Calcium-activated K+ channels of mouse beta-cells are controlled by both store and cytoplasmic Ca2+: experimental and theoretical studies

Molecular mechanism responsible for sex differences in electrical activity of mouse pancreatic β cells

In humans, type 2 diabetes mellitus shows a higher prevalence in men compared with women, a phenotype that has been attributed to a lower peripheral insulin sensitivity in men. Whether sex-specific differences in pancreatic β cell function also contribute is largely unknown. Here, we characterized the electrophysiological properties of β cells in intact male and female mouse islets. Elevation of glucose concentration above 5 mM triggered an electrical activity with a similar glucose dependence in β cells of both sexes. However, female β cells had a more depolarized membrane potential and increased firing frequency compared with males. The higher membrane depolarization in female β cells was caused by approximately 50% smaller Kv2.1 K+ currents compared with males but otherwise unchanged KATP, large-conductance and small-conductance Ca2+-activated K+ channels, and background TASK1/TALK1 K+ current densities. In female β cells, the higher depolarization caused a membrane potential-dependent inactivation of the voltage-gated Ca2+ channels (CaV), resulting in reduced Ca2+ entry. Nevertheless, this reduced Ca2+ influx was offset by a higher action potential firing frequency. Because exocytosis of insulin granules does not show a sex-specific difference, we conclude that the higher electrical activity promotes insulin release in females, improving glucose tolerance.

Disturbances in system dynamics of [Formula: see text] and [Formula: see text] perturbing insulin secretion in a pancreatic [Formula: see text]-cell due to type-2 diabetes

The individual study of [Formula: see text] and [Formula: see text] dynamics respectively in a [Formula: see text]-cell has yielded limited information about the cell functions. But the systems biology approaches for such studies have received very little attention by the research workers in the past. In the present work, a system-dynamics model for the interdependent [Formula: see text] and [Formula: see text] signaling that controls insulin secretion in a [Formula: see text]-cell has been suggested. A two-way feedback system of [Formula: see text] and [Formula: see text] has been considered and one-way feedback between [Formula: see text] and insulin has been implemented in the model. The finite element method along with the Crank-Nicolson method have been applied for simulation. Numerical results have been used to analyze the impact of perturbations in [Formula: see text] and [Formula: see text] dynamics on insulin secretion for normal and Type-2 diabetic conditions. The results reveal that Type-2 diabetes comes from abnormalities in insulin secretion caused by the perturbation in buffers and pumps (SERCA and PMCA).

Beta-Cell Ion Channels and Their Role in Regulating Insulin Secretion

Beta cells of the pancreatic islet express many different types of ion channels. These channels reside in the β-cell plasma membrane as well as subcellular organelles and their coordinated activity and sensitivity to metabolism regulate glucose-dependent insulin secretion. Here, we review the molecular nature, expression patterns, and functional roles of many β-cell channels, with an eye toward explaining the ionic basis of glucose-induced insulin secretion. Our primary focus is on K_ATP and voltage-gated Ca²⁺ channels as these primarily regulate insulin secretion; other channels in our view primarily help to sculpt the electrical patterns generated by activated β-cells or indirectly regulate metabolism. Lastly, we discuss why understanding the physiological roles played by ion channels is important for understanding the secretory defects that occur in type 2 diabetes. © 2021 American Physiological Society. Compr Physiol 11:1-21, 2021.

NMDA receptor inhibition increases, synchronizes, and stabilizes the collective pancreatic beta cell activity: Insights through multilayer network analysis

NMDA receptors promote repolarization in pancreatic beta cells and thereby reduce glucose-stimulated insulin secretion. Therefore, NMDA receptors are a potential therapeutic target for diabetes. While the mechanism of NMDA receptor inhibition in beta cells is rather well understood at the molecular level, its possible effects on the collective cellular activity have not been addressed to date, even though proper insulin secretion patterns result from well-synchronized beta cell behavior. The latter is enabled by strong intercellular connectivity, which governs propagating calcium waves across the islets and makes the heterogeneous beta cell population work in synchrony. Since a disrupted collective activity is an important and possibly early contributor to impaired insulin secretion and glucose intolerance, it is of utmost importance to understand possible effects of NMDA receptor inhibition on beta cell functional connectivity. To address this issue, we combined confocal functional multicellular calcium imaging in mouse tissue slices with network science approaches. Our results revealed that NMDA receptor inhibition increases, synchronizes, and stabilizes beta cell activity without affecting the velocity or size of calcium waves. To explore intercellular interactions more precisely, we made use of the multilayer network formalism by regarding each calcium wave as an individual network layer, with weighted directed connections portraying the intercellular propagation. NMDA receptor inhibition stabilized both the role of wave initiators and the course of waves. The findings obtained with the experimental antagonist of NMDA receptors, MK-801, were additionally validated with dextrorphan, the active metabolite of the approved drug dextromethorphan, as well as with experiments on NMDA receptor KO mice. In sum, our results provide additional and new evidence for a possible role of NMDA receptor inhibition in treatment of type 2 diabetes and introduce the multilayer network paradigm as a general strategy to examine effects of drugs on connectivity in multicellular systems.

Possible New Strategies for the Treatment of Congenital Hyperinsulinism

OBJECTIVE

Congenital hyperinsulinism (CHI) is a rare disease characterized by persistent hypoglycemia as a result of inappropriate insulin secretion, which can lead to irreversible neurological defects in infants. Poor efficacy and strong adverse effects of the current medications impede successful treatment. The aim of the study was to investigate new approaches to silence β-cells and thus attenuate insulin secretion.

RESEARCH DESIGN AND METHODS

In the scope of our research, we tested substances more selective and more potent than the gold standard diazoxide that also interact with neuroendocrine ATP-sensitive K⁺ (K_ATP) channels. Additionally, K_ATP channel-independent targets as Ca²⁺-activated K⁺ channels of intermediate conductance (K_Ca3.1) and L-type Ca²⁺ channels were investigated. Experiments were performed using human islet cell clusters isolated from tissue of CHI patients (histologically classified as pathological) and islet cell clusters obtained from C57BL/6N (WT) or SUR1 knockout (SUR1^-/-) mice. The cytosolic Ca²⁺ concentration ([Ca²⁺]_c) was used as a parameter for the pathway regulated by electrical activity and was determined by fura-2 fluorescence. The mitochondrial membrane potential (ΔΨ) was determined by rhodamine 123 fluorescence and single channel currents were measured by the patch-clamp technique.

RESULTS

The selective K_ATP channel opener NN414 (5 µM) diminished [Ca²⁺]_c in isolated human CHI islet cell clusters and WT mouse islet cell clusters stimulated with 10 mM glucose. In islet cell clusters lacking functional K_ATP channels (SUR1^-/-) the drug was without effect. VU0071063 (30 µM), another K_ATP channel opener considered to be selective, lowered [Ca²⁺]_c in human CHI islet cell clusters. The compound was also effective in islet cell clusters from SUR1^-/- mice, showing that [Ca²⁺]_c is influenced by additional effects besides K_ATP channels. Contrasting to NN414, the drug depolarized ΔΨ in murine islet cell clusters pointing to severe interference with mitochondrial metabolism. An opener of K_Ca3.1 channels, DCEBIO (100 µM), significantly decreased [Ca²⁺]_c in SUR1^-/- and human CHI islet cell clusters. To target L-type Ca²⁺ channels we tested two already approved drugs, dextromethorphan (DXM) and simvastatin. DXM (100 µM) efficiently diminished [Ca²⁺]_c in stimulated human CHI islet cell clusters as well as in stimulated SUR1^-/- islet cell clusters. Similar effects on [Ca²⁺]_c were observed in experiments with simvastatin (7.2 µM).

CONCLUSIONS

NN414 seems to provide a good alternative to the currently used K_ATP channel opener diazoxide. Targeting K_Ca3.1 channels by channel openers or L-type Ca²⁺ channels by DXM or simvastatin might be valuable approaches for treatment of CHI caused by mutations of K_ATP channels not sensitive to K_ATP channel openers.

Glucose-mediated inhibition of calcium-activated potassium channels limits α-cell calcium influx and glucagon secretion

Pancreatic α-cells exhibit oscillations in cytosolic Ca²⁺ (Ca²⁺_c), which control pulsatile glucagon (GCG) secretion. However, the mechanisms that modulate α-cell Ca²⁺_c oscillations have not been elucidated. As β-cell Ca²⁺_c oscillations are regulated in part by Ca²⁺-activated K⁺ (K_slow) currents, this work investigated the role of K_slow in α-cell Ca²⁺ handling and GCG secretion. α-Cells displayed K_slow currents that were dependent on Ca²⁺ influx through L- and P/Q-type voltage-dependent Ca²⁺ channels (VDCCs) as well as Ca²⁺ released from endoplasmic reticulum stores. α-Cell K_slow was decreased by small-conductance Ca²⁺-activated K⁺ (SK) channel inhibitors apamin and UCL 1684, large-conductance Ca²⁺-activated K⁺ (BK) channel inhibitor iberiotoxin (IbTx), and intermediate-conductance Ca²⁺-activated K⁺ (IK) channel inhibitor TRAM 34. Moreover, partial inhibition of α-cell K_slow with apamin depolarized membrane potential ( V_m) (3.8 ± 0.7 mV) and reduced action potential (AP) amplitude (10.4 ± 1.9 mV). Although apamin transiently increased Ca²⁺ influx into α-cells at low glucose (42.9 ± 10.6%), sustained SK (38.5 ± 10.4%) or BK channel inhibition (31.0 ± 11.7%) decreased α-cell Ca²⁺ influx. Total α-cell Ca²⁺_c was similarly reduced (28.3 ± 11.1%) following prolonged treatment with high glucose, but it was not decreased further by SK or BK channel inhibition. Consistent with reduced α-cell Ca²⁺_c following prolonged K_slow inhibition, apamin decreased GCG secretion from mouse (20.4 ± 4.2%) and human (27.7 ± 13.1%) islets at low glucose. These data demonstrate that K_slow activation provides a hyperpolarizing influence on α-cell V_m that sustains Ca²⁺ entry during hypoglycemic conditions, presumably by preventing voltage-dependent inactivation of P/Q-type VDCCs. Thus, when α-cell Ca²⁺_c is elevated during secretagogue stimulation, K_slow activation helps to preserve GCG secretion.

Cytokine-mediated changes in K+ channel activity promotes an adaptive Ca2+ response that sustains β-cell insulin secretion during inflammation

Cytokines present during low-grade inflammation contribute to β-cell dysfunction and diabetes. Cytokine signaling disrupts β-cell glucose-stimulated Ca2+ influx (GSCI) and endoplasmic reticulum (ER) Ca2+ ([Ca2+]ER) handling, leading to diminished glucose-stimulated insulin secretion (GSIS). However, cytokine-mediated changes in ion channel activity that alter β-cell Ca2+ handling remain unknown. Here we investigated the role of K+ currents in cytokine-mediated β-cell dysfunction. Kslow currents, which control the termination of intracellular Ca2+ ([Ca2+]i) oscillations, were reduced following cytokine exposure. As a consequence, [Ca2+]i and electrical oscillations were accelerated. Cytokine exposure also increased basal islet [Ca2+]i and decreased GSCI. The effect of cytokines on TALK-1 K+ currents were also examined as TALK-1 mediates Kslow by facilitating [Ca2+]ER release. Cytokine exposure decreased KCNK16 transcript abundance and associated TALK-1 protein expression, increasing [Ca2+]ER storage while maintaining 2nd phase GSCI and GSIS. This adaptive Ca2+ response was absent in TALK-1 KO islets, which exhibited decreased 2nd phase GSCI and diminished GSIS. These findings suggest that Kslow and TALK-1 currents play important roles in altered β-cell Ca2+ handling and electrical activity during low-grade inflammation. These results also reveal that a cytokine-mediated reduction in TALK-1 serves an acute protective role in β-cells by facilitating increased Ca2+ content to maintain GSIS.

Pancreatic β-Cell Electrical Activity and Insulin Secretion: Of Mice and Men

The pancreatic β-cell plays a key role in glucose homeostasis by secreting insulin, the only hormone capable of lowering the blood glucose concentration. Impaired insulin secretion results in the chronic hyperglycemia that characterizes type 2 diabetes (T2DM), which currently afflicts >450 million people worldwide. The healthy β-cell acts as a glucose sensor matching its output to the circulating glucose concentration. It does so via metabolically induced changes in electrical activity, which culminate in an increase in the cytoplasmic Ca2+ concentration and initiation of Ca2+-dependent exocytosis of insulin-containing secretory granules. Here, we review recent advances in our understanding of the β-cell transcriptome, electrical activity, and insulin exocytosis. We highlight salient differences between mouse and human β-cells, provide models of how the different ion channels contribute to their electrical activity and insulin secretion, and conclude by discussing how these processes become perturbed in T2DM.

Mathematical modeling of white adipocyte exocytosis predicts adiponectin secretion and quantifies the rates of vesicle exo- and endocytosis

Adiponectin is a hormone secreted from white adipocytes and takes part in the regulation of several metabolic processes. Although the pathophysiological importance of adiponectin has been thoroughly investigated, the mechanisms controlling its release are only partly understood. We have recently shown that adiponectin is secreted via regulated exocytosis of adiponectin-containing vesicles, that adiponectin exocytosis is stimulated by cAMP-dependent mechanisms, and that Ca²⁺ and ATP augment the cAMP-triggered secretion. However, much remains to be discovered regarding the molecular and cellular regulation of adiponectin release. Here, we have used mathematical modeling to extract detailed information contained within our previously obtained high-resolution patch-clamp time-resolved capacitance recordings to produce the first model of adiponectin exocytosis/secretion that combines all mechanistic knowledge deduced from electrophysiological experimental series. This model demonstrates that our previous understanding of the role of intracellular ATP in the control of adiponectin exocytosis needs to be revised to include an additional ATP-dependent step. Validation of the model by introduction of data of secreted adiponectin yielded a very close resemblance between the simulations and experimental results. Moreover, we could show that Ca²⁺-dependent adiponectin endocytosis contributes to the measured capacitance signal, and we were able to predict the contribution of endocytosis to the measured exocytotic rate under different experimental conditions. In conclusion, using mathematical modeling of published and newly generated data, we have obtained estimates of adiponectin exo- and endocytosis rates, and we have predicted adiponectin secretion. We believe that our model should have multiple applications in the study of metabolic processes and hormonal control thereof.

TALK-1 channels control β cell endoplasmic reticulum Ca2+ homeostasis

Ca2+ handling by the endoplasmic reticulum (ER) serves critical roles in controlling pancreatic β cell function and becomes perturbed during the pathogenesis of diabetes. ER Ca2+ homeostasis is determined by ion movements across the ER membrane, including K+ flux through K+ channels. We demonstrated that K+ flux through ER-localized TALK-1 channels facilitated Ca2+ release from the ER in mouse and human β cells. We found that β cells from mice lacking TALK-1 exhibited reduced basal cytosolic Ca2+ and increased ER Ca2+ concentrations, suggesting reduced ER Ca2+ leak. These changes in Ca2+ homeostasis were presumably due to TALK-1-mediated ER K+ flux, because we recorded K+ currents mediated by functional TALK-1 channels on the nuclear membrane, which is continuous with the ER. Moreover, overexpression of K+-impermeable TALK-1 channels in HEK293 cells did not reduce ER Ca2+ stores. Reduced ER Ca2+ content in β cells is associated with ER stress and islet dysfunction in diabetes, and islets from TALK-1-deficient mice fed a high-fat diet showed reduced signs of ER stress, suggesting that TALK-1 activity exacerbated ER stress. Our data establish TALK-1 channels as key regulators of β cell ER Ca2+ and suggest that TALK-1 may be a therapeutic target to reduce ER Ca2+ handling defects in β cells during the pathogenesis of diabetes.

Modeling of glucose-induced cAMP oscillations in pancreatic β cells: cAMP rocks when metabolism rolls

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.

Episodic hormone secretion: a comparison of the basis of pulsatile secretion of insulin and GnRH

Rhythms govern many endocrine functions. Examples of such rhythmic systems include the insulin-secreting pancreatic beta-cell, which regulates blood glucose, and the gonadotropin-releasing hormone (GnRH) neuron, which governs reproductive function. Although serving very different functions within the body, these cell types share many important features. Both GnRH neurons and beta-cells, for instance, are hypothesized to generate at least two rhythms endogenously: (1) a burst firing electrical rhythm and (2) a slower rhythm involving metabolic or other intracellular processes. This review discusses the importance of hormone rhythms to both physiology and disease and compares and contrasts the rhythms generated by each system.

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.

K(ATP) channels and islet hormone secretion: new insights and controversies

ATP-sensitive potassium channels (K(ATP) channels) link cell metabolism to electrical activity by controlling the cell membrane potential. They participate in many physiological processes but have a particularly important role in systemic glucose homeostasis by regulating hormone secretion from pancreatic islet cells. Glucose-induced closure of K(ATP) channels is crucial for insulin secretion. Emerging data suggest that K(ATP) channels also play a key part in glucagon secretion, although precisely how they do so remains controversial. This Review highlights the role of K(ATP) channels in insulin and glucagon secretion. We discuss how K(ATP) channels might contribute not only to the initiation of insulin release but also to the graded stimulation of insulin secretion that occurs with increasing glucose concentrations. The various hypotheses concerning the role of K(ATP) channels in glucagon release are also reviewed. Furthermore, we illustrate how mutations in K(ATP) channel genes can cause hyposecretion or hypersecretion of insulin, as in neonatal diabetes mellitus and congenital hyperinsulinism, and how defective metabolic regulation of the channel may underlie the hypoinsulinaemia and the hyperglucagonaemia that characterize type 2 diabetes mellitus. Finally, we outline how sulphonylureas, which inhibit K(ATP) channels, stimulate insulin secretion in patients with neonatal diabetes mellitus or type 2 diabetes mellitus, and suggest their potential use to target the glucagon secretory defects found in diabetes mellitus.

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.

Regulation of insulin secretion in human pancreatic islets

Pancreatic β cells secrete insulin, the body's only hormone capable of lowering plasma glucose levels. Impaired or insufficient insulin secretion results in diabetes mellitus. The β cell is electrically excitable; in response to an elevation of glucose, it depolarizes and starts generating action potentials. The electrophysiology of mouse β cells and the cell's role in insulin secretion have been extensively investigated. More recently, similar studies have been performed on human β cells. These studies have revealed numerous and important differences between human and rodent β cells. Here we discuss the properties of human pancreatic β cells: their glucose sensing, the ion channel complement underlying glucose-induced electrical activity that culminates in exocytotic release of insulin, the cellular control of exocytosis, and the modulation of insulin secretion by circulating hormones and locally released neurotransmitters. Finally, we consider the pathophysiology of insulin secretion and the interactions between genetics and environmental factors that may explain the current diabetes epidemic.

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

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

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

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

Analyzing electrical activities of pancreatic β cells using mathematical models

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

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

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

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

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

BK channels mediate a novel ionic mechanism that regulates glucose-dependent electrical activity and insulin secretion in mouse pancreatic β-cells

BK channels are large unitary conductance K(+) channels cooperatively activated by intracellular calcium and membrane depolarisation. We show that BK channels regulate electrical activity in β-cells of mouse pancreatic islets exposed to elevated glucose. In 11.1 mM glucose, the non-peptidyl BK channel blocker paxilline increased the height of β-cell action potentials (APs) by 21 mV without affecting burst- or silent-period durations. In isolated β-cells, paxilline increased AP height by 16 mV without affecting resting membrane potential. In voltage clamp, paxilline blocked a transient component of outward current activated by a short depolarisation, which accounted for at least 90% of the initial outward K(+) current. This BK current (I(BK)) was blocked by the Ca(2+) channel blockers Cd(2+) (200 μM) or nimodipine (1 μM), and potentiated by FPL-64176 (1 μM). I(BK) was also 56% blocked by the BK channel blocker iberiotoxin (100 nM). I(BK) activated more than 10-fold faster than the delayed rectifier I(Kv) over the physiological voltage range, and partially inactivated. An AP-like command revealed that I(BK) activated and deactivated faster than I(Kv) and accounted for 86% of peak I(K), explaining why I(BK) block increased AP height. A higher amplitude AP-like command, patterned on an AP recorded in 11.1 mM glucose plus paxilline, activated 4-fold more I(Kv) and significantly increased Ca(2+) entry. Paxilline increased insulin secretion in islets exposed to 11.1 mM glucose by 67%, but did not affect basal secretion in 2.8 mM glucose. These data suggest a modified model of β-cell AP generation where I(BK) and I(Kv) coordinate the AP repolarisation.

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.

Electrophysiology of islet cells

Stimulus-Secretion Coupling (SSC) of pancreatic islet cells comprises electrical activity. Changes of the membrane potential (V(m)) are regulated by metabolism-dependent alterations in ion channel activity. This coupling is best explored in beta-cells. The effect of glucose is directly linked to mitochondrial metabolism as the ATP/ADP ratio determines the open probability of ATP-sensitive K(+) channels (K(ATP) channels). Nucleotide sensitivity and concentration in the direct vicinity of the channels are controlled by several factors including phospholipids, fatty acids, and kinases, e.g., creatine and adenylate kinase. Closure of K(ATP) channels leads to depolarization of beta-cells via a yet unknown depolarizing current. Ca(2+) influx during action potentials (APs) results in an increase of the cytosolic Ca(2+) concentration ([Ca(2+)](c)) that triggers exocytosis. APs are elicited by the opening of voltage-dependent Na(+) and/or Ca(2+) channels and repolarized by voltage- and/or Ca(2+)-dependent K(+) channels. At a constant stimulatory glucose concentration APs are clustered in bursts that are interrupted by hyperpolarized interburst phases. Bursting electrical activity induces parallel fluctuations in [Ca(2+)](c) and insulin secretion. Bursts are terminated by I(Kslow) consisting of currents through Ca(2+)-dependent K(+) channels and K(ATP) channels. This review focuses on structure, characteristics, physiological function, and regulation of ion channels in beta-cells. Information about pharmacological drugs acting on K(ATP) channels, K(ATP) channelopathies, and influence of oxidative stress on K(ATP) channel function is provided. One focus is the outstanding significance of L-type Ca(2+) channels for insulin secretion. The role of less well characterized beta-cell channels including voltage-dependent Na(+) channels, volume sensitive anion channels (VSACs), transient receptor potential (TRP)-related channels, and hyperpolarization-activated cyclic nucleotide-gated (HCN) channels is discussed. A model of beta-cell oscillations provides insight in the interplay of the different channels to induce and maintain electrical activity. Regulation of beta-cell electrical activity by hormones and the autonomous nervous system is discussed. alpha- and delta-cells are also equipped with K(ATP) channels, voltage-dependent Na(+), K(+), and Ca(2+) channels. Yet the SSC of these cells is less clear and is not necessarily dependent on K(ATP) channel closure. Different ion channels of alpha- and delta-cells are introduced and SSC in alpha-cells is described in special respect of paracrine effects of insulin and GABA secreted from beta-cells.

Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.

Shortcomings of current models of glucose-induced insulin secretion

Glucose-induced insulin secretion by pancreatic beta-cells is generally schematized by a 'consensus model' that involves the following sequence of events: acceleration of glucose metabolism, closure of ATP-sensitive potassium channels (K(ATP) channels) in the plasma membrane, depolarization, influx of Ca(2+) through voltage-dependent calcium channels and a rise in cytosolic-free Ca(2+) concentration that induces exocytosis of insulin-containing granules. This model adequately depicts the essential triggering pathway but is incomplete. In this article, we first make a case for a model of dual regulation in which a metabolic amplifying pathway is also activated by glucose and augments the secretory response to the triggering Ca(2+) signal under physiological conditions. We next discuss experimental evidence, largely but not exclusively obtained from beta-cells lacking K(ATP) channels, which indicates that these channels are not the only possible transducers of glucose effects on the triggering Ca(2+)signal. We finally address the identity of the widely neglected background inward current (Cl(-) efflux vs. Na(+) or Ca(2+) influx through voltage-independent channels) that is necessary to cause beta-cell depolarization when glucose closes K(ATP) channels. More attention should be paid to the possibility that some components of this background current are influenced by glucose metabolism and have their place in a model of glucose-induced insulin secretion.

Evidence of diminished glucose stimulation and endoplasmic reticulum function in nonoscillatory pancreatic islets

Pulsatility is a fundamental feature of pancreatic islets and a hallmark of hormone secretion. Isolated pancreatic islets endogenously generate rhythms in secretion, metabolic activity, and intracellular calcium ([Ca(2+)](i)) that are important to normal physiological function. Few studies have directly compared oscillatory and nonoscillatory islets to identify possible differences in function. We investigated the hypothesis that the loss of these oscillations is a leading indicator of islet dysfunction by comparing oscillatory and nonoscillatory mouse islets for multiple parameters of function. Nonoscillatory islets displayed elevated basal [Ca(2+)](i) and diminished [Ca(2+)](i) response and insulin secretory response to 3-28 mm glucose stimulation compared with oscillatory islets, suggesting diminished glucose sensitivity. We investigated several possible mechanisms to explain these differences. No differences were observed in mitochondrial membrane potential, estimated ATP-sensitive potassium channel and L-type calcium channel activity, or cell death rates. Nonoscillatory islets, however, showed a reduced response to the sarco(endo)plasmic reticulum calcium ATPase inhibitor thapsigargin, suggesting a disruption in calcium homeostasis in the endoplasmic reticulum (ER) compared with oscillatory islets. The diminished ER calcium homeostasis among nonoscillatory islets was also consistent with the higher cytosolic calcium levels observed in 3 mm glucose. Inducing mild damage with low-dose proinflammatory cytokines reduced islet oscillatory capacity and produced similar effects on glucose-stimulated [Ca(2+)](i), basal [Ca(2+)](i), and thapsigargin response observed among untreated nonoscillatory islets. Our data suggest the loss of oscillatory capacity may be an early indicator of diminished islet glucose sensitivity and ER dysfunction, suggesting targets to improve islet assessment.

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.

Depletion of SK1 channel subunits leads to constitutive insulin secretion

In the pancreas, the role of the small-conductance, calcium-activated SK channels remains controversial. Here, we show that three SK subtypes are expressed in the rat insulinoma cells. Our findings demonstrate that rat SK1 (rSK1) channels ensure appropriate insulin secretion by establishing the cell's negative resting membrane potential and shortening the duration of the action potential. We also found that the depletion of rSK1 transcripts generated a condition in which beta cells constitutively secrete insulin, even in the absence of a stimulating molecule (such as glucose). Together, these results implicate SK1 subunits as key regulators of excitability and endocrine function in beta cells.

Cell coupling in mouse pancreatic beta-cells measured in intact islets of Langerhans

The perforated whole-cell configuration of the patch-clamp technique was applied to functionally identified beta-cells in intact mouse pancreatic islets to study the extent of cell coupling between adjacent beta-cells. Using a combination of current- and voltage-clamp recordings, the total gap junctional conductance between beta-cells in an islet was estimated to be 1.22 nS. The analysis of the current waveforms in a voltage-clamped cell (due to the firing of an action potential in a neighbouring cell) suggested that the gap junctional conductance between a pair of beta-cells was 0.17 nS. Subthreshold voltage-clamp depolarization (to -55 mV) gave rise to a slow capacitive current indicative of coupling between beta-cells, but not in non-beta-cells, with a time constant of 13.5 ms and a total charge movement of 0.2 pC. Our data suggest that a superficial beta-cell in an islet is in electrical contact with six to seven other beta-cells. No evidence for dye coupling was obtained when cells were dialysed with Lucifer yellow even when electrical coupling was apparent. The correction of the measured resting conductance for the contribution of the gap junctional conductance indicated that the whole-cell KATP channel conductance (GK,ATP) falls from approximately 2.5 nS in the absence of glucose to 0.1 nS at 15 mM glucose with an estimated IC50 of approximately 4mM. Theoretical considerations indicate that the coupling between beta-cells within the islet is sufficient to allow propagation of [Ca2+]i waves to spread with a speed of approximately 80 microms-1, similar to that observed experimentally in confocal [Ca2+]i imaging.

Regulation by glucose of oscillatory electrical activity and 5-HT/insulin release from single mouse pancreatic islets in absence of functional K(ATP) channels

The glucose sensitivity of bursting electrical activity and pulsatile insulin release from pancreatic islets was determined in absence of functional K(ATP) channels. Membrane potential, [Ca(2+)](i) and 5-HT/insulin release were measured by intracellular recording, fura-2 fluorescence and 5-HT amperometry, respectively. Single mouse islets, bathed in tolbutamide or glibenclamide and high extracellular Ca(2+) (Ca(2+)(o)), displayed bursting activity and concomitant fast [Ca(2+)](i) and 5-HT/insulin oscillations. Sulphonylurea block of K(ATP) channel current was unaffected by raising Ca(2+)(o). Raising glucose or alpha-ketoisocaproic acid (KIC) concentration from 3 to 30 mM increased spiking activity and burst plateau duration. Staurosporine did not impair glucose potentiation of electrical activity, ruling out the involvement of serine/threonine kinases. Glucose enhanced both [Ca(2+)](i) and 5-HT/insulin oscillatory activity, causing a approximately 3-fold increase in overall 5-HT release rate. Cells lacking bursting activity in high Ca(2+)(o) and low glucose (or KIC) developed a pattern of intensified spiking in response to 11 mM glucose. It is concluded that beta-cells exhibit graded oscillatory electrical and secretory responses to glucose in absence of functional K(ATP) channels. This suggests that, under physiological conditions, early glucose sensing may involve other channels besides the K(ATP) channel.

Direct regulation of BK channels by phosphatidylinositol 4,5-bisphosphate as a novel signaling pathway

Large conductance, calcium- and voltage-gated potassium (BK) channels are ubiquitous and critical for neuronal function, immunity, and smooth muscle contractility. BK channels are thought to be regulated by phosphatidylinositol 4,5-bisphosphate (PIP(2)) only through phospholipase C (PLC)-generated PIP(2) metabolites that target Ca(2+) stores and protein kinase C and, eventually, the BK channel. Here, we report that PIP(2) activates BK channels independently of PIP(2) metabolites. PIP(2) enhances Ca(2+)-driven gating and alters both open and closed channel distributions without affecting voltage gating and unitary conductance. Recovery from activation was strongly dependent on PIP(2) acyl chain length, with channels exposed to water-soluble diC4 and diC8 showing much faster recovery than those exposed to PIP(2) (diC16). The PIP(2)-channel interaction requires negative charge and the inositol moiety in the phospholipid headgroup, and the sequence RKK in the S6-S7 cytosolic linker of the BK channel-forming (cbv1) subunit. PIP(2)-induced activation is drastically potentiated by accessory beta(1) (but not beta(4)) channel subunits. Moreover, PIP(2) robustly activates BK channels in vascular myocytes, where beta(1) subunits are abundantly expressed, but not in skeletal myocytes, where these subunits are barely detectable. These data demonstrate that the final PIP(2) effect is determined by channel accessory subunits, and such mechanism is subunit specific. In HEK293 cells, cotransfection of cbv1+beta(1) and PI4-kinaseIIalpha robustly activates BK channels, suggesting a role for endogenous PIP(2) in modulating channel activity. Indeed, in membrane patches excised from vascular myocytes, BK channel activity runs down and Mg-ATP recovers it, this recovery being abolished by PIP(2) antibodies applied to the cytosolic membrane surface. Moreover, in intact arterial myocytes under physiological conditions, PLC inhibition on top of blockade of downstream signaling leads to drastic BK channel activation. Finally, pharmacological treatment that raises PIP(2) levels and activates BK channels dilates de-endothelized arteries that regulate cerebral blood flow. These data indicate that endogenous PIP(2) directly activates vascular myocyte BK channels to control vascular tone.

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.

Glucose stimulates Ca2+ influx and insulin secretion in 2-week-old beta-cells lacking ATP-sensitive K+ channels

In adult beta-cells glucose-induced insulin secretion involves two mechanisms (a) a K(ATP) channel-dependent Ca(2+) influx and rise of cytosolic [Ca(2+)](c) and (b) a K(ATP) channel-independent amplification of secretion without further increase of [Ca(2+)](c). Mice lacking the high affinity sulfonylurea receptor (Sur1KO), and thus K(ATP) channels, have been developed as a model of congenital hyperinsulinism. Here, we compared [Ca(2+)](c) and insulin secretion in overnight cultured islets from 2-week-old normal and Sur1KO mice. Control islets proved functionally mature: the magnitude and biphasic kinetics of [Ca(2+)](c) and insulin secretion changes induced by glucose, and operation of the amplifying pathway, were similar to adult islets. Sur1KO islets perifused with 1 mm glucose showed elevation of both basal [Ca(2+)](c) and insulin secretion. Stimulation with 15 mm glucose produced a transient drop of [Ca(2+)](c) followed by an overshoot and a sustained elevation, accompanied by a monophasic, 6-fold increase in insulin secretion. Glucose also increased insulin secretion when [Ca(2+)](c) was clamped by KCl. When Sur1KO islets were cultured in 5 instead of 10 mm glucose, [Ca(2+)](c) and insulin secretion were unexpectedly low in 1 mm glucose and increased following a biphasic time course upon stimulation by 15 mm glucose. This K(ATP) channel-independent first phase [Ca(2+)](c) rise was attributed to a Na(+)-, Cl(-)-, and Na(+)-pump-independent depolarization of beta-cells, leading to Ca(2+) influx through voltage-dependent calcium channels. Glucose indeed depolarized Sur1KO islets under these conditions. It is suggested that unidentified potassium channels are sensitive to glucose and subserve the acute and long-term metabolic control of [Ca(2+)](c) in beta-cells without functional K(ATP) channels.

Ca2+ microdomains and the control of insulin secretion

Nutrient-induced increases in intracellular free Ca(2+) concentrations are the key trigger for insulin release from pancreatic islet beta-cells. These Ca(2+) changes are tightly regulated temporally, occurring as Ca(2+) influx-dependent baseline oscillations. We explore here the concept that locally high [Ca(2+)] concentrations (i.e. Ca(2+) microdomains) may control exocytosis via the recruitment of key effector proteins to sites of exocytosis. Importantly, recent advances in the development of organelle- and membrane-targeted green fluorescent protein (GFP-) or aequorin-based Ca(2+) indicators, as well as in rapid imaging techniques, are providing new insights into the potential role of these Ca(2+) microdomains in beta-cells. We summarise here some of the evidence indicating that Ca(2+) microdomains beneath the plasma membrane and at the surface of large dense core vesicles may be important in the normal regulation of insulin secretion, and may conceivably contribute to "ATP-sensitive K(+)-channel independent" effects of glucose. We also discuss evidence that, in contrast to certain non-excitable cells, direct transfer of Ca(2+) from the ER to mitochondria via localised physical contacts between these organelles is relatively less important for efficient mitochondrial Ca(2+) uptake in beta-cells. Finally, we discuss evidence from single cell imaging that increases in cytosolic Ca(2+) are not required for the upstroke of oscillations in mitochondrial redox state, but may underlie the reoxidation process.

ABCC8 and ABCC9: ABC transporters that regulate K+ channels

The sulfonylurea receptors (SURs) ABCC8/SUR1 and ABCC9/SUR2 are members of the C-branch of the transport adenosine triphosphatase superfamily. Unlike their brethren, the SURs have no identified transport function; instead, evolution has matched these molecules with K(+) selective pores, either K(IR)6.1/KCNJ8 or K(IR)6.2/KCNJ11, to assemble adenosine triphosphate (ATP)-sensitive K(+) channels found in endocrine cells, neurons, and both smooth and striated muscle. Adenine nucleotides, the major regulators of ATP-sensitive K(+) (K(ATP)) channel activity, exert a dual action. Nucleotide binding to the pore reduces the activity or channel open probability, whereas Mg-nucleotide binding and/or hydrolysis in the nucleotide-binding domains of SUR antagonize this inhibitory action to stimulate channel openings. Mutations in either subunit can alter this balance and, in the case of the SUR1/KIR6.2 channels found in neurons and insulin-secreting pancreatic beta cells, are the cause of monogenic forms of hyperinsulinemic hypoglycemia and neonatal diabetes. Additionally, the subtle dysregulation of K(ATP) channel activity by a K(IR)6.2 polymorphism has been suggested as a predisposing factor in type 2 diabetes mellitus. Studies on K(ATP) channel null mice are clarifying the roles of these metabolically sensitive channels in a variety of tissues.

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.

Total insulin and IGF-I resistance in pancreatic beta cells causes overt diabetes

An appropriate beta cell mass is pivotal for the maintenance of glucose homeostasis. Both insulin and IGF-1 are important in regulation of beta cell growth and function (reviewed in ref. 2). To define the roles of these hormones directly, we created a mouse model lacking functional receptors for both insulin and IGF-1 only in beta cells (betaDKO), as the hormones have overlapping mechanisms of action and activate common downstream proteins. Notably, betaDKO mice were born with a normal complement of islet cells, but 3 weeks after birth, they developed diabetes, in contrast to mild phenotypes observed in single mutants. Normoglycemic 2-week-old betaDKO mice manifest reduced beta cell mass, reduced expression of phosphorylated Akt and the transcription factor MafA, increased apoptosis in islets and severely compromised beta cell function. Analyses of compound knockouts showed a dominant role for insulin signaling in regulating beta cell mass. Together, these data provide compelling genetic evidence that insulin and IGF-I-dependent pathways are not critical for development of beta cells but that a loss of action of these hormones in beta cells leads to diabetes. We propose that therapeutic improvement of insulin and IGF-I signaling in beta cells might protect against type 2 diabetes.

Pharmacological properties and functional role of Kslow current in mouse pancreatic beta-cells: SK channels contribute to Kslow tail current and modulate insulin secretion

The pharmacological properties of slow Ca²⁺-activated K⁺ current (K_slow) were investigated in mouse pancreatic β-cells and islets to understand how K_slow contributes to the control of islet bursting, [Ca²⁺]_i oscillations, and insulin secretion. K_slow was insensitive to apamin or the K_ATP channel inhibitor tolbutamide, but UCL 1684, a potent and selective nonpeptide SK channel blocker reduced the amplitude of K_slow tail current in voltage-clamped mouse β-cells. K_slow was also selectively and reversibly inhibited by the class III antiarrythmic agent azimilide (AZ). In isolated β-cells or islets, pharmacologic inhibition of K_slow by UCL 1684 or AZ depolarized β-cell silent phase potential, increased action potential firing, raised [Ca²⁺]_i, and enhanced glucose-dependent insulin secretion. AZ inhibition of K_slow also supported mediation by SK, rather than cardiac-like slow delayed rectifier channels since bath application of AZ to HEK 293 cells expressing SK3 cDNA reduced SK current. Further, AZ-sensitive K_slow current was extant in β-cells from KCNQ1 or KCNE1 null mice lacking cardiac slow delayed rectifier currents. These results strongly support a functional role for SK channel-mediated K_slow current in β-cells, and suggest that drugs that target SK channels may represent a new approach for increasing glucose-dependent insulin secretion. The apamin insensitivity of β-cell SK current suggests that β-cells express a unique SK splice variant or a novel heteromultimer consisting of different SK subunits.

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

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

Crosstalk between membrane potential and cytosolic Ca2+ concentration in beta cells from Sur1-/- mice

AIMS/HYPOTHESIS

Islets or beta cells from Sur1(-/-) mice were used to determine whether changes in plasma membrane potential (V(m)) remain coupled to changes in cytosolic Ca(2+) ([Ca(2+)](i)) in the absence of K(ATP) channels and thus provide a triggering signal for insulin secretion. The study also sought to elucidate whether [Ca(2+)](i) influences oscillations in V(m) in sur1(-/-) beta cells.

METHODS

Plasma membrane potential and ion currents were measured with microelectrodes and the patch-clamp technique. [Ca(2+)](i) was monitored with the fluorescent dye fura-2. Insulin secretion from isolated islets was determined by static incubations.

RESULTS

Membrane depolarisation of Sur1(-/-) islets by arginine or increased extracellular K(+), elevated [Ca(2+)](i) and augmented insulin secretion. Oligomycin completely abolished glucose-stimulated insulin release from Sur1(-/-) islets. Oscillations in V(m) were influenced by [Ca(2+)](i) as follows: (1) elevation of extracellular Ca(2+) lengthened phases of membrane hyperpolarisation; (2) simulating a burst of action potentials induced a Ca(2+)-dependent outward current that was augmented by increased Ca(2+) influx through L-type Ca(2+) channels; (3) Ca(2+) depletion of intracellular stores by cyclopiazonic acid increased the burst frequency in Sur1(-/-) islets, elevating [Ca(2+)](i) and insulin secretion; (4) store depletion activated a Ca(2+) influx that was not inhibitable by the L-type Ca(2+) channel blocker D600.

CONCLUSIONS/INTERPRETATION

Although V(m) is largely uncoupled from glucose metabolism in the absence of K(ATP) channels, increased electrical activity leads to elevations of [Ca(2+)](i) that are sufficient to stimulate insulin secretion. In Sur1(-/-) beta cells, [Ca(2+)](i) exerts feedback mechanisms on V(m) by activating a hyperpolarising outward current and by depolarising V(m) via store-operated ion channels.

Substrate effects on oscillations in metabolism, calcium and secretion in single mouse islets of Langerhans

Glucose induces complex patterns of oscillations in intracellular Ca2+ concentration ([Ca2+]i), metabolism and secretion in islets of Langerhans including "slow" and "fast" pulses with period of 2-5 min and 10-20 s respectively. In an effort to elucidate the origin of slow oscillations, individual mouse islets were exposed to different fuels including glyceraldehyde, pyruvate, methyl pyruvate and alpha-ketoisocaproate (KIC), all of which bypass key steps of glycolytic metabolism, while monitoring [Ca2+]i, oxygen consumption and secretion. Glyceraldehyde gave rise to slow oscillations only when substimulatory glucose was also added to the media. Glucosamine, an inhibitor of glucokinase, blocked these slow oscillations. KIC, pyruvate, and methyl pyruvate did not give rise to slow oscillations alone or with glucose present. The addition of glucose to islets bathed in nutrient-rich cell culture media accelerated metabolism and initiated slow oscillations while glyceraldehyde did not. It is concluded that glucose has a special role in accelerating metabolism and generating slow oscillations in isolated islets of Langerhans from mice. Combined with previous observations of Ca2+ dependency for all oscillations in islets, we propose that interactions between Ca2+ influx and glycolysis are responsible for the slow oscillations. In contrast, fast oscillations can occur independent of glycolytic flux.

Three roads to islet bursting: emergent oscillations in coupled phantom bursters

Glucose-induced membrane potential and Ca(2+) oscillations in isolated pancreatic beta-cells occur over a wide range of frequencies, from >6/min (fast) to <1/min (slow). However, cells within intact islets generally oscillate with periods of 10-60 s (medium). The phantom bursting concept addresses how beta-cells can generate such a wide range of frequencies. Here, we explore an updated phantom bursting model to determine how heterogeneity in a single parameter can explain both the broad frequency range observed in single cells and the rarity of medium oscillations. We then incorporate the single-cell model into an islet model with parameter heterogeneity. We show that strongly coupled islets must be composed of predominantly medium oscillating single cells or a mixture of fast and slow cells to robustly produce medium oscillations. Surprisingly, we find that this constraint does not hold for moderate coupling, and that robustly medium oscillating islets can arise from populations of single cells that are essentially all slow or all fast. Thus, with coupled phantom bursters, medium oscillating islets can be constructed out of cells that are either all fast, all slow, or a combination of the two.

Wave speeds of density dependent Nagumo diffusion equations – inspired by oscillating gap-junction conductance in the islets of Langerhans

The equation ut = (D(u)ux)x + f(u) arises in several biological examples and is known to have wave solutions for appropriate D and f. We give here a new formula for finding an approximation to the wave speed, relevant for comparing experiments with model simulations. This is done in details for the simple example D(u) = u + k and an N-shaped f, derived from a model of coupled pancreatic beta-cells, where the coupling conductance follows the electrical activity as it is found in experiments. On the way, we claim that the wave speed does not depend on the parameter g(K,ATP), mimicking the glucose concentration in the islet, in sharp contrast to the claim set forth in the article by Aslanidi et al.

Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

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

Filtering of calcium transients by the endoplasmic reticulum in pancreatic beta-cells

Calcium handling in pancreatic beta-cells is important for intracellular signaling, the control of electrical activity, and insulin secretion. The endoplasmic reticulum (ER) is a key organelle involved in the storage and release of intracellular Ca2+. Using mathematical modeling, we analyze the filtering properties of the ER and clarify the dual role that it plays as both a Ca2+ source and a Ca2+ sink. We demonstrate that recent time-dependent data on the free Ca2+ concentration in pancreatic islets and beta-cell clusters can be explained with a model that uses a passive ER that takes up Ca2+ when the cell is depolarized and the cytosolic Ca2+ concentration is elevated, and releases Ca2+ when the cell is repolarized and the cytosolic Ca2+ is at a lower concentration. We find that Ca2+-induced Ca2+ release is not necessary to explain the data, and indeed the model is inconsistent with the data if Ca2+-induced Ca2+ release is a dominating factor. Finally, we show that a three-compartment model that includes a subspace compartment between the ER and the plasma membrane provides the best agreement with the experimental Ca2+ data.

Complex bursting in pancreatic islets: a potential glycolytic mechanism

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis.

Microfluidic glucose stimulation reveals limited coordination of intracellular Ca2+ activity oscillations in pancreatic islets

The pancreatic islet is a functional microorgan involved in maintaining normoglycemia through regulated secretion of insulin and other hormones. Extracellular glucose stimulates insulin secretion from islet beta cells through an increase in redox state, which can be measured by NAD(P)H autofluorescence. Glucose concentrations over approximately 7 mM generate synchronous oscillations in beta cell intracellular Ca2+ concentration ([Ca2+]i), which lead to pulsatile insulin secretion. Prevailing models assume that the pancreatic islet acts as a functional syncytium, and the whole islet [Ca2+]i response has been modeled in terms of islet bursting and pacemaker models. To test these models, we developed a microfluidic device capable of partially stimulating an islet, while allowing observation of the NAD(P)H and [Ca2+]i responses. We show that beta cell [Ca2+]i oscillations occur only within regions stimulated with more than approximately 6.6 mM glucose. Furthermore, we show that tolbutamide, an antagonist of the ATP-sensitive K+ channel, allows these oscillations to travel farther into the nonstimulated regions of the islet. Our approach shows that the extent of Ca2+ propagation across the islet depends on a delicate interaction between the degree of coupling and the extent of ATP-sensitive K+-channel activation and illustrates an experimental paradigm that will have utility for many other biological systems.

Insulin feedback alters mitochondrial activity through an ATP-sensitive K+ channel-dependent pathway in mouse islets and beta-cells

Recent work suggests that insulin may exert both positive and negative feedback directly on pancreatic beta-cells. To investigate the hypothesis that insulin modulates beta-cell metabolism, mouse islets and beta-cell clusters were loaded with rhodamine 123 to dynamically monitor mitochondrial membrane potential (DeltaPsi(m)). Spontaneous oscillations in DeltaPsi(m) (period: 218 +/- 26 s) were observed in 17 of 30 islets exposed to 11.1 mmol/l glucose. Acute insulin application (100 nmol/l) hyperpolarized DeltaPsi(m), indicating a change in mitochondrial activity. The ATP-sensitive K(+) (K(ATP)) channel opener diazoxide or the l-type calcium channel blocker nifedipine mimicked the effect of insulin, suggesting that insulin activates K(ATP) channels to hyperpolarize DeltaPsi(m) by inhibiting calcium influx. Treatment with forskolin, which increases endogenous insulin secretion, also mimicked the effect of exogenous insulin, suggesting physiological feedback. Pretreatment with nifedipine or the K(ATP) inhibitor glyburide prevented insulin action, further implicating a K(ATP) channel pathway. Together, these data suggest a feedback mechanism whereby insulin receptor activation opens K(ATP) channels to inhibit further secretion. The resulting reduction in beta-cell calcium increases the energy stored in the mitochondrial gradient that drives ATP production. Insulin feedback onto mitochondria may thus help to calibrate the energy needs of the beta-cell on a minute-to-minute basis.

Oscillations of membrane potential and cytosolic Ca(2+) concentration in SUR1(-/-) beta cells

AIMS/HYPOTHESIS

SUR1(ABCC8)(-/-) mice lacking functional K(ATP) channels are an appropriate model to test the significance of K(ATP) channels in beta-cell function. We examined how this gene deletion interferes with stimulus-secretion coupling. We tested the influence of metabolic inhibition and galanin, whose mode of action is controversial.

METHODS

Plasma membrane potential (Vm) and currents were measured with microelectrodes or the patch-clamp technique; cytosolic Ca(2+) concentrations ([Ca(2+)](c)) and mitochondrial membrane potential (DeltaPsi) were measured using fluorescent dyes.

RESULTS

In contrast to the controls, SUR1(-/-) beta cells showed electrical activity even at a low glucose concentration. Continuous spike activity was measured with the patch-clamp technique, but with microelectrodes slow oscillations in Vm consisting of bursts of Ca(2+)-dependent action potentials were detected. [Ca(2+)](c) showed various patterns of oscillations or a sustained increase. Sodium azide did not hyperpolarize SUR1(-/-) beta cells. The depolarization of DeltaPsi evoked by sodium azide was significantly lower in SUR1(-/-) than SUR1(+/+) cells. Galanin transiently decreased action potential frequency and [Ca(2+)](c) in cells from both SUR1(-/-) and SUR1(+/+) mice.

CONCLUSION/INTERPRETATION

The strong dependence of Vm and [Ca(2+)](c) on glucose concentration observed in SUR1(+/+) beta cells is disrupted in the knock-out cells. This demonstrates that both parameters oscillate in the absence of functional K(ATP) channels. The lack of effect of metabolic inhibition by sodium azide shows that in SUR1(-/-) beta cells changes in ATP/ADP no longer link glucose metabolism and Vm. The results with galanin suggest that this peptide affects beta cells independently of K(ATP) currents and thus could contribute to the regulation of beta-cell function in SUR1(-/-) animals.