Calcium and glycolysis mediate multiple bursting modes in pancreatic islets

Subcellular Compartmentalization of Glucose Mediated Insulin Secretion

Regulation of blood glucose levels depends on the property of beta cells to couple glucose sensing with insulin secretion. This is accomplished by the concentration-dependent flux of glucose through glycolysis and oxidative phosphorylation, generating ATP. The resulting rise in cytosolic ATP/ADP inhibits KATP channels, inducing membrane depolarization and Ca2+ influx, which prompts insulin secretion. Evidence suggests that this coupling of glucose sensing with insulin secretion may be compartmentalized in the submembrane regions of the beta cell. We investigated the subcellular responses of key components involved in this coupling and found mitochondria in the submembrane zone, some tethered to the cytoskeleton near capillaries. Using Fluorescent Lifetime Imaging Microscopy (FLIM), we observed that submembrane mitochondria were the fastest to respond to glucose. In the most glucose-responsive beta cells, glucose triggers rapid, localized submembrane increases in ATP and Ca2+ as synchronized ~4-min oscillations, consistent with pulsatile insulin release after meals. These findings are consistent with the hypothesis that glucose sensing is coupled with insulin secretion in the submembrane zone of beta cells. This zonal adaptation would enhance both the speed and energy efficiency of beta cell responses to glucose, as only a subset of the most accessible mitochondria would be required to trigger insulin secretion.

A mechanism for slow rhythms in coordinated pancreatic islet activity

Insulin levels in the blood oscillate with a variety of periods, including rapid (5-10 min), ultradian (50-120 min), and circadian (24 h). Oscillations of insulin are beneficial for lowering blood glucose and disrupted rhythms are found in people with type 2 diabetes and their close relatives. These in vivo secretion dynamics imply that the oscillatory activity of individual islets of Langerhans are synchronized, although the mechanism for this is not known. One mechanism by which islets may synchronize is negative feedback of insulin on whole-body glucose levels. In previous work, we demonstrated that a negative feedback loop with a small time delay, to account for the time required for islets to be exposed to a new glucose concentration in vivo, results in small 3-6 islet populations synchronizing to produce fast closed-loop oscillations. However, these same islet populations could also produce slow closed-loop oscillations with periods longer than the natural islet oscillation periods. Here, we investigate the origin of the slow oscillations and the bistability with the fast oscillations using larger islet populations (20-50 islets). In contrast to what was observed earlier, larger islet populations mainly synchronize to longer-period oscillations that are approximately twice the delay time used in the feedback loop. A mean-field model was also used as a proxy for a large islet population to uncover the underlying mechanism for the slow rhythm. The heterogeneous intrinsic oscillation periods of the islets interferes with this rhythm mechanism when islet populations are small, and is similar to adding noise to the mean-field model. Thus, the effect of a time delay in the glucose feedback mechanism is similar to other examples of time-delayed systems in biology and may be a viable mechanism for ultradian oscillations.

Kinetic modelling of glycolytic oscillations

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

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays

This study aims to demonstrate the benefits of augmenting commercially available, real-time, in vitro glycolysis assays with phenomenological rate equation-based kinetic models, describing the contributions of the underpinning metabolic pathways. To this end, a commercially available glycolysis assay, sensitive to changes in extracellular acidification (extracellular pH), was used to derive the glycolysis pathway kinetics. The pathway was numerically modelled using a series of ordinary differential rate equations, to simulate the obtained experimental results. The sensitivity of the model to the key equation parameters was also explored. The cellular glycolysis pathway kinetics were determined for three different cell-lines, under nonmodulated and modulated conditions. Over the timescale studied, the assay demonstrated a two-phase metabolic response, representing the differential kinetics of glycolysis pathway rate as a function of time, and this behaviour was faithfully reproduced by the model simulations. The model enabled quantitative comparison of the pathway kinetics of three cell lines, and also the modulating effect of two known drugs. Moreover, the modelling tool allows the subtle differences between different cell lines to be better elucidated and also allows augmentation of the assay sensitivity. A simplistic numerical model can faithfully reproduce the differential pathway kinetics for three different cell lines, with and without pathway-modulating drugs, and furthermore provides insights into the cellular metabolism by elucidating the underlying mechanisms leading to the pathway end-product. This study demonstrates that augmenting a relatively simple, real-time, in vitro assay with a model of the underpinning metabolic pathway provides considerable insights into the observed differences in cellular systems.

Glycolytic oscillations under periodic drivings

In many living organisms displaying circadian rhythms, the intake of energy often occurs in a periodic manner. Glycolysis is a prototypical biochemical reaction that exhibits a self-sustained oscillation under continuous injection of glucose. Here we study the effect of periodic injection of glucose on the glycolytic oscillation from a dynamical systems perspective. In particular, we employ Goldbeter's allosteric model of phosphofructokinase as a model system for glycolytic oscillations, and explore the effect of periodic substrate influx of varying frequencies and amplitudes by building the phase diagrams of Lyapunov exponents and oscillatory periods. When the frequency of driving is tuned around the harmonic and sub/super-harmonic conditions of the natural frequency, the system is entrained to a frequency-locked state, forming an entrainment band that broadens with an increasing amplitude of driving. On the other hand, if the amplitude is substantial, the system may transition, albeit infrequent, to a chaotic state which defies prediction of dynamical behaviour. Our study offers in-depth understandings into the controllability of glycolytic oscillation as well as explaining physical underpinnings that enable the synchronous oscillations among a dense population of cells.

Deconstructing the integrated oscillator model for pancreatic β-cells

Electrical bursting oscillations in the β-cells of pancreatic islets have been a focus of investigation for more than fifty years. This has been aided by mathematical models, which are descendants of the pioneering Chay-Keizer model. This article describes the key biophysical and mathematical elements of this model, and then describes the path forward from there to the Integrated Oscillator Model (IOM). It is both a history and a deconstruction of the IOM that describes the various elements that have been added to the model over time, and the motivation for adding them. Finally, the article is a celebration of the 40th anniversary of the publication of the Chay-Keizer model.

Coordination of pancreatic islet rhythmic activity by delayed negative feedback

Secretion of insulin from the pancreas is pulsatile, driven by intrinsic oscillations within individual islets of Langerhans. The secretions are coordinated among the many islets distributed throughout the pancreas producing a synchronized rhythm in vivo that is essential for maintaining normal glucose levels. One hypothesized mechanism for the coordination of islet activity is negative feedback, whereby sequestration of glucose in response to elevated insulin leads to a reduction in the blood glucose level that is sensed by the islet population. This global signal of glucose then coordinates the individual islets. In this study, we tested how this coordination mechanism is affected by time delays in the negative feedback, using a microfluidic system to monitor Ca2+ levels in a small population of islets and implementing glucose control through a negative feedback system. We found that islet synchronization occurs even with time delays in the feedback of up to 7 min. We also found that a second, slower closed-loop oscillation period is produced during delayed feedback in which islet oscillations are clustered into episodes. The period of this second oscillatory mode increases with the time delay and appears to be a second stable behavior that coexists with the faster synchronized oscillation. The general conclusion is that islet coordination through negative feedback is a viable means of islet coordination that is robust to delays in the timing of the feedback, and could complement other potential coordination mechanisms such as entrainment by pancreatic ganglia.NEW & NOTEWORTHY Insulin secretion from islets of Langerhans is rhythmic, and these rhythms are coordinated to produce oscillatory plasma insulin levels. Using a combination of microfluidics and computational modeling, we demonstrate that coordination can occur through negative feedback of the type provided by the liver, even if that feedback is delayed by several minutes. We also demonstrate that a second, slower, mode of oscillations can occur when feedback is delayed where faster oscillations are grouped into episodes.

Pulsatile Basal Insulin Secretion Is Driven by Glycolytic Oscillations

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

Similarities in Calcium Oscillations Between Neonatal Mouse Islets and Mature Islets Exposed to Chronic Hyperglycemia

Pulsatility is important to islet function. As islets mature into fully developed insulin-secreting micro-organs, their ability to produce oscillatory intracellular calcium ([Ca2+]i) patterns in response to glucose also matures. In this study, we measured [Ca2+]i using fluorescence imaging to characterize oscillations from neonatal mice on postnatal (PN) days 0, 4, and 12 in comparison to adult islets. Under substimulatory (3-mM) glucose levels, [Ca2+]i was low and quiescent for adult islets as expected, as well as for PN day 12 islets. In contrast, one-third of islets on PN day 0 and 4 displayed robust [Ca2+]i oscillations in low glucose. In stimulatory glucose (11 mM) conditions, oscillations were present on all neonatal days but differed from patterns in adults. By PN day 12, [Ca2+]i oscillations were approaching characteristics of fully developed islets. The immature response pattern of neonatal islets was due, at least in part, to differences in adenosine 5'-triphosphate (ATP)-sensitive K+-channel activity estimated by [Ca2+]i responses to KATP channel agents diazoxide and tolbutamide. Neonatal [Ca2+]i patterns were also strikingly similar to patterns observed in mature islets exposed to hyperglycemic conditions (20 mM glucose for 48 hours): elevated [Ca2+]i and oscillations in low glucose along with reduced pulse mass in high glucose. Since a hallmark of diabetic islets is dedifferentiation, we propose that diabetic islets display features of "reverse maturation," demonstrating similar [Ca2+]i dynamics as neonatal islets. Pulsatility is thus an important emergent feature of neonatal islets. Our findings may provide insight into reversing β-cell dedifferentiation and to producing better functioning β cells from pluripotent stem cells.

Pancreatic α and β cells are globally phase-locked

The Ca²⁺ modulated pulsatile glucagon and insulin secretions by pancreatic α and β cells play a crucial role in glucose homeostasis. However, how α and β cells coordinate to produce various Ca²⁺ oscillation patterns is still elusive. Using a microfluidic device and transgenic mice, we recorded Ca²⁺ signals from islet α and β cells, and observed heterogeneous Ca²⁺ oscillation patterns intrinsic to each islet. After a brief period of glucose stimulation, α and β cells’ oscillations were globally phase-locked. While the activation of α cells displayed a fixed time delay of ~20 s to that of β cells, β cells activated with a tunable period. Moreover, islet α cell number correlated with oscillation frequency. We built a mathematical model of islet Ca²⁺ oscillation incorporating paracrine interactions, which quantitatively agreed with the experimental data. Our study highlights the importance of cell-cell interaction in generating stable but tunable islet oscillation patterns.

The Ca²⁺ modulated pulsatile glucagon and insulin secretions by pancreatic α and β cells are critical in glucose homeostasis. Here the authors show that the Ca²⁺ oscillations of α and β cells are phase-locked, and that the oscillation pattern is tuned by paracrine interactions between α and β cells.

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

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

Slow oscillations persist in pancreatic beta cells lacking phosphofructokinase M

Pulsatile insulin secretion by pancreatic beta cells is necessary for tight glucose control in the body. Glycolytic oscillations have been proposed as the mechanism for generating the electrical oscillations underlying pulsatile insulin secretion. The glycolytic enzyme 6-phosphofructokinase-1 (PFK) synthesizes fructose-1,6-bisphosphate (FBP) from fructose-6-phosphate. It has been proposed that the slow electrical and Ca2+ oscillations (periods of 3-5 min) observed in islets result from allosteric feedback activation of PFKM by FBP. Pancreatic beta cells express three PFK isozymes: PFKL, PFKM, and PFKP. A prior study of mice that were engineered to lack PFKM using a gene-trap strategy to delete Pfkm produced a mosaic reduction in global Pfkm expression, but the islets isolated from the mice still exhibited slow Ca2+ oscillations. However, these islets still expressed residual PFKM protein. Thus, to more fully test the hypothesis that beta cell PFKM is responsible for slow islet oscillations, we made a beta-cell-specific knockout mouse that completely lacked PFKM. While PFKM deletion resulted in subtle metabolic changes in vivo, islets that were isolated from these mice continued to exhibit slow oscillations in electrical activity, beta cell Ca2+ concentrations, and glycolysis, as measured using PKAR, an FBP reporter/biosensor. Furthermore, simulations obtained with a mathematical model of beta cell activity shows that slow oscillations can persist despite PFKM loss provided that one of the other PFK isoforms, such as PFKP, is present, even if its level of expression is unchanged. Thus, while we believe that PFKM may be the main regulator of slow oscillations in wild-type islets, PFKP can provide functional redundancy. Our model also suggests that PFKM likely dominates, in vivo, because it outcompetes PFKP with its higher FBP affinity and lower ATP affinity. We thus propose that isoform redundancy may rescue key physiological processes of the beta cell in the absence of certain critical genes.

Glucose-Stimulated Calcium Dynamics in Beta Cells From Male C57BL/6J, C57BL/6N, and NMRI Mice: A Comparison of Activation, Activity, and Deactivation Properties in Tissue Slices

Although mice are a very instrumental model in islet beta cell research, possible phenotypic differences between strains and substrains are largely neglected in the scientific community. In this study, we show important phenotypic differences in beta cell responses to glucose between C57BL/6J, C57BL/6N, and NMRI mice, i.e., the three most commonly used strains. High-resolution multicellular confocal imaging of beta cells in acute pancreas tissue slices was used to measure and quantitatively compare the calcium dynamics in response to a wide range of glucose concentrations. Strain- and substrain-specific features were found in all three phases of beta cell responses to glucose: a shift in the dose-response curve characterizing the delay to activation and deactivation in response to stimulus onset and termination, respectively, and distinct concentration-encoding principles during the plateau phase in terms of frequency, duration, and active time changes with increasing glucose concentrations. Our results underline the significance of carefully choosing and reporting the strain to enable comparison and increase reproducibility, emphasize the importance of analyzing a number of different beta cell physiological parameters characterizing the response to glucose, and provide a valuable standard for future studies on beta cell calcium dynamics in health and disease in tissue slices.

Symbiosis of Electrical and Metabolic Oscillations in Pancreatic β-Cells

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

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

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

RGS4-Deficiency Alters Intracellular Calcium and PKA-Mediated Control of Insulin Secretion in Glucose-Stimulated Beta Islets

A number of diverse G-protein signaling pathways have been shown to regulate insulin secretion from pancreatic β-cells. Accordingly, regulator of G-protein signaling (RGS) proteins have also been implicated in coordinating this process. One such protein, RGS4, is reported to show both positive and negative effects on insulin secretion from β-cells depending on the physiologic context under which it was studied. We here use an RGS4-deficient mouse model to characterize previously unknown G-protein signaling pathways that are regulated by RGS4 during glucose-stimulated insulin secretion from the pancreatic islets. Our data show that loss of RGS4 results in a marked deficiency in glucose-stimulated insulin secretion during both phase I and phase II of insulin release in intact mice and isolated islets. These deficiencies are associated with lower cAMP/PKA activity and a loss of normal calcium surge (phase I) and oscillatory (phase II) kinetics behavior in the RGS4-deficient β-cells, suggesting RGS4 may be important for regulation of both Gαi and Gαq signaling control during glucose-stimulated insulin secretion. Together, these studies add to the known list of G-protein coupled signaling events that are controlled by RGS4 during glucose-stimulated insulin secretion and highlight the importance of maintaining normal levels of RGS4 function in healthy pancreatic tissues.

Intercellular Communication in the Islet of Langerhans in Health and Disease

Blood glucose homeostasis requires proper function of pancreatic islets, which secrete insulin, glucagon, and somatostatin from the β-, α-, and δ-cells, respectively. Each islet cell type is equipped with intrinsic mechanisms for glucose sensing and secretory actions, but these intrinsic mechanisms alone cannot explain the observed secretory profiles from intact islets. Regulation of secretion involves interconnected mechanisms among and between islet cell types. Islet cells lose their normal functional signatures and secretory behaviors upon dispersal as compared to intact islets and in vivo. In dispersed islet cells, the glucose response of insulin secretion is attenuated from that seen from whole islets, coordinated oscillations in membrane potential and intracellular Ca2+ activity, as well as the two-phase insulin secretion profile, are missing, and glucagon secretion displays higher basal secretion profile and a reverse glucose-dependent response from that of intact islets. These observations highlight the critical roles of intercellular communication within the pancreatic islet, and how these communication pathways are crucial for proper hormonal and nonhormonal secretion and glucose homeostasis. Further, misregulated secretions of islet secretory products that arise from defective intercellular islet communication are implicated in diabetes. Intercellular communication within the islet environment comprises multiple mechanisms, including electrical synapses from gap junctional coupling, paracrine interactions among neighboring cells, and direct cell-to-cell contacts in the form of juxtacrine signaling. In this article, we describe the various mechanisms that contribute to proper islet function for each islet cell type and how intercellular islet communications are coordinated among the same and different islet cell types. © 2021 American Physiological Society. Compr Physiol 11:2191-2225, 2021.

Thermodynamic Optimality of Glycolytic Oscillations

Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out of thermodynamic equilibrium. Because of functional reasons, the period of a biochemical oscillation must be tuned to a specific value with precision; however, according to the thermodynamic uncertainty relation (TUR), the precision of the oscillatory period is constrained by the thermodynamic cost of generating it. After reviewing the basics of chemical oscillations using the Brusselator as a model system, we study the glycolytic oscillation generated by octameric phosphofructokinase (PFK), which is known to display a period of several minutes. By exploring the phase space of glycolytic oscillations, we find that the glycolytic oscillation under the cellular condition is realized in a cost-effective manner. Specifically, over the biologically relevant range of parameter values of glycolysis and octameric PFK, the entropy production from the glycolytic oscillation is minimal when the oscillation period is (5-10) min. Furthermore, the glycolytic oscillation is found at work near the phase boundary of limit cycles, suggesting that a moderate increase of glucose injection rate leads to the loss of oscillatory dynamics, which is reminiscent of the loss of pulsatile insulin release resulting from elevated blood glucose level.

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.

Many biological systems can be studied using network theory. How heterogeneous cell subpopulations come together to create complex multicellular behavior is of great value in understanding function and dysfunction in tissues. The pancreatic islet of Langerhans is a highly coupled structure that is important for maintaining blood glucose homeostasis. β-cell electrical activity is coordinated via gap junction communication. The function of the insulin-producing β-cell within the islet is disrupted in diabetes. As such, to understand the causes of islet dysfunction we need to understand how different cells within the islet contribute to its overall function via gap junction coupling. Using a computational model of β-cell electrophysiology, we investigated how small highly functional β-cell populations within the islet contribute to its function. We found that when small populations with greater functionality were introduced into the islet, they displayed signatures of this enhanced functionality. However, when these cells were removed, the islet, retained near-normal function. Thus, in a highly coupled system, such as an islet, the heterogeneity of cells allows small subpopulations to be dispensable, and thus their absence is unable to disrupt the larger cellular network. These findings can be applied to other electrical systems that have heterogeneous cell populations.

Phantom bursting may underlie electrical bursting in single pancreatic β-cells

Insulin is secreted by pancreatic β-cellsthat are electrically coupled into micro-organs called islets of Langerhans. The secretion is due to the influx of Ca²⁺ions that accompany electrical impulses, which are clustered into bursts. So-called "medium bursting" occurs in many β-cellsin intact islets, while in other islets the β-cellsexhibit "slow bursting", with a much longer period. Each burst brings in Ca²⁺ that, through exocytosis, results in insulin secretion. When isolated from an islet, β-cellsbehave very differently. The electrical activity is much noisier, and consists primarily of trains of irregularly-timed spikes, or fast or slow bursting. Medium bursting, so often seen in intact islets, is rarely if ever observed. In this study, we examine what the isolated cell behavior can tell us about the mechanism for bursting in intact islets. A previous mathematical study concluded that the slow bursting observed in isolated β-cells, and therefore most likely in islets, must be due to intrinsic glycolytic oscillations, since this mechanism for bursting is robust to noise. It was demonstrated that an alternate mechanism, phantom bursting, was very sensitive to noise, and therefore could not account for the slow bursting in single cells. We re-examine these conclusions, motivated by recent experimental and mathematical modeling evidence that slow bursting in intact islets is, at least in many cases, driven by the phantom bursting mechanism and not endogenous glycolytic oscillations. We employ two phantom bursting models, one minimal and the other more biophysical, to determine the sensitivity of medium and slow bursting to electrical current noise. In the minimal model, both forms of bursting are highly sensitive to noise. In the biophysical model, while medium bursting is sensitive to noise, slow bursting is much less sensitive. This suggests that the slow bursting seen in isolated β-cellsmay be due to a phantom bursting mechanism, and by extension, slow bursting in intact islets may also be driven by this mechanism.

Energetic substrate availability regulates synchronous activity in an excitatory neural network

Neural networks are required to meet significant metabolic demands associated with performing sophisticated computational tasks in the brain. The necessity for efficient transmission of information imposes stringent constraints on the metabolic pathways that can be used for energy generation at the synapse, and thus low availability of energetic substrates can reduce the efficacy of synaptic function. Here we study the effects of energetic substrate availability on global neural network behavior and find that glucose alone can sustain excitatory neurotransmission required to generate high-frequency synchronous bursting that emerges in culture. In contrast, obligatory oxidative energetic substrates such as lactate and pyruvate are unable to substitute for glucose, indicating that processes involving glucose metabolism form the primary energy-generating pathways supporting coordinated network activity. Our experimental results are discussed in the context of the role that metabolism plays in supporting the performance of individual synapses, including the relative contributions from postsynaptic responses, astrocytes, and presynaptic vesicle cycling. We propose a simple computational model for our excitatory cultures that accurately captures the inability of metabolically compromised synapses to sustain synchronous bursting when extracellular glucose is depleted.

Biophysical modeling of β-cells networks: Realistic architectures and heterogeneity effects

The β-cells dynamics is the regulator of insulin secretion in the pancreas, and its investigation is a central aspect in designing effective treatment strategies for diabetes. Despite great efforts, much is still unknown about the complex organization of such endocrine cells and realistic mathematical modeling represents a useful tool to elucidate key aspects of glucose control in humans. In this contribution, we study the human β-cells collective behaviour, by modeling their electric and metabolic coupling in a cluster, of size and architecture similar to human islets of Langerhans. We focus on the effect of coupling on various dynamics regimes observed in the islets, that are spiking and bursting on multiple timescales. In particular, we test the effect of hubs, that are highly glucose-sensitive β-cells, on the overall network dynamics, observing different modulation depending on the timescale of the dynamics. By properly taking into account the role of cells heterogeneity, recently emerged, our model effectively describes the effect of hubs on the synchronization of the islet response and the correlation of β-cells activity.

Tripartite cell networks for glucose homeostasis

Controlling the excess and shortage of energy is a fundamental task for living organisms. Diabetes is a representative metabolic disease caused by the malfunction of energy homeostasis. The islets of Langerhans in the pancreas release long-range messengers, hormones, into the blood to regulate the homeostasis of the primary energy fuel, glucose. The hormone and glucose levels in the blood show rhythmic oscillations with a characteristic period of 5-10 min, and the functional roles of the oscillations are not clear. Each islet has [Formula: see text] and [Formula: see text] cells that secrete glucagon and insulin, respectively. These two counter-regulatory hormones appear sufficient to increase and decrease glucose levels. However, pancreatic islets have a third cell type, [Formula: see text] cells, which secrete somatostatin. The three cell populations have a unique spatial organization in islets, and they interact to perturb their hormone secretions. The mini-organs of islets are scattered throughout the exocrine pancreas. Considering that the human pancreas contains approximately a million islets, the coordination of hormone secretion from the multiple sources of islets and cells within the islets should have a significant effect on human physiology. In this review, we introduce the hierarchical organization of tripartite cell networks, and recent biophysical modeling to systematically understand the oscillations and interactions of [Formula: see text], [Formula: see text], and [Formula: see text] cells. Furthermore, we discuss the functional roles and clinical implications of hormonal oscillations and their phase coordination for the diagnosis of type II diabetes.

Integrative and theoretical research on the architecture of a biological system and its disorder

An organism stems from assemblies of a variety of cells and proteins. This complex system serves as a unit, and it exhibits highly sophisticated functions in response to exogenous stimuli that change over time. The complete sequencing of the entire human genome has allowed researchers to address the enigmas of life and disease at the gene- or molecular-based level. The consequence of such studies is the rapid accumulation of a multitude of data at multiple levels, ranging from molecules to the whole body, that has necessitated the development of entirely new concepts, tools, and methodologies to analyze and integrate these data. This necessity has given birth to systems biology, an advanced theoretical and practical research framework that has totally changed the directions of not only basic life science but also medicine. During the symposium of the 95th Annual Meeting of The Physiological Society of Japan 2018, five researchers reported on their respective studies on systems biology. The topics included reactions of drugs, ion-transport architecture in an epithelial system, multi-omics in renal disease, cardiac electrophysiological systems, and a software platform for computer simulation. In this review article these authors have summarized recent achievements in the field and discuss next-generation studies on health and disease.

Gene expression patterns in synchronized islet populations

In vivo levels of insulin are oscillatory with a period of ~5-10 minutes, indicating that the islets of Langerhans within the pancreas are synchronized. While the synchronizing factors are still under investigation, one result of this behavior is expected to be coordinated and oscillatory intracellular factors, such as intracellular Ca²⁺ levels, throughout the islet population. In other cell types, oscillatory intracellular signals, like intracellular Ca²⁺, have been shown to affect specific gene expression. To test how the gene expression landscape may differ between a synchronized islet population with its reproducible intracellular oscillations and an unsynchronized islet population with heterogeneous oscillations, gene set enrichment analysis (GSEA) was used to compare an islet population that had been synchronized using a glucose wave with a 5-min period, and an unsynchronized islet population. In the population exposed to the glucose wave, 58/62 islets showed synchronization as evidenced by coordinated intracellular Ca²⁺ oscillations with an average oscillation period of 5.1 min, while in the unsynchronized population 29/62 islets showed slow oscillations with an average period of 5.2 min. The synchronized islets also had a significantly smaller drift of their oscillation period during the experiment as compared to the unsynchronized population. GSEA indicated that the synchronized population had reduced expression of gene sets related to protein translation, protein turnover, energy expenditure, and insulin synthesis, while those that were related to maintenance of cell morphology were increased.

Dissipative structures in biological systems: bistability, oscillations, spatial patterns and waves

The goal of this review article is to assess how relevant is the concept of dissipative structure for understanding the dynamical bases of non-equilibrium self-organization in biological systems, and to see where it has been applied in the five decades since it was initially proposed by Ilya Prigogine. Dissipative structures can be classified into four types, which will be considered, in turn, and illustrated by biological examples: (i) multistability, in the form of bistability and tristability, which involve the coexistence of two or three stable steady states, or in the form of birhythmicity, which involves the coexistence between two stable rhythms; (ii) temporal dissipative structures in the form of sustained oscillations, illustrated by biological rhythms; (iii) spatial dissipative structures, known as Turing patterns; and (iv) spatio-temporal structures in the form of propagating waves. Rhythms occur with widely different periods at all levels of biological organization, from neural, cardiac and metabolic oscillations to circadian clocks and the cell cycle; they play key roles in physiology and in many disorders. New rhythms are being uncovered while artificial ones are produced by synthetic biology. Rhythms provide the richest source of examples of dissipative structures in biological systems. Bistability has been observed experimentally, but has primarily been investigated in theoretical models in an increasingly wide range of biological contexts, from the genetic to the cell and animal population levels, both in physiological conditions and in disease. Bistable transitions have been implicated in the progression between the different phases of the cell cycle and, more generally, in the process of cell fate specification in the developing embryo. Turing patterns are exemplified by the formation of some periodic structures in the course of development and by skin stripe patterns in animals. Spatio-temporal patterns in the form of propagating waves are observed within cells as well as in intercellular communication. This review illustrates how dissipative structures of all sorts abound in biological systems.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Transitions between bursting modes in the integrated oscillator model for pancreatic β-cells

Insulin-secreting β-cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca²⁺ oscillations and pulsatile insulin secretion. The mechanism for this bursting activity has been the focus of mathematical modeling for more than three decades, and as new data are acquired old models are modified and new models are developed. Comprehensive models must now account for the various modes of bursting observed in islet β-cells, which include fast bursting, slow bursting, and compound bursting. One such model is the Integrated Oscillator Model (IOM), in which β-cell electrical activity, intracellular Ca²⁺, and glucose metabolism interact via numerous feedforward and feedback pathways. These interactions can produce metabolic oscillations with a sawtooth time course or a pulsatile time course, reflecting very different oscillation mechanisms. In this report, we determine conditions favorable to one form of oscillations or the other, and examine the transitions between modes of bursting and the relationship of the transitions to the patterns of metabolic oscillations. Importantly, this work clarifies what can be expected in experimental measurements of β-cell oscillatory activity, and suggests pathways through which oscillations of one type can be converted to oscillations of another type.

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

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

Metformin Inhibits Mouse Islet Insulin Secretion and Alters Intracellular Calcium in a Concentration-Dependent and Duration-Dependent Manner near the Circulating Range

Metformin is considered the first-line treatment for type 2 diabetes. While metformin primarily increases insulin sensitivity, evidence also suggests that metformin affects the activity of insulin-secreting pancreatic islets. This study was designed to systematically examine the direct effects of metformin by measuring insulin secretion and the kinetics of the calcium response to glucose stimulation in isolated mouse islets using varying concentrations (20 μM, 200 μM, and 1 mM) and durations (~1, 2, and 3 days) of metformin exposure. We observed both concentration- and duration-dependent inhibitory effects of metformin. Concentrations as little as 20 μM (nearing circulating therapeutic levels) were sufficient to reduce insulin secretion following 3-day treatment. Concentrations of 200 μM and 1 mM produced more pronounced effects more rapidly. With 1 mM metformin, islets showed severe impairments in calcium handling, inhibition of insulin secretion, and increased cell death. No stimulatory effects of metformin were observed for any experimental endpoint. We conclude that the direct effects of metformin on islets are inhibitory at near-physiological concentrations. Beneficial effects of metformin observed on islets under various stressors may occur by "resting" fatigued cellular processes. However, metformin may have unintended consequences on normally functioning islets within the circulating range that require further evaluation.

δ-cells and β-cells are electrically coupled and regulate α-cell activity via somatostatin

Key points

We used a mouse expressing a light‐sensitive ion channel in β‐cells to understand how α‐cell activity is regulated by β‐cells.

Light activation of β‐cells triggered a suppression of α‐cell activity via gap junction‐dependent activation of δ‐cells.

Mathematical modelling of human islets suggests that 23% of the inhibitory effect of glucose on glucagon secretion is mediated by β‐cells via gap junction‐dependent activation of δ‐cells/somatostatin secretion.

Abstract

Glucagon, the body's principal hyperglycaemic hormone, is released from α‐cells of the pancreatic islet. Secretion of this hormone is dysregulated in type 2 diabetes mellitus but the mechanisms controlling secretion are not well understood. Regulation of glucagon secretion by factors secreted by neighbouring β‐ and δ‐cells (paracrine regulation) have been proposed to be important. In this study, we explored the importance of paracrine regulation by using an optogenetic strategy. Specific light‐induced activation of β‐cells in mouse islets expressing the light‐gated channelrhodopsin‐2 resulted in stimulation of electrical activity in δ‐cells but suppression of α‐cell activity. Activation of the δ‐cells was rapid and sensitive to the gap junction inhibitor carbenoxolone, whereas the effect on electrical activity in α‐cells was blocked by CYN 154806, an antagonist of the somatostatin‐2 receptor. These observations indicate that optogenetic activation of the β‐cells propagates to the δ‐cells via gap junctions, and the consequential stimulation of somatostatin secretion inhibits α‐cell electrical activity by a paracrine mechanism. To explore whether this pathway is important for regulating α‐cell activity and glucagon secretion in human islets, we constructed computational models of human islets. These models had detailed architectures based on human islets and consisted of a collection of >500 α‐, β‐ and δ‐cells. Simulations of these models revealed that this gap junctional/paracrine mechanism accounts for up to 23% of the suppression of glucagon secretion by high glucose.

We used a mouse expressing a light‐sensitive ion channel in β‐cells to understand how α‐cell activity is regulated by β‐cells.

Light activation of β‐cells triggered a suppression of α‐cell activity via gap junction‐dependent activation of δ‐cells.

Mathematical modelling of human islets suggests that 23% of the inhibitory effect of glucose on glucagon secretion is mediated by β‐cells via gap junction‐dependent activation of δ‐cells/somatostatin secretion.

Dissipative structures and biological rhythms

Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca⁺⁺ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.

Insulin modulates the frequency of Ca2+ oscillations in mouse pancreatic islets

Pancreatic islets can adapt to oscillatory glucose to produce synchronous insulin pulses. Can islets adapt to other oscillatory stimuli, specifically insulin? To answer this question, we stimulated islets with pulses of exogenous insulin and measured their Ca²⁺ oscillations. We observed that sufficiently high insulin (> 500 nM) with an optimal pulse period (~ 4 min) could make islets to produce synchronous Ca²⁺ oscillations. Glucose and insulin, which are key stimulatory factors of islets, modulate islet Ca²⁺ oscillations differently. Glucose increases the active-to-silent ratio of phases, whereas insulin increases the period of the oscillation. To examine the dual modulation, we adopted a phase oscillator model that incorporated the phase and frequency modulations. This mathematical model showed that out-of-phase oscillations of glucose and insulin were more effective at synchronizing islet Ca²⁺ oscillations than in-phase stimuli. This finding suggests that a phase shift in glucose and insulin oscillations can enhance inter-islet synchronization.

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.

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.

Glucose Oscillations Can Activate an Endogenous Oscillator in Pancreatic Islets

Pancreatic islets manage elevations in blood glucose level by secreting insulin into the bloodstream in a pulsatile manner. Pulsatile insulin secretion is governed by islet oscillations such as bursting electrical activity and periodic Ca²⁺ entry in β-cells. In this report, we demonstrate that although islet oscillations are lost by fixing a glucose stimulus at a high concentration, they may be recovered by subsequently converting the glucose stimulus to a sinusoidal wave. We predict with mathematical modeling that the sinusoidal glucose signal’s ability to recover islet oscillations depends on its amplitude and period, and we confirm our predictions by conducting experiments with islets using a microfluidics platform. Our results suggest a mechanism whereby oscillatory blood glucose levels recruit non-oscillating islets to enhance pulsatile insulin output from the pancreas. Our results also provide support for the main hypothesis of the Dual Oscillator Model, that a glycolytic oscillator endogenous to islet β-cells drives pulsatile insulin secretion.

A global shift throughout the last century toward excessive nutrient intake relative to energy expenditure has fueled a dramatic increase in the incidence of diabetes in humans. The epidemic is primarily of type 2 diabetes, a disease characterized by the inability of the body to effectively control blood glucose levels. Insulin plays a key role in regulating blood glucose levels by restraining endogenous glucose output from the liver and promoting blood glucose uptake by tissue throughout the body. It is secreted in pulses by islets of Langerhans, endocrine cell aggregates dispersed throughout the pancreas. Loss of insulin pulsatility is an early event in the development of type 2 diabetes. Here, we demonstrate, with a combined modeling and experimental approach, that the loss of pulsatile insulin release that results from elevated glucose may be recovered by an oscillatory glucose stimulus. Our results have potential implications for enhancing insulin pulsatility and therefore mitigating the development of type 2 diabetes.

Paracrine regulation of glucagon secretion: the β/α/δ model

The regulation of glucagon secretion in the pancreatic α-cell is not well understood. It has been proposed that glucose suppresses glucagon secretion either directly through an intrinsic mechanism within the α-cell or indirectly through an extrinsic mechanism. Previously, we described a mathematical model for isolated pancreatic α-cells and used it to investigate possible intrinsic mechanisms of regulating glucagon secretion. We demonstrated that glucose can suppress glucagon secretion through both ATP-dependent potassium channels (K_ATP) and a store-operated current (SOC). We have now developed an islet model that combines previously published mathematical models of α- and β-cells with a new model of δ-cells and use it to explore the effects of insulin and somatostatin on glucagon secretion. We show that the model can reproduce experimental observations that the inhibitory effect of glucose remains even when paracrine modulators are no longer acting on the α-cell. We demonstrate how paracrine interactions can either synchronize α- and δ-cells to produce pulsatile oscillations in glucagon and somatostatin secretion or fail to do so. The model can also account for the paradoxical observation that glucagon can be out of phase with insulin, whereas α-cell calcium is in phase with insulin. We conclude that both paracrine interactions and the α-cell's intrinsic mechanisms are needed to explain the response of glucagon secretion to glucose.

A Unifying Organ Model of Pancreatic Insulin Secretion

The secretion of insulin by the pancreas has been the object of much attention over the past several decades. Insulin is known to be secreted by pancreatic β-cells in response to hyperglycemia: its blood concentrations however exhibit both high-frequency (period approx. 10 minutes) and low-frequency oscillations (period approx. 1.5 hours). Furthermore, characteristic insulin secretory response to challenge maneuvers have been described, such as frequency entrainment upon sinusoidal glycemic stimulation; substantial insulin peaks following minimal glucose administration; progressively strengthened insulin secretion response after repeated administration of the same amount of glucose; insulin and glucose characteristic curves after Intra-Venous administration of glucose boli in healthy and pre-diabetic subjects as well as in Type 2 Diabetes Mellitus. Previous modeling of β-cell physiology has been mainly directed to the intracellular chain of events giving rise to single-cell or cell-cluster hormone release oscillations, but the large size, long period and complex morphology of the diverse responses to whole-body glucose stimuli has not yet been coherently explained. Starting with the seminal work of Grodsky it was hypothesized that the population of pancreatic β-cells, possibly functionally aggregated in islets of Langerhans, could be viewed as a set of independent, similar, but not identical controllers (firing units) with distributed functional parameters. The present work shows how a single model based on a population of independent islet controllers can reproduce very closely a diverse array of actually observed experimental results, with the same set of working parameters. The model's success in reproducing a diverse array of experiments implies that, in order to understand the macroscopic behaviour of the endocrine pancreas in regulating glycemia, there is no need to hypothesize intrapancreatic pacemakers, influences between different islets of Langerhans, glycolitic-induced oscillations or β-cell sensitivity to the rate of change of glycemia.

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.

Integrated perfusion and separation systems for entrainment of insulin secretion from islets of Langerhans

A microfluidic system was developed to investigate the entrainment of insulin secretion from islets of Langerhans to oscillatory glucose levels. A gravity-driven perfusion system was integrated with a microfluidic system to deliver sinusoidal glucose waveforms to the islet chamber. Automated manipulation of the height of the perfusion syringes allowed precise control of the ratio of two perfusion solutions into a chamber containing 1-10 islets. Insulin levels in the perfusate were measured using an online competitive electrophoretic immunoassay with a sampling period of 10 s. The insulin immunoassay had a detection limit of 3 nM with RSDs of calibration points ranging from 2-8%. At 11 mM glucose, insulin secretion from single islets was oscillatory with a period ranging from 3-6 min. Application of a small amplitude sinusoidal wave of glucose with a period of 5 or 10 min, shifted the period of the insulin oscillations to this forcing period. Exposing groups of 6-10 islets to a sinusoidal glucose wave synchronized their behavior, producing a coherent pulsatile insulin response from the population. These results demonstrate the feasibility of the developed system for the study of oscillatory insulin secretion and can be easily modified for investigating the dynamic nature of other hormones released from different cell types.

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 ([Ca(2+)]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 [Ca(2+)]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 [Ca(2+)]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 [Ca(2+)]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.

Episodic hormone secretion: a comparison of the basis of pulsatile secretion of insulin and GnRH

Rhythms govern many endocrine functions. Examples of such rhythmic systems include the insulin-secreting pancreatic beta-cell, which regulates blood glucose, and the gonadotropin-releasing hormone (GnRH) neuron, which governs reproductive function. Although serving very different functions within the body, these cell types share many important features. Both GnRH neurons and beta-cells, for instance, are hypothesized to generate at least two rhythms endogenously: (1) a burst firing electrical rhythm and (2) a slower rhythm involving metabolic or other intracellular processes. This review discusses the importance of hormone rhythms to both physiology and disease and compares and contrasts the rhythms generated by each system.

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.

Alterations of the Ca²⁺ signaling pathway in pancreatic beta-cells isolated from db/db mice

Upon glucose elevation, pancreatic beta-cells secrete insulin in a Ca²⁺-dependent manner. In diabetic animal models, different aspects of the calcium signaling pathway in beta-cells are altered, but there is no consensus regarding their relative contributions to the development of beta-cell dysfunction. In this study, we compared the increase in cytosolic Ca²⁺ ([Ca²⁺]_i) via Ca²⁺ influx, Ca²⁺ mobilization from endoplasmic reticulum (ER) calcium stores, and the removal of Ca²⁺ via multiple mechanisms in beta-cells from both diabetic db/db mice and non-diabetic C57BL/6J mice. We refined our previous quantitative model to describe the slow [Ca²⁺]_i recovery after depolarization in beta-cells from db/db mice. According to the model, the activity levels of the two subtypes of the sarco-endoplasmic reticulum Ca²⁺-ATPase (SERCA) pump, SERCA2 and SERCA3, were severely down-regulated in diabetic cells to 65% and 0% of the levels in normal cells. This down-regulation may lead to a reduction in the Ca²⁺ concentration in the ER, a compensatory up-regulation of the plasma membrane Na⁺/Ca²⁺ exchanger (NCX) and a reduction in depolarization-evoked Ca²⁺ influx. As a result, the patterns of glucose-stimulated calcium oscillations were significantly different in db/db diabetic beta-cells compared with normal cells. Overall, quantifying the changes in the calcium signaling pathway in db/db diabetic beta-cells will aid in the development of a disease model that could provide insight into the adaptive transformations of beta-cell function during diabetes development.

60 Hz electric field changes the membrane potential during burst phase in pancreatic β-cells: in silico analysis

The production, distribution and use of electricity can generate low frequency electric and magnetic fields (50-60 Hz). Considering that some studies showed adverse effects on pancreatic β-cells exposed to these fields; the present study aimed to analyze the effects of 60 Hz electric fields on membrane potential during the silent and burst phases in pancreatic β-cells using a mathematical model. Sinusoidal 60 Hz electric fields with amplitude ranging from 0.5 to 4 mV were applied on pancreatic β-cells model. The sinusoidal electric field changed burst duration, inter-burst intervals (silent phase) and spike sizes. The parameters above presented dose-dependent response with the voltage amplitude applied. In conclusion, theoretical analyses showed that a 60 Hz electric field with low amplitudes changes the membrane potential in pancreatic β-cells.

Intercellular delay regulates the collective period of repressively coupled gene regulatory oscillator networks

Most biological rhythms are generated by a population of cellular oscillators coupled through intercellular signaling. Recent experimental evidence shows that the collective period may differ significantly from the autonomous period in the presence of intercellular delays. The phenomenon has been investigated using delay-coupled phase oscillators, but the proposed phase model contains no direct biological mechanism, which may weaken the model's reliability in unraveling biophysical principles. Based on a published gene regulatory oscillator model, we analyze the collective period of delay-coupled biological oscillators using the multivariable harmonic balance technique. We prove that, in contradiction to the common intuition that the collective period increases linearly with the coupling delay, the collective period turns out to be a periodic function of the intercellular delay. More surprisingly, the collective period may even decrease with the intercellular delay when the delay resides in certain regions. The collective period is given in a closed-form in terms of biochemical reaction constants and thus provides biological insights as well as guidance in synthetic-biological-oscillator design. Simulation results are given based on a segmentation clock model to confirm the theoretical predictions.