In vivo synchronous membrane potential oscillations in mouse pancreatic beta-cells: lack of co-ordination between islets

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.

Network Properties of Electrically Coupled Bursting Pituitary Cells

The endocrine cells of the anterior pituitary gland are electrically active when stimulated or, in some cases, when not inhibited. The activity pattern thought to be most effective in releasing hormones is bursting, which consists of depolarization with small spikes that are much longer than single spikes. Although a majority of the research on cellular activity patterns has been performed on dispersed cells, the environment in situ is characterized by networks of coupled cells of the same type, at least in the case of somatotrophs and lactotrophs. This produces some degree of synchronization of their activity, which can be greatly increased by hormones and changes in the physiological state. In this computational study, we examine how electrical coupling among model cells influences synchronization of bursting oscillations among the population. We focus primarily on weak electrical coupling, since strong coupling leads to complete synchronization that is not characteristic of pituitary cell networks. We first look at small networks to point out several unexpected behaviors of the coupled system, and then consider a larger random scale-free network to determine what features of the structural network formed through gap junctional coupling among cells produce a high degree of functional coupling, i.e., clusters of synchronized cells. We employ several network centrality measures, and find that cells that are closely related in terms of their closeness centrality are most likely to be synchronized. We also find that structural hubs (cells with extensive coupling to other cells) are typically not functional hubs (cells synchronized with many other cells). Overall, in the case of weak electrical coupling, it is hard to predict the functional network that arises from a structural network, or to use a functional network as a means for determining the structural network that gives rise to it.

"Take Me To Your Leader": An Electrophysiological Appraisal of the Role of Hub Cells in Pancreatic Islets

The coordinated electrical activity of β-cells within the pancreatic islet drives oscillatory insulin secretion. A recent hypothesis postulates that specially equipped "hub" or "leader" cells within the β-cell network drive islet oscillations and that electrically silencing or optically ablating these cells suppresses coordinated electrical activity (and thus insulin secretion) in the rest of the islet. In this Perspective, we discuss this hypothesis in relation to established principles of electrophysiological theory. We conclude that whereas electrical coupling between β-cells is sufficient for the propagation of excitation across the islet, there is no obvious electrophysiological mechanism that explains how hyperpolarizing a hub cell results in widespread inhibition of islet electrical activity and disruption of their coordination. Thus, intraislet diffusible factors should perhaps be considered as an alternate mechanism.

Critical and Supercritical Spatiotemporal Calcium Dynamics in Beta Cells

A coordinated functioning of beta cells within pancreatic islets is mediated by oscillatory membrane depolarization and subsequent changes in cytoplasmic calcium concentration. While gap junctions allow for intraislet information exchange, beta cells within islets form complex syncytia that are intrinsically nonlinear and highly heterogeneous. To study spatiotemporal calcium dynamics within these syncytia, we make use of computational modeling and confocal high-speed functional multicellular imaging. We show that model predictions are in good agreement with experimental data, especially if a high degree of heterogeneity in the intercellular coupling term is assumed. In particular, during the first few minutes after stimulation, the probability distribution of calcium wave sizes is characterized by a power law, thus indicating critical behavior. After this period, the dynamics changes qualitatively such that the number of global intercellular calcium events increases to the point where the behavior becomes supercritical. To better mimic normal in vivo conditions, we compare the described behavior during supraphysiological non-oscillatory stimulation with the behavior during exposure to a slightly lower and oscillatory glucose challenge. In the case of this protocol, we observe only critical behavior in both experiment and model. Our results indicate that the loss of oscillatory changes, along with the rise in plasma glucose observed in diabetes, could be associated with a switch to supercritical calcium dynamics and loss of beta cell functionality.

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

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

Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling

Based on bifurcation analysis, the synchronization behaviors of two identical pancreatic β-cells connected by electrical and chemical coupling are investigated, respectively. Various firing patterns are produced in coupled cells when a single cell exhibits tonic spiking or square-wave bursting individually, irrespectively of what the cells are connected by electrical or chemical coupling. On the one hand, cells can burst synchronously for both weak electrical and chemical coupling when an isolated cell exhibits tonic spiking itself. In particular, for electrically coupled cells, under the variation of the coupling strength there exist complex transition processes of synchronous firing patterns such as "fold/limit cycle" type of bursting, then anti-phase continuous spiking, followed by the "fold/torus" type of bursting, and finally in-phase tonic spiking. On the other hand, it is shown that when the individual cell exhibits square-wave bursting, suitable coupling strength can make the electrically coupled system generate "fold/Hopf" bursting via "fold/fold" hysteresis loop; whereas, the chemically coupled cells generate "fold/subHopf" bursting. Especially, chemically coupled bursters can exhibit inverse period-adding bursting sequence. Fast-slow dynamics analysis is applied to explore the generation mechanism of these bursting oscillations. The above analysis of bursting types and the transition may provide us with better insight into understanding the role of coupling in the dynamic behaviors of pancreatic β-cells.

Functional connectivity in islets of Langerhans from mouse pancreas tissue slices

We propose a network representation of electrically coupled beta cells in islets of Langerhans. Beta cells are functionally connected on the basis of correlations between calcium dynamics of individual cells, obtained by means of confocal laser-scanning calcium imaging in islets from acute mouse pancreas tissue slices. Obtained functional networks are analyzed in the light of known structural and physiological properties of islets. Focusing on the temporal evolution of the network under stimulation with glucose, we show that the dynamics are more correlated under stimulation than under non-stimulated conditions and that the highest overall correlation, largely independent of Euclidean distances between cells, is observed in the activation and deactivation phases when cells are driven by the external stimulus. Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets. Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way. Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

Glucose-stimulated calcium dynamics in islets of Langerhans in acute mouse pancreas tissue slices

In endocrine cells within islets of Langerhans calcium ions couple cell stimulation to hormone secretion. Since the advent of modern fluorimetry, numerous in vitro studies employing primarily isolated mouse islets have investigated the effects of various secretagogues on cytoplasmic calcium, predominantly in insulin-secreting beta cells. Due to technical limitations, insights of these studies are inherently limited to a rather small subpopulation of outermost cells. The results also seem to depend on various factors, like culture conditions and duration, and are not always easily reconcilable with findings in vivo. The main controversies regard the types of calcium oscillations, presence of calcium waves, and the level of synchronized activity. Here, we set out to combine the in situ acute mouse pancreas tissue slice preparation with noninvasive fluorescent calcium labeling and subsequent confocal laser scanning microscopy to shed new light on the existing controversies utilizing an innovative approach enabling the characterization of responses in many cells from all layers of islets. Our experiments reproducibly showed stable fast calcium oscillations on a sustained plateau rather than slow oscillations as the predominant type of response in acute tissue slices, and that calcium waves are the mechanistic substrate for synchronization of oscillations. We also found indirect evidence that even a large amplitude calcium signal was not sufficient and that metabolic activation was necessary to ensure cell synchronization upon stimulation with glucose. Our novel method helped resolve existing controversies and showed the potential to help answer important physiological questions, making it one of the methods of choice for the foreseeable future.

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.

Functional roles for noise in genetic circuits

The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or 'noise', in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward.

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.

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.

Oscillatory control of insulin secretion

Pancreatic beta-cells possess an inherent ability to generate oscillatory signals that trigger insulin release. Coordination of the secretory activity among beta-cells results in pulsatile insulin secretion from the pancreas, which is considered important for the action of the hormone in the target tissues. This review focuses on the mechanisms underlying oscillatory control of insulin secretion at the level of the individual beta-cell. Recent studies have demonstrated that oscillations of the cytoplasmic Ca(2+) concentration are synchronized with oscillations in beta-cell metabolism, intracellular cAMP concentration, phospholipase C activity and plasma membrane phosphoinositide lipid concentrations. There are complex interdependencies between the different messengers and signalling pathways that contribute to amplitude regulation and shaping of the insulin secretory response to nutrient stimuli and neurohormonal modulators. Several of these pathways may be important pharmacological targets for improving pulsatile insulin secretion in type 2 diabetes.

Novel aspects of the molecular mechanisms controlling insulin secretion

Pancreatic beta-cells secrete insulin by Ca(2+)-dependent exocytosis of secretory granules. beta-cell exocytosis involves SNARE (soluble NSF-attachment protein receptor) proteins similar to those controlling neurotransmitter release and depends on the close association of L-type Ca(2+) channels and granules. In most cases, the secretory granules fuse individually but there is ultrastructural and biophysical evidence of multivesicular exocytosis. Estimates of the secretory rate in beta-cells in intact islets indicate a release rate of approximately 15 granules per beta-cell per second, 100-fold higher than that observed in biochemical assays. Single-vesicle capacitance measurements reveal that the diameter of the fusion pore connecting the granule lumen with the exterior is approximately 1.4 nm. This is considerably smaller than the size of insulin and membrane fusion is therefore not obligatorily associated with release of the cargo, a feature that may contribute to the different rates of secretion detected by the biochemical and biophysical measurements. However, small molecules like ATP and GABA, which are stored together with insulin in the granules, are small enough to be released via the narrow fusion pore, which accordingly functions as a molecular sieve. We finally consider the possibility that defective fusion pore expansion accounts for the decrease in insulin secretion observed in pathophysiological states including long-term exposure to lipids.

RyR channels and glucose-regulated pancreatic beta-cells

Ryanodine receptor channel model is introduced to a dynamical model of pancreatic beta-cells to discuss the effects of RyR channels and glucose concentration on membrane potential. The results show Ca2+ concentration changes responding to enhance of glucose concentration is more quickly than that of activating RyR channels, and both methods can induce bursting action potential and increase free cytosolic Ca2+ concentration. An interesting finding is that moderate stimulation to RyR channels will result in a kind of "complex bursting", which is more effective in enhancing average Ca2+ concentration and insulin section.

Investigating the role of islet cytoarchitecture in its oscillation using a new beta-cell cluster model

The oscillatory insulin release is fundamental to normal glycemic control. The basis of the oscillation is the intercellular coupling and bursting synchronization of β cells in each islet. The functional role of islet β cell mass organization with respect to its oscillatory bursting is not well understood. This is of special interest in view of the recent finding of islet cytoarchitectural differences between human and animal models. In this study we developed a new hexagonal closest packing (HCP) cell cluster model. The model captures more accurately the real islet cell organization than the simple cubic packing (SCP) cluster that is conventionally used. Using our new model we investigated the functional characteristics of β-cell clusters, including the fraction of cells able to burst f_b, the synchronization index λ of the bursting β cells, the bursting period T_b, the plateau fraction p_f, and the amplitude of intracellular calcium oscillation [Ca]. We determined their dependence on cluster architectural parameters including number of cells n_β, number of inter-β cell couplings of each β cell n_c, and the coupling strength g_c. We found that at low values of n_β, n_c and g_c, the oscillation regularity improves with their increasing values. This functional gain plateaus around their physiological values in real islets, at n_β∼100, n_c∼6 and g_c∼200 pS. In addition, normal β-cell clusters are robust against significant perturbation to their architecture, including the presence of non-β cells or dead β cells. In clusters with n_β>∼100, coordinated β-cell bursting can be maintained at up to 70% of β-cell loss, which is consistent with laboratory and clinical findings of islets. Our results suggest that the bursting characteristics of a β-cell cluster depend quantitatively on its architecture in a non-linear fashion. These findings are important to understand the islet bursting phenomenon and the regulation of insulin secretion, under both physiological and pathological conditions.

Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion

Impairment of insulin secretion from the beta-cells of the pancreatic islets of Langerhans is central to the development of type 2 diabetes mellitus and has therefore been the subject of much investigation. Great advances have been made in this area, but the mechanisms underlying the pulsatility of insulin secretion remain controversial. The period of these pulses is 4-6 min and reflects oscillations in islet membrane potential and intracellular free Ca(2+). Pulsatile blood insulin levels appear to play an important physiological role in insulin action and are lost in patients with type 2 diabetes and their near relatives. We present evidence for a recently developed beta-cell model, the "dual oscillator model," in which oscillations in activity are due to both electrical and metabolic mechanisms. This model is capable of explaining much of the available data on islet activity and offers possible resolutions of a number of longstanding issues. The model, however, still lacks direct confirmation and raises new issues. In this article, we highlight both the successes of the model and the challenges that it poses for the field.

Effects of both glucose and IP3 concentrations on action potentials in pancreatic beta-cells

Considering the ATP-driven (SERCA) pump flux as function of glucose concentration and the calcium flux from the endoplasmic reticulum (ER) through the IP(3)R channel, the calcium-based phantom bursting model (PBM) of beta-cells (Bertram and Sherman in Bull Math Biol 66:1313, 2004) is theoretically extended to discuss the effects of glucose and inositol 1,4,5-trisphosphate (IP(3)) concentration on the membrane potential activities. When IP(3) concentration is fixed, it is found that there is a critical glucose concentration at which electrical bursting oscillations transfer into spiking, and the critical concentration of glucose is increased with the increasing of IP(3) concentration. To get the bursting oscillations in beta-cells, our theoretical results show that the stimulatory glucose concentration should be more than 10 mM, which is consistent with the normal physiological IP(3) level. When the stochastic opening and closing of IP(3)R channels are considered, it is shown that the membrane potential oscillation transfers from spiking to bursting with the channel number decreasing, and the average cytosolic free Ca(2+) concentration is increased with the increase of glucose concentration.

Connexin36 and pancreatic beta-cell functions

Most cell types are functionally coupled by connexin (Cx) channels, i.e. exchange cytoplasmic ions and small metabolites through gap junction domains of their membrane. This form of direct cell-to-cell communication occurs in all existing animals, whatever their position in the phylogenetic scale, and up to humans. Pancreatic beta-cells are no exception, and normally cross-talk with their neighbors via channels made of Cx36. These exchanges importantly contribute to coordinate and synchronize the function of individual cells within pancreatic islets, particularly in the context of glucose-induced insulin secretion. Compelling evidence now indicates that Cx36-mediated coupling, and/or the Cx36 protein per se, play significant regulatory roles in various beta-cell functions, ranging from the biosynthesis, storage and release of insulin. Recent preliminary data further suggest that the protein may also be implicated in the balance of beta-cell growth versus necrosis and apoptosis, and in the regulated expression of specific genes. Here, we review this evidence, discuss the possible involvement of Cx36 in the pathophysiology of diabetes, and evaluate the relevance of this connexin in the therapeutic approaches to the disease.

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.

Individual mice can be distinguished by the period of their islet calcium oscillations: is there an intrinsic islet period that is imprinted in vivo?

Pulsatile insulin secretion in vivo is believed to be derived, in part, from the intrinsic glucose-dependent intracellular calcium concentration ([Ca2+]i) pulsatility of individual islets. In isolation, islets display fast, slow, or mixtures of fast and slow [Ca2+]i oscillations. We show that the period of islet [Ca2+]i oscillations is unique to each mouse, with the islets from an individual mouse demonstrating similar rhythms to one another. Based on their rhythmic period, mice were broadly classified as being either fast (0.65 +/- 0.1 min; n = 6 mice) or slow (4.7 +/- 0.2 min; n = 15 mice). To ensure this phenomenon was not an artifact of islet-to-islet communication, we confirmed that islets cultured in isolation (period: 2.9 +/- 0.1 min) were not statistically different from islets cultured together from the same mouse (3.1 +/- 0.1 min, P > 0.52, n = 5 mice). We also compared pulsatile insulin patterns measured in vivo with islet [Ca2+]i patterns measured in vitro from six mice. Mice with faster insulin pulse periods corresponded to faster islet [Ca2+]i patterns, whereas slower insulin patterns corresponded to slower [Ca2+]i patterns, suggesting that the insulin rhythm of each mouse is preserved to some degree by its islets in vitro. We propose that individual mice have characteristic oscillatory [Ca2+]i patterns, which are imprinted in vivo through an unknown mechanism.

Involvement of gap junctional communication in secretion

Glands were the first type of tissues in which the permissive role of gap junctions in the cell-to-cell transfer of membrane-impermeant molecules was shown. During the 40 years that have followed this seminal finding, gap junctions have been documented in all types of multicellular secretory systems, whether of the exocrine, endocrine or pheromonal nature. Also, compelling evidence now indicates that gap junction-mediated coupling, and/or the connexin proteins per se, play significant regulatory roles in various aspects of gland functions, ranging from the biosynthesis, storage and release of a variety of secretory products, to the control of the growth and differentiation of secretory cells, and to the regulation of gland morphogenesis. This review summarizes this evidence in the light of recent reports.

Glucose metabolism and oscillatory behavior of pancreatic islets

A variety of oscillations are observed in pancreatic islets. We establish a model incorporating two oscillatory systems of different time scales: One is the well-known bursting model in pancreatic cells and the other is the glucose-insulin feedback model which considers direct and indirect feedback of secreted insulin. These two are coupled to interact with each other in the combined model, and two basic assumptions are made on the basis of biological observations: The conductance gK(ATP) for the ATP-dependent potassium current is a decreasing function of the glucose concentration whereas the insulin secretion rate is given by a function of the intracellular calcium concentration. Obtained via extensive numerical simulations are complex oscillations including clusters of bursts, slow and fast calcium oscillations, and so on. We also consider how the intracellular glucose concentration depends upon the extracellular glucose concentration, and examine the inhibitory effects of insulin.

Stabilizing role of calcium store-dependent plasma membrane calcium channels in action-potential firing and intracellular calcium oscillations

In many biological systems, cells display spontaneous calcium oscillations (CaOs) and repetitive action-potential firing. These phenomena have been described separately by models for intracellular inositol trisphosphate (IP3)-mediated CaOs and for plasma membrane excitability. In this study, we present an integrated model that combines an excitable membrane with an IP3-mediated intracellular calcium oscillator. The IP3 receptor is described as an endoplasmic reticulum (ER) calcium channel with open and close probabilities that depend on the cytoplasmic concentration of IP3 and Ca2+. We show that simply combining this ER model for intracellular CaOs with a model for membrane excitability of normal rat kidney (NRK) fibroblasts leads to instability of intracellular calcium dynamics. To ensure stable long-term periodic firing of action potentials and CaOs, it is essential to incorporate calcium transporters controlled by feedback of the ER store filling, for example, store-operated calcium channels in the plasma membrane. For low IP3 concentrations, our integrated NRK cell model is at rest at -70 mV. For higher IP3 concentrations, the CaOs become activated and trigger repetitive firing of action potentials. At high IP3 concentrations, the basal intracellular calcium concentration becomes elevated and the cell is depolarized near -20 mV. These predictions are in agreement with the different proliferative states of cultures of NRK fibroblasts. We postulate that the stabilizing role of calcium channels and/or other calcium transporters controlled by feedback from the ER store is essential for any cell in which calcium signaling by intracellular CaOs involves both ER and plasma membrane calcium fluxes.

How noise and coupling induce bursting action potentials in pancreatic {beta}-cells

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as well as that by channel-gating stochasticity and examine its effects on the action potential behavior of the beta-cell model. It is observed numerically that such noise in general helps single cells to produce a variety of electrical activities. In addition, we also probe coupling via gap junctions between neighboring cells, with heterogeneity induced by noise, to find that it enhances regular bursts.

Intra- and inter-islet synchronization of metabolically driven insulin secretion

Insulin secretion from pancreatic beta-cells is pulsatile with a period of 5-10 min and is believed to be responsible for plasma insulin oscillations with similar frequency. To observe an overall oscillatory insulin profile it is necessary that the insulin secretion from individual beta-cells is synchronized within islets, and that the population of islets is also synchronized. We have recently developed a model in which pulsatile insulin secretion is produced as a result of calcium-driven electrical oscillations in combination with oscillations in glycolysis. We use this model to investigate possible mechanisms for intra-islet and inter-islet synchronization. We show that electrical coupling is sufficient to synchronize both electrical bursting activity and metabolic oscillations. We also demonstrate that islets can synchronize by mutually entraining each other by their effects on a simple model "liver," which responds to the level of insulin secretion by adjusting the blood glucose concentration in an appropriate way. Since all islets are exposed to the blood, the distributed islet-liver system can synchronize the individual islet insulin oscillations. Thus, we demonstrate how intra-islet and inter-islet synchronization of insulin oscillations may be achieved.

Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

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

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

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

Stretch activation of Ca2+ transients in pancreatic beta cells by mobilization of intracellular stores

INTRODUCTION

Nonadrenergic, noncholinergic neurons have been proposed to synchronize pulsatile insulin release from the islets in the pancreas by triggering transient increases of the cytoplasmic Ca2+ concentration ([Ca2+]i) in beta-cells via an inositol trisphoshate-dependent mechanism.

AIMS

To test whether pancreatic beta-cells respond to stretch activation with similar types of transients and whether these Ca signals propagate to other beta-cells in the presence and absence of cell contacts.

METHODOLOGY

Single cells and small aggregates were prepared from beta-cell-rich islets from mice. After 2-5 days of culture, [Ca2+]i was measured with digital imaging and the indicator fura-2 during superfusion with a medium containing 20 mmol/L glucose and 50 micromol/L methoxyverapamil. Membrane stretch was induced by osmotic swelling or focal touch stimulation.

RESULTS

Lowering the medium osmolarity with 100-102 mOSM/L by removal of sucrose or by dilution resulted in a 2-3-fold increase in the number of transients during an initial 5-minute period. Sucrose omission was stimulatory also after isosmolar replacement with readily penetrating urea. The intracellular Ca2+-ATPase inhibitor thapsigargin suppressed both the spontaneously occurring transients and those initiated by volume expansion. Touch stimuli induced [Ca2+]i transients, which rapidly propagated to cells within the same aggregate or lacking contact.

CONCLUSION

The observations support the idea that beta-cells both receive and regenerate extracellular signals triggering [Ca2+]i transients. Touch stimulation is a useful tool for investigating the propagation of [Ca2+]i signals between pancreatic beta-cells lacking physical contact.

A model for glucose-induced wave propagation in pancreatic islets of Langerhans

A reaction-diffusion type model is constructed, describing the spatio-temporal dynamics of the basic intracellular variables assumed to be involved in the initiation of the insulin secretion process by beta -cells in the pancreatic islets of Langerhans. The model includes equations for the electric membrane potential of the cells, with respective kinetics for ionic currents, for concentrations of both free and stored intracellular calcium, and for the intra- and extracellular concentrations of glucose. An empirical expression connecting the equation for the intracellular glucose concentration to the electrical equation is introduced. The model reproduces the events observed in experiments in vitro upon external glucose application to the islets of Langerhans, such as usual bursting oscillations of the membrane potential and corresponding oscillations of the intracellular calcium concentration. It also allows simulation of electric wave propagation through the islet, initiated by the spatial gradient of glucose concentration within the islet. The gradient emerges due to glucose diffusing into the islets from the external medium, being high at the edges. The latter results show that glucose diffusion presents a means for wave initiation in the islets, which supports our previous assumption (Aslanidi et al., 2001).

Primary in vivo oscillations of metabolism in the pancreas

The role of metabolism in the generation of plasma insulin oscillations was investigated by simultaneous in vivo recordings of oxygen tension (pO(2)) in the endocrine and exocrine pancreas and portal blood insulin concentrations in the anesthetized rat. At the start of the experiment, the blood glucose concentration of seven rats was 6.2 +/- 0.1 mmol/l and the arterial blood pressure was 116 +/- 5 mmHg. These values did not differ from those obtained at the end of the experiment. Islet pO(2) was measured by impaling superficially located islets with a miniaturized Clark electrode. The pO(2) measurements revealed slow (0.21 +/- 0.03 min(-1)) with superimposed rapid (3.1 +/- 0.3 min(-1)) oscillations. The average pO(2) was 39 +/- 5 mmHg. Simultaneous recordings of pO(2) in the exocrine pancreas were significantly lower (16 +/- 6 mmHg), but showed a slow and a rapid oscillatory activity with similar frequencies as seen in the endocrine pancreas. Corresponding measurements of portal insulin concentrations revealed insulin oscillations at a frequency of 0.22 +/- 0.02 min(-1). The results are the first in vivo recordings of an oscillatory islet parameter with a frequency corresponding to that of plasma insulin oscillations; they support a primary role of metabolic oscillations in the induction of plasma insulin oscillations.

Pulsatile insulin secretion: detection, regulation, and role in diabetes

Insulin concentrations oscillate at a periodicity of 5-15 min per oscillation. These oscillations are due to coordinate insulin secretory bursts, from millions of islets. The generation of common secretory bursts requires strong within-islet and within-pancreas coordination to synchronize the secretory activity from the beta-cell population. The overall contribution of this pulsatile mechanism dominates and accounts for the majority of insulin release. This review discusses the methods involved in the detection and quantification of periodicities and individual secretory bursts. The mechanism by which overall insulin secretion is regulated through changes in the pulsatile component is discussed for nerves, metabolites, hormones, and drugs. The impaired pulsatile secretion of insulin in type 2 diabetes has resulted in much focus on the impact of the insulin delivery pattern on insulin action, and improved action from oscillatory insulin exposure is demonstrated on liver, muscle, and adipose tissues. Therefore, not only is the dominant regulation of insulin through changes in secretory burst mass and amplitude, but the changes may affect insulin action. Finally, the role of impaired pulsatile release in early type 2 diabetes suggests a predictive value of studies on insulin pulsatility in the development of this disease.

Control mechanisms of the oscillations of insulin secretion in vitro and in vivo

The mechanisms driving the pulsatility of insulin secretion in vivo and in vitro are still unclear. Because glucose metabolism and changes in cytosolic free Ca(2+) ([Ca(2+)](c)) in beta-cells play a key role in the control of insulin secretion, and because oscillations of these two factors have been observed in single isolated islets and beta-cells, pulsatile insulin secretion could theoretically result from [Ca(2+)](c) or metabolism oscillations. We could not detect metabolic oscillations independent from [Ca(2+)](c) changes in beta-cells, and imposed metabolic oscillations were poorly effective in inducing oscillations of secretion when [Ca(2+)](c) was kept stable, which suggests that metabolic oscillations are not the direct regulator of the oscillations of secretion. By contrast, tight temporal and quantitative correlations between the changes in [Ca(2+)](c) and insulin release strongly suggest that [Ca(2+)](c) oscillations are the direct drivers of insulin secretion oscillations. Metabolism may play a dual role, inducing [Ca(2+)](c) oscillations (via changes in ATP-sensitive K(+) channel activity and membrane potential) and amplifying the secretory response by increasing the efficiency of Ca(2+) on exocytosis. The mechanisms underlying the oscillations of insulin secretion by the isolated pancreas and those observed in vivo remain elusive. It is not known how the functioning of distinct islets is synchronized, and the possible role of intrapancreatic ganglia in this synchronization requires confirmation. That pulsatile insulin secretion is beneficial in vivo, by preventing insulin resistance, is suggested by the greater hypoglycemic effect of exogenous insulin when it is infused in a pulsatile rather than continuous manner. The observation that type 2 diabetic patients have impaired pulsatile insulin secretion has prompted the suggestion that such dysregulation contributes to the disease and justifies the efforts toward understanding of the mechanism underlying the pulsatility of insulin secretion both in vitro and in vivo.

Role of oscillations in membrane potential, cytoplasmic Ca2+, and metabolism for plasma insulin oscillations

A model for the relationship between ionic and metabolic oscillations and plasma insulin oscillations is presented. It is argued that the pancreatic beta-cell in vivo displays two intrinsic frequencies that are important for the regulation of plasma insulin oscillations. The rapid oscillatory activity (2--7 oscillations [osc] per minute), which is evident in both ionic and metabolic events, causes the required elevation in cytoplasmic Ca(2+) concentration ([Ca(2+)](i)) for the exocytosis of insulin granules. This activity is important for regulation of the amplitude of plasma insulin oscillations. The frequency of the rapid oscillatory ionic activities is regulated by glucose and allows the beta-cell to respond in an analogous way, with gradual changes in [Ca(2+)](i) and insulin release in response to the alterations in glucose concentration. The slower oscillatory activity (0.2--0.4 osc/min), which is evident in the metabolism of the beta-cell, has a frequency corresponding to the frequency observed in plasma insulin oscillations. The frequency is not affected by changes in the glucose concentration. This activity is suggested to generate energy in a pulsatile fashion, which sets the frequency of the plasma insulin oscillations. It is proposed that the slow oscillations in [Ca(2+)](i) observed in vitro are a manifestation of the metabolic oscillations and do not represent an in vivo phenomenon.

Nitric oxide induces synchronous Ca2+ transients in pancreatic beta cells lacking contact

AIMS

To evaluate the role of nitric oxide (NO) in the coordination of the Ca2+ signals generating pulsatile insulin release in pancreatic beta cells isolated from ob/ob mice.

METHODOLOGY

Using ratiometric fura-2 technique for recording glucose-induced cytoplasmic Ca2+ transients, it was possible to demonstrate a synchronization of beta cells lacking contact.

RESULTS

The frequency of the transients increased 10-fold in the presence of 20 n M glucagon. Additional increase in frequency with maintenance of synchronization was observed when the beta cells were exposed to 100 microM of the NO donors sodium nitroprusside and hydroxylamine. Bolus additions of 0.1-10 microM gaseous NO resulted in prompt appearance of cytoplasmic Ca2+ transients. An activator of soluble guanylate cyclase (mesoporphyrin) increased the frequency of the transients, and inhibition of this enzyme with 1H-(1,2,4) oxadiazolo [4,3-a] quinoxalin-1-one had the opposite effect.

CONCLUSION

The results support the idea that nitrergic nerves generate beta-cell transients of Ca2+ synchronizing the activity of the numerous islets in the pancreas.

The generation of oscillations in networks of electrically coupled cells

In several biological systems, the electrical coupling of nonoscillating cells generates synchronized membrane potential oscillations. Because the isolated cell is nonoscillating and electrical coupling tends to equalize the membrane potentials of the coupled cells, the mechanism underlying these oscillations is unclear. Here we present a dynamic mechanism by which the electrical coupling of identical nonoscillating cells can generate synchronous membrane potential oscillations. We demonstrate this mechanism by constructing a biologically feasible model of electrically coupled cells, characterized by an excitable membrane and calcium dynamics. We show that strong electrical coupling in this network generates multiple oscillatory states with different spatio-temporal patterns and discuss their possible role in the cooperative computations performed by the system.

Excitation wave propagation as a possible mechanism for signal transmission in pancreatic islets of Langerhans

In response to glucose application, beta-cells forming pancreatic islets of Langerhans start bursting oscillations of the membrane potential and intracellular calcium concentration, inducing insulin secretion by the cells. Until recently, it has been assumed that the bursting activity of beta-cells in a single islet of Langerhans is synchronized across the whole islet due to coupling between the cells. However, time delays of several seconds in the activity of distant cells are usually observed in the islets of Langerhans, indicating that electrical/calcium wave propagation through the islets can occur. This work presents both experimental and theoretical evidence for wave propagation in the islets of Langerhans. Experiments with Fura-2 fluorescence monitoring of spatiotemporal calcium dynamics in the islets have clearly shown such wave propagation. Furthermore, numerical simulations of the model describing a cluster of electrically coupled beta-cells have supported our view that the experimentally observed calcium waves are due to electric pulses propagating through the cluster. This point of view is also supported by independent experimental results. Based on the model equations, an approximate analytical expression for the wave velocity is introduced, indicating which parameters can alter the velocity. We point to the possible role of the observed waves as signals controlling the insulin secretion inside the islets of Langerhans, in particular, in the regions that cannot be reached by any external stimuli such as high glucose concentration outside the islets.

Synchronous glucose-dependent [Ca(2+)](i) oscillations in mouse pancreatic islets of Langerhans recorded in vivo

Using microfluorescence in combination with image-analysis techniques we monitored intracellular calcium ([Ca(2+)](i)) dynamics in mouse islets of Langerhans loaded with fura-2 and recorded in vivo. [Ca(2+)](i) oscillates in the glycaemias range 5-10 mM, the duration of the oscillations being directly proportional to the blood glucose concentration. The analysis of different areas within the same islet shows that [Ca(2+)](i) oscillations are synchronous throughout the islet. These results show that in vivo, individual islets of Langerhans behave as a functional syncytium and suggest the existence of secretory pulses of insulin.

Dynamical complexity and temporal plasticity in pancreatic beta-cells

We discuss some of the biological and mathematical issues involved in understanding and modelling the bursting electrical activity in pancreatic beta-cells. These issues include single-cell versus islet behaviour, parameter heterogeneity, channel noise, the effects of hormones, neurotransmitters, and ions, and multiple slow biophysical processes. Some of the key experimental and modelling studies are described, and some of the major open questions are discussed.

Pathophysiology of impaired pulsatile insulin release

Plasma insulin displays 5-10 min oscillations. In Type 2 diabetes the regularity of the oscillations disappears, which may lead to insulin receptor down-regulation and glucose intolerance and explain why pulsatile delivery of the hormone has a greater hypoglycemic effect than continuous delivery. The rhythm is intrinsic to the islet. Variations in metabolism, cytoplasmic Ca(2+) concentration ([Ca(2+)](i)), other hormones, neuronal signaling and possibly beta-cell insulin receptor expression have been implicated in the regulation of plasma insulin oscillations. Most of these factors are important for amplitude-regulation of the insulin pulses. Although evidence exists supporting a role of both metabolism and [Ca(2+)](i) as pacemakers of the pulses, metabolic oscillations probably have a primary role and [Ca(2+)](i) oscillations a permissive role. Results from islets from animal models of diabetes suggest that altered plasma insulin pattern could be due to lowering of pulse amplitude of insulin oscillations rather than alterations in their frequency. Supporting a role of metabolism, altered plasma insulin oscillations were found in MODY2, MIDD and glycogenosis Type VII, which are linked to alterations in glucokinase, mitochondrial tRNALeu(UUR) and phosphofructokinase. Plasma insulin oscillations require coordination of islet secretory activities in the pancreas. The intrapancreatic ganglia have been suggested as coordinators. The diabetes-associated neuropathy may contribute to the deranged pattern as indicated by glucose intolerance in chagasic patients. Continued investigation of the role and regulation of pulsatile insulin release will lead to better understanding of the pathophysiology of impaired pulsatile insulin release, which could lead to new approaches to restore normal plasma insulin oscillations in diabetes and related diseases.

Regulation by tolbutamide and diazoxide of the electrical activity in mouse pancreatic beta-cells recorded in vivo

1. The glucose-dependence of beta-cell electrical activity and the effects of tolbutamide and diazoxide were studied in anaesthetized mice. 2. In untreated animals there was a direct relationship between glycaemia and the burst pattern of electrical activity. Animals with high glucose concentration showed continuous electrical activity. The application of insulin led to a steady decrease in blood glucose concentration and a transition from continuous to oscillatory activity at 7.7+/-0.1 mM glucose (mean+/-s.d.) and a subsequent transition from oscillatory to silent at 4.7+/-0.6 mM glucose. 3. At physiological blood glucose concentrations the electrical activity was oscillatory. The injection of tolbutamide (1800 mg kg[-1]) transformed this oscillatory pattern into one of continuous electrical activity. The increased electrical activity was associated with a decrease in blood glucose concentration from 7.1+/-0.9 (control) to 5.5+/-1.0 mM (10 min after tolbutamide injection). The effects of tolbutamide are consistent with a direct blocking effect on the K(ATP) channel that leads to membrane depolarization. 4. The injection of diazoxide (6000 mg kg[-1]) hyperpolarized the cells and transformed the oscillatory pattern into a silent one. This is consistent with a direct stimulant effect by diazoxide on the K(ATP) channel. The use of tolbutamide or diazoxide correspondingly led to the lengthening or shortening of the active phase of electrical activity, respectively. This indicates that in vivo, such activity can be modulated by the relative degree of activation or inhibition of the K(ATP) channel. 5. These results indicate that under physiological conditions, tolbutamide and diazoxide have direct and opposite effects on the electrical activity of pancreatic beta-cells, most likely through their action on K(ATP) channels. This is consistent with previous work carried out on in vitro models and explains the drugs hypo- and hyperglycaemic effects.

Oscillation of gap junction electrical coupling in the mouse pancreatic islets of Langerhans

1. Pancreatic beta-cells oscillate synchronously when grouped in islets. Coupling seems essential to maintain this oscillatory behaviour, as isolated cells are unable to oscillate. This allows the islet to be used as a model system for studying the role of coupling in the generation of oscillatory patterns. 2. Pairs of beta-cells were intracellularly recorded in islets. beta-Cells oscillated synchronously. Propagated voltage deflections were observed as a function of glucose concentration and of the distance between the recording electrodes. Space constants were smaller in the silent than in the active phases, suggesting a higher intercellular connection in the active phases. 3. Coupling coefficients and estimated coupling conductances were larger in the active than in the silent phases. 4. Coupling coefficients and coupling conductances changed dynamically and in phase with the membrane potential oscillations, pointing to an active modulation of the gap junctions. 5. We hypothesize a role for coupling in the generation of the oscillatory events, providing different levels of permeability dependent on the state of conductance during the oscillatory phases.

Oscillatory patterns of electrical activity in mouse pancreatic islets of Langerhans recorded in vivo

Pancreatic beta-cells secrete insulin as a function of blood glucose concentration. One of the key steps in stimulus-secretion coupling is the depolarisation of the membrane and the appearance of bursts of calcium action potentials. Recently, the characteristics and glucose dependence of the oscillations in electrical activity in vivo have been described. The experiments described here were designed to determine the temporal evolution of such electrical activity when no experimental changes in the glycaemia are imposed. The absolute duration of the active and silent phases has been analysed and compared with the values obtained in vitro. We have found that in vivo, at glycaemia ranging from 6.0 to 7.5 mM, the electrical activity of the islets of Langerhans is permanently oscillatory, the mean duration of the depolarisation phase being 28 s. In general, the oscillatory pattern remains very constant for relatively long (up to 60 min) periods of time. In some experiments, slow or transitory changes in the degree of beta-cell activation could be observed, as well as the existence, in a very few cases, of oscillatory non-periodic patterns. Key words beta-cells middle dot Pancreas middle dot Electrophysiology middle dot Oscillations