Modeling of Ca2+ flux in pancreatic beta-cells: role of the plasma membrane and intracellular stores

Model of Calcium Dynamics Regulating [Formula: see text], ATP and Insulin Production in a Pancreatic [Formula: see text]-Cell

The calcium signals regulate the production and secretion of many signaling molecules like inositol trisphosphate ([Formula: see text]) and adenosine triphosphate (ATP) in various cells including pancreatic [Formula: see text]-cells. The calcium signaling mechanisms regulating [Formula: see text], ATP and insulin responsible for various functions of [Formula: see text]-cells are still not well understood. Any disturbance in these mechanisms can alter the functions of [Formula: see text]-cells leading to diabetes and metabolic disorders. Therefore, a mathematical model is proposed by incorporating the reaction-diffusion equation for calcium dynamics and a system of first-order differential equations for [Formula: see text], ATP-production and insulin secretion with initial and boundary conditions. The model incorporates the temporal dependence of [Formula: see text]-production and degradation, ATP production and insulin secretion on calcium dynamics in a [Formula: see text]-cell. The piecewise linear finite element method has been used for the spatial dimension and the Crank-Nicolson scheme for the temporal dimension to obtain numerical results. The effect of changes in source influxes and buffers on calcium dynamics and production of [Formula: see text], ATP and insulin levels in a [Formula: see text]-cell has been analyzed. It is concluded that the dysfunction of source influx and buffers can cause significant variations in calcium levels and dysregulation of [Formula: see text], ATP and insulin production, which can lead to various metabolic disorders, diabetes, obesity, etc. The proposed model provides crucial information about the changes in mechanisms of calcium dynamics causing proportionate disturbances in [Formula: see text], ATP and insulin levels in pancreatic cells, which can be helpful for devising protocols for diagnosis and treatment of various metabolic diseases.

How Merkel cells transduce mechanical stimuli: A biophysical model of Merkel cells

Merkel cells combine with Aβ afferents, producing slowly adapting type 1(SA1) responses to mechanical stimuli. However, how Merkel cells transduce mechanical stimuli into neural signals to Aβ afferents is still unclear. Here we develop a biophysical model of Merkel cells for mechanical transduction by incorporating main ingredients such as Ca2+ and K+ voltage-gated channels, Piezo2 channels, internal Ca2+ stores, neurotransmitters release, and cell deformation. We first validate our model with several experiments. Then we reveal that Ca2+ and K+ channels on the plasma membrane shape the depolarization of membrane potentials, further regulating the Ca2+ transients in the cells. We also show that Ca2+ channels on the plasma membrane mainly inspire the Ca2+ transients, while internal Ca2+ stores mainly maintain the Ca2+ transients. Moreover, we show that though Piezo2 channels are rapidly adapting mechanical-sensitive channels, they are sufficient to inspire sustained Ca2+ transients in Merkel cells, which further induce the release of neurotransmitters for tens of seconds. Thus our work provides a model that captures the membrane potentials and Ca2+ transients features of Merkel cells and partly explains how Merkel cells transduce the mechanical stimuli by Piezo2 channels.

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

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

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.

Modeling Calcium Signaling in S. cerevisiae Highlights the Role and Regulation of the Calmodulin-Calcineurin Pathway in Response to Hypotonic Shock

Calcium homeostasis and signaling processes in Saccharomyces cerevisiae, as well as in any eukaryotic organism, depend on various transporters and channels located on both the plasma and intracellular membranes. The activity of these proteins is regulated by a number of feedback mechanisms that act through the calmodulin-calcineurin pathway. When exposed to hypotonic shock (HTS), yeast cells respond with an increased cytosolic calcium transient, which seems to be conditioned by the opening of stretch-activated channels. To better understand the role of each channel and transporter involved in the generation and recovery of the calcium transient—and of their feedback regulations—we defined and analyzed a mathematical model of the calcium signaling response to HTS in yeast cells. The model was validated by comparing the simulation outcomes with calcium concentration variations before and during the HTS response, which were observed experimentally in both wild-type and mutant strains. Our results show that calcium normally enters the cell through the High Affinity Calcium influx System and mechanosensitive channels. The increase of the plasma membrane tension, caused by HTS, boosts the opening probability of mechanosensitive channels. This event causes a sudden calcium pulse that is rapidly dissipated by the activity of the vacuolar transporter Pmc1. According to model simulations, the role of another vacuolar transporter, Vcx1, is instead marginal, unless calcineurin is inhibited or removed. Our results also suggest that the mechanosensitive channels are subject to a calcium-dependent feedback inhibition, possibly involving calmodulin. Noteworthy, the model predictions are in accordance with literature results concerning some aspects of calcium homeostasis and signaling that were not specifically addressed within the model itself, suggesting that it actually depicts all the main cellular components and interactions that constitute the HTS calcium pathway, and thus can correctly reproduce the shaping of the calcium signature by calmodulin- and calcineurin-dependent complex regulations. The model predictions also allowed to provide an interpretation of different regulatory schemes involved in calcium handling in both wild-type and mutants yeast strains. The model could be easily extended to represent different calcium signals in other eukaryotic 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.

Neural Network Differential Equations For Ion Channel Modelling

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality-termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.

Spatially compartmentalized phase regulation of a Ca2+-cAMP-PKA oscillatory circuit

Signaling networks are spatiotemporally organized to sense diverse inputs, process information, and carry out specific cellular tasks. In β cells, Ca2+, cyclic adenosine monophosphate (cAMP), and Protein Kinase A (PKA) exist in an oscillatory circuit characterized by a high degree of feedback. Here, we describe a mode of regulation within this circuit involving a spatial dependence of the relative phase between cAMP, PKA, and Ca2+. We show that in mouse MIN6 β cells, nanodomain clustering of Ca2+-sensitive adenylyl cyclases (ACs) drives oscillations of local cAMP levels to be precisely in-phase with Ca2+ oscillations, whereas Ca2+-sensitive phosphodiesterases maintain out-of-phase oscillations outside of the nanodomain. Disruption of this precise phase relationship perturbs Ca2+ oscillations, suggesting the relative phase within an oscillatory circuit can encode specific functional information. This work unveils a novel mechanism of cAMP compartmentation utilized for localized tuning of an oscillatory circuit and has broad implications for the spatiotemporal regulation of signaling networks.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Opportunities and Challenges in Building a Spatiotemporal Multi-scale Model of the Human Pancreatic β Cell

The construction of a predictive model of an entire eukaryotic cell that describes its dynamic structure from atomic to cellular scales is a grand challenge at the intersection of biology, chemistry, physics, and computer science. Having such a model will open new dimensions in biological research and accelerate healthcare advancements. Developing the necessary experimental and modeling methods presents abundant opportunities for a community effort to realize this goal. Here, we present a vision for creation of a spatiotemporal multi-scale model of the pancreatic β-cell, a relevant target for understanding and modulating the pathogenesis of diabetes.

Closing in on the Mechanisms of Pulsatile Insulin Secretion

Insulin secretion from pancreatic islet β-cells occurs in a pulsatile fashion, with a typical period of ∼5 min. The basis of this pulsatility in mouse islets has been investigated for more than four decades, and the various theories have been described as either qualitative or mathematical models. In many cases the models differ in their mechanisms for rhythmogenesis, as well as other less important details. In this Perspective, we describe two main classes of models: those in which oscillations in the intracellular Ca²⁺ concentration drive oscillations in metabolism, and those in which intrinsic metabolic oscillations drive oscillations in Ca²⁺ concentration and electrical activity. We then discuss nine canonical experimental findings that provide key insights into the mechanism of islet oscillations and list the models that can account for each finding. Finally, we describe a new model that integrates features from multiple earlier models and is thus called the Integrated Oscillator Model. In this model, intracellular Ca²⁺ acts on the glycolytic pathway in the generation of oscillations, and it is thus a hybrid of the two main classes of models. It alone among models proposed to date can explain all nine key experimental findings, and it serves as a good starting point for future studies of pulsatile insulin secretion from human islets.

Upregulation of an inward rectifying K+ channel can rescue slow Ca2+ oscillations in K(ATP) channel deficient pancreatic islets

Plasma insulin oscillations are known to have physiological importance in the regulation of blood glucose. In insulin-secreting β-cells of pancreatic islets, K(ATP) channels play a key role in regulating glucose-dependent insulin secretion. In addition, they convey oscillations in cellular metabolism to the membrane by sensing adenine nucleotides, and are thus instrumental in mediating pulsatile insulin secretion. Blocking K(ATP) channels pharmacologically depolarizes the β-cell plasma membrane and terminates islet oscillations. Surprisingly, when K(ATP) channels are genetically knocked out, oscillations in islet activity persist, and relatively normal blood glucose levels are maintained. Compensation must therefore occur to overcome the loss of K(ATP) channels in K(ATP) knockout mice. In a companion study, we demonstrated a substantial increase in Kir2.1 protein occurs in β-cells lacking K(ATP) because of SUR1 deletion. In this report, we demonstrate that β-cells of SUR1 null islets have an upregulated inward rectifying K⁺ current that helps to compensate for the loss of K(ATP) channels. This current is likely due to the increased expression of Kir2.1 channels. We used mathematical modeling to determine whether an ionic current having the biophysical characteristics of Kir2.1 is capable of rescuing oscillations that are similar in period to those of wild-type islets. By experimentally testing a key model prediction we suggest that Kir2.1 current upregulation is a likely mechanism for rescuing the oscillations seen in islets from mice deficient in K(ATP) channels.

Pulsatile insulin secretion is important for the proper regulation of blood glucose, and disruption of this pulsatility is a hallmark of type II diabetes. An ion channel was discovered more than three decades ago that conveys the metabolic state of insulin-secreting β-cells to the plasma membrane because it is blocked by ATP and opened by ADP, and thereby controls the activity of these electrically-excitable cells on a rapid time scale according to the prevailing blood glucose level. In addition to setting the appropriate level of insulin secretion, K(ATP) channels play a key role in generating the oscillations in cellular activity that underlie insulin pulsatility. It is therefore surprising that oscillations in activity persist in islets in which the K(ATP) channels are genetically knocked out. In this combined modeling and experimental study, we demonstrate that the role played by K(ATP) current in wild-type β-cells can be taken over by an inward-rectifying K⁺ current which, we show here, is upregulated in β-cells from SUR1 knockout mice. This result helps to resolve a mystery in the field that has remained elusive for more than a decade, since the first studies showing oscillations in SUR1^-/- islets.

Development of a detailed model of calcium dynamics at the postsynaptic spine of an excitatory synapse

Postsynaptic calcium dynamics play a critical role in synaptic plasticity, but are often difficult to measure in experimental protocols due to their relatively fast rise and decay times, and the small spine dimensions. To circumvent these limitations, we propose to develop a computational model of calcium dynamics in the postsynaptic spine. This model integrates the main elements that participate in calcium concentration influx, efflux, diffusion and buffering. These consist of (i) spine geometry; (ii) calcium influx through NMDA receptors and voltage-dependent calcium channels (VDCC); (iii) calcium efflux with plasma membrane calcium pumps (PMCA) and sodium-calcium exchangers (NCX); (iv) intracellular calcium stores; and (v) calcium buffers. We herein present computational results we obtained and compare them with experimentally measured data, thereby validating the proposed model. Overall the development of such postsynaptic calcium model may help us better understand the intricacies of interplay between the different elements that shape calcium dynamics and impact synaptic plasticity in normal functions and pathologies. This model also constitutes a first step in the development of a nonlinear input-output calcium dynamics model for multi-scale, large scale neuronal simulations.

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.

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.

Routes of Ca2+ Shuttling during Ca2+ Oscillations: FOCUS ON THE ROLE OF MITOCHONDRIAL Ca2+ HANDLING AND CYTOSOLIC Ca2+ BUFFERS

In some cell types, Ca²⁺ oscillations are strictly dependent on Ca²⁺ influx across the plasma membrane, whereas in others, oscillations also persist in the absence of Ca²⁺ influx. We observed that, in primary mesothelial cells, the plasmalemmal Ca²⁺ influx played a pivotal role. However, when the Ca²⁺ transport across the plasma membrane by the “lanthanum insulation method” was blocked prior to the induction of the serum-induced Ca²⁺ oscillations, mitochondrial Ca²⁺ transport was found to be able to substitute for the plasmalemmal Ca²⁺ exchange function, thus rendering the oscillations independent of extracellular Ca²⁺. However, in a physiological situation, the Ca²⁺-buffering capacity of mitochondria was found not to be essential for Ca²⁺ oscillations. Moreover, brief spontaneous Ca²⁺ changes were observed in the mitochondrial Ca²⁺ concentration without apparent changes in the cytosolic Ca²⁺ concentration, indicating the presence of a mitochondrial autonomous Ca²⁺ signaling mechanism. In the presence of calretinin, a Ca²⁺-buffering protein, the amplitude of cytosolic spikes during oscillations was decreased, and the amount of Ca²⁺ ions taken up by mitochondria was reduced. Thus, the increased calretinin expression observed in mesothelioma cells and in certain colon cancer might be correlated to the increased resistance of these tumor cells to proapoptotic/pronecrotic signals. We identified and characterized (experimentally and by modeling) three Ca²⁺ shuttling pathways in primary mesothelial cells during Ca²⁺ oscillations: Ca²⁺ shuttled between (i) the endoplasmic reticulum (ER) and mitochondria, (ii) the ER and the extracellular space, and (iii) the ER and cytoplasmic Ca²⁺ buffers.

Modeling K,ATP--dependent excitability in pancreatic islets

In pancreatic ?-cells, K,ATP channels respond to changes in glucose to regulate cell excitability and insulin release. Confirming a high sensitivity of electrical activity to K,ATP activity, mutations that cause gain of K,ATP function cause neonatal diabetes. Our aim was to quantitatively assess the contribution of K,ATP current to the regulation of glucose-dependent bursting by reproducing experimentally observed changes in excitability when K,ATP conductance is altered by genetic manipulation. A recent detailed computational model of single cell pancreatic ?-cell excitability reproduces the ?-cell response to varying glucose concentrations. However, initial simulations showed that the model underrepresents the significance of K,ATP activity and was unable to reproduce K,ATP conductance-dependent changes in excitability. By altering the ATP and glucose dependence of the L-type Ca(2+) channel and the Na-K ATPase to better fit experiment, appropriate dependence of excitability on K,ATP conductance was reproduced. Because experiments were conducted in islets, which contain cell-to-cell variability, we extended the model from a single cell to a three-dimensional model (10×10×10 cell) islet with 1000 cells. For each cell, the conductance of the major currents was allowed to vary as was the gap junction conductance between cells. This showed that single cell glucose-dependent behavior was then highly variable, but was uniform in coupled islets. The study highlights the importance of parameterization of detailed models of ?-cell excitability and suggests future experiments that will lead to improved characterization of ?-cell excitability and the control of insulin secretion.

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.

Pulsatile insulin secretion, impaired glucose tolerance and type 2 diabetes

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

Defects in β-cell Ca2+ dynamics in age-induced diabetes

Little is known about the molecular mechanisms underlying age-dependent deterioration in β-cell function. We now demonstrate that age-dependent impairment in insulin release, and thereby glucose homeostasis, is associated with subtle changes in Ca(2+) dynamics in mouse β-cells. We show that these changes are likely to be accounted for by impaired mitochondrial function and to involve phospholipase C/inositol 1,4,5-trisphosphate-mediated Ca(2+) mobilization from intracellular stores as well as decreased β-cell Ca(2+) influx over the plasma membrane. We use three mouse models, namely, a premature aging phenotype, a mature aging phenotype, and an aging-resistant phenotype. Premature aging is studied in a genetically modified mouse model with an age-dependent accumulation of mitochondrial DNA mutations. Mature aging is studied in the C57BL/6 mouse, whereas the 129 mouse represents a model that is more resistant to age-induced deterioration. Our data suggest that aging is associated with a progressive decline in β-cell mitochondrial function that negatively impacts on the fine tuning of Ca(2+) dynamics. This is conceptually important since it emphasizes that even relatively modest changes in β-cell signal transduction over time lead to compromised insulin release and a diabetic phenotype.

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.

Cellular communication and heterogeneity in pancreatic islet insulin secretion dynamics

Coordinated pulses of electrical activity and insulin secretion are a hallmark of the islet of Langerhans. These coordinated behaviors are lost when β cells are dissociated, which also leads to increased insulin secretion at low glucose levels. Islets without gap junctions exhibit asynchronous electrical activity similar to dispersed cells, but their secretion at low glucose levels is still clamped off, putatively by a juxtacrine mechanism. Mice lacking β cell gap junctions have near-normal average insulin levels, but are glucose intolerant due to reduced first-phase and pulsatile insulin secretion, illustrating the importance of temporal dynamics. Here, we review the quantitative data on islet synchronization and the current mathematical models that have been developed to explain these behaviors and generate greater understanding of the underlying mechanisms.

Glucose stimulates calcium-activated chloride secretion in small intestinal cells

The sodium-coupled glucose transporter-1 (SGLT1)-based oral rehydration solution (ORS) used in the management of acute diarrhea does not substantially reduce stool output, despite the fact that glucose stimulates the absorption of sodium and water. To explain this phenomenon, we investigated the possibility that glucose might also stimulate anion secretion. Transepithelial electrical measurements and isotope flux measurements in Ussing chambers were used to study the effect of glucose on active chloride and fluid secretion in mouse small intestinal cells and human Caco-2 cells. Confocal fluorescence laser microscopy and immunohistochemistry measured intracellular changes in calcium, sodium-glucose linked transporter, and calcium-activated chloride channel (anoctamin 1) expression. In addition to enhancing active sodium absorption, glucose increased intracellular calcium and stimulated electrogenic chloride secretion. Calcium imaging studies showed increased intracellular calcium when intestinal cells were exposed to glucose. Niflumic acid, but not glibenclamide, inhibited glucose-stimulated chloride secretion in mouse small intestines and in Caco-2 cells. Glucose-stimulated chloride secretion was not seen in ileal tissues incubated with the intracellular calcium chelater BAPTA-AM and the sodium-potassium-2 chloride cotransporter 1 (NKCC1) blocker bumetanide. These observations establish that glucose not only stimulates active Na absorption, a well-established phenomenon, but also induces a Ca-activated chloride secretion. This may explain the failure of glucose-based ORS to markedly reduce stool output in acute diarrhea. These results have immediate potential to improve the treatment outcomes for acute and/or chronic diarrheal diseases by replacing glucose with compounds that do not stimulate chloride secretion.

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.

A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties

Fate decision processes of T lymphocytes are crucial for health and disease. Whether a T lymphocyte is activated, divides, gets anergic, or initiates apoptosis depends on extracellular triggers and intracellular signaling. Free cytosolic calcium dynamics plays an important role in this context. The relative contributions of store-derived calcium entry and calcium entry from extracellular space to T lymphocyte activation are still a matter of debate. Here we develop a quantitative mathematical model of T lymphocyte calcium dynamics in order to establish a tool which allows to disentangle cause-effect relationships between ion fluxes and observed calcium time courses. The model is based on single transmembrane protein characteristics which have been determined in independent experiments. This reduces the number of unknown parameters in the model to a minimum and ensures the predictive power of the model. Simulation results are subsequently used for an analysis of whole cell calcium dynamics measured under various experimental conditions. The model accounts for a variety of these conditions, which supports the suitability of the modeling approach. The simulation results suggest a model in which calcium dynamics dominantly relies on the opening of channels in calcium stores while calcium entry through calcium-release activated channels (CRAC) is more associated with the maintenance of the T lymphocyte calcium levels and prevents the cell from calcium depletion. Our findings indicate that CRAC guarantees a long-term stable calcium level which is required for cell survival and sustained calcium enhancement.

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.

Ion channels and regulation of insulin secretion in human β-cells: a computational systems analysis

In mammals an increase in glucose leads to block of ATP dependent potassium channels in pancreatic β cells leading to membrane depolarization. This leads to the repetitive firing of action potentials that increases calcium influx and triggers insulin granule exocytosis. Several important differences between species in this process suggest that a dedicated human-oriented approach is advantageous as extrapolating from rodent data may be misleading in several respects. We examined depolarization-induced spike activity in pancreatic human islet-attached β-cells employing whole-cell patch-clamp methods. We also reviewed the literature concerning regulation of insulin secretion by channel activity and constructed a data-based computer model of human β cell function. The model couples the Hodgkin-Huxley-type ionic equations to the equations describing intracellular Ca²⁺ homeostasis and insulin release. On the basis of this model we employed computational simulations to better understand the behavior of action potentials, calcium handling and insulin secretion in human β cells under a wide range of experimental conditions. This computational system approach provides a framework to analyze the mechanisms of human β cell insulin secretion.

Beneficial Effects of Pentanema vestitum Linn. Whole Plant on the Glucose and Other Biochemical Parameters of Alloxan Induced Diabetic Rabbits

The residents of Lower Dir and Malakand agency, Khyber Pakhtunkhwa, Pakistan, use the dry powder of whole plant of Pentanema vestitum for the treatment of asthma and diabetes. No documented reports are available about the therapeutic action of Pentanema vestitum. The present study was aimed to explore the antihyperglycemic effect of 70% methanol extract of Pentanema vestitum whole plant in glucose-induced nondiabetic hyperglycemic and alloxan-induced diabetic rabbits. During this study, the effects of plant extract on the serum lipid profile, GPT, ALP, bilirubin and creatinine of diabetic rabbits were also studied. The extract of Pentanema vestitum whole plant exhibited significant (P < 0.05) antihyperglycemic activity in glucose-induced hyperglycemic rabbits. Treatment of alloxan-induced diabetic rabbits with extract significantly (P < 0.05) reduced the elevated levels of serum glucose, GPT, ALP, bilirubin and creatinine. During the study of lipid profile, the extract proved to be antihyperlipidemic and HDL boosting in diabetic rabbit models. From the finding of the present research, it was concluded that the 70% methanol extract of Pentanema vestitum whole plant has beneficial effects on serum levels of glucose, lipid profile, GPT, ALP, bilirubin, and creatinine of diabetic rabbits.

MATLAB implementation of a dynamic clamp with bandwidth of >125 kHz capable of generating I Na at 37 °C

We describe the construction of a dynamic clamp with a bandwidth of >125 kHz that utilizes a high-performance, yet low-cost, standard home/office PC interfaced with a high-speed (16 bit) data acquisition module. High bandwidth is achieved by exploiting recently available software advances (code-generation technology and optimized real-time kernel). Dynamic-clamp programs are constructed using Simulink, a visual programming language. Blocks for computation of membrane currents are written in the high-level MATLAB language; no programming in C is required. The instrument can be used in single- or dual-cell configurations, with the capability to modify programs while experiments are in progress. We describe an algorithm for computing the fast transient Na(+) current (I Na) in real time and test its accuracy and stability using rate constants appropriate for 37 °C. We then construct a program capable of supplying three currents to a cell preparation: I Na, the hyperpolarizing-activated inward pacemaker current (I f) and an inward-rectifier K(+) current (I K1). The program corrects for the IR drop due to electrode current flow and also records all voltages and currents. We tested this program on dual patch-clamped HEK293 cells where the dynamic clamp controls a current-clamp amplifier and a voltage-clamp amplifier controls membrane potential, and current-clamped HEK293 cells where the dynamic clamp produces spontaneous pacing behavior exhibiting Na(+) spikes in otherwise passive cells.

Buffering capacity explains signal variation in symbiotic calcium oscillations

Legumes form symbioses with rhizobial bacteria and arbuscular mycorrhizal fungi that aid plant nutrition. A critical component in the establishment of these symbioses is nuclear-localized calcium (Ca(2+)) oscillations. Different components on the nuclear envelope have been identified as being required for the generation of the Ca(2+) oscillations. Among these an ion channel, Doesn't Make Infections1, is preferentially localized on the inner nuclear envelope and a Ca(2+) ATPase is localized on both the inner and outer nuclear envelopes. Doesn't Make Infections1 is conserved across plants and has a weak but broad similarity to bacterial potassium channels. A possible role for this cation channel could be hyperpolarization of the nuclear envelope to counterbalance the charge caused by the influx of Ca(2+) into the nucleus. Ca(2+) channels and Ca(2+) pumps are needed for the release and reuptake of Ca(2+) from the internal store, which is hypothesized to be the nuclear envelope lumen and endoplasmic reticulum, but the release mechanism of Ca(2+) remains to be identified and characterized. Here, we develop a mathematical model based on these components to describe the observed symbiotic Ca(2+) oscillations. This model can recapitulate Ca(2+) oscillations, and with the inclusion of Ca(2+)-binding proteins it offers a simple explanation for several previously unexplained phenomena. These include long periods of frequency variation, changes in spike shape, and the initiation and termination of oscillations. The model also predicts that an increase in buffering capacity in the nucleoplasm would cause a period of rapid oscillations. This phenomenon was observed experimentally by adding more of the inducing signal.

A computational systems analysis of factors regulating α cell glucagon secretion

Glucagon, a peptide hormone secreted from the α-cells of the pancreatic islets, is critical for blood glucose homeostasis. We reviewed the literature and employed a computational systems analysis of intracellular metabolic and electrical regulation of glucagon secretion to better understand these processes. The mathematical model of α-cell metabolic parameters is based on our previous model for pancreatic β-cells. We also formulated an ionic model for action potentials that incorporates Ca ( 2+) , K (+) , Na (+) and Cl (-) currents. Metabolic and ionic models are coupled to the equations describing Ca ( 2+) homeostasis and glucagon secretion that depends on activation of specific voltage-gated Ca ( 2+) channels. Paracrine and endocrine regulations were analyzed with an emphasis on their effects on a hyperpolarization of membrane potential. This general model simulates and gives insight into the mechanisms of regulation of glucagon secretion under a wide range of experimental conditions. We also reviewed and analyzed dysfunctional mechanisms in α-cells to determine key pharmacological targets for modulating glucagon secretion in type 1 and 2 diabetes.

β-Cell subcellular localization of glucose-stimulated Mn uptake by X-ray fluorescence microscopy: implications for pancreatic MRI

Manganese (Mn) is a calcium (Ca) analog that has long been used as a magnetic resonance imaging (MRI) contrast agent for investigating cardiac tissue functionality, for brain mapping and for neuronal tract tracing studies. Recently, we have extended its use to investigate pancreatic β-cells and showed that, in the presence of MnCl(2), glucose-activated pancreatic islets yield significant signal enhancement in T(1)-weigheted MR images. In this study, we exploited for the first time the unique capabilities of X-ray fluorescence microscopy (XFM) to both visualize and quantify the metal in pancreatic β-cells at cellular and subcellular levels. MIN-6 insulinoma cells grown in standard tissue culture conditions had only a trace amount of Mn, 1.14 ± 0.03 × 10(-11)µg/µm(2), homogenously distributed across the cell. Exposure to 2 mM glucose and 50 µM MnCl(2) for 20 min resulted in nonglucose-dependent Mn uptake and the overall cell concentration increased to 8.99 ± 2.69 × 10(-11) µg/µm(2). When cells were activated by incubation in 16 mM glucose in the presence of 50 µM MnCl(2), a significant increase in cytoplasmic Mn was measured, reaching 2.57 ± 1.34 × 10(-10) µg/µm(2). A further rise in intracellular concentration was measured following KCl-induced depolarization, with concentrations totaling 1.25 ± 0.33 × 10(-9) and 4.02 ± 0.71 × 10(-10) µg/µm(2) in the cytoplasm and nuclei, respectively. In both activated conditions Mn was prevalent in the cytoplasm and localized primarily in a perinuclear region, possibly corresponding to the Golgi apparatus and involving the secretory pathway. These data are consistent with our previous MRI findings, confirming that Mn can be used as a functional imaging reporter of pancreatic β-cell activation and also provide a basis for understanding how subcellular localization of Mn will impact MRI contrast.

Mathematical models for insulin secretion in pancreatic β-cells

Insulin secretion is one of the most characteristic features of β-cell physiology. As it plays a central role in glucose regulation, a number of experimental and theoretical studies have been performed since the discovery of the pancreatic β-cell. This review article aims to give an overview of the mathematical approaches to insulin secretion. Beginning with the bursting electrical activity in pancreatic β-cells, we describe effects of the gap-junction coupling between β-cells on the dynamics of insulin secretion. Then, implications of paracrine interactions among such islet cells as α-, β-, and δ-cells are discussed. Finally, we present mathematical models which incorporate effects of glycolysis and mitochondrial glucose metabolism on the control of insulin secretion.

Disruption of the chemokine-like receptor-1 (CMKLR1) gene is associated with reduced adiposity and glucose intolerance

Adipose tissue secretes a variety of bioactive signaling molecules, termed adipokines, which regulate numerous biological functions including appetite, energy balance, glucose homeostasis, and inflammation. Chemerin is a novel adipokine that regulates adipocyte differentiation and metabolism by binding to and activating the G protein-coupled receptor, chemokine like receptor-1 (CMKLR1). In the present study, we investigated the impact of CMKLR1 deficiency on adipose development, glucose homeostasis, and inflammation in vivo. Herein we report that regardless of diet (low or high fat), CMKLR1(-/-) mice had lower food consumption, total body mass, and percent body fat compared with wild-type controls. CMKLR1(-/-) mice also exhibited decreased hepatic and white adipose tissue TNFα and IL-6 mRNA levels coincident with decreased hepatic dendritic cell infiltration, decreased adipose CD3+ T cells, and increased adipose natural killer cells. CMKLR1(-/-) mice were glucose intolerant compared with wild-type mice, and this was associated with decreased glucose stimulated insulin secretion as well as decreased skeletal muscle and white adipose tissue glucose uptake. Collectively these data provide compelling evidence that CMKLR1 influences adipose tissue development, inflammation, and glucose homeostasis and may contribute to the metabolic derangement characteristic of obesity and obesity-related diseases.

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

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

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

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

Oral administration of levan polysaccharide reduces the alloxan-induced oxidative stress in rats

This study aimed to evaluate the effect of a polysaccharide named levan, which was produced by new isolated bacteria, on oxidative stress and hyperglycemia in alloxan-induced diabetic rats. Levan polysaccharide was given in drinking water for 60 days at a daily dose equivalent to 2%. The oral administration of levan in diabetic rats caused a decrease in glucose level in plasma and an increase of superoxide dismutase (SOD), catalase (CAT) and glutathione peroxidase (GPX) activities in both pancreas and liver. Furthermore, a protective action against hepatic and pancreatic toxicity in diabetic rats was clearly observed. Furthermore, a significant decrease in hepatic and pancreatic indices toxicity was observed, i.e., alkalines phosphatases (ALP), aspartate and lactate transaminases (AST and ALT), lactate deshydrogenases (LDH) activities and the thiobarbituric acid-reactive substances (TBARs). These beneficial effects of levan were confirmed by histological findings in hepatic and pancreatic tissues of diabetic rats. This study demonstrates for the first time that levan is efficient in inhibiting hyperglycemia and oxidative stress induced by diabetes and suggests that administration of levan may be helpful in the prevention of diabetic complications associated with oxidative stress.

Coupling of metabolic, second messenger pathways and insulin granule dynamics in pancreatic beta-cells: a computational analysis

Insulin secretory responses to nutrient stimuli and hormonal modulators in pancreatic beta-cells are controlled by a variety of secondary messengers. We have analyzed numerous mechanisms responsible for regulated exocytosis in these cells and present an integrated mathematical model of cytosolic Ca²⁺, cAMP and granule dynamics. The insulin-containing granules in the beta-cell were divided into four classes: a large "reserve" granule pool, a smaller pool of the morphologically docked granules that is chemically 'primed' for release or the "readily releasable pool", and a pool of "restless newcomer granules" that undergoes preferential exocytosis. The model incorporates glucose and other aspects of metabolism, the cAMP amplifying pathway, insulin granule dynamics and the exocyst concept for granule binding. The values of most of the model parameters were inferred from available experimental data. The model can generate both the fast first phase and slow biphasic insulin secretion found experimentally in response to a step increase of membrane potential or of glucose. The numerical simulations have also reproduced a variety of experimental conditions, such as periodic stimulation by high K⁺ and the potentiation induced in islets by pre-incubation with cAMP pathway activators. The explicit incorporation of Ca²⁺ channels, Ca²⁺ and cAMP dynamics allows the model to be further connected to current models for calcium and metabolic dynamics and provides an interpretation of the roles of the triggering and amplifying pathways of glucose-stimulated insulin secretion. The model may be important in the identification of pharmacological targets for improving insulin secretion in type 2 diabetes.

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.

Systems analysis of GLP-1 receptor signaling in pancreatic β-cells

Glucagon-like peptide-1 (GLP-1) elevates intracellular concentration of cAMP ([cAMP]) and facilitates glucose-dependent insulin secretion in pancreatic β-cells. There has been much evidence to suggest that multiple key players such as the GLP-1 receptor, G(s) protein, adenylate cyclase (AC), phosphodiesterase (PDE), and intracellular Ca(2+) concentration ([Ca(2+)]) are involved in the regulation of [cAMP]. However, because of complex interactions among these signaling factors, the kinetics of the reaction cascade as well as the activities of ACs and PDEs have not been determined in pancreatic β-cells. We have constructed a minimal mathematical model of GLP-1 receptor signal transduction based on experimental findings obtained mostly in β-cells and insulinoma cell lines. By fitting this theoretical reaction scheme to key experimental records of the GLP-1 response, the parameters determining individual reaction steps were estimated. The model reconstructed satisfactorily the dynamic changes in [cAMP] and predicted the activities of cAMP effectors, protein kinase A (PKA), and cAMP-regulated guanine nucleotide exchange factor [cAMP-GEF or exchange protein directly activated by cAMP (Epac)] during GLP-1 stimulation. The simulations also predicted the presence of two sequential desensitization steps of the GLP1 receptor that occur with fast and very slow reaction rates. The cross talk between glucose- and GLP-1-dependent signal cascades for cAMP synthesis was well reconstructed by integrating the direct regulation of AC and PDE by [Ca(2+)]. To examine robustness of the signaling system in controlling [cAMP], magnitudes of AC and PDE activities were compared in the presence or absence of GLP-1 and/or the PDE inhibitor IBMX.(1).

Toward integration of biological and physiological functions at multiple levels

An aim of systems physiology today can be stated as to establish logical and quantitative bridges between phenomenological attributes of physiological entities such as cells and organs and physical attributes of biological entities, i.e., biological molecules, allowing us to describe and better understand physiological functions in terms of underlying biological functions. This article illustrates possible schema that can be used for promoting systems physiology by integrating quantitative knowledge of biological and physiological functions at multiple levels of time and space with the use of information technology infrastructure. Emphasis will be made for systematic, modular, hierarchical, and standardized descriptions of mathematical models of the functions and advantages for the use of them.

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.