Rhythm of the beta-cell oscillator is not governed by a single regulator: multiple systems contribute to oscillatory behavior

A trio of biological rhythms and their relevance in rhythmic mechanical stimulation of cell cultures

The primary aim of this article is to provide a biological rhythm model based on previous theoretical and experimental findings to promote more comprehensive studies of rhythmic mechanical stimulation of cell cultures, which relates to tissue engineering and regenerative medicine fields. Through an interdisciplinary approach where different standpoints from biology and musicology are combined, we explore some of the core rhythmic features of biological and cellular rhythmic processes and present them as a trio model that aims to afford a basic but fundamental understanding of the connections between various biological rhythms. It is vital to highlight such links since rhythmic mechanical stimulation and its effect on cell cultures are vastly underexplored even though the cellular response to mechanical stimuli (mechanotransduction) has been studied widely and relevant experimental evidence suggests mechanotransduction processes are rhythmic.

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.

Coexistence between silent and bursting states in a biophysical Hodgkin-Huxley-type of model

Classification of the dynamical mechanisms that support bistability between bursting oscillations and silence has not yet been clarified in detail. The purpose of this paper is to demonstrate that the coexistence of a stable equilibrium point with a state of continuous bursting can occur in a slightly modified, biophysical model that describe the dynamics of pancreatic beta-cells. To realize this form of coexistence, we have introduced an additional voltage-dependent potassium current that is activated in the region around the original, unstable equilibrium point. It is interesting to note that this modification also leads the model to display a blue-sky catastrophe in the transition region between chaotic and bursting states.

The Pancreatic β-Cell: A Bioenergetic Perspective

The pancreatic β-cell secretes insulin in response to elevated plasma glucose. This review applies an external bioenergetic critique to the central processes of glucose-stimulated insulin secretion, including glycolytic and mitochondrial metabolism, the cytosolic adenine nucleotide pool, and its interaction with plasma membrane ion channels. The control mechanisms responsible for the unique responsiveness of the cell to glucose availability are discussed from bioenergetic and metabolic control standpoints. The concept of coupling factor facilitation of secretion is critiqued, and an attempt is made to unravel the bioenergetic basis of the oscillatory mechanisms controlling secretion. The need to consider the physiological constraints operating in the intact cell is emphasized throughout. The aim is to provide a coherent pathway through an extensive, complex, and sometimes bewildering literature, particularly for those unfamiliar with the field.

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.

An Automated Perifusion System for Modifying Cell Culture Conditions over Time

BACKGROUND

Cells are continuously exposed to changes in their environment. Endocrine systems, in particular, communicate by rhythms and feedback loops. In this study, we developed an automated system to produce such conditions for cultured cells in a precisely timed manner. We utilized a programmable pair of syringe pumps for inflow and a peristaltic pump for outflow to create rhythmic pulses at 5-min intervals in solutions that mimic the endogenous patterns of insulin produced by pancreatic islets as a test case.

RESULTS

This perifusion system was first tested by measuring trypan blue absorbance, which was intermittently added and washed out at 3:3 and 2:3 min (in:out). Absorbance corresponded with patterns of trypan blue delivery. We then created patterns of forced oscillations in islets by intermittently switching between solutions containing 28 millimolar (mM) glucose (producing high levels of intracellular calcium ([Ca²⁺]_i) and insulin secretion) and 28 mM glucose + calcium-channel blocker nifedipine (producing low levels of [Ca²⁺]_i and insulin secretion). Forced perifusion effects were monitored by fura-2 AM fluorescence measurements of [Ca²⁺]_i. Islets showed uniform oscillations in [Ca²⁺]_i at time intervals consistent with the perifusion pattern, mimicking endogenous pulsatility.

CONCLUSIONS

This study highlights a valuable method to modify the environment of the cell culture over a period of hours to days.

Restoration of high-frequency glucose-entrained insulin oscillations in obese subjects with type 2 diabetes after biliopancreatic diversion

BACKGROUND

Minimal glucose infusions are known to entrain insulin oscillations in patients with normal glucose tolerance (NGT) but not in patients with type 2 diabetes (T2D).

OBJECTIVES

To investigate whether weight loss after a version of biliopancreatic diversion (BPD) can restore the glucose entrainment of high-frequency insulin oscillations in morbidly obese NGT or T2D patients.

SETTING

University Hospital, Greece.

METHODS

We prospectively studied 9 NGT controls (body mass index [BMI] 23.3±1.6 kg/m²), 9 obese NGT patients (BMI 51.1±12.7 kg/m²), and 9 obese T2D patients (BMI 56.8±11.6 kg/m²). Patients were studied before and 1.5 years after BPD. Insulin was sampled every minute for 90 minutes. Glucose (6 mg/kg weight) was infused every 10 minutes for 1 minute. Regularity of insulin pulses was estimated by autocorrelation analysis, spectral analysis, approximate entropy/sample entropy (ApEn/SampEn), and insulin pulsatility by deconvolution analysis.

RESULTS

Postoperatively, glucose and insulin concentrations of NGT and T2D patients decreased to control levels and BMI to 31.3±6.3 for NGT patients and 34.9±9.9 kg/m² for T2D patients. Preoperatively, glucose entrainment was absent in all T2D and in 4 NGT patients as assessed with spectral analysis and in 8 and 4, respectively, as assessed with autocorrelation and deconvolution analysis. Postoperatively, it was restored to normal in all patients. ApEn/SampEn decreased significantly only in the T2D group postoperatively.

CONCLUSION

BPD restores the glucose entrainment of high-frequency insulin oscillations in obese NGT and T2D patients after marked weight loss and normalizes glucose levels and insulin sensitivity, thus demonstrating recovery of β-cell glucose sensing.

Calcium modulation of exocytosis-linked plasma membrane potential oscillations in INS-1 832/13 cells

Oscillations in plasma membrane potential initiated by substrate-dependent blockade of ATP-sensitive K+ channels in insulin-secreting INS-1 832/13 are differentially linked to distinct voltage-activated Ca2+ channels and drive exocytosis. Ca2+ feeds back to control oscillation frequency, amplitude and prevalence.

Pulsatile insulin secretion, impaired glucose tolerance and type 2 diabetes

Type 2 diabetes (T2DM) results when increases in beta cell function and/or mass cannot compensate for rising insulin resistance. Numerous studies have documented the longitudinal changes in metabolism that occur during the development of glucose intolerance and lead to T2DM. However, the role of changes in insulin secretion, both amount and temporal pattern, has been understudied. Most of the insulin secreted from pancreatic beta cells of the pancreas is released in a pulsatile pattern, which is disrupted in T2DM. Here we review the evidence that changes in beta cell pulsatility occur during the progression from glucose intolerance to T2DM in humans, and contribute significantly to the etiology of the disease. We review the evidence that insulin pulsatility improves the efficacy of secreted insulin on its targets, particularly hepatic glucose production, but also examine evidence that pulsatility alters or is altered by changes in peripheral glucose uptake. Finally, we summarize our current understanding of the biophysical mechanisms responsible for oscillatory insulin secretion. Understanding how insulin pulsatility contributes to normal glucose homeostasis and is altered in metabolic disease states may help improve the treatment of T2DM.

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.

Unpredictable feeding impairs glucose tolerance in growing lambs

Irregular eating is associated with insulin resistance and metabolic disease in adults but may affect young, growing children differently. We investigated the metabolic effects of unpredictable feeding in female juvenile lambs randomly assigned to receive, for six weeks, maintenance feed given twice daily in equal portions (Control Group, C; n = 24) or the same weekly feed amount in aliquots of variable size at unpredictable times (Unpredictable Group, U; n = 21). Intravenous glucose tolerance tests (IVGTT), insulin tolerance tests (ITT), and measurement of diurnal plasma cortisol concentrations were performed pre and post the dietary intervention. Groups were compared using t test and RM ANOVA. Weight gain was similar in both groups (C 18±2%; U 16±2% of initial body weight). Glucose area under the curve (AUC) was unchanged in C (AUC pre 818±34, post 801±33 mmol.min.l⁻¹), but increased by 20% in U (pre 830±25, post 1010±19 mmol.min.l⁻¹; p<0.0001), with an inadequate insulin response to glucose load (log(AUC insulin first 40 minutes) post intervention C 1.49±0.04 vs U 1.36±0.04 ng.min.ml⁻¹; p = 0.03). Insulin tolerance and diurnal variation of plasma cortisol concentrations were not different between groups. Unpredictable feeding impairs insulin response to glucose in growing lambs despite high quality food and normal weight gain. Irregular eating warrants investigation as a potentially remediable risk factor for disordered glucose metabolism.

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.

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.

Catechol metabolites of endogenous estrogens induce redox cycling and generate reactive oxygen species in breast epithelial cells

Estrogens are major risk factors for the development of breast cancer; they can be metabolized to catechols, which are further oxidized to DNA-reactive quinones and semiquinones (SQs). These metabolites are mutagenic and may contribute to the carcinogenic activity of estrogens. Redox cycling of the SQs and subsequent generation of reactive oxygen species (ROS) is also an important mechanism leading to DNA damage. The SQs of exogenous estrogens have been shown to redox cycle, however, redox cycling and the generation of ROS by endogenous estrogens has never been characterized. In the present studies, we determined whether the catechol metabolites of endogenous estrogens, including 2-hydroxyestradiol, 4-hydroxyestradiol, 4-hydroxyestrone and 2-hydroxyestriol, can redox cycle in breast epithelial cells. These catechol estrogens, but not estradiol, estrone, estriol or 2-methoxyestradiol, were found to redox cycle and generate hydrogen peroxide (H(2)O(2)) and hydroxyl radicals in lysates of three different breast epithelial cell lines: MCF-7, MDA-MB-231 and MCF-10A. The generation of ROS required reduced nicotinamide adenine dinucleotide phosphate as a reducing equivalent and was inhibited by diphenyleneiodonium, a flavoenzyme inhibitor, indicating that redox cycling is mediated by flavin-containing oxidoreductases. Using extracellular microsensors, catechol estrogen metabolites stimulated the release of H(2)O(2) by adherent cells, indicating that redox cycling occurs in viable intact cells. Taken together, these data demonstrate that catechol metabolites of endogenous estrogens undergo redox cycling in breast epithelial cells, resulting in ROS production. Depending on the localized concentrations of catechol estrogens and enzymes that mediate redox cycling, this may be an important mechanism contributing to the development of breast cancer.

Oscillatory glucose flux in INS 1 pancreatic β cells: a self-referencing microbiosensor study

Signaling and insulin secretion in β cells have been reported to demonstrate oscillatory modes, with abnormal oscillations associated with type 2 diabetes. We investigated cellular glucose influx in β cells with a self-referencing (SR) microbiosensor based on nanomaterials with enhanced performance. Dose-response analyses with glucose and metabolic inhibition studies were used to study oscillatory patterns and transporter kinetics. For the first time, we report a stable and regular oscillatory uptake of glucose (averaged period 2.9±0.6 min), which corresponds well with an oscillator model. This oscillatory behavior is part of the feedback control pathway involving oxygen, cytosolic Ca(2+)/ATP, and insulin secretion (periodicity approximately 3 min). Glucose stimulation experiments show that the net Michaelis-Menten constant (6.1±1.5 mM) is in between GLUT2 and GLUT9. Phloretin inhibition experiments show an EC(50) value of 28±1.6 μM phloretin for class I GLUT proteins and a concentration of 40±0.6 μM phloretin caused maximum inhibition with residual nonoscillating flux, suggesting that the transporters not inhibited by phloretin are likely responsible for the remaining nonoscillatory uptake, and that impaired uptake via GLUT2 may be the cause of the oscillation loss in type 2 diabetes. Transporter studies using the SR microbiosensor will contribute to diabetes research and therapy development by exploring the nature of oscillatory transport mechanisms.

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.

Glucagon-like peptide-1 induced signaling and insulin secretion do not drive fuel and energy metabolism in primary rodent pancreatic beta-cells

Background

Glucagon like peptide-1 (GLP-1) and its analogue exendin-4 (Ex-4) enhance glucose stimulated insulin secretion (GSIS) and activate various signaling pathways in pancreatic β-cells, in particular cAMP, Ca²⁺ and protein kinase-B (PKB/Akt). In many cells these signals activate intermediary metabolism. However, it is not clear whether the acute amplification of GSIS by GLP-1 involves in part metabolic alterations and the production of metabolic coupling factors.

Methodology/Prinicipal Findings

GLP-1 or Ex-4 at high glucose caused release (∼20%) of the total rat islet insulin content over 1 h. While both GLP-1 and Ex-4 markedly potentiated GSIS in isolated rat and mouse islets, neither had an effect on β-cell fuel and energy metabolism over a 5 min to 3 h time period. GLP-1 activated PKB without changing glucose usage and oxidation, fatty acid oxidation, lipolysis or esterification into various lipids in rat islets. Ex-4 caused a rise in [Ca²⁺]_i and cAMP but did not enhance energy utilization, as neither oxygen consumption nor mitochondrial ATP levels were altered.

Conclusions/Significance

The results indicate that GLP-1 barely affects β-cell intermediary metabolism and that metabolic signaling does not significantly contribute to GLP-1 potentiation of GSIS. The data also indicate that insulin secretion is a minor energy consuming process in the β-cell, and that the β-cell is different from most cell types in that its metabolic activation appears to be primarily governed by a “push” (fuel substrate driven) process, rather than a “pull” mechanism secondary to enhanced insulin release as well as to Ca²⁺, cAMP and PKB signaling.

Role for malic enzyme, pyruvate carboxylation, and mitochondrial malate import in glucose-stimulated insulin secretion

Pyruvate cycling has been implicated in glucose-stimulated insulin secretion (GSIS) from pancreatic beta-cells. The operation of some pyruvate cycling pathways is proposed to necessitate malate export from the mitochondria and NADP(+)-dependent decarboxylation of malate to pyruvate by cytosolic malic enzyme (ME1). Evidence in favor of and against a role of ME1 in GSIS has been presented by others using small interfering RNA-mediated suppression of ME1. ME1 was also proposed to account for methyl succinate-stimulated insulin secretion (MSSIS), which has been hypothesized to occur via succinate entry into the mitochondria in exchange for malate and subsequent malate conversion to pyruvate. In contrast to rat, mouse beta-cells lack ME1 activity, which was suggested to explain their lack of MSSIS. However, this hypothesis was not tested. In this report, we demonstrate that although adenoviral-mediated overexpression of ME1 greatly augments GSIS in rat insulinoma INS-1 832/13 cells, it does not restore MSSIS, nor does it significantly affect GSIS in mouse islets. The increase in GSIS following ME1 overexpression in INS-1 832/13 cells did not alter the ATP-to-ADP ratio but was accompanied by increases in malate and citrate levels. Increased malate and citrate levels were also observed after INS-1 832/13 cells were treated with the malate-permeable analog dimethyl malate. These data suggest that although ME1 overexpression augments anaplerosis and GSIS in INS-1 832/13 cells, it is not likely involved in MSSIS and GSIS in pancreatic islets.

Effects of palmitate on ER and cytosolic Ca2+ homeostasis in beta-cells

There are strong links between obesity, elevated free fatty acids, and type 2 diabetes. Specifically, the saturated fatty acid palmitate has pleiotropic effects on beta-cell function and survival. In the present study, we sought to determine the mechanism by which palmitate affects intracellular Ca2+, and in particular the role of the endoplasmic reticulum (ER). In human beta-cells and MIN6 cells, palmitate rapidly increased cytosolic Ca2+ through a combination of Ca2+ store release and extracellular Ca2+ influx. Palmitate caused a reversible lowering of ER Ca2+, measured directly with the fluorescent protein-based ER Ca2+ sensor D1ER. Using another genetically encoded indicator, we observed long-lasting oscillations of cytosolic Ca2+ in palmitate-treated cells. In keeping with this observed ER Ca2+ depletion, palmitate induced rapid phosphorylation of the ER Ca2+ sensor protein kinase R-like ER kinase (PERK) and subsequently ER stress and beta-cell death. We detected little palmitate-induced insulin secretion, suggesting that these Ca2+ signals are poorly coupled to exocytosis. In summary, we have characterized Ca2+-dependent mechanisms involved in altered beta-cell function and survival induced by the free fatty acid palmitate. We present the first direct evidence that free fatty acids reduce ER Ca2+ and shed light on pathways involved in lipotoxicity and the pathogenesis of type 2 diabetes.

Oscillatory control of insulin secretion

Pancreatic beta-cells possess an inherent ability to generate oscillatory signals that trigger insulin release. Coordination of the secretory activity among beta-cells results in pulsatile insulin secretion from the pancreas, which is considered important for the action of the hormone in the target tissues. This review focuses on the mechanisms underlying oscillatory control of insulin secretion at the level of the individual beta-cell. Recent studies have demonstrated that oscillations of the cytoplasmic Ca(2+) concentration are synchronized with oscillations in beta-cell metabolism, intracellular cAMP concentration, phospholipase C activity and plasma membrane phosphoinositide lipid concentrations. There are complex interdependencies between the different messengers and signalling pathways that contribute to amplitude regulation and shaping of the insulin secretory response to nutrient stimuli and neurohormonal modulators. Several of these pathways may be important pharmacological targets for improving pulsatile insulin secretion in type 2 diabetes.

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.

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.

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.