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.     

Low Level Pro-inflammatory Cytokines Decrease Connexin36 Gap Junction Coupling in Mouse and Human Islets through Nitric Oxide-mediated Protein Kinase Cδ

Pro-inflammatory cytokines contribute to the decline in islet function during the development of diabetes. Cytokines can disrupt insulin secretion and calcium dynamics; however, the mechanisms underlying this are poorly understood. Connexin36 gap junctions coordinate glucose-induced calcium oscillations and pulsatile insulin secretion across the islet. Loss of gap junction coupling disrupts these dynamics, similar to that observed during the development of diabetes. This study investigates the mechanisms by which pro-inflammatory cytokines mediate gap junction coupling. Specifically, as cytokine-induced NO can activate PKCδ, we aimed to understand the role of PKCδ in modulating cytokine-induced changes in gap junction coupling. Isolated mouse and human islets were treated with varying levels of a cytokine mixture containing TNF-α, IL-1β, and IFN-γ. Islet dysfunction was measured by insulin secretion, calcium dynamics, and gap junction coupling. Modulators of PKCδ and NO were applied to determine their respective roles in modulating gap junction coupling. High levels of cytokines caused cell death and decreased insulin secretion. Low levels of cytokine treatment disrupted calcium dynamics and decreased gap junction coupling, in the absence of disruptions to insulin secretion. Decreases in gap junction coupling were dependent on NO-regulated PKCδ, and altered membrane organization of connexin36. This study defines several mechanisms underlying the disruption to gap junction coupling under conditions associated with the development of diabetes. These mechanisms will allow for greater understanding of islet dysfunction and suggest ways to ameliorate this dysfunction during the development of diabetes.     

Small subpopulations of β-cells do not drive islet oscillatory [Ca2+] dynamics via gap junction communication

The islets of Langerhans exist as multicellular networks that regulate blood glucose levels. The majority of cells in the islet are excitable, insulin-producing β-cells that are electrically coupled via gap junction channels. β-cells are known to display heterogeneous functionality. However, due to gap junction coupling, β-cells show coordinated [Ca²⁺] oscillations when stimulated with glucose, and global quiescence when unstimulated. Small subpopulations of highly functional β-cells have been suggested to control [Ca²⁺] dynamics across the islet. When these populations were targeted by optogenetic silencing or photoablation, [Ca²⁺] dynamics across the islet were largely disrupted. In this study, we investigated the theoretical basis of these experiments and how small populations can disproportionality control islet [Ca²⁺] dynamics. Using a multicellular islet model, we generated normal, skewed or bimodal distributions of β-cell heterogeneity. We examined how islet [Ca²⁺] dynamics were disrupted when cells were targeted via hyperpolarization or populations were removed; to mimic optogenetic silencing or photoablation, respectively. Targeted cell populations were chosen based on characteristics linked to functional subpopulation, including metabolic rate of glucose oxidation or [Ca²⁺] oscillation frequency. Islets were susceptible to marked suppression of [Ca²⁺] when ~10% of cells with high metabolic activity were hyperpolarized; where hyperpolarizing cells with normal metabolic activity had little effect. However, when highly metabolic cells were removed from the model, [Ca²⁺] oscillations remained. Similarly, when ~10% of cells with either the highest frequency or earliest elevations in [Ca²⁺] were removed from the islet, the [Ca²⁺] oscillation frequency remained largely unchanged. Overall, these results indicate small populations of β-cells with either increased metabolic activity or increased frequency are unable to disproportionately control islet-wide [Ca²⁺] via gap junction coupling. Therefore, we need to reconsider the physiological basis for such small β-cell populations or the mechanism by which they may be acting to control normal islet function.     

Intrinsic Islet Heterogeneity and Gap Junction Coupling Determine Spatiotemporal Ca2+ Wave Dynamics

Insulin is released from the islets of Langerhans in discrete pulses that are linked to synchronized oscillations of intracellular free calcium ([Ca²⁺]_i). Associated with each synchronized oscillation is a propagating calcium wave mediated by Connexin36 (Cx36) gap junctions. A computational islet model predicted that waves emerge due to heterogeneity in β-cell function throughout the islet. To test this, we applied defined patterns of glucose stimulation across the islet using a microfluidic device and measured how these perturbations affect calcium wave propagation. We further investigated how gap junction coupling regulates spatiotemporal [Ca²⁺]_i dynamics in the face of heterogeneous glucose stimulation. Calcium waves were found to originate in regions of the islet having elevated excitability, and this heterogeneity is an intrinsic property of islet β-cells. The extent of [Ca²⁺]_i elevation across the islet in the presence of heterogeneity is gap-junction dependent, which reveals a glucose dependence of gap junction coupling. To better describe these observations, we had to modify the computational islet model to consider the electrochemical gradient between neighboring β-cells. These results reveal how the spatiotemporal [Ca²⁺]_i dynamics of the islet depend on β-cell heterogeneity and cell-cell coupling, and are important for understanding the regulation of coordinated insulin release across the islet.     

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.     

On-line analysis of gap junctions reveals more efficient electrical than dye coupling between islet cells

Pancreatic beta-cells constitute a well-communicating multicellular network that permits a coordinated and synchronized signal transmission within the islet of Langerhans that is necessary for proper insulin release. Gap junctions are the molecular keys that mediate functional cellular connections, which are responsible for electrical and metabolic coupling in the majority of cell types. Although the role of gap junctions in beta-cell electrical coupling is well documented, metabolic communication is still a matter of discussion. Here, we have addressed this issue by use of a fluorescence recovery after photobleaching (FRAP) approach. This technique has been validated as a reliable and noninvasive approach to monitor functional gap junctions in real time. We show that control pancreatic islet cells did not exchange a gap junction-permeant molecule in either clustered cells or intact islets of Langerhans under conditions that allowed cell-to-cell exchange of current-carrying ions. Conversely, we have detected that the same probe was extensively transferred between islet cells of transgenic mice expressing connexin 32 (Cx32) that have enhanced junctional coupling properties. The results indicate that the electrical coupling of native islet cells is more extensive than dye communication. Dye-coupling domains in islet cells appear more restricted than previously inferred with other methods.     

New insights into the role of connexins in pancreatic islet function and diabetes

Multi-cellular systems require complex signaling mechanisms for proper tissue function, to mediate signaling between cells in close proximity and at distances. This holds true for the islets of Langerhans, which are multicellular micro-organs located in the pancreas responsible for glycemic control, through secretion of insulin and other hormones. Coupling of electrical and metabolic signaling between islet β-cells is required for proper insulin secretion and effective glycemic control. β-cell specific coupling is established through gap junctions composed of connexin36, which results in coordinated insulin release across the islet. Islet connexins have been implicated in both Type-1 and Type-2 diabetes; however a clear link remains to be determined. The goal of this review is to discuss recent discoveries regarding the role of connexins in regulating insulin secretion, the regulation of connexins within the islet, and recent studies which support a role for connexins in diabetes. Further studies which investigate the regulation of connexins in the islet and their role in diabetes may lead to novel diabetes therapies which regulate islet function and β-cell survival through modulation of gap junction coupling.     

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.     

Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e., regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.     

Initiation and entrainment of multicellular automaticity via diffusion limited extracellular domains

Electrically excitable cells often spontaneously and synchronously depolarize in vitro and in vivo preparations. It remains unclear how cells entrain and autorhythmically activate above the intrinsic mean activation frequency of isolated cells with or without pacemaking mechanisms. Recent studies suggest that cyclic ion accumulation and depletion in diffusion-limited extracellular volumes modulate electrophysiology by ephaptic mechanisms (nongap junction or synaptic coupling). This report explores how potassium accumulation and depletion in a restricted extracellular domain induces spontaneous action potentials in two different computational models of excitable cells without gap junctional coupling: Hodgkin-Huxley and Luo-Rudy. Importantly, neither model will spontaneously activate on its own without external stimuli. Simulations demonstrate that cells sharing a diffusion-limited extracellular compartment can become autorhythmic and entrained despite intercellular electrical heterogeneity. Autorhythmic frequency is modulated by the cleft volume and potassium fluxes through the cleft. Additionally, inexcitable cells can suppress or induce autorhythmic activity in an excitable cell via a shared cleft. Diffusion-limited shared clefts can also entrain repolarization. Critically, this model predicts a mechanism by which diffusion-limited shared clefts can initiate, entrain, and modulate multicellular automaticity in the absence of gap junctions.     

Why pancreatic islets burst but single beta cells do not. The heterogeneity hypothesis.

Previous mathematical modeling of beta cell electrical activity has involved single cells or, recently, clusters of identical cells. Here we model clusters of heterogeneous cells that differ in size, channel density, and other parameters. We use gap-junctional electrical coupling, with conductances determined by an experimental histogram. We find that, for reasonable parameter distributions, only a small proportion of isolated beta cells will burst when uncoupled, at any given value of a glucose-sensing parameter. However, a coupled, heterogeneous cluster of such cells, if sufficiently large (approximately 125 cells), will burst synchronously. Small clusters of such cells will burst only with low probability. In large clusters, the dynamics of intracellular calcium compare well with experiments. Also, these clusters possess a dose-response curve of increasing average electrical activity with respect to a glucose-sensing parameter that is sharp when the cluster is coupled, but shallow when the cluster is decoupled into individual cells. This is in agreement with comparative experiments on cells in suspension and islets.     

Modeling K,ATP-Dependent Excitability in Pancreatic Islets

In pancreatic β-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 β-cell excitability reproduces the β-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 Ca²⁺ 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 β-cell excitability and suggests future experiments that will lead to improved characterization of β-cell excitability and the control of insulin secretion.     

Size distribution of mouse Langerhans islets

Pancreatic beta-cells are clustered in islets of Langerhans, which are typically a few hundred micrometers in a variety of mammals. In this study, we propose a theoretical model for the growth of pancreatic islets and derive the islet size distribution, based on two recent observations: First, the neogenesis of new islets becomes negligible after some developmental stage. Second, islets grow via a random process, where any cell in an islet proliferates with the same rate regardless of the present size of the islet. Our model predicts either log-normal or Weibull distributions of the islet sizes, depending on whether cells in an islet proliferate coherently or independently. To confirm this, we also measure the islet size by selectively staining islets, which are exposed from exocrine tissues in mice after enzymatic treatment. Indeed revealed are skewed distributions with the peak size of approximately 100 cells, which fit well to the theoretically derived ones. Interestingly, most islets turned out to be bigger than the expected minimal size (approximately 10 or so cells) necessary for stable synchronization of beta-cells through electrical gap-junction coupling. The collaborative behavior among cells is known to facilitate synchronized insulin secretion and tends to saturate beyond the critical (saturation) size of approximately 100 cells. We further probe how the islets change as normal mice grow from young (6 weeks) to adult (5 months) stages. It is found that islets may not grow too large to maintain appropriate ratios between cells of different types. Our results implicate that growing of mouse islets may be regulated by several physical constraints such as the minimal size required for stable cell-to-cell coupling and the upper limit to keep the ratios between cell types. Within the lower and upper limits the observed size distributions of islets can be faithfully regenerated by assuming random and uncoordinated proliferation of each beta-cell at appropriate rates.     

Phase synchronization and coherence resonance of stochastic calcium oscillations in coupled hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the effects of gap junction permeable to calcium and of the total Ca(2+) channel number located on endoplasmic reticulum on intercellular synchronization. Figures of ratio between mean oscillating frequency of coupled cells describe visually the process of phase-locking. By virtue of a set of phase analysis, we can observe a gradual transition from synchronous behavior to nonsynchronous behavior. Furthermore, a signal-to-noise ratio in two dimensional parameter space (coupling strength-total Ca(2+) channel number) has suggested that, coherence resonance will occur for appropriate noise and coupling.     

Magnitude and modulation of pancreatic β-cell gap junction electrical conductance in situ

The parallel gap junction electrical conductance between a -cell and its nearest neighbors was measured by using an intracellular microelectrode to clamp the voltage of a -cell within a bursting islet of Langerhans. The holding current records consisted of bursts of inward current due to the synchronized oscillations in membrane potential of the surrounding cells. The membrane potential record of the impaled cell, obtained in current clamp mode, was used to estimate the behavior of the surrounding cells during voltage clamp, and the coupling conductance was calculated by dividing the magnitude of the current bursts by that of the voltage bursts. The histogram of coupling conductance magnitude from 26 cells was bimodal with peaks at 2.5 and 3.5 nS, indicating heterogeneity in extent of electrical communication within the islet of Langerhans. Gap junction conductance reversibly decreased when the temperature was lowered from 37 to 30°C and when the extracellular calcium concentration was raised from 2.56 to 7.56 mm. The coupling conductance decreased slightly during the active phase of the burst. Activation of adenylate cyclase with forskolin (10 m) resulted in an increase in cell-to-cell electrical coupling. We conclude that -cell gap junction conductance can be measured in situ under near physiological conditions. Furthermore, the magnitude and physiological regulation of -cell gap junction conductance suggest that intercellular electrical communication plays an important role in the function of the endocrine pancreas.The authors thank Dr. Arthur Sherman for sharing his insights on in situ coupling measurements, and for helpful discussions throughout the work. DM acknowledges partial support by a National Institutes of Health training grant to the Johns Hopkins University, Department of Biomedical Engineering (5 T32 GM7057). This work was supported in part by a National Science Foundation PYI award (ECS-9058419) to NFS.     

Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells

A continuum model for a heterogeneous collection of excitable cells electrically coupled through gap junctions is introduced and analysed using spatial averaging, asymptotic and numerical techniques. Heterogeneity is modelled by imposing a spatial dependence on parameters which define the single cell model and a diffusion term is used to model the gap junction coupling. For different parameter values, single cell models can exhibit bursting, beating and a myriad of other complex oscillations. A procedure for finding asymptotic estimates of the thresholds between these (synchronous) behaviors in the cellular aggregates is described for the heterogeneous case where the coupling strength is strong. This procedure is tested on a model of a strongly coupled heterogeneous collection of bursting and beating cells. Since isolated pancreatic β-cells have been observed to both burst and beat, this test of the spatial averaging techniques provides a possible explanation to measured discrepancies between the electrical activities of isolated β-cells and coupled collections (islets) of β-cells. This work was supported by the National Science Foundation Grant DMS-97-04-966.     

Co-expression and regulation of connexins 36 and 43 in cultured neonatal rat pancreatic islets

Fetal and neonatal pancreatic islets present a lower insulin secretory response as compared with adult islets. Prolonged culturing leads to an improvement of the glucose-induced insulin secretion response in neonatal pancreatic islets that may involve regulation of gap junction mediated cell communication. In this study, we investigated the effect of culturing neonatal islet cells for varying periods of time and with different glucose medium concentrations on the cellular expression of the endocrine pancreatic gap junction associated connexin (Cx) 36 and Cx43. We report here that the 7-d culture induced upregulation of the expression of these junctional proteins in neonatal islets in a time-dependent manner. A correlation was observed between the increased mRNA and protein expression of Cx36 and Cx43 and the increased insulin secretion following islet culturing. In addition, increasing glucose concentration within the culture medium induced a concentration-dependent enhancement of Cx36 islet expression, but not of Cx43 expression in cultured neonatal islets. In conclusion, we suggest that the regulation of gap junctional proteins by culture medium containing factors and glucose may be an important event for the maturation process of beta cells observed at in vitro conditions.     

Learning Theories Reveal Loss of Pancreatic Electrical Connectivity in Diabetes as an Adaptive Response

Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secreting the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however, explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.     

Critical Role of Gap Junction Coupled KATP Channel Activity for Regulated Insulin Secretion

Pancreatic β-cells secrete insulin in response to closure of ATP-sensitive K⁺ (K_ATP) channels, which causes membrane depolarization and a concomitant rise in intracellular Ca²⁺ (Ca_i). In intact islets, β-cells are coupled by gap junctions, which are proposed to synchronize electrical activity and Ca_i oscillations after exposure to stimulatory glucose (>7 mM). To determine the significance of this coupling in regulating insulin secretion, we examined islets and β-cells from transgenic mice that express zero functional K_ATP channels in approximately 70% of their β-cells, but normal K_ATP channel density in the remainder. We found that K_ATP channel activity from approximately 30% of the β-cells is sufficient to maintain strong glucose dependence of metabolism, Ca_i, membrane potential, and insulin secretion from intact islets, but that glucose dependence is lost in isolated transgenic cells. Further, inhibition of gap junctions caused loss of glucose sensitivity specifically in transgenic islets. These data demonstrate a critical role of gap junctional coupling of K_ATP channel activity in control of membrane potential across the islet. Control via coupling lessens the effects of cell–cell variation and provides resistance to defects in excitability that would otherwise lead to a profound diabetic state, such as occurs in persistent neonatal diabetes mellitus.