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

Kinetic modelling of glycolytic oscillations

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

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.

Metabolic cycles and signals for insulin secretion

In this review, we focus on recent developments in our understanding of nutrient-induced insulin secretion that challenge a key aspect of the "canonical" model, in which an oxidative phosphorylation-driven rise in ATP production closes K_ATP channels. We discuss the importance of intrinsic β cell metabolic oscillations; the phasic alignment of relevant metabolic cycles, shuttles, and shunts; and how their temporal and compartmental relationships align with the triggering phase or the secretory phase of pulsatile insulin secretion. Metabolic signaling components are assigned regulatory, effectory, and/or homeostatic roles vis-à-vis their contribution to glucose sensing, signal transmission, and resetting the system. Taken together, these functions provide a framework for understanding how allostery, anaplerosis, and oxidative metabolism are integrated into the oscillatory behavior of the secretory pathway. By incorporating these temporal as well as newly discovered spatial aspects of β cell metabolism, we propose a much-refined Mito_Cat-Mito_Ox model of the signaling process for the field to evaluate.

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.

Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

Insulin is secreted in a pulsatile pattern, with important physiological ramifications. In pancreatic β-cells, which are the cells that synthesize insulin, insulin exocytosis is elicited by pulses of elevated intracellular Ca²⁺ initiated by bursts of electrical activity. In parallel with these electrical and Ca²⁺ oscillations are oscillations in metabolism, and the periods of all of these oscillatory processes are similar. A key question that remains unresolved is whether the electrical oscillations are responsible for the metabolic oscillations via the effects of Ca²⁺, or whether the metabolic oscillations are responsible for the electrical oscillations due to the effects of ATP on ATP-sensitive ion channels? Mathematical modeling is a useful tool for addressing this and related questions as modeling can aid in the design of well-focused experiments that can test the predictions of particular models and subsequently be used to improve the models in an iterative fashion. In this article, we discuss a recent mathematical model, the Integrated Oscillator Model (IOM), that was the product of many years of development. We use the model to demonstrate that the relationship between calcium and metabolism in beta cells is symbiotic: in some contexts, the electrical oscillations drive the metabolic oscillations, while in other contexts it is the opposite. We provide new insights regarding these results and illustrate that what might at first appear to be contradictory data are actually compatible when viewed holistically with the IOM.

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.

Metabolic regulation of calcium signaling in beta cells

The cytoplasmic Ca²⁺ concentration ([Ca²⁺]_cyt) regulates a vast number of cellular functions, including insulin secretion from beta cells. The major physiological insulin secretagogue, glucose, triggers [Ca²⁺]_cyt oscillations in beta cells. Synchronization of the oscillations among the beta cells within an islet underlies the generation of pulsatile insulin secretion. This review describes the mechanisms generating [Ca²⁺]_cyt oscillations, the interactions between [Ca²⁺]_cyt and cell metabolism, as well as the contribution of various organelles to the shaping of [Ca²⁺]_cyt signals and insulin secretion. It also discusses how Ca²⁺ signals are coordinated and spread throughout the islets and data indicating that altered Ca²⁺ signaling is associated with beta cell dysfunction and development of type 2 diabetes.

Lipid-associated metabolic signalling networks in pancreatic beta cell function

Significant advances have been made in deciphering the mechanisms underlying fuel-stimulated insulin secretion by pancreatic beta cells. The contribution of the triggering/ATP-sensitive potassium (K_ATP)-dependent Ca²⁺ signalling and K_ATP-independent amplification pathways, that include anaplerosis and lipid signalling of glucose-stimulated insulin secretion (GSIS), are well established. A proposed model included a key role for a metabolic partitioning 'switch', the acetyl-CoA carboxylase (ACC)/malonyl-CoA/carnitine palmitoyltransferase-1 (CPT-1) axis, in beta cell glucose and fatty acid signalling for insulin secretion. This model has gained overwhelming support from a number of studies in recent years and is now refined through its link to the glycerolipid/NEFA cycle that provides lipid signals through its lipolysis arm. Furthermore, acetyl-CoA carboxylase may also control beta cell growth. Here we review the evidence supporting a role for the ACC/malonyl-CoA/CPT-1 axis in the control of GSIS and its particular importance under conditions of elevated fatty acids (e.g. fasting, excess nutrients, hyperlipidaemia and diabetes). We also document how it is linked to a more global lipid signalling system that includes the glycerolipid/NEFA cycle.

How Heterogeneity in Glucokinase and Gap-Junction Coupling Determines the Islet [Ca2+] Response

Understanding how cell subpopulations in a tissue impact overall system function is challenging. There is extensive heterogeneity among insulin-secreting β-cells within islets of Langerhans, including their insulin secretory response and gene expression profile, and this heterogeneity can be altered in diabetes. Several studies have identified variations in nutrient sensing between β-cells, including glucokinase (GK) levels, mitochondrial function, or expression of genes important for glucose metabolism. Subpopulations of β-cells with defined electrical properties can disproportionately influence islet-wide free-calcium activity ([Ca2+]) and insulin secretion via gap-junction electrical coupling. However, it is poorly understood how subpopulations of β-cells with altered glucose metabolism may impact islet function. To address this, we utilized a multicellular computational model of the islet in which a population of cells deficient in GK activity and glucose metabolism was imposed on the islet or in which β-cells were heterogeneous in glucose metabolism and GK kinetics were altered. This included simulating GK gene (GCK) mutations that cause monogenic diabetes. We combined these approaches with experimental models in which gck was genetically deleted in a population of cells or GK was pharmacologically inhibited. In each case, we modulated gap-junction electrical coupling. Both the simulated islet and the experimental system required 30-50% of the cells to have near-normal glucose metabolism, fewer than cells with normal KATP conductance. Below this number, the islet lacked any glucose-stimulated [Ca2+] elevations. In the absence of electrical coupling, the change in [Ca2+] was more gradual. As such, electrical coupling allows a large minority of cells with normal glucose metabolism to promote glucose-stimulated [Ca2+]. If insufficient numbers of cells are present, which we predict can be caused by a subset of GCK mutations that cause monogenic diabetes, electrical coupling exacerbates [Ca2+] suppression. This demonstrates precisely how metabolically heterogeneous β-cell populations interact to impact islet function.

Metabolic activation-driven mitochondrial hyperpolarization predicts insulin secretion in human pancreatic beta-cells

Mitochondrial metabolism plays a central role in insulin secretion in pancreatic beta-cells. Generation of protonmotive force and ATP synthesis from glucose-originated pyruvate are critical steps in the canonical pathway of glucose-stimulated insulin secretion. Mitochondrial metabolism is intertwined with pathways that are thought to amplify insulin secretion with mechanisms distinct from the canonical pathway, and the relative importance of these two pathways is controversial. Here I show that glucose-induced mitochondrial membrane potential (MMP) hyperpolarization is necessary for, and predicts, the rate of insulin secretion in primary cultured human beta-cells. When glucose concentration is elevated, increased metabolism results in a substantial MMP hyperpolarization, as well as in increased rates of ATP synthesis and turnover marked by faster cell respiration. Using modular kinetic analysis I explored what properties of cellular energy metabolism enable a large glucose-induced change in MMP in human beta-cells. I found that an ATP-dependent pathway activates glucose or substrate oxidation, acting as a positive feedback in energy metabolism. This activation mechanism is essential for concomitant fast respiration and high MMP, and for a high magnitude glucose-induced MMP hyperpolarization and therefore for insulin secretion.

Metabolic fate of glucose and candidate signaling and excess-fuel detoxification pathways in pancreatic β-cells

Glucose metabolism promotes insulin secretion in β-cells via metabolic coupling factors that are incompletely defined. Moreover, chronically elevated glucose causes β-cell dysfunction, but little is known about how cells handle excess fuels to avoid toxicity. Here we sought to determine which among the candidate pathways and coupling factors best correlates with glucose-stimulated insulin secretion (GSIS), define the fate of glucose in the β-cell, and identify pathways possibly involved in excess-fuel detoxification. We exposed isolated rat islets for 1 h to increasing glucose concentrations and measured various pathways and metabolites. Glucose oxidation, oxygen consumption, and ATP production correlated well with GSIS and saturated at 16 mm glucose. However, glucose utilization, glycerol release, triglyceride and glycogen contents, free fatty acid (FFA) content and release, and cholesterol and cholesterol esters increased linearly up to 25 mm glucose. Besides being oxidized, glucose was mainly metabolized via glycerol production and release and lipid synthesis (particularly FFA, triglycerides, and cholesterol), whereas glycogen production was comparatively low. Using targeted metabolomics in INS-1(832/13) cells, we found that several metabolites correlated well with GSIS, in particular some Krebs cycle intermediates, malonyl-CoA, and lower ADP levels. Glucose dose-dependently increased the dihydroxyacetone phosphate/glycerol 3-phosphate ratio in INS-1(832/13) cells, indicating a more oxidized state of NAD in the cytosol upon glucose stimulation. Overall, the data support a role for accelerated oxidative mitochondrial metabolism, anaplerosis, and malonyl-CoA/lipid signaling in β-cell metabolic signaling and suggest that a decrease in ADP levels is important in GSIS. The results also suggest that excess-fuel detoxification pathways in β-cells possibly comprise glycerol and FFA formation and release extracellularly and the diversion of glucose carbons to triglycerides and cholesterol esters.

Ca2+ Effects on ATP Production and Consumption Have Regulatory Roles on Oscillatory Islet Activity

Pancreatic islets respond to elevated blood glucose by secreting pulses of insulin that parallel oscillations in β-cell metabolism, intracellular Ca(2+) concentration, and bursting electrical activity. The mechanisms that maintain an oscillatory response are not fully understood, yet several models have been proposed. Only some can account for experiments supporting that metabolism is intrinsically oscillatory in β-cells. The dual oscillator model (DOM) implicates glycolysis as the source of oscillatory metabolism. In the companion article, we use recently developed biosensors to confirm that glycolysis is oscillatory and further elucidate the coordination of metabolic and electrical signals in the insulin secretory pathway. In this report, we modify the DOM by incorporating an established link between metabolism and intracellular Ca(2+) to reconcile model predictions with experimental observations from the companion article. With modification, we maintain the distinguishing feature of the DOM, oscillatory glycolysis, but introduce the ability of Ca(2+) influx to reshape glycolytic oscillations by promoting glycolytic efflux. We use the modified model to explain measurements from the companion article and from previously published experiments with islets.

Phase Analysis of Metabolic Oscillations and Membrane Potential in Pancreatic Islet β-Cells

Metabolism in islet β-cells displays oscillations that can trigger pulses of electrical activity and insulin secretion. There has been a decades-long debate among islet biologists about whether metabolic oscillations are intrinsic or occur in response to oscillations in intracellular Ca(2+) that result from bursting electrical activity. In this article, the dynamics of oscillatory metabolism were investigated using five different optical reporters. Reporter activity was measured simultaneously with membrane potential bursting to determine the phase relationships between the metabolic oscillations and electrical activity. Our experimental findings suggest that Ca(2+) entry into β-cells stimulates the rate of mitochondrial metabolism, accounting for the depletion of glycolytic intermediates during each oscillatory burst. We also performed Ca(2+) clamp tests in which we clamped membrane potential with the KATP channel-opener diazoxide and KCl to fix Ca(2+) at an elevated level. These tests confirm that metabolic oscillations do not require Ca(2+) oscillations, but show that Ca(2+) plays a larger role in shaping metabolic oscillations than previously suspected. A dynamical picture of the mechanisms of oscillations emerged that requires the restructuring of contemporary mathematical β-cell models, including our own dual oscillator model. In the companion article, we modified our model to account for these new data.

Pancreatic Beta Cell G-Protein Coupled Receptors and Second Messenger Interactions: A Systems Biology Computational Analysis

Insulin secretory in pancreatic beta-cells responses to nutrient stimuli and hormonal modulators include multiple messengers and signaling pathways with complex interdependencies. Here we present a computational model that incorporates recent data on glucose metabolism, plasma membrane potential, G-protein-coupled-receptors (GPCR), cytoplasmic and endoplasmic reticulum calcium dynamics, cAMP and phospholipase C pathways that regulate interactions between second messengers in pancreatic beta-cells. The values of key model parameters were inferred from published experimental data. The model gives a reasonable fit to important aspects of experimentally measured metabolic and second messenger concentrations and provides a framework for analyzing the role of metabolic, hormones and neurotransmitters changes on insulin secretion. Our analysis of the dynamic data provides support for the hypothesis that activation of Ca²⁺-dependent adenylyl cyclases play a critical role in modulating the effects of glucagon-like peptide 1 (GLP-1), glucose-dependent insulinotropic polypeptide (GIP) and catecholamines. The regulatory properties of adenylyl cyclase isoforms determine fluctuations in cytoplasmic cAMP concentration and reveal a synergistic action of glucose, GLP-1 and GIP on insulin secretion. On the other hand, the regulatory properties of phospholipase C isoforms determine the interaction of glucose, acetylcholine and free fatty acids (FFA) (that act through the FFA receptors) on insulin secretion. We found that a combination of GPCR agonists activating different messenger pathways can stimulate insulin secretion more effectively than a combination of GPCR agonists for a single pathway. This analysis also suggests that the activators of GLP-1, GIP and FFA receptors may have a relatively low risk of hypoglycemia in fasting conditions whereas an activator of muscarinic receptors can increase this risk. This computational analysis demonstrates that study of second messenger pathway interactions will improve understanding of critical regulatory sites, how different GPCRs interact and pharmacological targets for modulating insulin secretion in type 2 diabetes.

Calcium and Metabolic Oscillations in Pancreatic Islets: Who's Driving the Bus?*

Pancreatic islets exhibit bursting oscillations in response to elevated blood glucose. These oscillations are accompanied by oscillations in the free cytosolic Ca2+ concentration (Cac ), which drives pulses of insulin secretion. Both islet Ca2+ and metabolism oscillate, but there is some debate about their interrelationship. Recent experimental data show that metabolic oscillations in some cases persist after the addition of diazoxide (Dz), which opens K(ATP) channels, hyperpolarizing β-cells and preventing Ca2+ entry and Ca2+ oscillations. Further, in some islets in which metabolic oscillations were eliminated with Dz, increasing the cytosolic Ca2+ concentration by the addition of KCl could restart the metabolic oscillations. Here we address why metabolic oscillations persist in some islets but not others, and why raising Cac restarts oscillations in some islets but not others. We answer these questions using the dual oscillator model (DOM) for pancreatic islets. The DOM can reproduce the experimental data and shows that the model supports two different mechanisms for slow metabolic oscillations, one that requires calcium oscillations and one that does not.

Phase transitions in the multi-cellular regulatory behavior of pancreatic islet excitability

The pancreatic islets of Langerhans are multicellular micro-organs integral to maintaining glucose homeostasis through secretion of the hormone insulin. β-cells within the islet exist as a highly coupled electrical network which coordinates electrical activity and insulin release at high glucose, but leads to global suppression at basal glucose. Despite its importance, how network dynamics generate this emergent binary on/off behavior remains to be elucidated. Previous work has suggested that a small threshold of quiescent cells is able to suppress the entire network. By modeling the islet as a Boolean network, we predicted a phase-transition between globally active and inactive states would emerge near this threshold number of cells, indicative of critical behavior. This was tested using islets with an inducible-expression mutation which renders defined numbers of cells electrically inactive, together with pharmacological modulation of electrical activity. This was combined with real-time imaging of intracellular free-calcium activity [Ca²⁺]_i and measurement of physiological parameters in mice. As the number of inexcitable cells was increased beyond ∼15%, a phase-transition in islet activity occurred, switching from globally active wild-type behavior to global quiescence. This phase-transition was also seen in insulin secretion and blood glucose, indicating physiological impact. This behavior was reproduced in a multicellular dynamical model suggesting critical behavior in the islet may obey general properties of coupled heterogeneous networks. This study represents the first detailed explanation for how the islet facilitates inhibitory activity in spite of a heterogeneous cell population, as well as the role this plays in diabetes and its reversal. We further explain how islets utilize this critical behavior to leverage cellular heterogeneity and coordinate a robust insulin response with high dynamic range. These findings also give new insight into emergent multicellular dynamics in general which are applicable to many coupled physiological systems, specifically where inhibitory dynamics result from coupled networks.

As science has successfully broken down the elements of many biological systems, the network dynamics of large-scale cellular interactions has emerged as a new frontier. One way to understand how dynamical elements within large networks behave collectively is via mathematical modeling. Diabetes, which is of increasing international concern, is commonly caused by a deterioration of these complex dynamics in a highly coupled micro-organ called the islet of Langerhans. Therefore, if we are to understand diabetes and how to treat it, we must understand how coupling affects ensemble dynamics. While the role of network connectivity in islet excitation under stimulatory conditions has been well studied, how connectivity also suppresses activity under fasting conditions remains to be elucidated. Here we use two network models of islet connectivity to investigate this process. Using genetically altered islets and pharmacological treatments, we show how suppression of islet activity is solely dependent on a threshold number of inactive cells. We found that the islet exhibits critical behavior in the threshold region, rapidly transitioning from global activity to inactivity. We therefore propose how the islet and multicellular systems in general can generate a robust stimulated response from a heterogeneous cell population.

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.

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

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

Slow oscillations of KATP conductance in mouse pancreatic islets provide support for electrical bursting driven by metabolic oscillations

We used the patch clamp technique in situ to test the hypothesis that slow oscillations in metabolism mediate slow electrical oscillations in mouse pancreatic islets by causing oscillations in KATP channel activity. Total conductance was measured over the course of slow bursting oscillations in surface β-cells of islets exposed to 11.1 mM glucose by either switching from current clamp to voltage clamp at different phases of the bursting cycle or by clamping the cells to -60 mV and running two-second voltage ramps from -120 to -50 mV every 20 s. The membrane conductance, calculated from the slopes of the ramp current-voltage curves, oscillated and was larger during the silent phase than during the active phase of the burst. The ramp conductance was sensitive to diazoxide, and the oscillatory component was reduced by sulfonylureas or by lowering extracellular glucose to 2.8 mM, suggesting that the oscillatory total conductance is due to oscillatory KATP channel conductance. We demonstrate that these results are consistent with the Dual Oscillator model, in which glycolytic oscillations drive slow electrical bursting, but not with other models in which metabolic oscillations are secondary to calcium oscillations. The simulations also confirm that oscillations in membrane conductance can be well estimated from measurements of slope conductance and distinguished from gap junction conductance. Furthermore, the oscillatory conductance was blocked by tolbutamide in isolated β-cells. The data, combined with insights from mathematical models, support a mechanism of slow (∼5 min) bursting driven by oscillations in metabolism, rather than by oscillations in the intracellular free calcium concentration.

G6PC2: a negative regulator of basal glucose-stimulated insulin secretion

Elevated fasting blood glucose (FBG) is associated with increased risk for the development of type 2 diabetes and cardiovascular-associated mortality. Genome-wide association studies (GWAS) have linked polymorphisms in G6PC2 with variations in FBG and body fat, although not insulin sensitivity or glucose tolerance. G6PC2 encodes an islet-specific, endoplasmic reticulum-resident glucose-6-phosphatase catalytic subunit. A combination of in situ perfused pancreas, in vitro isolated islet, and in vivo analyses were used to explore the function of G6pc2 in mice. G6pc2 deletion had little effect on insulin sensitivity and glucose tolerance, whereas body fat was reduced in female G6pc2 knockout (KO) mice on both a chow and high-fat diet, observations that are all consistent with human GWAS data. G6pc2 deletion resulted in a leftward shift in the dose-response curve for glucose-stimulated insulin secretion (GSIS). As a consequence, under fasting conditions in which plasma insulin levels were identical, blood glucose levels were reduced in G6pc2 KO mice, again consistent with human GWAS data. Glucose-6-phosphatase activity was reduced, whereas basal cytoplasmic calcium levels were elevated in islets isolated from G6pc2 KO mice. These data suggest that G6pc2 represents a novel, negative regulator of basal GSIS that acts by hydrolyzing glucose-6-phosphate, thereby reducing glycolytic flux.

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.

Mathematical model of metabolism and electrophysiology of amino acid and glucose stimulated insulin secretion: in vitro validation using a β-cell line

We integrated biological experimental data with mathematical modelling to gain insights into the role played by L-alanine in amino acid-stimulated insulin secretion (AASIS) and in D-glucose-stimulated insulin secretion (GSIS), details important to the understanding of complex β-cell metabolic coupling relationships. We present an ordinary differential equations (ODEs) based simplified kinetic model of core metabolic processes leading to ATP production (glycolysis, TCA cycle, L-alanine-specific reactions, respiratory chain, ATPase and proton leak) and Ca(2+) handling (essential channels and pumps in the plasma membrane) in pancreatic β-cells and relate these to insulin secretion. Experimental work was performed using a clonal rat insulin-secreting cell line (BRIN-BD11) to measure the consumption or production of a range of important biochemical parameters (D-glucose, L-alanine, ATP, insulin secretion) and Ca(2+) levels. These measurements were then used to validate the theoretical model and fine-tune the parameters. Mathematical modelling was used to predict L-lactate and L-glutamate concentrations following D-glucose and/or L-alanine challenge and Ca(2+) levels upon stimulation with a non metabolizable L-alanine analogue. Experimental data and mathematical model simulations combined suggest that L-alanine produces a potent insulinotropic effect via both a stimulatory impact on β-cell metabolism and as a direct result of the membrane depolarization due to Ca(2+) influx triggered by L-alanine/Na(+) co-transport. Our simulations indicate that both high intracellular ATP and Ca(2+) concentrations are required in order to develop full insulin secretory responses. The model confirmed that K(+) ATP channel independent mechanisms of stimulation of intracellular Ca(2+) levels, via generation of mitochondrial coupling messengers, are essential for promotion of the full and sustained insulin secretion response in β-cells.

Metabolome response to glucose in the β-cell line INS-1 832/13

Glucose-stimulated insulin secretion (GSIS) from pancreatic β-cells is triggered by metabolism of the sugar to increase ATP/ADP ratio that blocks the KATP channel leading to membrane depolarization and insulin exocytosis. Other metabolic pathways believed to augment insulin secretion have yet to be fully elucidated. To study metabolic changes during GSIS, liquid chromatography with mass spectrometry was used to determine levels of 87 metabolites temporally following a change in glucose from 3 to 10 mM glucose and in response to increasing concentrations of glucose in the INS-1 832/13 β-cell line. U-[(13)C]Glucose was used to probe flux in specific metabolic pathways. Results include a rapid increase in ATP/ADP, anaplerotic tricarboxylic acid cycle flux, and increases in the malonyl CoA pathway, support prevailing theories of GSIS. Novel findings include that aspartate used for anaplerosis does not derive from the glucose fuel added to stimulate insulin secretion, glucose flux into glycerol-3-phosphate, and esterification of long chain CoAs resulting in rapid consumption of long chain CoAs and de novo generation of phosphatidic acid and diacylglycerol. Further, novel metabolites with potential roles in GSIS such as 5-aminoimidazole-4-carboxamide ribotide (ZMP), GDP-mannose, and farnesyl pyrophosphate were found to be rapidly altered following glucose exposure.

Association between a common KCNJ11 polymorphism (rs5219) and new-onset posttransplant diabetes in patients treated with Tacrolimus

KCNJ11 polymorphisms have been linked to the risk of developing type 2 diabetes. Our aim was to define the contribution of KCNJ11 to new-onset diabetes after transplantation (NODAT) among patients treated with Tacrolimus (Tac). A total of 115 NODAT and 205 non-NODAT were genotyped for rs5219 (p.E23K). AA+AG genotypes were significantly associated with NODAT-risk (p=0.004; OR=2.10). The reported effect of this KCNJ11 polymorphism on insulin release by beta cells could explain this association.

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.

Mechanism of KATP hyperactivity and sulfonylurea tolerance due to a diabetogenic mutation in L0 helix of sulfonylurea receptor 1 (ABCC8)

Activating mutations in different domains of the ABCC8 gene-coded sulfonylurea receptor 1 (SUR1) cause neonatal diabetes. Here we show that a diabetogenic mutation in an unexplored helix preceding the ABC core of SUR1 dramatically increases open probability of (SUR1/Kir6.2)(4) channel (KATP) by reciprocally changing rates of its transitions to and from the long-lived, inhibitory ligand-stabilized closed state. This kinetic mechanism attenuates ATP and sulfonylurea inhibition, but not Mg-nucleotide stimulation, of SUR1/Kir6.2. The results suggest a key role for L0 helix in KATP gating and together with previous findings from mutant KATP clarify why many patients with neonatal diabetes require high doses of sulfonylureas.

Mechanisms of glucose sensing in the pancreatic β-cell: A computational systems-based analysis

Pancreatic β-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm with a subsequent influx of calcium and the eventual secretion of insulin. The mechanisms of glucose sensing in the pancreatic β-cell involve the coupling of cytoplasmic and mitochondrial processes. Our analysis, based on mathematical models of data from multiple sources has implications for β-cell function and the treatment of type 2 diabetes (Fridlyand and Philipson, 2010). This β-cell glucose response model correctly predicts changes in the ATP/ADP ratio, cytoplasmic and mitochondrial calcium levels, and other metabolic parameters in response to alterations in substrate delivery at steady-state and during cytoplasmic calcium oscillations. Here we consider how peculiarities of β-cell pathways that result in dysfunction can be a consequence of specific mechanisms of glucose sensitivity, using our computational systems-based analysis. We found that the mitochondrial membrane potential must be relatively low in β-cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in cellular respiratory activity. Our analysis additionally demonstrates how activity of lactate dehydrogenase, uncoupling proteins, and the redox shuttles all working in concert can regulate β-cell function. We further show that a decreased mitochondrial membrane potential may lead to a low rate of production of reactive oxygen species in β-cells under physiological conditions. This computational systems analysis aids in providing a more complete understanding of the complex process of β-cell glucose sensing.

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.

Unique cellular and mitochondrial defects mediate FK506-induced islet β-cell dysfunction

OBJECTIVE

To determine biological mechanisms involved in posttransplantation diabetes mellitus caused by the immunosuppressant tacrolimus (FK506).

METHODS

INS-1 cells and isolated rat islets were incubated with vehicle or FK506 and harvested at 24-hr intervals. Cells were assessed for viability, apoptosis, proliferation, cell insulin secretion, and content. Gene expression studies by microarray analysis, quantitative polymerase chain reaction, and motifADE analysis of the microarray data identified potential FK506-mediated pathways and regulatory motifs. Mitochondrial functions, including cell respiration, mitochondrial content, and bioenergetics were assessed.

RESULTS

Cell replication, viability, insulin secretion, oxygen consumption, and mitochondrial content were decreased (P<0.05) 1.2-, 1.27-, 1.77-, 1.32-, and 1.43-fold, respectively, after 48-hr FK506 treatment. Differences increased with time. FK506 (50 ng/mL) and cyclosporine A (800 ng/mL) had comparable effects. FK506 significantly decreased mitochondrial content and mitochondrial bioenergetics and showed a trend toward decreased oxygen consumption in isolated islets. Cell apoptosis and proliferation, mitochondrial DNA copy number, and ATP:ADP ratios were not significantly affected. Pathway analysis of microarray data showed FK506 modification of pathways involving ATP metabolism, membrane trafficking, and cytoskeleton remodeling. PGC1-α mRNA was down-regulated by FK506. MotifADE identified nuclear factor of activated T-cells, an important mediator of β-cell survival and function, as a potential factor mediating both up- and down-regulation of gene expression.

CONCLUSIONS

At pharmacologically relevant concentrations, FK506 decreases insulin secretion and reduces mitochondrial density and function without changing apoptosis rates, suggesting that posttransplantation diabetes induced by FK506 may be mediated by its effects on mitochondrial function.

Interactive effects of cadmium and hypoxia on metabolic responses and bacterial loads of eastern oysters Crassostrea virginica Gmelin

Pollution by toxic metals including cadmium (Cd) and hypoxia are important stressors in estuaries and coastal waters which may interactively affect sessile benthic organisms, such as oysters. We studied metabolic responses to prolonged hypoxic acclimation (2 weeks at 5% O2) in control and Cd-exposed (30 d at 50 μg L(-1) Cd) oysters Crassostrea virginica, and analyzed the effects of these stressors on abundance of Vibrio spp. in oysters. Hypoxia-acclimated oysters retained normal standard metabolic rates (SMR) at 5% O2, in contrast to a decline of SMR observed during acute hypoxia. However, oysters spent more time actively ventilating in hypoxia than normoxia resulting in enhanced Cd uptake and 2.7-fold higher tissue Cd burdens in hypoxia. Cd exposure led to a significant decrease in tissue glycogen stores, increase in free glucose levels and elevated activity of glycolytic enzymes (hexokinase and aldolase) indicating a greater dependence on carbohydrate catabolism. A compensatory increase in activities of two key mitochondrial enzymes (citrate synthase and cytochrome c oxidase) was found during prolonged hypoxia in control oysters but suppressed in Cd-exposed ones. Cd exposure also resulted in a significant increase in abundance of Vibrio parahaemolyticus and Vibrio vulnificus levels during normoxia and hypoxia, respectively. Overall, Cd- and hypoxia-induced changes in metabolic profile, Cd accumulation and bacterial flora of oysters indicate that these stressors can synergistically impact energy homeostasis, performance and survival of oysters in polluted estuaries and have significant consequences for transfer of Cd and bacterial pathogens to the higher levels of the food chain.

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

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

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

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

Glucose sensing in the pancreatic beta cell: a computational systems analysis

Background

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of K_ATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.

Methods

We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F₁F₀ ATPase. Redox shuttles and mitochondrial Ca²⁺ handling were also modeled.

Results

The model correctly predicts changes in the ATP/ADP ratio, Ca²⁺ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca²⁺ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca²⁺ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.

Conclusion

This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic β-cells.

Pancreatic islet cells: a model for calcium-dependent peptide release

In mammals the concentration of blood glucose is kept close to 5 mmol∕l. Different cell types in the islet of Langerhans participate in the control of glucose homeostasis. β-cells, the most frequent type in pancreatic islets, are responsible for the synthesis, storage, and release of insulin. Insulin, released with increases in blood glucose promotes glucose uptake into the cells. In response to glucose changes, pancreatic α-, β-, and δ-cells regulate their electrical activity and Ca(2+) signals to release glucagon, insulin, and somatostatin, respectively. While all these signaling steps are stimulated in hypoglycemic conditions in α-cells, the activation of these events require higher glucose concentrations in β and also in δ-cells. The stimulus-secretion coupling process and intracellular Ca(2+) ([Ca(2+)](i)) dynamics that allow β-cells to secrete is well-accepted. Conversely, the mechanisms that regulate α- and δ-cell secretion are still under study. Here, we will consider the glucose-induced signaling mechanisms in each cell type and the mathematical models that explain Ca(2+) dynamics.

Accounting for near-normal glucose sensitivity in Kir6.2[AAA] transgenic mice

K(ir)6.2[AAA] transgenic mouse islets exhibit mosaicism such that approximately 70% of the beta-cells have nonfunctional ATP-sensitive potassium (K(ATP)) channels, whereas the remainder have normal K(ATP) function. Despite this drastic reduction, the glucose dose-response curve is only shifted by approximately 2 mM. We use a previously published mathematical model, in which K(ATP) conductance is increased by rises in cytosolic calcium through indirect effects on metabolism, to investigate how cells could compensate for the loss of K(ATP) conductance. Compensation is favored by the assumption that only a small fraction of K(ATP) channels are open during oscillations, which renders it easy to upregulate the open fraction via a modest elevation of calcium. We show further that strong gap-junctional coupling of both membrane potential and calcium is needed to overcome the stark heterogeneity of cell properties in these mosaic islets.

Use of virtual cell in studies of cellular dynamics

The Virtual Cell (VCell) is a unique computational environment for modeling and simulation of cell biology. It has been specifically designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists. The models created with VCell can range from the simple, to evaluate hypotheses or to interpret experimental data, to complex multilayered models used to probe the predicted behavior of spatially resolved, highly nonlinear systems. In this chapter, we discuss modeling capabilities of VCell and demonstrate representative examples of the models published by the VCell users.

Beta-catenin is involved in alterations in mitochondrial activity in non-transformed intestinal epithelial and colon cancer cells

BACKGROUND

Alteration in respiratory activity and mitochondrial DNA (mtDNA) transcription seems to be an important feature of cancer cells. Leukotriene D(4) (LTD(4)) is a proinflammatory mediator implicated in the pathology of chronic inflammation and cancer. We have shown earlier that LTD(4) causes translocation of beta-catenin both to the mitochondria, in which it associates with the survival protein Bcl-2 identifying a novel role for beta-catenin in cell survival, and to the nucleus in which it activates the TCF/LEF transcription machinery.

METHODS

Here we have used non-transformed intestinal epithelial Int 407 cells and Caco-2 colon cancer cells, transfected or not with wild type and mutated (S33Y) beta-catenin to analyse its effect on mitochondria activity. We have measured the ATP/ADP ratio, and transcription of the mtDNA genes ND2, ND6 and 16 s in these cells stimulated or not with LTD(4).

RESULTS

We have shown for the first time that LTD(4) triggers a cellular increase in NADPH dehydrogenase activity and ATP/ADP ratio. In addition, LTD(4) significantly increased the transcription of mtDNA genes. Overexpression of wild-type beta-catenin or a constitutively active beta-catenin mutant mimicked the effect of LTD(4) on ATP/ADP ratio and mtDNA transcription. These elevations in mitochondrial activity resulted in increased reactive oxygen species levels and subsequent activations of the p65 subunit of NF-kappaB.

CONCLUSIONS

The present novel data show that LTD(4), presumably through beta-catenin accumulation in the mitochondria, affects mitochondrial activity, lending further credence to the idea that inflammatory signalling pathways are intrinsically linked with potential oncogenic signals.

A model of action potentials and fast Ca2+ dynamics in pancreatic beta-cells

We examined the ionic mechanisms mediating depolarization-induced spike activity in pancreatic beta-cells. We formulated a Hodgkin-Huxley-type ionic model for the action potential (AP) in these cells based on voltage- and current-clamp results together with measurements of Ca(2+) dynamics in wild-type and Kv2.1 null mouse islets. The model contains an L-type Ca(2+) current, a "rapid" delayed-rectifier K(+) current, a small slowly-activated K(+) current, a Ca(2+)-activated K(+) current, an ATP-sensitive K(+) current, a plasma membrane calcium-pump current and a Na(+) background current. This model, coupled with an equation describing intracellular Ca(2+) homeostasis, replicates beta-cell AP and Ca(2+) changes during one glucose-induced spontaneous spike, the effects of blocking K(+) currents with different inhibitors, and specific complex spike in mouse islets lacking Kv2.1 channels. The currents with voltage-independent gating variables can also be responsible for burst behavior. Original features of this model include new equations for L-type Ca(2+) current, assessment of the role of rapid delayed-rectifier K(+) current, and Ca(2+)-activated K(+) currents, demonstrating the important roles of the Ca(2+)-pump and background currents in the APs and bursts. This model provides acceptable fits to voltage-clamp, AP, and Ca(2+) concentration data based on in silico analysis.

The hyperbolic effect of density and strength of inter beta-cell coupling on islet bursting: a theoretical investigation

BACKGROUND

Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP) model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each beta-cell is coupled to, nc, and the coupling strength, gc.

RESULTS

BETA-cell clusters of different sizes with number of beta-cells nbeta ranging from 1-343, nc from 0-12, and gc from 0-1000 pS, were simulated. Three functional measures of islet bursting characteristics--fraction of bursting beta-cells fb, synchronization index lambda, and bursting period Tb, were quantified. The results revealed a hyperbolic dependence on the combined effect of nc and gc. From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures fb, lambda and Tb increasing monotonically with CCI when it is small, and plateau around CCI = 1.

CONCLUSION

CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet beta-cell mass and function.

A novel ABCC8 (SUR1)-dependent mechanism of metabolism-excitation uncoupling

ATP/ADP-sensing (sulfonylurea receptor (SUR)/K(IR)6)(4) K(ATP) channels regulate the excitability of our insulin secreting and other vital cells via the differential MgATP/ADP-dependent stimulatory actions of their tissue-specific ATP-binding cassette regulatory subunits (sulfonylurea receptors), which counterbalance the nearly constant inhibitory action of ATP on the K(+) inwardly rectifying pore. Mutations in SUR1 that abolish its stimulation have been found in infants persistently releasing insulin. Activating mutations in SUR1 have been shown to cause neonatal diabetes. Here, analyses of K(IR)6.2-based channels with diabetogenic receptors reveal that MgATP-dependent hyper-stimulation of mutant SUR can compromise the ability of K(ATP) channels to function as metabolic sensors. I demonstrate that the channel hyperactivity rises exponentially with the number of hyperstimulating subunits, so small subpopulations of channels with more than two mutant SUR can dominate hyperpolarizing currents in heterozygous patients. I uncovered an attenuated tolbutamide inhibition of the hyperstimulated mutant, which is normally sensitive to the drug under non-stimulatory conditions. These findings show the key role of SUR in sensing the metabolic index in humans and urge others to (re)test mutant SUR/K(IR)6 channels from probands in physiologic MgATP.

Modeling a simplified regulatory system of blood glucose at molecular levels

In this paper, we propose a new mathematical control system for a simplified regulatory system of blood glucose by taking into account the dynamics of glucose and glycogen in liver and the dynamics of insulin and glucagon receptors at the molecular level. Numerical simulations show that the proposed feedback control system agrees approximately with published experimental data. Sensitivity analysis predicts that feedback control gains of insulin receptors and glucagon receptors are robust. Using the model, we develop a new formula to compute the insulin sensitivity. The formula shows that the insulin sensitivity depends on various parameters that determine the insulin influence on insulin-dependent glucose utilization and reflect the efficiency of binding of insulin to its receptors. Using Lyapunov indirect method, we prove that the new control system is input-output stable. The stability result provides theoretical evidence for the phenomenon that the blood glucose fluctuates within a narrow range in response to the exogenous glucose input from food. We also show that the regulatory system is controllable and observable. These structural system properties could explain why the glucose level can be regulated.

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

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

Glucose-induced cytosolic pH changes in beta-cells and insulin secretion are not causally related: studies in islets lacking the Na+/H+ exchangeR NHE1

The contribution of Na(+)/H(+) exchange (achieved by NHE proteins) to the regulation of beta-cell cytosolic pH(c), and the role of pH(c) changes in glucose-induced insulin secretion are disputed and were examined here. Using real-time PCR, we identified plasmalemmal NHE1 and intracellular NHE7 as the two most abundant NHE isoforms in mouse islets. We, therefore, compared insulin secretion, cytosolic free Ca(2+) ([Ca(2+)](c)) and pH(c) in islets from normal mice and mice bearing an inactivating mutation of NHE1 (Slc9A1-swe/swe). The experiments were performed in HCO(-)(3)/CO(2) or HEPES/NaOH buffers. PCR and functional approaches showed that NHE1 mutant islets do not express compensatory pH-regulating mechanisms. NHE1 played a greater role than HCO(-)(3)-dependent mechanisms in the correction of an acidification imposed by a pulse of NH(4)Cl. In contrast, basal pH(c) (in low glucose) and the alkalinization produced by high glucose were independent of NHE1. Dimethylamiloride, a classic blocker of Na(+)/H(+) exchange, did not affect pH(c) but increased insulin secretion in NHE1 mutant islets, indicating unspecific effects. In control islets, glucose similarly increased [Ca(2+)](c) and insulin secretion in HCO(-)(3) and HEPES buffer, although pH(c) changed in opposite directions. The amplification of insulin secretion that glucose produces when [Ca(2+)](c) is clamped at an elevated level by KCl was also unrelated to pH(c) and pH(c) changes. All effects of glucose on [Ca(2+)](c) and insulin secretion proved independent of NHE1. In conclusion, NHE1 protects beta-cells against strong acidification, but has no role in stimulus-secretion coupling. The changes in pH(c) produced by glucose involve HCO(-)(3)-dependent mechanisms. Variations in beta-cell pH(c) are not causally related to changes in insulin secretion.

The electrophysiology of the beta-cell based on single transmembrane protein characteristics

The electrophysiology of beta-cells is at the origin of insulin secretion. beta-Cells exhibit a complex behavior upon stimulation with glucose including repeated bursts and continuous spiking. Mathematical modeling is most suitable to improve knowledge about the function of various transmembrane currents provided the model is based on reliable data. This is the first attempt to build a mathematical model for the beta-cell electrophysiology in a bottom-up approach that relies on single protein conductance data. The results of previous whole-cell-based models are reconsidered. The full simulation including all prominent transmembrane proteins in beta-cells is used to provide a functional interpretation of their role in beta-cell bursting and an updated vantage point of beta-cell electrophysiology. As a result of a number of in silico knock-out and block experiments the novel model makes some unexpected predictions: single-channel conductance data imply that large-conductance calcium-gated potassium currents acquire the potential of driving oscillations at supralarge glucose levels. A more complex burst interruption model is presented. It also turns out that, depending on the species, sodium currents may be more relevant than considered so far. Experiments are proposed to verify these predictions.

Metabolic and ionic coupling factors in amino acid-stimulated insulin release in pancreatic beta-HC9 cells

Fuel stimulation of insulin secretion from pancreatic beta-cells is thought to be mediated by metabolic coupling factors that are generated by energized mitochondria, including protons, adenine nucleotides, and perhaps certain amino acids (AA), as for instance aspartate, glutamate, or glutamine (Q). The goal of the present study was to evaluate the role of such factors when insulin release (IR) is stimulated by glucose or AA, alone or combined, using (31)P, (23)Na and (1)H NMR technology, respirometry, and biochemical analysis to study the metabolic events that occur in continuously superfused mouse beta-HC9 cells contained in agarose beads and enhanced by the phosphodiesterase inhibitor IBMX. Exposing beta-HC9 cells to high glucose or 3.5 mM of a physiological mixture of 18 AA (AAM) plus 2 mM glutamine caused a marked stimulation of insulin secretion associated with increased oxygen consumption, cAMP release, and phosphorylation potential as evidenced by higher phosphocreatine and lower P(i) peak areas of (31)P NMR spectra. Diazoxide blocked stimulation of IR completely, suggesting involvement of ATP-dependent potassium (K(ATP)) channels in this process. However, levels of MgATP and MgADP concentrations, which regulate channel activity, changed only slowly and little, whereas the rate of insulin release increased fast and very markedly. The involvement of other candidate coupling factors was therefore considered. High glucose or AAM + Q increased pH(i). The availability of temporal pH profiles allowed the precise computation of the phosphate potential (ATP/P(i) x ADP) in fuel-stimulated IR. Intracellular Na+ levels were greatly elevated by AAM + Q. However, glutamine alone or together with 2-amino-2-norbornanecarboxylic acid (which activates glutamate dehydrogenase) decreased beta-cell Na levels. Stimulation of beta-cells by glucose in the presence of AAM + Q (0.5 mM) was associated with rising cellular concentrations of glutamate and glutamine and strikingly lower aspartate levels. Methionine sulfoximine, an inhibitor of glutamine synthetase, blocked the glucose enhancement of AMM + Q-induced IR and associated changes in glutamine and aspartate but did not prevent the accumulation of glutamate. The results of this study demonstrate again that an increased phosphate potential and a functional K(ATP) channel are essential for metabolic coupling during fuel-stimulated insulin release but illustrate that determining the identity and relative importance of all participating coupling factors and second messengers remains a challenge largely unmet.

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

Pulsatile insulin output, paralleled by oscillations in intracellular Ca(2+), reflect oscillating metabolism within beta-cells in response to secretory fuels. Here we question whether oscillatory periodicity is conserved or varied from stimulation to stimulation, whether glycolysis is essential for the manifestation of an oscillatory response, and if an environment of nutrient oversupply affects oscillatory regularity. We have determined that a beta-cell oscillatory Ca(2+) pattern is independent of the type of applied secretory fuel (glucose, methyl-pyruvate, or alpha-ketoisocaproate). In addition, single cells respond with the same pattern when repeatedly stimulated, regardless of the type of stimulatory fuel. Presence of substimulatory glucose is not necessary to obtain an oscillatory responses to methyl-pyruvate or alpha-ketoisocaproate. Glucose-6-phosphate, as a measure of glycolytic flux, is not detectable under these conditions. These data suggest that multiple systems, rather than a single enzyme component, can contribute to the beta-cell oscillatory behavior. Prolonged exposure to high levels of palmitate impaired oscillatory regularity in the individual beta-cells. This supports the hypothesis that a high-fat environment might contribute to loss of regular oscillatory pattern in diabetic subjects, acting, at least in part, at the level of the single beta-cell.

Rapid turnover of phosphatidylinositol-4,5-bisphosphate in insulin-secreting cells mediated by Ca2+ and the ATP-to-ADP ratio

Phosphatidylinositol-4,5-bisphosphate (PIP(2)) is important for a variety of cellular processes as a precursor for second messengers and by regulating ion channels, the cytoskeleton, and vesicle traffic in many types of cells, including insulin-secreting beta-cells. Here, we applied evanescent wave microscopy and the PIP(2)-binding pleckstrin homology domain from phospholipase C (PLC)-delta fused to the green fluorescent protein to characterize the regulation of plasma membrane PIP(2) in individual insulin-secreting MIN6 beta-cells. Elevation of the glucose concentration from 3 to 11 mmol/l evoked antisynchronous oscillations of [PIP(2)] and cytoplasmic Ca(2+)concentration, consistent with PLC being periodically activated by the voltage-dependent Ca(2+) influx. The effect of adenine nucleotides on [PIP(2)] was studied in cells permeabilized with alpha-toxin. ATP dose- dependently stimulated PIP(2) synthesis with half-maximal effect at 300 mumol/l. Omission of the nucleotide resulted in rapid loss of PIP(2) with t(1/2) < 40 s. ADP also stimulated PIP(2) formation, but this effect reflected local ATP formation and was prevented by the adenylate kinase inhibitor diadenosine-pentaphosphate. The ATP-induced PIP(2) synthesis was counteracted by the ADP analog adenosine-5'-O-2-thiodiphosphate. We conclude that plasma membrane PIP(2) is dynamically regulated by intracellular Ca(2+) and the ATP-to-ADP ratio in insulin-secreting cells. The rapid turnover allows maintenance of PIP(2) levels while generating second messengers of critical importance for insulin secretion.

Expression of key substrate cycle enzymes in rat spermatogenic cells: Fructose 1,6 bisphosphatase and 6 phosphofructose 1-kinase

A substrate cycle composed of phosphofructo 1-kinase I (PFK) and fructose 1,6 bisphosphatase I (FBPase) has been proposed in rat spermatids. This substrate cycle can explain the ability of glucose to induce a decrease in intracellular ATP, a phenomenon that was related to regulation of [Ca(2+)]i in these cells. In spite of the importance of this metabolic cycle, the expression and activities of the enzymes that compose such cycle have not been systematically studied in spermatogenic cells. Here, we show that PFK and FBPase activities were present in pachytene spermatocytes and round spermatids extracts. Expression of PFK at the mRNA and protein levels showed a relatively similar expression in spermatogenic cells, but a stronger expression in Sertoli cells. Instead, expression of FBPase at the mRNA and protein levels was stronger in round and elongating spermatids as compared to other spermatogenic cells. A similar pattern was observed when evidencing FBPase activity by a NADPH-nitroblue tetrazolium-linked cytochemical assay in isolated pachytene spermatocytes and round spermatids. Rat spermatids also showed the ability to convert lactate to fructose- and glucose-6-P, indicating that both glycolytic and gluconeogenic fluxes are present in these cells. Our results indicate that a coordinated expression of key substrate cycle enzymes, at the level of PFK/FBPase, appear in the last stages of spermatogenic cell differentiation, suggesting that the co-regulation of these enzymes are required for the ability of these cells to respond to glucose and induce metabolic and Ca(2+) signals that can be important for sperm development and function.