Calcium and delayed potassium currents in mouse pancreatic beta-cells under voltage-clamp conditions

The Dynamics of Calcium Signaling in Beta Cells-A Discussion on the Comparison of Experimental and Modelling Data

The stimulus-secretion coupling of the pancreatic beta cell is particularly complex, as it integrates the availability of glucose and other nutrients with the neuronal and hormonal input to generate rates of insulin secretion that are appropriate for the entire organism. It is beyond dispute however, that the cytosolic Ca²⁺ concentration plays a particularly prominent role in this process, as it not only triggers the fusion of insulin granules with the plasma membrane, but also regulates the metabolism of nutrient secretagogues and affects the function of ion channels and transporters. In order to obtain a better understanding of the interdependence of these processes and, ultimately, of the entire beta cell as a working system, models have been developed based on a set of nonlinear ordinary differential equations, and were tested and parametrized on a limited set of experiments. In the present investigation, we have used a recently published version of the beta cell model to test its ability to describe further measurements from our own experimentation and from the literature. The sensitivity of the parameters is quantified and discussed; furthermore, the possible influence of the measuring technique is taken into account. The model proved to be powerful in correctly describing the depolarization pattern in response to glucose and the reaction of the cytosolic Ca²⁺ concentration to stepwise increases of the extracellular K⁺ concentration. Additionally, the membrane potential during a KATP channel block combined with a high extracellular K⁺ concentration could be reproduced. In some cases, however, a slight change of a single parameter led to an abrupt change in the cellular response, such as the generation of a Ca²⁺ oscillation with high amplitude and high frequency. This raises the question as to whether the beta cell may be a partially unstable system or whether further developments in modeling are needed to achieve a generally valid description of the stimulus-secretion coupling of the beta cell.

Contribution of Mitochondria to Insulin Secretion by Various Secretagogues

Significance: Mitochondria determine glucose-stimulated insulin secretion (GSIS) in pancreatic β-cells by elevating ATP synthesis. As the metabolic and redox hub, mitochondria provide numerous links to the plasma membrane channels, insulin granule vesicles (IGVs), cell redox, NADH, NADPH, and Ca²⁺ homeostasis, all affecting insulin secretion. Recent Advances: Mitochondrial redox signaling was implicated in several modes of insulin secretion (branched-chain ketoacid [BCKA]-, fatty acid [FA]-stimulated). Mitochondrial Ca²⁺ influx was found to enhance GSIS, reflecting cytosolic Ca²⁺ oscillations induced by action potential spikes (intermittent opening of voltage-dependent Ca²⁺ and K⁺ channels) or the superimposed Ca²⁺ release from the endoplasmic reticulum (ER). The ATPase inhibitory factor 1 (IF1) was reported to tune the glucose sensitivity range for GSIS. Mitochondrial protein kinase A was implicated in preventing the IF1-mediated inhibition of the ATP synthase. Critical Issues: It is unknown how the redox signal spreads up to the plasma membrane and what its targets are, what the differences in metabolic, redox, NADH/NADPH, and Ca²⁺ signaling, and homeostasis are between the first and second GSIS phase, and whether mitochondria can replace ER in the amplification of IGV exocytosis. Future Directions: Metabolomics studies performed to distinguish between the mitochondrial matrix and cytosolic metabolites will elucidate further details. Identifying the targets of cell signaling into mitochondria and of mitochondrial retrograde metabolic and redox signals to the cell will uncover further molecular mechanisms for insulin secretion stimulated by glucose, BCKAs, and FAs, and the amplification of secretion by glucagon-like peptide (GLP-1) and metabotropic receptors. They will identify the distinction between the hub β-cells and their followers in intact and diabetic states. Antioxid. Redox Signal. 36, 920-952.

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.

Hubs, diversity, and synchronization in FitzHugh-Nagumo oscillator networks: Resonance effects and biophysical implications

Using the FitzHugh-Nagumo equations to represent the oscillatory electrical behavior of β-cells, we develop a coupled oscillator network model with cubic lattice topology, showing that the emergence of pacemakers or hubs in the system can be viewed as a natural consequence of oscillator population diversity. The optimal hub to nonhub ratio is determined by the position of the diversity-induced resonance maximum for a given set of FitzHugh-Nagumo equation parameters and is predicted by the model to be in a range that is fully consistent with experimental observations. The model also suggests that hubs in a β-cell network should have the ability to "switch on" and "off" their pacemaker function. As a consequence, their relative amount in the population can vary in order to ensure an optimal oscillatory performance of the network in response to environmental changes, such as variations of an external stimulus.

Physiology of pancreatic β-cells: Ion channels and molecular mechanisms implicated in stimulus-secretion coupling

The human and mouse islet of Langerhans is an endocrine organ composed of five different cells types; insulin-secreting β-cells, glucagon-producing α-cells, somatostatin-producing δ-cells, pancreatic polypeptide-secreting PP cells and ɛ-cells that secretes ghrelin. The most important cells are the pancreatic β-cells that comprise around 45-50% of human islets and 75-80% in the mouse. Pancreatic β-cells secrete insulin at high glucose concentration, thereby finely regulating glycaemia by the hypoglycaemic effects of this hormone. Different ion channels are implicated in the stimulus-secretion coupling of insulin. An increase in the intracellular ATP concentration leads to closure K_ATP channels, depolarizing the cell and opening voltage-gated calcium channels. The increase of intracellular calcium concentration induced by calcium entry through voltage-gated calcium channels promotes insulin secretion. Here, we briefly describe the diversity of ion channels present in pancreatic β-cells and the different mechanisms that are responsible to induce insulin secretion in human and mouse cells. Moreover, we described the pathophysiology due to alterations in the physiology of the main ion channels present in pancreatic β-cell and its implication to predispose metabolic disorders as type 2 diabetes mellitus.

The Pancreatic β-Cell: The Perfect Redox System

Pancreatic β-cell insulin secretion, which responds to various secretagogues and hormonal regulations, is reviewed here, emphasizing the fundamental redox signaling by NADPH oxidase 4- (NOX4-) mediated H₂O₂ production for glucose-stimulated insulin secretion (GSIS). There is a logical summation that integrates both metabolic plus redox homeostasis because the ATP-sensitive K⁺ channel (K_ATP) can only be closed when both ATP and H₂O₂ are elevated. Otherwise ATP would block K_ATP, while H₂O₂ would activate any of the redox-sensitive nonspecific calcium channels (NSCCs), such as TRPM2. Notably, a 100%-closed K_ATP ensemble is insufficient to reach the -50 mV threshold plasma membrane depolarization required for the activation of voltage-dependent Ca²⁺ channels. Open synergic NSCCs or Cl^- channels have to act simultaneously to reach this threshold. The resulting intermittent cytosolic Ca²⁺-increases lead to the pulsatile exocytosis of insulin granule vesicles (IGVs). The incretin (e.g., GLP-1) amplification of GSIS stems from receptor signaling leading to activating the phosphorylation of TRPM channels and effects on other channels to intensify integral Ca²⁺-influx (fortified by endoplasmic reticulum Ca²⁺). ATP plus H₂O₂ are also required for branched-chain ketoacids (BCKAs); and partly for fatty acids (FAs) to secrete insulin, while BCKA or FA β-oxidation provide redox signaling from mitochondria, which proceeds by H₂O₂ diffusion or hypothetical SH relay via peroxiredoxin "redox kiss" to target proteins.

Dextromethorphan and Dextrorphan Influence Insulin Secretion by Interacting with KATP and L-type Ca2+ Channels in Pancreatic β-Cells

The NMDA receptor antagonist dextromethorphan (DXM) and its metabolite dextrorphan (DXO) have been recommended for treatment of type 2 diabetes mellitus because of their beneficial effects on insulin secretion. This study investigates how different key points of the stimulus-secretion coupling in mouse islets and β-cells are influenced by DXM or DXO. Both compounds elevated insulin secretion, electrical activity, and [Ca²⁺]_c in islets at a concentration of 100 µM along with a stimulating glucose concentration. DXO and DXM increased insulin secretion approximately 30-fold at a substimulatory glucose concentration (3 mM). Patch-clamp experiments revealed that 100 µM DXM directly inhibited K_ATP channels by about 70%. Of note, DXM decreased the current through L-type Ca²⁺ channels about 25%, leading to a transient reduction in Ca²⁺ action potentials. This interaction might explain why elevating DXM to 500 µM drastically decreased insulin release. DXO inhibited K_ATP channels almost equally. In islets of K_ATP channel-deficient sulfonylurea receptor 1 knockout mice, the elevating effects of 100 µM DXM on [Ca²⁺]_c and insulin release were completely lost. By contrast, 100 µM DXO still increased glucose-stimulated insulin release around 60%. In summary, DXM-induced alterations in stimulus-secretion coupling of wild-type islets result from a direct block of K_ATP channels and are partly counteracted by inhibition of L-type Ca²⁺ channels. The stimulatory effect of DXO seems to be based on a combined antagonism on K_ATP channels and NMDA receptors and already occurs under resting conditions. Consequently, both compounds seem not to be suitable candidates for treatment of type 2 diabetes mellitus. SIGNIFICANCE STATEMENT: This study shows that the use of dextromethorphan as an antidiabetic drug can cause unpredictable alterations in insulin secretion by direct interaction with K_ATP and L-type Ca²⁺ channels besides its actual target, the NMDA receptor.

Effects of maintaining eucalcemia following immunoactivation in lactating Holstein dairy cows

Periparturient hypocalcemia is a common metabolic disorder and it is ostensibly associated with negative health and production outcomes. Acute infection also markedly decreases circulating Ca, but the reasons for and consequences of it on physiological and immunological parameters are unknown. Objectives were to evaluate the effects of maintaining eucalcemia on production, metabolic, and immune variables following an intravenous lipopolysaccharide (LPS) challenge. Twelve multiparous lactating Holstein cows (717 ± 20 kg of body weight; 176 ± 34 d in milk; parity 3 ± 0.2) were enrolled in a study containing 2 experimental periods (P); during P1 (3 d), cows consumed feed ad libitum and baseline values were obtained. At the initiation of P2 (4 d), cows were randomly assigned to 1 of 2 treatments: (1) LPS administered (LPS-Con; 0.5 μg/kg of body weight LPS; n = 6) or (2) LPS administered + eucalcemic clamp (LPS-Ca; 0.5 μg/kg of body weight LPS; Ca infusion; n = 6). Cows were fasted for the first 12 h during P2. After LPS administration, ionized Ca was determined every 15 min for 6 h and every 30 min for an additional 6 h and intravenous Ca infusion was adjusted in LPS-Ca cows to maintain eucalcemia. Blood ionized Ca was decreased 23% for the first 12 h postbolus in LPS-Con cows, and by design, Ca infusion prevented hypocalcemia. To maintain eucalcemia for the 12 h, 13.7 g of Ca was infused. The total Ca deficit (including Ca not secreted into milk) accumulated over the 12 h was 10.4 and 20.2 g for the LPS-Con and LPS-Ca treatments, respectively. Mild hyperthermia (0.8°C) occurred for ∼6 h post-LPS administration relative to P1. From 6 to 7 h postbolus rectal temperature from LPS-Ca cows was increased (0.6°C) relative to LPS-Con cows. On d 1 of P2, milk yield decreased (61%) in both treatments relative to P1. Relative to LPS-Con cows, milk yield decreased (15%) in LPS-Ca cows during P2. Overall, circulating LPS-binding protein continuously increased postbolus, and at 24 h LPS-binding protein levels in LPS-Ca cows were increased (80%) relative to LPS-Con cows. During P2, serum amyloid A increased (4-fold) in both treatments relative to P1. Administering LPS initially decreased circulating neutrophils, then cell counts progressively increased with time. Calcium infusion decreased neutrophil counts (40%) from 9 to 12 h postbolus relative to LPS-Con cows. Neutrophil function, as assessed by oxidative burst and myeloperoxidase production, did not differ due to treatment. In summary, maintaining eucalcemia (via intravenous Ca infusion) during an immune challenge appeared to intensify inflammation and adversely affect lactation performance.

β Cells Operate Collectively to Help Maintain Glucose Homeostasis

Residing in the islets of Langerhans in the pancreas, β cells contribute to glucose homeostasis by managing the body's insulin supply. Although it has been acknowledged that healthy β cells engage in heavy cell-to-cell communication to perform their homeostatic function, the exact role and effects of such communication remain partly understood. We offer a novel, to our knowledge, perspective on the subject in the form of 1) a dynamical network model that faithfully mimics fast calcium oscillations in response to above-threshold glucose stimulation and 2) empirical data analysis that reveals a qualitative shift in the cross-correlation structure of measured signals below and above the threshold glucose concentration. Combined together, these results point to a glucose-induced transition in β-cell activity thanks to increasing coordination through gap-junctional signaling and paracrine interactions. Our data and the model further suggest how the conservation of entire cell-cell conductance, observed in coupled but not uncoupled β cells, emerges as a collective phenomenon. An overall implication is that improving the ability to monitor β-cell signaling should offer means to better understand the pathogenesis of diabetes mellitus.

Cooperative maintenance of cellular identity in systems with intercellular communication defects

The cooperative dynamics of cellular populations emerging from the underlying interactions determines cellular functions and thereby their identity in tissues. Global deviations from this dynamics, on the other hand, reflect pathological conditions. However, how these conditions are stabilized from dysregulation on the level of the single entities is still unclear. Here, we tackle this question using the generic Hodgkin-Huxley type of models that describe physiological bursting dynamics of pancreatic β-cells and introduce channel dysfunction to mimic pathological silent dynamics. The probability for pathological behavior in β-cell populations is ∼100% when all cells have these defects, despite the negligible size of the silent state basin of attraction for single cells. In stark contrast, in a more realistic scenario for a mixed population, stabilization of the pathological state depends on the size of the subpopulation which acquired the defects. However, the probability to exhibit stable pathological dynamics in this case is less than 10%. These results, therefore, suggest that the physiological bursting dynamics of a population of β-cells is cooperatively maintained, even under intercellular communication defects induced by dysfunctional channels of single cells.

Pharmacological polysulfide suppresses glucose-stimulated insulin secretion in an ATP-sensitive potassium channel-dependent manner

Hydrogen sulfide (H₂S) is an endogenous gaseous transmitter synthesized in various cell types. It is well established that H₂S functions in many physiological processes, including the relaxation of vascular smooth muscle, mediation of neurotransmission, regulation of inflammation, and modulation of insulin signaling. In recent years, it has been revealed that polysulfides, substances with a varying number of sulfur atoms (H₂Sn), are generated endogenously from H₂S in the presence of oxygen. A series of studies describes that sulfane sulfur has the unique ability to bind reversibly to other sulfur atoms to form hydropersulfides and polysulfides, and that polysulfides activate ion channels and promote calcium influx. Furthermore, polysulfides regulate tumor suppressor activity, promote the activation of transcription factors targeting antioxidant genes and regulate blood pressure by vascular smooth muscle relaxation. Insulin secretion from pancreatic β cells plays a critical role in response to increased blood glucose concentration. H₂S has emerged as an important regulator of glycemic control and exhibits characteristic regulation of glucose homeostasis. However, the effects of polysulfides on glucose-stimulated insulin secretion (GSIS) are largely unknown. In this study, we demonstrated that pharmacological polysulfide salts including Na₂S₂, Na₂S₃, and Na₂S₄ considerably inhibit GSIS in mouse and rat pancreatic β-cell-derived MIN6 and INS-1 cell lines, and that the effect is dependent on the activation of ATP-sensitive potassium channels. In addition, we demonstrated that a mixture of Na₂S and diethylamine NONOate inhibits GSIS in a similar way to the pharmacological administration of polysulfide salts.

Random Matrix Analysis of Ca2+ Signals in β-Cell Collectives

Even within small organs like pancreatic islets, different endocrine cell types and subtypes form a heterogeneous collective to sense the chemical composition of the extracellular solution and compute an adequate hormonal output. Erroneous cellular processing and hormonal output due to challenged heterogeneity result in various disorders with diabetes mellitus as a flagship metabolic disease. Here we attempt to address the aforementioned functional heterogeneity with comparing pairwise cell-cell cross-correlations obtained from simultaneous measurements of cytosolic calcium responses in hundreds of islet cells in an optical plane to statistical properties of correlations predicted by the random matrix theory (RMT). We find that the bulk of the empirical eigenvalue spectrum is almost completely described by RMT prediction, however, the deviating eigenvalues that exist below and above RMT spectral edges suggest that there are local and extended modes driving the correlations. We also show that empirical nearest neighbor spacing of eigenvalues follows universal RMT properties regardless of glucose stimulation, but that number variance displays clear separation from RMT prediction and can differentiate between empirical spectra obtained under non-stimulated and stimulated conditions. We suggest that RMT approach provides a sensitive tool to assess the functional cell heterogeneity and its effects on the spatio-temporal dynamics of a collective of beta cells in pancreatic islets in physiological resting and stimulatory conditions, beyond the current limitations of molecular and cellular biology.

Insulin Release Mechanism Modulated by Toxins Isolated from Animal Venoms: From Basic Research to Drug Development Prospects

Venom from mammals, amphibians, snakes, arachnids, sea anemones and insects provides diverse sources of peptides with different potential medical applications. Several of these peptides have already been converted into drugs and some are still in the clinical phase. Diabetes type 2 is one of the diseases with the highest mortality rate worldwide, requiring specific attention. Diverse drugs are available (e.g., Sulfonylureas) for effective treatment, but with several adverse secondary effects, most of them related to the low specificity of these compounds to the target. In this context, the search for specific and high-affinity compounds for the management of this metabolic disease is growing. Toxins isolated from animal venom have high specificity and affinity for different molecular targets, of which the most important are ion channels. This review will present an overview about the electrical activity of the ion channels present in pancreatic β cells that are involved in the insulin secretion process, in addition to the diversity of peptides that can interact and modulate the electrical activity of pancreatic β cells. The importance of prospecting bioactive peptides for therapeutic use is also reinforced.

The inhibitor of connexin Cx36 channels, mefloquine, inhibits voltage-dependent Ca2+ channels and insulin secretion

The antimalarial agent, mefloquine, inhibits the function of connexin Cx36 gap junctions and hemichannels and has thus become a tool to investigate their physiological relevance in pancreatic islets. In view of earlier reports on a KATP channel-block by mefloquine, the specificity of mefloquine as a pharmacological tool was investigated. Mouse pancreatic islets and single beta cells were used to measure membrane potential, whole cell currents, Ca2+ channel activity, cytosolic Ca2+ concentration ([Ca2+]i) and insulin secretion. Mefloquine was tested in the concentration range of 5-50 μM 25 μM mefloquine was as effective as 500 μM tolbutamide to depolarize the plasma membrane of beta cells, but did not induce action potentials. Rather, it abolished tolbutamide-induced action potentials and the associated increase of [Ca2+]i. In the range of 5-50 μM mefloquine inhibited voltage-dependent Ca2+ currents in primary beta cells as effectively as 1 μM nisoldipine, a specific blocker of L-type Ca2+ channels. The Ca2+ channel opening effect of Bay K8644 was completely antagonized by mefloquine. Likewise, the increase of [Ca2+]i and of insulin secretion stimulated by 40 mM KCl, but not that by 30 mM glucose was antagonized by 50 μM mefloquine. Neither at 5 μM nor at 50 μM did mefloquin stimulate insulin secretion at basal glucose. In conclusion, mefloquine blocks KATP channels and L-type Ca2+ channels in pancreatic beta cells in the range from 5 to 50 μM. Thus it inhibits depolarization-induced insulin secretion, but in the presence of a stimulatory glucose concentration additional effects of mefloquine, possibly on intracellular Ca2+ mobilization, and the metabolic amplification by glucose permit a sustained rate of secretion.

Low Resting Membrane Potential and Low Inward Rectifier Potassium Currents Are Not Inherent Features of hiPSC-Derived Cardiomyocytes

Human induced pluripotent stem cell (hiPSC) cardiomyocytes (CMs) show less negative resting membrane potential (RMP), which is attributed to small inward rectifier currents (IK1). Here, IK1 was measured in hiPSC-CMs (proprietary and commercial cell line) cultured as monolayer (ML) or 3D engineered heart tissue (EHT) and, for direct comparison, in CMs from human right atrial (RA) and left ventricular (LV) tissue. RMP was measured in isolated cells and intact tissues. IK1 density in ML- and EHT-CMs from the proprietary line was similar to LV and RA, respectively. IK1 density in EHT-CMs from the commercial line was 2-fold smaller than in the proprietary line. RMP in EHT of both lines was similar to RA and LV. Repolarization fraction and IK,ACh response discriminated best between RA and LV and indicated predominantly ventricular phenotype in hiPSC-CMs/EHT. The data indicate that IK1 is not necessarily low in hiPSC-CMs, and technical issues may underlie low RMP in hiPSC-CMs.

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.

A TRPV1-to-secretagogin regulatory axis controls pancreatic β-cell survival by modulating protein turnover

Ca2+-sensor proteins are generally implicated in insulin release through SNARE interactions. Here, secretagogin, whose expression in human pancreatic islets correlates with their insulin content and the incidence of type 2 diabetes, is shown to orchestrate an unexpectedly distinct mechanism. Single-cell RNA-seq reveals retained expression of the TRP family members in β-cells from diabetic donors. Amongst these, pharmacological probing identifies Ca2+-permeable transient receptor potential vanilloid type 1 channels (TRPV1) as potent inducers of secretagogin expression through recruitment of Sp1 transcription factors. Accordingly, agonist stimulation of TRPV1s fails to rescue insulin release from pancreatic islets of glucose intolerant secretagogin knock-out(-/-) mice. However, instead of merely impinging on the SNARE machinery, reduced insulin availability in secretagogin-/- mice is due to β-cell loss, which is underpinned by the collapse of protein folding and deregulation of secretagogin-dependent USP9X deubiquitinase activity. Therefore, and considering the desensitization of TRPV1s in diabetic pancreata, a TRPV1-to-secretagogin regulatory axis seems critical to maintain the structural integrity and signal competence of β-cells.

Modulation of Ionic Channels and Insulin Secretion by Drugs and Hormones in Pancreatic Beta Cells

Pancreatic beta cells, unique cells that secrete insulin in response to an increase in glucose levels, play a significant role in glucose homeostasis. Glucose-stimulated insulin secretion (GSIS) in pancreatic beta cells has been extensively explored. In this mechanism, glucose enters the cells and subsequently the metabolic cycle. During this process, the ATP/ADP ratio increases, leading to ATP-sensitive potassium (KATP) channel closure, which initiates depolarization that is also dependent on the activity of TRP nonselective ion channels. Depolarization leads to the opening of voltage-gated Na(+) channels (Nav) and subsequently voltage-dependent Ca(2+) channels (Cav). The increase in intracellular Ca(2+) triggers the exocytosis of insulin-containing vesicles. Thus, electrical activity of pancreatic beta cells plays a central role in GSIS. Moreover, many growth factors, incretins, neurotransmitters, and hormones can modulate GSIS, and the channels that participate in GSIS are highly regulated. In this review, we focus on the principal ionic channels (KATP, Nav, and Cav channels) involved in GSIS and how classic and new proteins, hormones, and drugs regulate it. Moreover, we also discuss advances on how metabolic disorders such as metabolic syndrome and diabetes mellitus change channel activity leading to changes in insulin secretion.

Fractal Behavior of the Pancreatic β-Cell Near the Percolation Threshold: Effect of the KATP Channel On the Electrical Response

The molecular system built with true chemical bonds or strong molecular interaction can be described using conceptual mathematical tools. Modeling of the natural generated ionic currents on the human pancreatic β-cell activity had been already studied using complicated analytical models. In our present contribution, we prove the same using our simple electrical model. The ionic currents are associated with different proteins membrane channels (K-Ca, K(v), K(ATP), Ca(v)-L) and Na/Ca Exchanger (NCX). The proteins are Ohmic conductors and are modeled by conductance randomly distributed. Switches are placed in series with conductances in order to highlight the channel activity. However, the KATP channel activity is stimulated by glucose, and the NCX's conductance change according to the intracellular calcium concentration. The percolation threshold of the system is calculated by the fractal nature of the infinite cluster using the Tarjan's depth-first-search algorithm. It is shown that the behavior of the internal concentration of Ca(2+) and the membrane potential are modulated by glucose. The results confirm that the inhibition of KATP channels depolarizes the membrane and increases the influx of [Ca(2+)]i through NCX and Ca(v)-L channel for high glucose concentrations.

A new dimethyl labeling-based SID-MRM-MS method and its application to three proteases involved in insulin maturation

The absolute quantification of target proteins in proteomics involves stable isotope dilution coupled with multiple reactions monitoring mass spectrometry (SID-MRM-MS). The successful preparation of stable isotope-labeled internal standard peptides is an important prerequisite for the SID-MRM absolute quantification methods. Dimethyl labeling has been widely used in relative quantitative proteomics and it is fast, simple, reliable, cost-effective, and applicable to any protein sample, making it an ideal candidate method for the preparation of stable isotope-labeled internal standards. MRM mass spectrometry is of high sensitivity, specificity, and throughput characteristics and can quantify multiple proteins simultaneously, including low-abundance proteins in precious samples such as pancreatic islets. In this study, a new method for the absolute quantification of three proteases involved in insulin maturation, namely PC1/3, PC2 and CPE, was developed by coupling a stable isotope dimethyl labeling strategy for internal standard peptide preparation with SID-MRM-MS quantitative technology. This method offers a new and effective approach for deep understanding of the functional status of pancreatic β cells and pathogenesis in diabetes.

Concerted Trafficking Regulation of Kv2.1 and KATP Channels by Leptin in Pancreatic β-Cells

In pancreatic β-cells, voltage-gated potassium 2.1 (Kv2.1) channels are the dominant delayed rectifier potassium channels responsible for action potential repolarization. Here, we report that leptin, a hormone secreted by adipocytes known to inhibit insulin secretion, causes a transient increase in surface expression of Kv2.1 channels in rodent and human β-cells. The effect of leptin on Kv2.1 surface expression is mediated by the AMP-activated protein kinase (AMPK). Activation of AMPK mimics whereas inhibition of AMPK occludes the effect of leptin. Inhibition of Ca(2+)/calmodulin-dependent protein kinase kinase β, a known upstream kinase of AMPK, also blocks the effect of leptin. In addition, the cAMP-dependent protein kinase (PKA) is involved in Kv2.1 channel trafficking regulation. Inhibition of PKA prevents leptin or AMPK activators from increasing Kv2.1 channel density, whereas stimulation of PKA is sufficient to promote Kv2.1 channel surface expression. The increased Kv2.1 surface expression by leptin is dependent on actin depolymerization, and pharmacologically induced actin depolymerization is sufficient to enhance Kv2.1 surface expression. The signaling and cellular mechanisms underlying Kv2.1 channel trafficking regulation by leptin mirror those reported recently for ATP-sensitive potassium (KATP) channels, which are critical for coupling glucose stimulation with membrane depolarization. We show that the leptin-induced increase in surface KATP channels results in more hyperpolarized membrane potentials than control cells at stimulating glucose concentrations, and the increase in Kv2.1 channels leads to a more rapid repolarization of membrane potential in cells firing action potentials. This study supports a model in which leptin exerts concerted trafficking regulation of KATP and Kv2.1 channels to coordinately inhibit insulin secretion.

Time-stepping techniques to enable the simulation of bursting behavior in a physiologically realistic computational islet

Physiologically realistic simulations of computational islets of beta cells require the long-time solution of several thousands of coupled ordinary differential equations (ODEs), resulting from the combination of several ODEs in each cell and realistic numbers of several hundreds of cells in an islet. For a reliable and accurate solution of complex nonlinear models up to the desired final times on the scale of several bursting periods, an appropriate ODE solver designed for stiff problems is eventually a necessity, since other solvers may not be able to handle the problem or are exceedingly inefficient. But stiff solvers are potentially significantly harder to use, since their algorithms require at least an approximation of the Jacobian matrix. For sophisticated models, systems of several complex ODEs in each cell, it is practically unworkable to differentiate these intricate nonlinear systems analytically and to manually program the resulting Jacobian matrix in computer code. This paper demonstrates that automatic differentiation can be used to obtain code for the Jacobian directly from code for the ODE system, which allows a full accounting for the sophisticated model equations. This technique is also feasible in source-code languages Fortran and C, and the conclusions apply to a wide range of systems of coupled, nonlinear reaction equations. However, when we combine an appropriately supplied Jacobian with slightly modified memory management in the ODE solver, simulations on the realistic scale of one thousand cells in the islet become possible that are several orders of magnitude faster than the original solver in the software Matlab, a language that is particularly user friendly for programming complicated model equations. We use the efficient simulator to analyze electrical bursting and show non-monotonic average burst period between fast and slow cells for increasing coupling strengths. We also find that interestingly, the arrangement of the connected fast and slow heterogeneous cells impacts the peak bursting period monotonically.

Ionic mechanisms in pancreatic β cell signaling

The function and survival of pancreatic β cells critically rely on complex electrical signaling systems composed of a series of ionic events, namely fluxes of K(+), Na(+), Ca(2+) and Cl(-) across the β cell membranes. These electrical signaling systems not only sense events occurring in the extracellular space and intracellular milieu of pancreatic islet cells, but also control different β cell activities, most notably glucose-stimulated insulin secretion. Three major ion fluxes including K(+) efflux through ATP-sensitive K(+) (KATP) channels, the voltage-gated Ca(2+) (CaV) channel-mediated Ca(2+) influx and K(+) efflux through voltage-gated K(+) (KV) channels operate in the β cell. These ion fluxes set the resting membrane potential and the shape, rate and pattern of firing of action potentials under different metabolic conditions. The KATP channel-mediated K(+) efflux determines the resting membrane potential and keeps the excitability of the β cell at low levels. Ca(2+) influx through CaV1 channels, a major type of β cell CaV channels, causes the upstroke or depolarization phase of the action potential and regulates a wide range of β cell functions including the most elementary β cell function, insulin secretion. K(+) efflux mediated by KV2.1 delayed rectifier K(+) channels, a predominant form of β cell KV channels, brings about the downstroke or repolarization phase of the action potential, which acts as a brake for insulin secretion owing to shutting down the CaV channel-mediated Ca(2+) entry. These three ion channel-mediated ion fluxes are the most important ionic events in β cell signaling. This review concisely discusses various ionic mechanisms in β cell signaling and highlights KATP channel-, CaV1 channel- and KV2.1 channel-mediated ion fluxes.

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.

Store-operated calcium entry could prevent continuous spiking of membrane potential to sustain normal intracellular calcium oscillations and normal potential bursting in pancreatic β-cells

We propose a dynamical store-operated calcium entry (SOCE) model to analyze the complex role of SOCE in modulating calcium oscillations and electrical activity in pancreatic β-cells and provide a new mathematical insight. Using this model, we simulate the SOCE role in a number of cases with different SOCE conductances. When the SOCE conductance is set to 0 or very small (5 pS), our numerical simulation conforms to the experimental observation that endoplasmic reticulum (ER) calcium can sustain normal calcium oscillations and the depletion of ER calcium transforms the normal calcium oscillations into a sustained calcium increase with oscillations of much higher frequency and much smaller amplitude, and transforms the normal membrane potential oscillations to a pattern of continuous spiking. When the SOCE conductance is increased to 20 pS and the ER calcium is depleted, our numerical simulation conforms to the other experimental observation that the normal calcium and potential oscillations are sustained and augmented a little bit. Moreover, the oscillation frequency is increased a very little bit. A further increase of the conductance to 35 pS slows down the oscillation a little bit. This numerical evidence suggests that a sufficiently large SOCE can prevent the continuous spiking of membrane potential to sustain the normal calcium oscillations and the normal membrane potential bursting. A careful examination of our simulated dynamics of the ATP/ADP ratio, the ATP-sensitive outward K(+) current, and the voltage-gated inward Ca(2+) current reveals that intracellular periodic Ca(2+) peaks perhaps resulted from SOCE might play a role in stabilizing the membrane potential at its resting level (avoiding the continuous spiking) for a certain period of time by accelerating ATP consumption, reducing the ratio ATP/ADP, opening the ATP-sensitive potassium channel, and repolarizing the membrane potential.

A stochastic mathematical model to study the autoimmune progression towards type 1 diabetes

BACKGROUND

The integrity of the interactions and the 3D architecture among beta cell populations in pancreatic islets is critical for proper biosynthesis, storage and release of insulin. The aim of this study was to evaluate the effect on electrophysiological signalling of beta cells that is produced by progressive lymphocytic islet cell infiltration (insulitis), by modelling the disruption of pancreatic islet anatomy as a consequence of insulitis and altered glucose concentrations.

METHODS

On the basis of histopathological images of murine islets from non-obese diabetic mice, we simulated the electrophysiological dynamics of a 3D cluster of mouse beta cells via a stochastic model. Progressive damage was modelled at different glucose concentrations, representing the different glycaemic states in the autoimmune progression towards type 1 diabetes.

RESULTS

At 31% of dead beta cells (normoglycaemia) and 69% (hyperglycaemia), the system appeared to be biologically robust to maintain regular Ca(2+) ion oscillations guaranteeing an effective insulin release. Simulations at 84%, 94% and 98% grades (severe hyperglycemia) showed that intracellular calcium oscillations were absent. In such conditions, insulin pulsatility is not expected to occur.

CONCLUSIONS

Our results suggest that the islet tissue is biophysically robust enough to compensate for high rates of beta cell loss. These predictions can be experimentally tested in vitro by quantifying space and time electrophysiological dynamics of animal islets kept at different glucose gradients. The model indicates the necessity of maintaining glycaemia within the physiological range as soon as possible after diabetes onset to avoid a dramatic interruption of Ca(2+) pulsatility and the consequent drop of insulin release.

ATP regulates sodium channel kinetics in pancreatic islet beta cells

Pancreatic beta cells act as glucose sensors, in which intracellular ATP ([ATP](i)) are altered with glucose concentration change. The characterization of voltage-gated sodium channels under different [ATP](i) remains unclear. Here, we demonstrated that increasing [ATP](i) within a certain range of concentrations (2-8 mM) significantly enhanced the voltage-gated sodium channel currents, compared with 2 mM cytosolic ATP. This enhancement was attenuated by even high intracellular ATP (12 mM). Furthermore, elevated ATP modulated the sodium channel kinetics in a dose-dependent manner. Increased [ATP](i) shifted both the current-voltage curve and the voltage-dependent inactivation curve of sodium channel to the right. Finally, the sodium channel recovery from inactivation was significantly faster when the intracellular ATP level was increased, especially in 8 mM [ATP](i), which is an attainable concentration by the high glucose stimulation. In summary, our data suggested that elevated cytosolic ATP enhanced the activity of Na(+) channels, which may play essential roles in modulating β cell excitability and insulin release when blood glucose concentration increases.

Protein-mediated interactions of pancreatic islet cells

The islets of Langerhans collectively form the endocrine pancreas, the organ that is soley responsible for insulin secretion in mammals, and which plays a prominent role in the control of circulating glucose and metabolism. Normal function of these islets implies the coordination of different types of endocrine cells, noticeably of the beta cells which produce insulin. Given that an appropriate secretion of this hormone is vital to the organism, a number of mechanisms have been selected during evolution, which now converge to coordinate beta cell functions. Among these, several mechanisms depend on different families of integral membrane proteins, which ensure direct (cadherins, N-CAM, occludin, and claudins) and paracrine communications (pannexins) between beta cells, and between these cells and the other islet cell types. Also, other proteins (integrins) provide communication of the different islet cell types with the materials that form the islet basal laminae and extracellular matrix. Here, we review what is known about these proteins and their signaling in pancreatic β -cells, with particular emphasis on the signaling provided by Cx36, given that this is the integral membrane protein involved in cell-to-cell communication, which has so far been mostly investigated for effects on beta cell functions.

Regulation of insulin synthesis and secretion and pancreatic Beta-cell dysfunction in diabetes

Pancreatic β-cell dysfunction plays an important role in the pathogenesis of both type 1 and type 2 diabetes. Insulin, which is produced in β-cells, is a critical regulator of metabolism. Insulin is synthesized as preproinsulin and processed to proinsulin. Proinsulin is then converted to insulin and C-peptide and stored in secretary granules awaiting release on demand. Insulin synthesis is regulated at both the transcriptional and translational level. The cis-acting sequences within the 5' flanking region and trans-activators including paired box gene 6 (PAX6), pancreatic and duodenal homeobox- 1(PDX-1), MafA, and β-2/Neurogenic differentiation 1 (NeuroD1) regulate insulin transcription, while the stability of preproinsulin mRNA and its untranslated regions control protein translation. Insulin secretion involves a sequence of events in β-cells that lead to fusion of secretory granules with the plasma membrane. Insulin is secreted primarily in response to glucose, while other nutrients such as free fatty acids and amino acids can augment glucose-induced insulin secretion. In addition, various hormones, such as melatonin, estrogen, leptin, growth hormone, and glucagon like peptide-1 also regulate insulin secretion. Thus, the β-cell is a metabolic hub in the body, connecting nutrient metabolism and the endocrine system. Although an increase in intracellular [Ca2+] is the primary insulin secretary signal, cAMP signaling- dependent mechanisms are also critical in the regulation of insulin secretion. This article reviews current knowledge on how β-cells synthesize and secrete insulin. In addition, this review presents evidence that genetic and environmental factors can lead to hyperglycemia, dyslipidemia, inflammation, and autoimmunity, resulting in β-cell dysfunction, thereby triggering the pathogenesis of diabetes.

Regulation of insulin synthesis and secretion and pancreatic Beta-cell dysfunction in diabetes

Pancreatic β-cell dysfunction plays an important role in the pathogenesis of both type 1 and type 2 diabetes. Insulin, which is produced in β-cells, is a critical regulator of metabolism. Insulin is synthesized as preproinsulin and processed to proinsulin. Proinsulin is then converted to insulin and C-peptide and stored in secretary granules awaiting release on demand. Insulin synthesis is regulated at both the transcriptional and translational level. The cis-acting sequences within the 5' flanking region and trans-activators including paired box gene 6 (PAX6), pancreatic and duodenal homeobox- 1(PDX-1), MafA, and β-2/Neurogenic differentiation 1 (NeuroD1) regulate insulin transcription, while the stability of preproinsulin mRNA and its untranslated regions control protein translation. Insulin secretion involves a sequence of events in β-cells that lead to fusion of secretory granules with the plasma membrane. Insulin is secreted primarily in response to glucose, while other nutrients such as free fatty acids and amino acids can augment glucose-induced insulin secretion. In addition, various hormones, such as melatonin, estrogen, leptin, growth hormone, and glucagon like peptide-1 also regulate insulin secretion. Thus, the β-cell is a metabolic hub in the body, connecting nutrient metabolism and the endocrine system. Although an increase in intracellular [Ca2+] is the primary insulin secretary signal, cAMP signaling- dependent mechanisms are also critical in the regulation of insulin secretion. This article reviews current knowledge on how β-cells synthesize and secrete insulin. In addition, this review presents evidence that genetic and environmental factors can lead to hyperglycemia, dyslipidemia, inflammation, and autoimmunity, resulting in β-cell dysfunction, thereby triggering the pathogenesis of diabetes.

The diabetic β-cell: hyperstimulated vs. hyperexcited

Hyperglycaemia has multiple effects on β-cells, some clearly prosecretory, including hyperplasia and elevated insulin content, but eventually, a 'glucotoxic' effect which leads to pancreatic β-cell dysfunction, reduced β-cell mass and insulin deficiency, is an important part of diabetes pathophysiology. Myriad underlying cellular and molecular processes could lead to such dysfunction. High glucose will stimulate glycolysis and oxidative phosphorylation, which will in turn increase β-cell membrane excitability through K(ATP) channel closure. Chronic hyperexcitability will then lead to persistently elevated [Ca(2+)](i), a key trigger to insulin secretion. Thus, at least a part of the consequence of 'hyperstimulation' by glucose has been suggested to be a result of 'hyperexcitability' and chronically elevated [Ca(2+)](i). This link is lost when the [glucose], K(ATP) -channel activity link is broken, either pharmacologically or genetically. In isolated islets, such studies reveal that hyperexcitability causes a largely reversible chronic loss of insulin content, but in vivo chronic hyperexcitability per se does not lead to β-cell death or loss of insulin content. On the other hand, chronic inexcitability in vivo leads to systemic diabetes and consequential β-cell death, even while [Ca(2+)](i) remains low.

Bulk-like endocytosis plays an important role in the recycling of insulin granules in pancreatic beta cells

Although bulk endocytosis has been found in a number of neuronal and endocrine cells, the molecular mechanism and physiological function of bulk endocytosis remain elusive. In pancreatic beta cells, we have observed bulk-like endocytosis evoked both by flash photolysis and trains of depolarization. Bulk-like endocytosis is a clathrin-independent process that is facilitated by enhanced extracellular Ca(2+) entry and suppressed by the inhibition of dynamin function. Moreover, defects in bulk-like endocytosis are accompanied by hyperinsulinemia in primary beta cells dissociated from diabetic KKAy mice, which suggests that bulk-like endocytosis plays an important role in maintaining the exo-endocytosis balance and beta cell secretory capability.

Novel standards in the measurement of rat insulin granules combining electron microscopy, high-content image analysis and in silico modelling

AIMS/HYPOTHESIS

Knowledge of number, size and content of insulin secretory granules is pivotal for understanding the physiology of pancreatic beta cells. Here we re-evaluated key structural features of rat beta cells, including insulin granule size, number and distribution as well as cell size.

METHODS

Electron micrographs of rat beta cells fixed either chemically or by high-pressure freezing were compared using a high-content analysis approach. These data were used to develop three-dimensional in silico beta cell models, the slicing of which would reproduce the experimental datasets.

RESULTS

As previously reported, chemically fixed insulin secretory granules appeared as hollow spheres with a mean diameter of ∼350 nm. Remarkably, most granules fixed by high-pressure freezing lacked the characteristic halo between the dense core and the limiting membrane and were smaller than their chemically fixed counterparts. Based on our analyses, we conclude that the mean diameter of rat insulin secretory granules is 243 nm, corresponding to a surface area of 0.19 μm(2). Rat beta cells have a mean volume of 763 μm(3) and contain 5,000-6,000 granules.

CONCLUSIONS/INTERPRETATION

A major reason for the lower mean granule number/rat beta cell relative to previous accounts is a reduced estimation of the mean beta cell volume. These findings imply that each granule contains about twofold more insulin, while its exocytosis increases membrane capacitance about twofold less than assumed previously. Our integrated approach defines new standards for quantitative image analysis of beta cells and could be applied to other cellular systems.

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.

Regulation of calcium in pancreatic α- and β-cells in health and disease

The glucoregulatory hormones insulin and glucagon are released from the β- and α-cells of the pancreatic islets. In both cell types, secretion is secondary to firing of action potentials, Ca²⁺-influx via voltage-gated Ca²⁺-channels, elevation of [Ca²⁺]_i and initiation of Ca²⁺-dependent exocytosis. Here we discuss the mechanisms that underlie the reciprocal regulation of insulin and glucagon secretion by changes in plasma glucose, the roles played by different types of voltage-gated Ca²⁺-channel present in α- and β-cells and the modulation of hormone secretion by Ca²⁺-dependent and -independent processes. We also consider how subtle changes in Ca²⁺-signalling may have profound impact on β-cell performance and increase risk of developing type-2 diabetes.

Thiopental-induced insulin secretion via activation of IP3-sensitive calcium stores in rat pancreatic β-cells

While glucose-stimulated insulin secretion depends on Ca(2+) influx through voltage-gated Ca(2+) channels in the cell membrane of the pancreatic β-cell, there is also ample evidence for an important role of intracellular Ca(2+) stores in insulin secretion, particularly in relation to drug stimuli. We report here that thiopental, a common anesthetic agent, triggers insulin secretion from the intact pancreas and primary cultured rat pancreatic β-cells. We investigated the underlying mechanisms by measurements of whole cell K(+) and Ca(2+) currents, membrane potential, cytoplasmic Ca(2+) concentration ([Ca(2+)](i)), and membrane capacitance. Thiopental-induced insulin secretion was first detected by enzyme-linked immunoassay, then further assessed by membrane capacitance measurement, which revealed kinetics distinct from glucose-induced insulin secretion. The thiopental-induced secretion was independent of cell membrane depolarization and closure of ATP-sensitive potassium (K(ATP)) channels. However, accompanied by the insulin secretion stimulated by thiopental, we recorded a significant intracellular [Ca(2+)] increase that was not from Ca(2+) influx across the cell membrane, but from intracellular Ca(2+) stores. The thiopental-induced [Ca(2+)](i) rise in β-cells was sensitive to thapsigargin, a blocker of the endoplasmic reticulum Ca(2+) pump, as well as to heparin (0.1 mg/ml) and 2-aminoethoxydiphenyl borate (2-APB; 100 μM), drugs that inhibit inositol 1,4,5-trisphosphate (IP(3)) binding to the IP(3) receptor, and to U-73122, a phospholipase C inhibitor, but insensitive to ryanodine. Thapsigargin also diminished thiopental-induced insulin secretion. Thus, we conclude that thiopental-induced insulin secretion is mediated by activation of the intracellular IP(3)-sensitive Ca(2+) store.

Electrophysiology of pancreatic β-cells in intact mouse islets of Langerhans

When exposed to intermediate glucose concentrations (6-16 mol/l), pancreatic β-cells in intact islets generate bursts of action potentials (superimposed on depolarised plateaux) separated by repolarised electrically silent intervals. First described more than 40 years ago, these oscillations have continued to intrigue β-cell electrophysiologists. To date, most studies of β-cell ion channels have been performed on isolated cells maintained in tissue culture (that do not burst). Here we will review the electrophysiological properties of β-cells in intact, freshly isolated, mouse pancreatic islets. We will consider the role of ATP-regulated K⁺-channels (K(ATP)-channels), small-conductance Ca²⁺-activated K⁺-channels and voltage-gated Ca²⁺-channels in the generation of the bursts. Our data indicate that K(ATP)-channels not only constitute the glucose-regulated resting conductance in the β-cell but also provide a variable K⁺-conductance that influence the duration of the bursts of action potentials and the silent intervals. We show that inactivation of the voltage-gated Ca²⁺-current is negligible at voltages corresponding to the plateau potential and consequently unlikely to play a major role in the termination of the burst. Finally, we propose a model for glucose-induced β-cell electrical activity based on observations made in intact pancreatic islets.

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

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

Analyzing electrical activities of pancreatic β cells using mathematical models

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

A fast solution switching system with temperature control for single cell measurements

This article describes a perfusion system for biophysical single cell experiments at the physiological temperature. Our system regulates temperature of test solutions using a small heat exchanger that includes several capillaries. Water circulating inside the heat exchanger warms or cools test solutions flowing inside the capillaries. Temperature-controlled solutions are delivered directly to a single cell(s) through a multibarreled manifold that switches solutions bathing a cell in less than 1s. This solution exchange is optimal for patch clamp, single-cell microamperometry, and microfluorometry experiments. Using this system, we demonstrate that exocytosis from pancreatic β cells and activation of TRPV1 channels are temperature sensitive. We also discuss how to measure local temperature near a single cell under investigation.

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.

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.

Voltage-dependent metabolic regulation of Kv2.1 channels in pancreatic beta-cells

Voltage-gated potassium channels (Kv channels) play a crucial role in formation of action potentials in response to glucose stimulation in pancreatic beta-ells. We previously reported that the Kv channel is regulated by glucose metabolism, particularly by MgATP. We examined whether the regulation of Kv channels is voltage-dependent and mechanistically related with phosphorylation of the channels. In rat pancreatic beta-cells, suppression of glucose metabolism with low glucose concentrations of 2.8mM or less or by metabolic inhibitors decreased the Kv2.1-channel activity at positive membrane potentials, while increased it at potentials negative to -10 mV, suggesting that modulation of Kv channels by glucose metabolism is voltage-dependent. Similarly, in HEK293 cells expressing the recombinant Kv2.1 channels, 0mM but not 10mM MgATP modulated the channel activity in a manner similar to that in beta-cells. Both steady-state activation and inactivation kinetics of the channel were shifted toward the negative potential in association with the voltage-dependent modulation of the channels by cytosolic dialysis of alkaline phosphatase in beta-cells. The modulation of Kv-channel current-voltage relations were also observed during and after glucose-stimulated electrical excitation. These results suggest that the cellular metabolism including MgATP production and/or channel phosphorylation/dephosphorylation underlie the physiological modulation of Kv2.1 channels during glucose-induced insulin secretion.

Hyperinsulinism and diabetes: genetic dissection of beta cell metabolism-excitation coupling in mice

The role of metabolism-excitation coupling in insulin secretion has long been apparent, but in recent years, in parallel with studies of human hyperinsulinism and diabetes, genetic manipulation of proteins involved in glucose transport, metabolism, and excitability in mice has brought the central importance of this pathway into sharp relief. We focus on these animal studies and how they provide important insights into not only metabolic and electrical regulation of insulin secretion, but also downstream consequences of alterations in this pathway and the etiology and treatment of insulin-secretion diseases in humans.

Somatostatin release, electrical activity, membrane currents and exocytosis in human pancreatic delta cells

AIMS/HYPOTHESIS

The aim of this study was to characterise electrical activity, ion channels, exocytosis and somatostatin release in human delta cells/pancreatic islets.

METHODS

Glucose-stimulated somatostatin release was measured from intact human islets. Membrane potential, currents and changes in membrane capacitance (reflecting exocytosis) were recorded from individual human delta cells identified by immunocytochemistry.

RESULTS

Somatostatin secretion from human islets was stimulated by glucose and tolbutamide and inhibited by diazoxide. Human delta cells generated bursting or sporadic electrical activity, which was enhanced by tolbutamide but unaffected by glucose. Delta cells contained a tolbutamide-insensitive, Ba(2+)-sensitive inwardly rectifying K(+) current and two types of voltage-gated K(+) currents, sensitive to tetraethylammonium/stromatoxin (delayed rectifying, Kv2.1/2.2) and 4-aminopyridine (A current). Voltage-gated tetrodotoxin (TTX)-sensitive Na(+) currents contributed to the action potential upstroke but TTX had no effect on somatostatin release. Delta cells are equipped with Ca(2+) channels blocked by isradipine (L), omega-agatoxin (P/Q) and NNC 55-0396 (T). Blockade of any of these channels interferes with delta cell electrical activity and abolishes glucose-stimulated somatostatin release. Capacitance measurements revealed a slow component of depolarisation-evoked exocytosis sensitive to omega-agatoxin.

CONCLUSIONS/INTERPRETATION

Action potential firing in delta cells is modulated by ATP-sensitive K(+)-channel activity. The membrane potential is stabilised by Ba(2+)-sensitive inwardly rectifying K(+) channels. Voltage-gated L- and T-type Ca(2+) channels are required for electrical activity, whereas Na(+) currents and P/Q-type Ca(2+) channels contribute to (but are not necessary for) the upstroke of the action potential. Action potential repolarisation is mediated by A-type and Kv2.1/2.2 K(+) channels. Exocytosis is tightly linked to Ca(2+)-influx via P/Q-type Ca(2+) channels. Glucose stimulation of somatostatin secretion involves both K(ATP) channel-dependent and -independent processes.