however, with the K(ATP) channel opener diazoxide. The synchronizing action of carbachol depended on the glucose concentration used, suggesting that glucose metabolism was necessary for synchronization to occur. To understand how transiently perturbing islet [Ca(2+)](i) produced sustained synchronization, we used a mathematical model of islet oscillations in which complex oscillatory behavior results from the interaction between a fast electrical subsystem and a slower metabolic oscillator. Transient synchronization simulated by the model was mediated by resetting of the islet oscillators to a similar initial phase followed by transient "ringing" behavior, during which the model islets oscillated with a similar frequency. These results suggest that neurohormone release from intrapancreatic neurons could help synchronize islets in situ. Defects in this coordinating mechanism could contribute to the disrupted insulin secretion observed in Type 2 diabetes.

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.

Identifying the targets of the amplifying pathway for insulin secretion in pancreatic beta-cells by kinetic modeling of granule exocytosis

A kinetic model for insulin secretion in pancreatic beta-cells is adapted from a model for fast exocytosis in chromaffin cells. The fusion of primed granules with the plasma membrane is assumed to occur only in the "microdomain" near voltage-sensitive L-type Ca(2+)-channels, where [Ca(2+)] can reach micromolar levels. In contrast, resupply and priming of granules are assumed to depend on the cytosolic [Ca(2+)]. Adding a two-compartment model to handle the temporal distribution of Ca(2+) between the microdomain and the cytosol, we obtain a unified model that can generate both the fast granule fusion and the slow insulin secretion found experimentally in response to a step of membrane potential. The model can simulate the potentiation induced in islets by preincubation with glucose and the reduction in second-phase insulin secretion induced by blocking R-type Ca(2+)-channels (Ca(V)2.3). The model indicates that increased second-phase insulin secretion induced by the amplifying signal is controlled by the "resupply" step of the exocytosis cascade. In contrast, enhancement of priming is a good candidate for amplification of first-phase secretion by glucose, cyclic adenosine 3':5'-cyclic monophosphate, and protein kinase C. Finally, insulin secretion is enhanced when the amplifying signal oscillates in phase with the triggering Ca(2+)-signal.

RyR channels and glucose-regulated pancreatic beta-cells

Ryanodine receptor channel model is introduced to a dynamical model of pancreatic beta-cells to discuss the effects of RyR channels and glucose concentration on membrane potential. The results show Ca2+ concentration changes responding to enhance of glucose concentration is more quickly than that of activating RyR channels, and both methods can induce bursting action potential and increase free cytosolic Ca2+ concentration. An interesting finding is that moderate stimulation to RyR channels will result in a kind of "complex bursting", which is more effective in enhancing average Ca2+ concentration and insulin section.

Regulation of cAMP dynamics by Ca2+ and G protein-coupled receptors in the pancreatic beta-cell: a computational approach

In this report we describe a mathematical model for the regulation of cAMP dynamics in pancreatic beta-cells. Incretin hormones such as glucagon-like peptide 1 (GLP-1) increase cAMP and augment insulin secretion in pancreatic beta-cells. Imaging experiments performed in MIN6 insulinoma cells expressing a genetically encoded cAMP biosensor and loaded with fura-2, a calcium indicator, showed that cAMP oscillations are differentially regulated by periodic changes in membrane potential and GLP-1. We modeled the interplay of intracellular calcium (Ca(2+)) and its interaction with calmodulin, G protein-coupled receptor activation, adenylyl cyclases (AC), and phosphodiesterases (PDE). Simulations with the model demonstrate that cAMP oscillations are coupled to cytoplasmic Ca(2+) oscillations in the beta-cell. Slow Ca(2+) oscillations (<1 min(-1)) produce low-frequency cAMP oscillations, and faster Ca(2+) oscillations (>3-4 min(-1)) entrain high-frequency, low-amplitude cAMP oscillations. The model predicts that GLP-1 receptor agonists induce cAMP oscillations in phase with cytoplasmic Ca(2+) oscillations. In contrast, observed antiphasic Ca(2+) and cAMP oscillations can be simulated following combined glucose and tetraethylammonium-induced changes in membrane potential. The model provides additional evidence for a pivotal role for Ca(2+)-dependent AC and PDE activation in coupling of Ca(2+) and cAMP signals. Our results reveal important differences in the effects of glucose/TEA and GLP-1 on cAMP dynamics in MIN6 beta-cells.

Investigating the role of islet cytoarchitecture in its oscillation using a new beta-cell cluster model

The oscillatory insulin release is fundamental to normal glycemic control. The basis of the oscillation is the intercellular coupling and bursting synchronization of β cells in each islet. The functional role of islet β cell mass organization with respect to its oscillatory bursting is not well understood. This is of special interest in view of the recent finding of islet cytoarchitectural differences between human and animal models. In this study we developed a new hexagonal closest packing (HCP) cell cluster model. The model captures more accurately the real islet cell organization than the simple cubic packing (SCP) cluster that is conventionally used. Using our new model we investigated the functional characteristics of β-cell clusters, including the fraction of cells able to burst f_b, the synchronization index λ of the bursting β cells, the bursting period T_b, the plateau fraction p_f, and the amplitude of intracellular calcium oscillation [Ca]. We determined their dependence on cluster architectural parameters including number of cells n_β, number of inter-β cell couplings of each β cell n_c, and the coupling strength g_c. We found that at low values of n_β, n_c and g_c, the oscillation regularity improves with their increasing values. This functional gain plateaus around their physiological values in real islets, at n_β∼100, n_c∼6 and g_c∼200 pS. In addition, normal β-cell clusters are robust against significant perturbation to their architecture, including the presence of non-β cells or dead β cells. In clusters with n_β>∼100, coordinated β-cell bursting can be maintained at up to 70% of β-cell loss, which is consistent with laboratory and clinical findings of islets. Our results suggest that the bursting characteristics of a β-cell cluster depend quantitatively on its architecture in a non-linear fashion. These findings are important to understand the islet bursting phenomenon and the regulation of insulin secretion, under both physiological and pathological conditions.

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.

Tissue-dependent loss of phosphofructokinase-M in mice with interrupted activity of the distal promoter: impairment in insulin secretion

Phosphofructokinase is a key enzyme of glycolysis that exists as homo- and heterotetramers of three subunit isoforms: muscle, liver, and C type. Mice with a disrupting tag inserted near the distal promoter of the phosphofructokinase-M gene showed tissue-dependent differences in loss of that isoform: 99% in brain and 95-98% in islets, but only 50-75% in skeletal muscle and little if any loss in heart. This correlated with the continued presence of proximal transcripts specifically in muscle tissues. These data strongly support the proposed two-promoter system of the gene, with ubiquitous use of the distal promoter and additional use of the proximal promoter selectively in muscle. Interestingly, the mice were glucose intolerant and had somewhat elevated fasting and fed blood glucose levels; however, they did not have an abnormal insulin tolerance test, consistent with the less pronounced loss of phosphofructokinase-M in muscle. Isolated perifused islets showed about 50% decreased glucose-stimulated insulin secretion and reduced amplitude and regularity of secretory oscillations. Oscillations in cytoplasmic free Ca(2+) and the rise in the ATP/ADP ratio appeared normal. Secretory oscillations still occurred in the presence of diazoxide and high KCl, indicating an oscillation mechanism not requiring dynamic Ca(2+) changes. The results suggest the importance of phosphofructokinase-M for insulin secretion, although glucokinase is the overall rate-limiting glucose sensor. Whether the Ca(2+) oscillations and residual insulin oscillations in this mouse model are due to the residual 2-5% phosphofructokinase-M or to other phosphofructokinase isoforms present in islets or involve another metabolic oscillator remains to be determined.

Phantom bursting is highly sensitive to noise and unlikely to account for slow bursting in beta-cells: considerations in favor of metabolically driven oscillations

Pancreatic beta-cells show bursting electrical activity with a wide range of burst periods ranging from a few seconds, often seen in isolated cells, over tens of seconds (medium bursting), usually observed in intact islets, to several minutes. The phantom burster model [Bertram, R., Previte, J., Sherman, A., Kinard, T.A., Satin, L.S., 2000. The phantom burster model for pancreatic beta-cells. Biophys. J. 79, 2880-2892] provided a framework, which covered this span, and gave an explanation of how to obtain medium bursting combining two processes operating on different time scales. However, single cells are subjected to stochastic fluctuations in plasma membrane currents, which are likely to disturb the bursting mechanism and transform medium bursters into spikers or very fast bursters. We present a polynomial, minimal, phantom burster model and show that noise modifies the plateau fraction and lowers the burst period dramatically in phantom bursters. It is therefore unlikely that slow bursting in single cells is driven by the slow phantom bursting mechanism, but could instead be driven by oscillations in glycolysis, which we show are stable to random ion channel fluctuations. Moreover, so-called compound bursting can be converted to apparent slow bursting by noise, which could explain why compound bursting and mixed Ca(2+) oscillations are seen mainly in intact islets.

A silicon pancreatic Beta cell for diabetes

The paper will consider how silicon devices such as ion-sensitive field effect transistors can be used to model metabolic functions in biology. In a first example, a biologically inspired silicon beta cell is presented to serve as the main building block of an artificial pancreas. This is to be used for real-time glucose sensing and insulin release for diabetics. This system presents the first silicon implementation of a metabolic cell capable of exhibiting variable bursting behavior upon glucose stimulation. Based on the Hodgkin and Huxley formalism, this approach achieves dynamics similar to that of biological beta cells by using devices biased in the subthreshold regime. In addition to mimicking the physiological behavior of the beta cell, the circuit achieves good power efficiency, measured to be 4.5 muW.

Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets

Insulin secretion from pancreatic beta-cells is oscillatory, with a typical period of 2-7 min, reflecting oscillations in membrane potential and the cytosolic Ca(2+) concentration. Our central hypothesis is that the slow 2-7 min oscillations are due to glycolytic oscillations, whereas faster oscillations that are superimposed are due to Ca(2+) feedback onto metabolism or ion channels. We extend a previous mathematical model based on this hypothesis to include a more detailed description of mitochondrial metabolism. We demonstrate that this model can account for typical oscillatory patterns of membrane potential and Ca(2+) concentration in islets. It also accounts for temporal data on oxygen consumption in islets. A recent challenge to the notion that glycolytic oscillations drive slow Ca(2+) oscillations in islets are data showing that oscillations in Ca(2+), mitochondrial oxygen consumption, and NAD(P)H levels are all terminated by membrane hyperpolarization. We demonstrate that these data are in fact compatible with a model in which glycolytic oscillations are the key player in rhythmic islet activity. Finally, we use the model to address the recent finding that the activity of islets from some mice is uniformly fast, whereas that from islets of other mice is slow. We propose a mechanism for this dichotomy.

Oscillatory membrane potential response to glucose in islet beta-cells: a comparison of islet-cell electrical activity in mouse and rat

In contrast to mouse, rat islet beta-cell membrane potential is reported not to oscillate in response to elevated glucose despite demonstrated oscillations in calcium and insulin secretion. We aim to clarify the electrical activity of rat islet beta-cells and characterize and compare the electrical activity of both alpha- and beta-cells in rat and mouse islets. We recorded electrical activity from alpha- and beta-cells within intact islets from both mouse and rat using the perforated whole-cell patch clamp technique. Fifty-six percent of both mouse and rat beta-cells exhibited an oscillatory response to 11.1 mm glucose. Responses to both 11.1 mm and 2.8 mm glucose were identical in the two species. Rat beta-cells exhibited incremental depolarization in a glucose concentration-dependent manner. We also demonstrated electrical activity in human islets recorded under the same conditions. In both mouse and rat alpha-cells 11 mm glucose caused hyperpolarization of the membrane potential, whereas 2.8 mm glucose produced action potential firing. No species differences were observed in the response of alpha-cells to glucose. This paper is the first to demonstrate and characterize oscillatory membrane potential fluctuations in the presence of elevated glucose in rat islet beta-cells in comparison with mouse. The findings promote the use of rat islets in future electrophysiological studies, enabling consistency between electrophysiological and insulin secretion studies. An inverse response of alpha-cell membrane potential to glucose furthers our understanding of the mechanisms underlying glucose sensitive glucagon secretion.

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

A new type of equation to describe enzyme-catalyzed reactions was developed, which allows the description of processes both at or near equilibrium and far from equilibrium, as they are both known to occur in the living cell. These equations combine kinetic as well as energetic characteristics within one single equation, and they describe the steady state as well as oscillations, as is shown for the glucose metabolism of the pancreatic beta-cell. A simulation of oxidative glucose metabolism could be elaborated, which allows to analyse in detail, how membrane and metabolic oscillations of the pancreatic beta-cell are generated, and how they are kinetically coupled. Glucose metabolism shows steady-state behaviour at a resting glucose concentration ([Glu]) of 4 mM. The steady state is switched to the oscillatory state by a first increase of the conductance of the glucokinase-catalyzed reaction at an elevated [Glu] of 10 mM. This is in fact sufficient to decrease the cytosolic adenosine diphosphate concentration ([ADP](c)) at constant intracellular [Ca(2+)]. The associated changes of the ATP and ADP species can reduce the conductance of ATP-sensitive K(+) channels (K(ATP)), thereby initiating bursts of the cell membrane potential (Delta(c)phi) with a concomitant influx of Ca(2+) ions from the extracellular space into the cell. The production of oscillations of [ADP](c), [Ca(2+)](c), and all other variables, including those of mitochondria, are brought about on the one hand by a [Ca(2+)](m) dependent activation of mitochondrial ATP production, on the other hand by a [Ca(2+)](c)-dependent activation of ATP utilisation in the cytosol. Both processes must be coordinated in such a way that ATP production slightly precedes its utilisation. Oscillatory frequencies (fast/slow) are determined by the conductance (high/low, respectively) of flux through pyruvate dehydrogenase and/or citric acid cycle. The simulation shows that the so-called pyruvate paradox possibly results from a relatively low membrane conductance of beta-cells for pyruvate.

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.

Pancreatic beta-cells secrete insulin in fast- and slow-release forms

Insulin vesicles contain a chemically rich mixture of cargo that includes ions, small molecules, and proteins. At present, it is unclear if all components of this cargo escape from the vesicle at the same rate or to the same extent during exocytosis. Here, we demonstrate through real-time imaging that individual rat and human pancreatic beta-cells secrete insulin in heterogeneous forms that disperse either rapidly or slowly. In healthy pancreatic beta-cells maintained in culture, most vesicles discharge insulin in its fast-release form, a form that leaves individual vesicles in a few hundred milliseconds. The fast-release form of insulin leaves vesicles as rapidly as C-peptide leaves vesicles. Healthy beta-cells also secrete a slow-release form of insulin that leaves vesicles more slowly than C-peptide, over times ranging from seconds to minutes. Individual beta-cells make vesicles with both forms of insulin, though not all vesicles contain both forms of insulin. In addition, we confirm that insulin vesicles store their cargo in two functionally distinct compartments: an acidic solution, or halo, and a condensed core. Thus, our results suggest two important features of the condensed core: 1) It exists in different states among the vesicles undergoing exocytosis and 2) its dissolution determines the availability of insulin during exocytosis.

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.