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

Mechanisms and Functions of Sweet Reception in Oral and Extraoral Organs

The oral detection of sugars relies on two types of receptor systems. The first is the G-protein-coupled receptor TAS1R2/TAS1R3. When activated, this receptor triggers a downstream signaling cascade involving gustducin, phospholipase Cβ2 (PLCβ2), and transient receptor potential channel M5 (TRPM5). The second type of receptor is the glucose transporter. When glucose enters the cell via this transporter, it is metabolized to produce ATP. This ATP inhibits the opening of KATP channels, leading to cell depolarization. Beside these receptor systems, sweet-sensitive taste cells have mechanisms to regulate their sensitivity to sweet substances based on internal and external states of the body. Sweet taste receptors are not limited to the oral cavity; they are also present in extraoral organs such as the gastrointestinal tract, pancreas, and brain. These extraoral sweet receptors are involved in various functions, including glucose absorption, insulin release, sugar preference, and food intake, contributing to the maintenance of energy homeostasis. Additionally, sweet receptors may have unique roles in certain organs like the trachea and bone. This review summarizes past and recent studies on sweet receptor systems, exploring the molecular mechanisms and physiological functions of sweet (sugar) detection in both oral and extraoral organs.

STIM1 regulates pancreatic β-cell behaviour: A modelling study

Pancreatic β-cells are equipped with the molecular machinery allowing them to respond to high glucose levels in the form of electrical activity and Ca2+ oscillations. These oscillations drive insulin secretion. Two key ionic mechanisms involved in this response are the Store-Operated Current and the current through ATP-dependent K+ channels. Both currents have been shown to be regulated by the protein STIM1, but this dual regulation by STIM1 has not been studied before. In this paper, we use mathematical modelling to gain insight into the role of STIM1 in the β-cell response. We extended a previous β-cell model to include the dynamics of STIM1 and described the dependence of the ATP-dependent K+ current on STIM1. Our simulations suggest that the total concentration of STIM1 modifies the bursting frequency, the burst duration and the intracellular Ca2+ levels. These results are in good agreement with experimental reports, and the contribution of the studied currents to electrical activity and Ca2+ dynamics is discussed. The model predicts that in the absence of STIM1 the excitability of the plasma membrane increases and that the glucose threshold for electrical activity is shifted to lower concentrations. These computational predictions may be related to impaired insulin secretion under conditions of reduced STIM1 in the diabetic state.

A primer on modelling pancreatic islets: from models of coupled β-cells to multicellular islet models

Pancreatic islets are mini-organs composed of hundreds or thousands of ɑ, β and δ-cells, which, respectively, secrete glucagon, insulin and somatostatin, key hormones for the regulation of blood glucose. In pancreatic islets, hormone secretion is tightly regulated by both internal and external mechanisms, including electrical communication and paracrine signaling between islet cells. Given its complexity, the experimental study of pancreatic islets has been complemented with computational modeling as a tool to gain a better understanding about how all the mechanisms involved at different levels of organization interact. In this review, we describe how multicellular models of pancreatic cells have evolved from the early models of electrically coupled β-cells to models in which experimentally derived architectures and both electrical and paracrine signals have been considered.

A pathway model of glucose-stimulated insulin secretion in the pancreatic β-cell

The pancreas plays a critical role in maintaining glucose homeostasis through the secretion of hormones from the islets of Langerhans. Glucose-stimulated insulin secretion (GSIS) by the pancreatic β-cell is the main mechanism for reducing elevated plasma glucose. Here we present a systematic modeling workflow for the development of kinetic pathway models using the Systems Biology Markup Language (SBML). Steps include retrieval of information from databases, curation of experimental and clinical data for model calibration and validation, integration of heterogeneous data including absolute and relative measurements, unit normalization, data normalization, and model annotation. An important factor was the reproducibility and exchangeability of the model, which allowed the use of various existing tools. The workflow was applied to construct a novel data-driven kinetic model of GSIS in the pancreatic β-cell based on experimental and clinical data from 39 studies spanning 50 years of pancreatic, islet, and β-cell research in humans, rats, mice, and cell lines. The model consists of detailed glycolysis and phenomenological equations for insulin secretion coupled to cellular energy state, ATP dynamics and (ATP/ADP ratio). Key findings of our work are that in GSIS there is a glucose-dependent increase in almost all intermediates of glycolysis. This increase in glycolytic metabolites is accompanied by an increase in energy metabolites, especially ATP and NADH. One of the few decreasing metabolites is ADP, which, in combination with the increase in ATP, results in a large increase in ATP/ADP ratios in the β-cell with increasing glucose. Insulin secretion is dependent on ATP/ADP, resulting in glucose-stimulated insulin secretion. The observed glucose-dependent increase in glycolytic intermediates and the resulting change in ATP/ADP ratios and insulin secretion is a robust phenomenon observed across data sets, experimental systems and species. Model predictions of the glucose-dependent response of glycolytic intermediates and biphasic insulin secretion are in good agreement with experimental measurements. Our model predicts that factors affecting ATP consumption, ATP formation, hexokinase, phosphofructokinase, and ATP/ADP-dependent insulin secretion have a major effect on GSIS. In conclusion, we have developed and applied a systematic modeling workflow for pathway models that allowed us to gain insight into key mechanisms in GSIS in the pancreatic β-cell.

Ca2+ release or Ca2+ entry, that is the question: what governs Ca2+ oscillations in pancreatic β cells?

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model.

TRPC3 Regulates Islet Beta-Cell Insulin Secretion

Insulin release is tightly controlled by glucose-stimulated calcium (GSCa) through hitherto equivocal pathways. This study investigates TRPC3, a non-selective cation channel, as a critical regulator of insulin secretion and glucose control. TRPC3's involvement in glucose-stimulated insulin secretion (GSIS) is studied in human and animal islets. TRPC3-dependent in vivo insulin secretion is investigated using pharmacological tools and Trpc3-/- mice. TRPC3's involvement in islet glucose uptake and GSCa is explored using fluorescent glucose analogue 2-[N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl) amino]-2-deoxy-D-glucose and calcium imaging. TRPC3 modulation by a small-molecule activator, GSK1702934A, is evaluated in type 2 diabetic mice. TRPC3 is functionally expressed in human and mouse islet beta cells. TRPC3-controlled insulin secretion is KATP -independent and primarily mediated by diacylglycerol channel regulation of the cytosolic calcium oscillations following glucose stimulation. Conversely, glucose uptake in islets is independent of TRPC3. TRPC3 pharmacologic inhibition and knockout in mice lead to defective insulin secretion and glucose intolerance. Subsequently, TRPC3 activation through targeted small-molecule enhances insulin secretion and alleviates diabetes hallmarks in animals. This study imputes a function for TRPC3 at the onset of GSIS. These insights strengthen one's knowledge of insulin secretion physiology and set forth the TRPC3 channel as an appealing candidate for drug development in the treatment of diabetes.

A Review of Fibraurea tinctoria and Its Component, Berberine, as an Antidiabetic and Antioxidant

Diabetes mellitus is a group of metabolic disorders characterized by hyperglycemia caused by resistance to insulin action, inadequate insulin secretion, or excessive glucagon production. Numerous studies have linked diabetes mellitus and oxidative stress. People with diabetes usually exhibit high oxidative stress due to persistent and chronic hyperglycemia, which impairs the activity of the antioxidant defense system and promotes the formation of free radicals. Recently, several studies have focused on exploring natural antioxidants to improve diabetes mellitus. Fibraurea tinctoria has long been known as the native Borneo used in traditional medicine to treat diabetes. Taxonomically, this plant is part of the Menispermaceae family, widely known for producing various alkaloids. Among them are protoberberine alkaloids such as berberine. Berberine is an isoquinoline alkaloid with many pharmacological activities. Berberine is receiving considerable interest because of its antidiabetic and antioxidant activities, which are based on many biochemical pathways. Therefore, this review explores the pharmacological effects of Fibraurea tinctoria and its active constituent, berberine, against oxidative stress and diabetes, emphasizing its mechanistic aspects. This review also summarizes the pharmacokinetics and toxicity of berberine and in silico studies of berberine in several diseases and its protein targets.

Pulsatile Basal Insulin Secretion Is Driven by Glycolytic Oscillations

In fasted and fed states, blood insulin levels are oscillatory. While this phenomenon is well studied at high glucose levels, comparatively little is known about its origin under basal conditions. We propose a possible mechanism for basal insulin oscillations based on oscillations in glycolysis, demonstrated using an established mathematical model. At high glucose, this is superseded by a calcium-dependent mechanism.

From Isles of Königsberg to Islets of Langerhans: Examining the Function of the Endocrine Pancreas Through Network Science

Islets of Langerhans are multicellular microorgans located in the pancreas that play a central role in whole-body energy homeostasis. Through secretion of insulin and other hormones they regulate postprandial storage and interprandial usage of energy-rich nutrients. In these clusters of hormone-secreting endocrine cells, intricate cell-cell communication is essential for proper function. Electrical coupling between the insulin-secreting beta cells through gap junctions composed of connexin36 is particularly important, as it provides the required, most important, basis for coordinated responses of the beta cell population. The increasing evidence that gap-junctional communication and its modulation are vital to well-regulated secretion of insulin has stimulated immense interest in how subpopulations of heterogeneous beta cells are functionally arranged throughout the islets and how they mediate intercellular signals. In the last decade, several novel techniques have been proposed to assess cooperation between cells in islets, including the prosperous combination of multicellular imaging and network science. In the present contribution, we review recent advances related to the application of complex network approaches to uncover the functional connectivity patterns among cells within the islets. We first provide an accessible introduction to the basic principles of network theory, enumerating the measures characterizing the intercellular interactions and quantifying the functional integration and segregation of a multicellular system. Then we describe methodological approaches to construct functional beta cell networks, point out possible pitfalls, and specify the functional implications of beta cell network examinations. We continue by highlighting the recent findings obtained through advanced multicellular imaging techniques supported by network-based analyses, giving special emphasis to the current developments in both mouse and human islets, as well as outlining challenges offered by the multilayer network formalism in exploring the collective activity of islet cell populations. Finally, we emphasize that the combination of these imaging techniques and network-based analyses does not only represent an innovative concept that can be used to describe and interpret the physiology of islets, but also provides fertile ground for delineating normal from pathological function and for quantifying the changes in islet communication networks associated with the development of diabetes mellitus.

Endoplasmic Reticulum (ER) Stress and Its Role in Pancreatic β-Cell Dysfunction and Senescence in Type 2 Diabetes

An increased life span and accompanying nutritional affluency have led to a rapid increase in diseases associated with aging, such as obesity and type 2 diabetes, imposing a tremendous economic and health burden on society. Pancreatic β-cells are crucial for controlling glucose homeostasis by properly producing and secreting the glucose-lowering hormone insulin, and the dysfunction of β-cells determines the outcomes for both type 1 and type 2 diabetes. As the native structure of insulin is formed within the endoplasmic reticulum (ER), ER homeostasis should be appropriately maintained to allow for the proper metabolic homeostasis and functioning of β-cells. Recent studies have found that cellular senescence is critically linked with cellular stresses, including ER stress, oxidative stress, and mitochondrial stress. These studies implied that β-cell senescence is caused by ER stress and other cellular stresses and contributes to β-cells’ dysfunction and the impairment of glucose homeostasis. This review documents and discusses the current understanding of cellular senescence, β-cell function, ER stress, its associated signaling mechanism (unfolded protein response), and the effect of ER stress on β-cell senescence and dysfunction.

Oscillations in K(ATP) conductance drive slow calcium oscillations in pancreatic β-cells

ATP-sensitive K+ (K(ATP)) channels were first reported in the β-cells of pancreatic islets in 1984, and it was soon established that they are the primary means by which the blood glucose level is transduced to cellular electrical activity and consequently insulin secretion. However, the role that the K(ATP) channels play in driving the bursting electrical activity of islet β-cells, which drives pulsatile insulin secretion, remains unclear. One difficulty is that bursting is abolished when several different ion channel types are blocked pharmacologically or genetically, making it challenging to distinguish causation from correlation. Here, we demonstrate a means for determining whether activity-dependent oscillations in K(ATP) conductance play the primary role in driving electrical bursting in β-cells. We use mathematical models to predict that if K(ATP) is the driver, then contrary to intuition, the mean, peak, and nadir levels of ATP/ADP should be invariant to changes in glucose within the concentration range that supports bursting. We test this in islets using Perceval-HR to image oscillations in ATP/ADP. We find that mean, peak, and nadir levels are indeed approximately invariant, supporting the hypothesis that oscillations in K(ATP) conductance are the main drivers of the slow bursting oscillations typically seen at stimulatory glucose levels in mouse islets. In conclusion, we provide, for the first time to our knowledge, causal evidence for the role of K(ATP) channels not only as the primary target for glucose regulation but also for their role in driving bursting electrical activity and pulsatile insulin secretion.

Impact of β-Amyloids Induced Disruption of Ca2+ Homeostasis in a Simple Model of Neuronal Activity

Alzheimer’s disease is characterized by a marked dysregulation of intracellular Ca²⁺ homeostasis. In particular, toxic β-amyloids (Aβ) perturb the activities of numerous Ca²⁺ transporters or channels. Because of the tight coupling between Ca²⁺ dynamics and the membrane electrical activity, such perturbations are also expected to affect neuronal excitability. We used mathematical modeling to systematically investigate the effects of changing the activities of the various targets of Aβ peptides reported in the literature on calcium dynamics and neuronal excitability. We found that the evolution of Ca²⁺ concentration just below the plasma membrane is regulated by the exchanges with the extracellular medium, and is practically independent from the Ca²⁺ exchanges with the endoplasmic reticulum. Thus, disruptions of Ca²⁺ homeostasis interfering with signaling do not affect the electrical properties of the neurons at the single cell level. In contrast, the model predicts that by affecting the activities of L-type Ca²⁺ channels or Ca²⁺-activated K⁺ channels, Aβ peptides promote neuronal hyperexcitability. On the contrary, they induce hypo-excitability when acting on the plasma membrane Ca²⁺ ATPases. Finally, the presence of pores of amyloids in the plasma membrane can induce hypo- or hyperexcitability, depending on the conditions. These modeling conclusions should help with analyzing experimental observations in which Aβ peptides interfere at several levels with Ca²⁺ signaling and neuronal activity.

Comparative analysis of reconstructed architectures from mice and human islets

Intra-islet communication via electrical, paracrine and autocrine signals, is highly dependent on the organization of cells within the islets and is key for an adequate response to changes in blood glucose and other stimuli. In spite of the fact that relevant structural differences between mouse and human islet architectures have been described, the functional implications of these differences remain only partially understood. In this work, aiming to contribute to a better understanding of the relationship between structural and functional properties of pancreatic islets, we reconstructed human and mice islets in order to perform a structural comparison based on both morphologic and network-derived metrics. According to our results, human islets constitute a more efficient network from a connectivity viewpoint, mainly due to the higher proportion of heterotypic contacts between islet cells in comparison to mice islets.

Eugenosedin-A improves obesity-related hyperglycemia by regulating ATP-sensitive K+ channels and insulin secretion in pancreatic β cells

Eugenosedin-A (Eu-A) has been shown to protect against hyperglycemia- and hyperlipidemia-induced metabolic syndrome. We investigated the relationship of K_ATP channel activities and insulin secretion by Eu-A in vitro in pancreatic β-cells, and examined the effect of Eu-A on streptozotocin (STZ)/nicotinamide (NA)-induced type 2 diabetes mellitus (T2DM) in vivo. We isolated pancreatic islets from adult male Wistar rats (250-350 g) and identified pancreatic β-cells by the cell size, capacitance and membrane potential. Perforated patch-clamp and inside-out recordings were used to monitor the membrane potential (current-clamp mode) and channel activity (voltage-clamp mode) of β-cells. The membrane potential of β-cells was raised by Eu-A and reversed by the K_ATP channel activator diazoxide. Eu-A inhibited the K_ATP channel activity measured at - 60 mV and increased the intracellular calcium concentration ([Ca²⁺]_i), resulting in enhanced insulin secretion. Eu-A also reduced Kir6.2 protein on the cell membrane and scattered in the cytosol under normal glucose conditions (5.6 mM). In our animal study, rats were divided into normal and STZ/NA-induced T2DM groups. Normal rats fed with regular chow were divided into control and control+Eu-A (5 mg/kg/day, i.p.) groups. The STZ/NA-induced diabetic rats fed with a high-fat diet (HFD) were divided into three groups: T2DM, T2DM+Eu-A (5 mg/kg/day, i.p.), and T2DM+glibenclamide (0.5 mg/kg/day, i.p.; a K_ATP channel inhibitor). Both Eu-A and glibenclamide decreased the rats' blood glucose, prevented weight gain, and enhanced insulin secretion. We found that Eu-A blocked pancreatic β-cell K_ATP channels, caused membrane potential depolarization, and stimulated Ca²⁺ influx, thus increasing insulin secretion. Furthermore, Eu-A decreased blood glucose and increased insulin levels in T2DM rats. These results suggested that Eu-A might have clinical benefits for the control of T2DM and its complications.

On the Electrophysiological Component of Pancreatic Alpha-Cell Models

Glucagon, the main hormone responsible for increasing blood glucose levels, is secreted by pancreatic alphacells in a Ca²⁺ dependent process associated to membrane potential oscillations developed by the dynamic operation of K⁺, Na⁺ and Ca²⁺ channels. The mechanisms behind membrane potential and Ca²⁺ oscillations in alpha-cells are still under debate, and some new research works have used alpha-cell models to describe electrical activity. In this paper we studied the dynamics of electrical activity of three alpha-cell models using the Lead Potential Analysis method and Bifurcation Diagrams. Our aim is to highlight the differences in their dynamic behavior and therefore, in their response to glucose. Both issues are relevant to understand the stimulus-secretion coupling in alpha-cells and then, the mechanisms behind their dysregulation in Type 2 Diabetes.Clinical Relevance - A reliable description of the electrophysiological mechanisms in pancreatic alpha-cells is key to understand and treat the dysregulation of these cells in patients with Type 2 Diabetes.

Glucose-induced [Ca2+]i oscillations in β cells are composed of trains of spikes within a subplasmalemmal microdomain

Electrical activity and oscillations of cytosolic Ca²⁺ concentrations ([Ca²⁺]_i) that trigger insulin release in response to glucose are key functions of pancreatic β cells. Although oscillatory Ca²⁺ signals have been intensively studied in β cells, their lower frequency did not match that of electrical activity. In addition, the measured peak [Ca²⁺]_i did not reach levels that are typically required by synaptotagmins to elicit the release of insulin-containing vesicles in live-cell experiments. We therefore sought to resolve the Ca²⁺ dynamics in the subplasmalemmal microdomain that is critical for triggering fast exocytosis. Applying total internal reflection fluorescence (TIRF) microscopy in insulin-producing INS-1E and primary mouse β cells, we resolved extraordinary fast trains of Ca²⁺ spiking (frequency > 3 s^-1) in response to glucose exposure. Using a low-affinity [Ca²⁺]_i indicator dye, we provide experimental evidence that Ca²⁺ spikes reach low micromolar apparent concentrations in the vicinity of the plasma membrane_. Analysis of Ca²⁺ spikes evoked by repeated depolarization for 10 ms closely matched the Ca²⁺ dynamics observed upon glucose application. To our knowledge, this is the first study that experimentally demonstrates Ca²⁺ spikes in β cells with velocities that resemble those of bursting or continuously appearing trains of action potentials (APs) in non-patched cells.

Bayesian metamodeling of complex biological systems across varying representations

Comprehensive modeling of a whole cell requires an integration of vast amounts of information on various aspects of the cell and its parts. To divide and conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models. Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity. These input models are 1) converted to a standardized statistical representation relying on probabilistic graphical models, 2) coupled by modeling their mutual relations with the physical world, and 3) finally harmonized with respect to each other. To illustrate Bayesian metamodeling, we provide a proof-of-principle metamodel of glucose-stimulated insulin secretion by human pancreatic β-cells. The input models include a coarse-grained spatiotemporal simulation of insulin vesicle trafficking, docking, and exocytosis; a molecular network model of glucose-stimulated insulin secretion signaling; a network model of insulin metabolism; a structural model of glucagon-like peptide-1 receptor activation; a linear model of a pancreatic cell population; and ordinary differential equations for systemic postprandial insulin response. Metamodeling benefits from decentralized computing, while often producing a more accurate, precise, and complete model that contextualizes input models as well as resolves conflicting information. We anticipate Bayesian metamodeling will facilitate collaborative science by providing a framework for sharing expertise, resources, data, and models, as exemplified by the Pancreatic β-Cell Consortium.

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.

Mathematical Modeling for the Physiological and Clinical Investigation of Glucose Homeostasis and Diabetes

Mathematical modeling in the field of glucose metabolism has a longstanding tradition. The use of models is motivated by several reasons. Models have been used for calculating parameters of physiological interest from experimental data indirectly, to provide an unambiguous quantitative representation of pathophysiological mechanisms, to determine indices of clinical usefulness from simple experimental tests. With the growing societal impact of type 2 diabetes, which involves the disturbance of the glucose homeostasis system, development and use of models in this area have increased. Following the approaches of physiological and clinical investigation, the focus of the models has spanned from representations of whole body processes to those of cells, i.e., from in vivo to in vitro research. Model-based approaches for linking in vivo to in vitro research have been proposed, as well as multiscale models merging the two areas. The success and impact of models has been variable. Two kinds of models have received remarkable interest: those widely used in clinical applications, e.g., for the assessment of insulin sensitivity and β-cell function and some models representing specific aspects of the glucose homeostasis system, which have become iconic for their efficacy in describing clearly and compactly key physiological processes, such as insulin secretion from the pancreatic β cells. Models are inevitably simplified and approximate representations of a physiological system. Key to their success is an appropriate balance between adherence to reality, comprehensibility, interpretative value and practical usefulness. This has been achieved with a variety of approaches. Although many models concerning the glucose homeostasis system have been proposed, research in this area still needs to address numerous issues and tackle new opportunities. The mathematical representation of the glucose homeostasis processes is only partial, also because some mechanisms are still only partially understood. For in vitro research, mathematical models still need to develop their potential. This review illustrates the problems, approaches and contribution of mathematical modeling to the physiological and clinical investigation of glucose homeostasis and diabetes, focusing on the most relevant and stimulating models.

Electrophysiological models of the human pancreatic δ-cell: From single channels to the firing of action potentials

Minimal mathematical models were developed to describe the electrophysiological properties of human δ-cells. Markov models of single channels were first developed based on the analysis of electrophysiological data. Monte Carlo simulations of voltage-clamp experiments were performed in an iteratively optimization procedure to estimate the number of channels required to reproduce the main characteristics of the macroscopic currents recorded experimentally. A membrane model of the firing of action potentials was then developed based on the kinetic schemes of single channels and the number of channels estimated. We showed that macroscopic currents of human δ-cells can be reproduced by minimal models of single channels when the appropriate number of channels is considered. In addition, our simulations suggest that human δ-cells are capable of generating action potentials through the interaction of the ionic currents involved. Finally, we determined the relative contribution of the currents underlying the firing of action potentials in human pancreatic δ-cells, which allowed us to propose a qualitative model of an action potential in terms of the underlying ionic currents.

From Hyper- to Hypoinsulinemia and Diabetes: Effect of KCNH6 on Insulin Secretion

Glucose-stimulated insulin secretion from islet β cells is mediated by K_ATP channels. However, the role of non-K_ATP K⁺ channels in insulin secretion is largely unknown. Here, we show that a non-K_ATP K⁺ channel, KCNH6, plays a key role in insulin secretion and glucose hemostasis in humans and mice. KCNH6 p.P235L heterozygous mutation co-separated with diabetes in a four-generation pedigree. Kcnh6 knockout (KO) or Kcnh6 p.P235L knockin (KI) mice had a phenotype characterized by changing from hypoglycemia with hyperinsulinemia to hyperglycemia with insulin deficiency. Islets from the young KO mice had increased intracellular calcium concentration and increased insulin secretion. However, islets from the adult KO mice not only had increased intracellular calcium levels but also had remarkable ER stress and apoptosis, associated with loss of β cell mass and decreased insulin secretion. Therefore, dysfunction of KCNH6 causes overstimulation of insulin secretion in the short term and β cell failure in the long term.

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.

Calcium Signaling and Contractility in Cardiac Myocyte of Wolframin Deficient Rats

Wolframin (Wfs1) is a membrane protein of the sarco/endoplasmic reticulum. Wfs1 mutations are responsible for the Wolfram syndrome, characterized by diabetic and neurological symptoms. Although Wfs1 is expressed in cardiac muscle, its role in this tissue is not clear. We have characterized the effect of invalidation of Wfs1 on calcium signaling-related processes in isolated ventricular myocytes of exon5-Wfs1 deficient rats (Wfs1-e5/-e5) before the onset of overt disease. Calcium transients and contraction were measured in field-stimulated isolated myocytes using confocal microscopy with calcium indicator fluo-3 AM and sarcomere length detection. Calcium currents and their calcium release-dependent inactivation were characterized in whole-cell patch-clamp experiments. At 4 months, Wfs1-e5/-e5 animals were euglycemic, and echocardiographic examination revealed fully compensated cardiac function. In field-stimulated isolated ventricular myocytes, both the amplitude and the duration of contraction of Wfs1-e5/-e5 animals were elevated relative to control Wfs1+/+ littermates. Increased contractility of myocytes resulted largely from prolonged cytosolic calcium transients. Neither the amplitude of calcium currents nor their voltage dependence of activation differed between the two groups. Calcium currents in Wfs1-e5/-e5 myocytes showed a larger extent of inactivation by short voltage prepulses applied to selectively induce calcium release-dependent inactivation of calcium current. Neither the calcium content of the sarcoplasmic reticulum, measured by application of 20 mmol/l caffeine, nor the expression of SERCA2, determined from Western blots, differed significantly in myocytes of Wfs1-e5/-e5 animals compared to control ones. These experiments point to increased duration of calcium release in ventricular myocytes of Wfs1-e5/-e5 animals. We speculate that the lack of functional wolframin might cause changes leading to upregulation of RyR2 channels resulting in prolongation of channel openings and/or a delay in termination of calcium release.

Decoding the regulatory mechanism of glucose and insulin induced phosphatidylinositol 3,4,5-trisphosphate dynamics in β-cells

In MIN6 pancreatic β-cells, glucose and insulin act in a synergistic manner to regulate the dynamics of Phosphatidylinositol (3,4,5)-trisphosphate (PIP₃). However, the precise regulatory mechanism behind such an experimentally observed synergy is poorly understood. In this article, we propose a phenomenological mathematical model for studying the glucose and insulin driven PIP₃ activation dynamics under various stimulatory conditions to unfold the mechanism responsible for the observed synergy. The modeling study reveals that the experimentally observed oscillation in PIP₃ dynamics with disparate time scales for different external glucose doses is mainly orchestrated by the complex dynamic regulation of cytosolic Ca²⁺ in β-cells. The model accounts for the dose-dependent activation of PIP₃ as a function of externally added insulin, and further shows that even in the absence of Ca²⁺ signaling, externally added glucose can still maintain a basal level of endogenous insulin secretion via the fatty acid metabolism pathway. Importantly, the model analysis suggests that the glucose mediated ROS (reactive oxygen species) activation often contributes considerably to the synergistic activation of PIP₃ by glucose and insulin in a context dependent manner. Under the physiological conditions that keep β-cells in an insulin responsive state, the effect of glucose induced ROS signaling plays a moderate role in PIP₃ activation. As β-cells approach an insulin resistant state, the glucose induced ROS signaling significantly affects the PIP₃ dynamics. Our findings provide a plausible mechanistic insight into the experimentally observed synergy, and can lead to novel therapeutic strategies.

Investigation of the role of ion channels in human pancreatic β-cell hubs: A mathematical modeling study

In many cellular networks, the structure of the network follows a scale-free organization, where a limited number of cells are strongly coupled to other cells. These cells are called hub cells and their critical roles are well accepted. Despite their importance, there have been only a few studies investigating the characteristic features of these cells. In this paper, a computational approach is proposed to study the possible role of different ion channels in distinguishing between the hub and non-hub cells. The results show that the P/Q-type and T-type calcium channels may have an especial role in the β-cell hubs because the high-level expressions of these channels make a pancreatic β-cell more potent to force other coupled cells to follow it. In addition, in order to consider the variation of the coupling strength with voltage, a novel mathematical model is proposed for the gap junction coupling between the pancreatic β-cells. The proposed approach is validated based on the data from the literature.

Effects of polysaccharide from Portulaca oleracea L. on voltage-gated Na+ channel of INS-1 cells

Our previous work showed that polysaccharide isolated from Portulaca oleracea L. (POP) has an insulinotropic effect. The voltage-gated Na⁺ channel (VGSC) in the excitement phase plays an important role. This work aims to study the effect of POP on the voltage-gated Na⁺ channel current (I_Na) and its channel dynamic characteristics in insulin-secreting β-cell line (INS-1) cells of rat. Our results revealed that POP can inhibit the amplitude of I_Na and improve cell survival in a concentration-dependent manner. POP concentration of 0.5 mg mL^-1 reduced the amplitude of I_Na, suppressed the I_Na of steady-state activation, shifted the steady-state inactivation curves of I_Na to negative potentials, prolonged the time course of I_Na recovery from inactivation, and enhanced the activity-dependent attenuation of I_Na. Furthermore, 0.5 mg mL^-1 POP or low concentration of tetrodotoxin (TTX, a VGSC-specific blocker) partially inhibited I_Na and also improved insulin synthesis and cell survival. Collectively, these results revealed that POP protects INS-1 cells and enhances the insulin synthesis in INS-1 cells, and the mechanism through the partial inhibition on I_Na channel is strongly recommended.

The triggering pathway to insulin secretion: Functional similarities and differences between the human and the mouse β cells and their translational relevance

In β cells, stimulation by metabolic, hormonal, neuronal, and pharmacological factors is coupled to secretion of insulin through different intracellular signaling pathways. Our knowledge about the molecular machinery supporting these pathways and the patterns of signals it generates comes mostly from rodent models, especially the laboratory mouse. The increased availability of human islets for research during the last few decades has yielded new insights into the specifics in signaling pathways leading to insulin secretion in humans. In this review, we follow the most central triggering pathway to insulin secretion from its very beginning when glucose enters the β cell to the calcium oscillations it produces to trigger fusion of insulin containing granules with the plasma membrane. Along the way, we describe the crucial building blocks that contribute to the flow of information and focus on their functional role in mice and humans and on their translational implications.

Encompassing ATP, DNA, insulin, and protein content for quantification and assessment of human pancreatic islets

Islet transplantation has made major progress to treat patients with type 1 diabetes. Islet mass and quality are critically important to ensure successful transplantation. Currently, islet status is evaluated using insulin secretion, oxygen consumption rate, or adenosine triphosphate (ATP) measurement. These parameters are evaluated independently and do not effectively predict islet status post-transplant. Therefore, assessing human pancreatic islets by encompassing ATP, DNA, insulin, and protein content from a single tissue sample would serve as a better predictor for islet status. In this study, a single step procedure for extracting ATP, DNA, insulin, and protein content from human pancreatic islets was described and the biomolecule contents were quantified. Additionally, different mathematical calculations integrating total ATP, DNA, insulin, and protein content were randomly tested under various conditions to predict islet status. The results demonstrated that the ATP assay was efficient and the biomolecules were effectively quantified. Furthermore, the mathematical formula we developed could be optimized to predict islet status. In conclusion, our results indicate a proof-of-concept that a simple logarithmic formula can predict overall islet status for various conditions when total islet ATP, DNA, insulin, and protein content are simultaneously assessed from a single tissue sample.

The Pancreatic β-Cell: A Bioenergetic Perspective

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

Survival and growth of C57BL/6J mice lacking the BK channel, Kcnma1: lower adult body weight occurs together with higher body fat

Big conductance potassium (BK) channels contribute to K⁺ flow and electrical behavior in many cell types. Mice made null for the gene (Kcnma1) producing the BK channel (BK^KO) exhibit numerous deficits in physiological functions. Breeding mice lacking a single allele of Kcnma1 (C57BL/6J background) had litter sizes of approximately eight pups. For the period of maternal care (P0–P21), pup deaths peaked at P1 with a second less severe interval of death peaking near P13. Early deaths were twice as likely during a 20‐month period of building construction compared with the quiescent period after cessation of construction. Births during construction were not consistent with Mendelian predictions indicating the likelihood of a specific disadvantage induced by this environmental stressor. Later BK^KO pup deaths (~P13) also were more numerous than Mendelian expectations. After weaning, weight gain was slower for BK^KO mice compared with wild‐type littermates: 5 g less for male BK^KO mice and 4 g less for female BK^KO mice. Body composition determined by quantitative magnetic resonance indicated a higher fat proportion for wild‐type female mice compared with males, as well as a higher hydration ratio. Both male and female BK^KO mice showed higher fat proportions than wild‐type, with female BK^KO mice exhibiting greater variation. Together, these results indicate that BK^KO mice suffered disadvantages that lead to prenatal and perinatal death. A metabolic difference likely related to glucose handling led to the smaller body size and distinct composition for BK^KO mice, suggesting a diversion of energy supplies from growth to fat storage.

Potentiation of Calcium Influx and Insulin Secretion in Pancreatic Beta Cell by the Specific TREK-1 Blocker Spadin

Inhibition of the potassium channels TREK-1 by spadin (SPA) is currently thought to be a promising therapeutic target for the treatment of depression. Since these channels are expressed in pancreatic β-cells, we investigated their role in the control of insulin secretion and glucose homeostasis. In this study, we confirmed the expression of TREK-1 channels in the insulin secreting MIN6-B1 β-cell line and in mouse islets. We found that their blockade by SPA potentiated insulin secretion induced by potassium chloride dependent membrane depolarization. Inhibition of TREK-1 by SPA induced a decrease of the resting membrane potential (ΔV_m ~ 12 mV) and increased the cytosolic calcium concentration. In mice, administration of SPA enhanced the plasma insulin level stimulated by glucose, confirming its secretagogue effect observed in vitro. Taken together, this work identifies SPA as a novel potential pharmacological agent able to control insulin secretion and glucose homeostasis.

Membrane Potential and Calcium Dynamics in Beta Cells from Mouse Pancreas Tissue Slices: Theory, Experimentation, and Analysis

Beta cells in the pancreatic islets of Langerhans are precise biological sensors for glucose and play a central role in balancing the organism between catabolic and anabolic needs. A hallmark of the beta cell response to glucose are oscillatory changes of membrane potential that are tightly coupled with oscillatory changes in intracellular calcium concentration which, in turn, elicit oscillations of insulin secretion. Both membrane potential and calcium changes spread from one beta cell to the other in a wave-like manner. In order to assess the properties of the abovementioned responses to physiological and pathological stimuli, the main challenge remains how to effectively measure membrane potential and calcium changes at the same time with high spatial and temporal resolution, and also in as many cells as possible. To date, the most wide-spread approach has employed the electrophysiological patch-clamp method to monitor membrane potential changes. Inherently, this technique has many advantages, such as a direct contact with the cell and a high temporal resolution. However, it allows one to assess information from a single cell only. In some instances, this technique has been used in conjunction with CCD camera-based imaging, offering the opportunity to simultaneously monitor membrane potential and calcium changes, but not in the same cells and not with a reliable cellular or subcellular spatial resolution. Recently, a novel family of highly-sensitive membrane potential reporter dyes in combination with high temporal and spatial confocal calcium imaging allows for simultaneously detecting membrane potential and calcium changes in many cells at a time. Since the signals yielded from both types of reporter dyes are inherently noisy, we have developed complex methods of data denoising that permit for visualization and pixel-wise analysis of signals. Combining the experimental approach of high-resolution imaging with the advanced analysis of noisy data enables novel physiological insights and reassessment of current concepts in unprecedented detail.

Modeling Ca(2+) currents and buffered diffusion of Ca(2+) in human β-cells during voltage clamp experiments

Macroscopic Ca(2+) currents of the human β-cells were characterized using the Hodgkin-Huxley formalism. Expressions describing the Ca(2+)-dependent inactivation process of the L-type Ca(2+) channels in terms of the concentration of Ca(2+) were obtained. By coupling the modeled Ca(2+) currents to a three-dimensional model of buffered diffusion of Ca(2+), we simulated the Ca(2+) transients formed in the immediate vicinity of the cell membrane during voltage clamp experiments performed in high buffering conditions. Our modeling approach allowed us to consider the distribution of the Ca(2+) sources over the cell membrane. The effect of exogenous (EGTA) and endogenous Ca(2+) buffers on the temporal course of the Ca(2+) transients was evaluated. We show that despite the high Ca(2+) buffering capacity, nanodomains are formed in the submembrane space, where a peak Ca(2+) concentration between ∼76 and 143 µM was estimated from our simulations. In addition, the contribution of each Ca(2+) current to the formation of the Ca(2+) nanodomains was also addressed. Here we provide a general framework to incorporate the spatial aspects to the models of the pancreatic β-cell, such as a more detailed and realistic description of Ca(2+) dynamics in response to electrical activity in physiological conditions can be provided by future models.

Cross-talks between microRNAs and mRNAs in pancreatic tissues of streptozotocin-induced type 1 diabetic mice

Network cross-talks between microRNAs (miRNAs) and mRNAs may be useful to elucidate the pathological mechanisms of pancreatic islet cells in diabetic individuals. The aim of the present study was to investigate the cross-talks between miRNAs and mRNAs in pancreatic tissues of streptozotocin-induced diabetic mice through microarray and bioinformatic methods. Based on the miRNA microarray, 64 upregulated and 72 downregulated miRNAs were observed in pancreatic tissues in diabetic mice compared to the normal controls. Based on the mRNA microarrray, 507 upregulated mRNAs and 570 downregulated mRNAs were identified in pancreatic tissues in diabetic mice compared to the normal controls. Notably, there were 246 binding points between upregulated miRNA and downregulated mRNAs; simultaneously, there were 583 binding points between downregulated miRNA and upregulated mRNAs. These changed mRNA may potentially involve the following signaling pathways: Insulin secretion, pancreatic secretion, mammalian target of rapamycin signaling pathway, forkhead box O signaling pathway and phosphatidylinositol 3-kinase-protein kinase B signaling. The fluctuating effects of miRNAs and matched mRNAs indicated that miRNAs may have wide cross-talks with mRNAs in pancreatic tissues of type 1 diabetic mice. The cross-talks may play important roles in contributing to impaired islet functions and the development of diabetes. However, further functional validation should be conducted in the future.