Metabolic and electrical oscillations: partners in controlling pulsatile insulin secretion

Gain of function mutation in K(ATP) channels and resulting upregulation of coupling conductance are partners in crime in the impairment of Ca2+ oscillations in pancreatic ß-cells

Gain of function mutations in the pore forming Kir6 subunits of the ATP sensitive K+ channels (K(ATP) channels) of pancreatic β-cells are the major cause of neonatal diabetes in humans. In this study, we show that in insulin secreting mouse β-cell lines, gain of function mutations in Kir6.1 result in a significant connexin36 (Cx36) overexpression, which form gap junctional connections and mediate electrical coupling between β-cells within pancreatic islets. Using computational modeling, we show that upregulation in Cx36 might play a functional role in the impairment of glucose stimulated Ca2+ oscillations in a cluster of β-cells with Kir6.1 gain of function mutations in their K(ATP) channels (GoF-K(ATP) channels). Our results show that without an increase in Cx36 expression, a gain of function mutation in Kir6.1 might not be sufficient to diminish glucose stimulated Ca2+ oscillations in a β-cell cluster. We also show that a reduced Cx36 expression, which leads to loss of coordination in a wild-type β-cell cluster, restores coordinated Ca2+ oscillations in a β-cell cluster with GoF-K(ATP) channels. Our results indicate that in a heterogenous β-cell cluster with GoF-K(ATP) channels, there is an inverted u-shaped nonmonotonic relation between the cluster activity and Cx36 expression. These results show that in a neonatal diabetic β-cell model, gain of function mutations in the Kir6.1 cause Cx36 overexpression, which aggravates the impairment of glucose stimulated Ca2+ 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.

TALK-1-mediated alterations of β-cell mitochondrial function and insulin secretion impair glucose homeostasis on a diabetogenic diet

Mitochondrial Ca2+ ([Ca2+]m) homeostasis is critical for β-cell function and becomes disrupted during the pathogenesis of diabetes. [Ca2+]m uptake is dependent on elevations in cytoplasmic Ca2+ ([Ca2+]c) and endoplasmic reticulum Ca2+ ([Ca2+]ER) release, both of which are regulated by the two-pore domain K+ channel TALK-1. Here, utilizing a novel β-cell TALK-1-knockout (β-TALK-1-KO) mouse model, we found that TALK-1 limited β-cell [Ca2+]m accumulation and ATP production. However, following exposure to a high-fat diet (HFD), ATP-linked respiration, glucose-stimulated oxygen consumption rate, and glucose-stimulated insulin secretion (GSIS) were increased in control but not TALK1-KO mice. Although β-TALK-1-KO animals showed similar GSIS before and after HFD treatment, these mice were protected from HFD-induced glucose intolerance. Collectively, these data identify that TALK-1 channel control of β-cell function reduces [Ca2+]m and suggest that metabolic remodeling in diabetes drives dysglycemia.

Novel regulators of islet function identified from genetic variation in mouse islet Ca2+ oscillations

Insufficient insulin secretion to meet metabolic demand results in diabetes. The intracellular flux of Ca2+ into β-cells triggers insulin release. Since genetics strongly influences variation in islet secretory responses, we surveyed islet Ca2+ dynamics in eight genetically diverse mouse strains. We found high strain variation in response to four conditions: (1) 8 mM glucose; (2) 8 mM glucose plus amino acids; (3) 8 mM glucose, amino acids, plus 10 nM glucose-dependent insulinotropic polypeptide (GIP); and (4) 2 mM glucose. These stimuli interrogate β-cell function, α- to β-cell signaling, and incretin responses. We then correlated components of the Ca2+ waveforms to islet protein abundances in the same strains used for the Ca2+ measurements. To focus on proteins relevant to human islet function, we identified human orthologues of correlated mouse proteins that are proximal to glycemic-associated single-nucleotide polymorphisms in human genome-wide association studies. Several orthologues have previously been shown to regulate insulin secretion (e.g. ABCC8, PCSK1, and GCK), supporting our mouse-to-human integration as a discovery platform. By integrating these data, we nominate novel regulators of islet Ca2+ oscillations and insulin secretion with potential relevance for human islet function. We also provide a resource for identifying appropriate mouse strains in which to study these regulators.

Restoring connexin-36 function in diabetogenic environments precludes mouse and human islet dysfunction

The secretion of insulin from β-cells in the islet of Langerhans is governed by a series of metabolic and electrical events, which can fail during the progression of type 2 diabetes (T2D). β-cells are electrically coupled via connexin-36 (Cx36) gap junction channels, which coordinates the pulsatile dynamics of [Ca2+ ] and insulin release across the islet. Factors such as pro-inflammatory cytokines and free fatty acids disrupt gap junction coupling under in vitro conditions. Here we test whether gap junction coupling and coordinated [Ca2+ ] dynamics are disrupted in T2D, and whether recovery of gap junction coupling can recover islet function. We examine islets from donors with T2D, from db/db mice, and islets treated with pro-inflammatory cytokines (TNF-α, IL-1β, IFN-ɣ) or free fatty acids (palmitate). We modulate gap junction coupling using Cx36 over-expression or pharmacological activation via modafinil. We also develop a peptide mimetic (S293) of the c-terminal regulatory site of Cx36 designed to compete against its phosphorylation. Cx36 gap junction permeability and [Ca2+ ] dynamics were disrupted in islets from both human donors with T2D and db/db mice, and in islets treated with pro-inflammatory cytokines or palmitate. Cx36 over-expression, modafinil treatment and S293 peptide all enhanced Cx36 gap junction coupling and protected against declines in coordinated [Ca2+ ] dynamics. Cx36 over-expression and S293 peptide also reduced apoptosis induced by pro-inflammatory cytokines. Critically, S293 peptide rescued gap junction coupling and [Ca2+ ] dynamics in islets from both db/db mice and a sub-set of T2D donors. Thus, recovering or enhancing Cx36 gap junction coupling can improve islet function in diabetes. KEY POINTS: Connexin-36 (Cx36) gap junction permeability and associated coordination of [Ca2+ ] dynamics is diminished in human type 2 diabetes (T2D) and mouse models of T2D. Enhancing Cx36 gap junction permeability protects against disruptions to the coordination of [Ca2+ ] dynamics. A novel peptide mimetic of the Cx36 c-terminal regulatory region protects against declines in Cx36 gap junction permeability. Pharmacological elevation in Cx36 or Cx36 peptide mimetic recovers [Ca2+ ] dynamics and glucose-stimulated insulin secretion in human T2D and mouse models of T2D.

A pathway model of glucose-stimulated insulin secretion in the pancreatic β-cell

The pancreas plays a critical role in maintaining glucose homeostasis through the secretion of hormones from the islets of Langerhans. Glucose-stimulated insulin secretion (GSIS) by the pancreatic β-cell is the main mechanism for reducing elevated plasma glucose. Here we present a systematic modeling workflow for the development of kinetic pathway models using the Systems Biology Markup Language (SBML). Steps include retrieval of information from databases, curation of experimental and clinical data for model calibration and validation, integration of heterogeneous data including absolute and relative measurements, unit normalization, data normalization, and model annotation. An important factor was the reproducibility and exchangeability of the model, which allowed the use of various existing tools. The workflow was applied to construct a novel data-driven kinetic model of GSIS in the pancreatic β-cell based on experimental and clinical data from 39 studies spanning 50 years of pancreatic, islet, and β-cell research in humans, rats, mice, and cell lines. The model consists of detailed glycolysis and phenomenological equations for insulin secretion coupled to cellular energy state, ATP dynamics and (ATP/ADP ratio). Key findings of our work are that in GSIS there is a glucose-dependent increase in almost all intermediates of glycolysis. This increase in glycolytic metabolites is accompanied by an increase in energy metabolites, especially ATP and NADH. One of the few decreasing metabolites is ADP, which, in combination with the increase in ATP, results in a large increase in ATP/ADP ratios in the β-cell with increasing glucose. Insulin secretion is dependent on ATP/ADP, resulting in glucose-stimulated insulin secretion. The observed glucose-dependent increase in glycolytic intermediates and the resulting change in ATP/ADP ratios and insulin secretion is a robust phenomenon observed across data sets, experimental systems and species. Model predictions of the glucose-dependent response of glycolytic intermediates and biphasic insulin secretion are in good agreement with experimental measurements. Our model predicts that factors affecting ATP consumption, ATP formation, hexokinase, phosphofructokinase, and ATP/ADP-dependent insulin secretion have a major effect on GSIS. In conclusion, we have developed and applied a systematic modeling workflow for pathway models that allowed us to gain insight into key mechanisms in GSIS in the pancreatic β-cell.

Ca2+ release or Ca2+ entry, that is the question: what governs Ca2+ oscillations in pancreatic β cells?

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model.

A Consensus Model of Glucose-Stimulated Insulin Secretion in the Pancreatic β -Cell

The pancreas plays a critical role in maintaining glucose homeostasis through the secretion of hormones from the islets of Langerhans. Glucose-stimulated insulin secretion (GSIS) by the pancreatic β -cell is the main mechanism for reducing elevated plasma glucose. Here we present a systematic modeling workflow for the development of kinetic pathway models using the Systems Biology Markup Language (SBML). Steps include retrieval of information from databases, curation of experimental and clinical data for model calibration and validation, integration of heterogeneous data including absolute and relative measurements, unit normalization, data normalization, and model annotation. An important factor was the reproducibility and exchangeability of the model, which allowed the use of various existing tools. The workflow was applied to construct the first consensus model of GSIS in the pancreatic β -cell based on experimental and clinical data from 39 studies spanning 50 years of pancreatic, islet, and β -cell research in humans, rats, mice, and cell lines. The model consists of detailed glycolysis and equations for insulin secretion coupled to cellular energy state (ATP/ADP ratio). Key findings of our work are that in GSIS there is a glucose-dependent increase in almost all intermediates of glycolysis. This increase in glycolytic metabolites is accompanied by an increase in energy metabolites, especially ATP and NADH. One of the few decreasing metabolites is ADP, which, in combination with the increase in ATP, results in a large increase in ATP/ADP ratios in the β -cell with increasing glucose. Insulin secretion is dependent on ATP/ADP, resulting in glucose-stimulated insulin secretion. The observed glucose-dependent increase in glycolytic intermediates and the resulting change in ATP/ADP ratios and insulin secretion is a robust phenomenon observed across data sets, experimental systems and species. Model predictions of the glucose-dependent response of glycolytic intermediates and insulin secretion are in good agreement with experimental measurements. Our model predicts that factors affecting ATP consumption, ATP formation, hexokinase, phosphofructokinase, and ATP/ADP-dependent insulin secretion have a major effect on GSIS. In conclusion, we have developed and applied a systematic modeling workflow for pathway models that allowed us to gain insight into key mechanisms in GSIS in the pancreatic β -cell.

Visualizing hypoxic modulation of beta cell secretions via a sensor augmented oxygen gradient

One distinct advantage of microfluidic-based cell assays is their scalability for multiple concentrations or gradients. Microfluidic scaling can be extremely powerful when combining multiple parameters and modalities. Moreover, in situ stimulation and detection eliminates variability between individual bioassays. However, conventional microfluidics must combat diffusion, which limits the spatial distance and time for molecules traveling through microchannels. Here, we leveraged a multilayered microfluidic approach to integrate a novel oxygen gradient (0-20%) with an enhanced hydrogel sensor to study pancreatic beta cells. This enabled our microfluidics to achieve spatiotemporal detection that is difficult to achieve with traditional microfluidics. Using this device, we demonstrated the in situ detection of calcium, insulin, and ATP (adenosine triphosphate) in response to glucose and oxygen stimulation. Specifically, insulin was quantified at levels as low as 25 pg/mL using our imaging technique. Furthermore, by analyzing the spatial detection data dynamically over time, we uncovered a new relationship between oxygen and beta cell oscillations. We observed an optimum oxygen level between 10 and 12%, which is neither hypoxic nor normoxic in the conventional cell culture sense. These results provide evidence to support the current islet oscillator model. In future applications, this spatial microfluidic technique can be adapted for discrete protein detection in a robust platform to study numerous oxygen-dependent tissue dysfunctions.

The Dynamics of Calcium Signaling in Beta Cells-A Discussion on the Comparison of Experimental and Modelling Data

The stimulus-secretion coupling of the pancreatic beta cell is particularly complex, as it integrates the availability of glucose and other nutrients with the neuronal and hormonal input to generate rates of insulin secretion that are appropriate for the entire organism. It is beyond dispute however, that the cytosolic Ca²⁺ concentration plays a particularly prominent role in this process, as it not only triggers the fusion of insulin granules with the plasma membrane, but also regulates the metabolism of nutrient secretagogues and affects the function of ion channels and transporters. In order to obtain a better understanding of the interdependence of these processes and, ultimately, of the entire beta cell as a working system, models have been developed based on a set of nonlinear ordinary differential equations, and were tested and parametrized on a limited set of experiments. In the present investigation, we have used a recently published version of the beta cell model to test its ability to describe further measurements from our own experimentation and from the literature. The sensitivity of the parameters is quantified and discussed; furthermore, the possible influence of the measuring technique is taken into account. The model proved to be powerful in correctly describing the depolarization pattern in response to glucose and the reaction of the cytosolic Ca²⁺ concentration to stepwise increases of the extracellular K⁺ concentration. Additionally, the membrane potential during a KATP channel block combined with a high extracellular K⁺ concentration could be reproduced. In some cases, however, a slight change of a single parameter led to an abrupt change in the cellular response, such as the generation of a Ca²⁺ oscillation with high amplitude and high frequency. This raises the question as to whether the beta cell may be a partially unstable system or whether further developments in modeling are needed to achieve a generally valid description of the stimulus-secretion coupling of the beta cell.

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.

Metabolic cycles and signals for insulin secretion

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

β Cell-specific deletion of Zfp148 improves nutrient-stimulated β cell Ca2+ responses

Insulin secretion from pancreatic β cells is essential for glucose homeostasis. An insufficient response to the demand for insulin results in diabetes. We previously showed that β cell-specific deletion of Zfp148 (β-Zfp148KO) improves glucose tolerance and insulin secretion in mice. Here, we performed Ca2+ imaging of islets from β‑Zfp148KO and control mice fed both a chow and a Western-style diet. β-Zfp148KO islets demonstrated improved sensitivity and sustained Ca2+ oscillations in response to elevated glucose levels. β-Zfp148KO islets also exhibited elevated sensitivity to amino acid-induced Ca2+ influx under low glucose conditions, suggesting enhanced mitochondrial phosphoenolpyruvate-dependent (PEP-dependent), ATP-sensitive K+ channel closure, independent of glycolysis. RNA-Seq and proteomics of β-Zfp148KO islets revealed altered levels of enzymes involved in amino acid metabolism (specifically, SLC3A2, SLC7A8, GLS, GLS2, PSPH, PHGDH, and PSAT1) and intermediary metabolism (namely, GOT1 and PCK2), consistent with altered PEP cycling. In agreement with this, β-Zfp148KO islets displayed enhanced insulin secretion in response to l-glutamine and activation of glutamate dehydrogenase. Understanding pathways controlled by ZFP148 may provide promising strategies for improving β cell function that are robust to the metabolic challenge imposed by a Western diet.

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.

Novel association between a transient receptor potential cation channel subfamily M member 5 expression quantitative trait locus rs35197079 and decreased susceptibility of gestational diabetes mellitus in a Chinese population

AIMS/INTRODUCTION

Emerging evidence suggests that expression quantitative trait loci (eQTLs) are more likely to associate with complex diseases. Transient receptor potential cation channel subfamily M member 5 (TRPM5) is a ubiquitously expressed voltage-gated cation channel that acts indispensably to trigger insulin secretion in pancreatic β-cells. The present study evaluated the association between TRPM5 eQTL single-nucleotide polymorphisms and the risk of gestational diabetes mellitus (GDM) in a Chinese population.

MATERIALS AND METHODS

A total of 380 unrelated Chinese pregnant women including 241 GDM patients and 139 controls were included in this study. The eQTL single-nucleotide polymorphisms of TRPM5 were obtained from the GTEx eQTL Browser, and were subsequently genotyped using the Agena MassARRAY iPLEX platform.

RESULTS

Logistic regression analysis and linear regression analysis showed that rs35197079 and rs74848824 were significantly associated with reduced GDM risk and lower fasting plasma glucose levels after adjusting confounder factors in dominant genetic models. Stratification analysis based on pre-pregnancy body mass index validated a strong association between rs35197079 and GDM susceptibility in underweight and normal weight individuals. Luciferase and electrophoretic mobility shift assays carried out in rat pancreatic β-cells showed that rs35197079 was functional.

CONCLUSIONS

The TRPM5 eQTL single-nucleotide polymorphism rs35197079 was associated with decreased GDM susceptibility in a Chinese population, especially in underweight and normal weight pregnant women, and it was functional in modulating gene transcription.

Beta-Cell Ion Channels and Their Role in Regulating Insulin Secretion

Beta cells of the pancreatic islet express many different types of ion channels. These channels reside in the β-cell plasma membrane as well as subcellular organelles and their coordinated activity and sensitivity to metabolism regulate glucose-dependent insulin secretion. Here, we review the molecular nature, expression patterns, and functional roles of many β-cell channels, with an eye toward explaining the ionic basis of glucose-induced insulin secretion. Our primary focus is on K_ATP and voltage-gated Ca²⁺ channels as these primarily regulate insulin secretion; other channels in our view primarily help to sculpt the electrical patterns generated by activated β-cells or indirectly regulate metabolism. Lastly, we discuss why understanding the physiological roles played by ion channels is important for understanding the secretory defects that occur in type 2 diabetes. © 2021 American Physiological Society. Compr Physiol 11:1-21, 2021.

Synchronisation of glycolytic activity in yeast cells

Glycolysis is the central metabolic pathway of almost every cell and organism. Under appropriate conditions, glycolytic oscillations may occur in individual cells as well as in entire cell populations or tissues. In many biological systems, glycolytic oscillations drive coherent oscillations of other metabolites, for instance in cardiomyocytes near anorexia, or in pancreas where they lead to a pulsatile release of insulin. Oscillations at the population or tissue level require the cells to synchronize their metabolism. We review the progress achieved in studying a model organism for glycolytic oscillations, namely yeast. Oscillations may occur on the level of individual cells as well as on the level of the cell population. In yeast, the cell-to-cell interaction is realized by diffusion-mediated intercellular communication via a messenger molecule. The present mini-review focuses on the synchronisation of glycolytic oscillations in yeast. Synchronisation is a quorum-sensing phenomenon because the collective oscillatory behaviour of a yeast cell population ceases when the cell density falls below a threshold. We review the question, under which conditions individual cells in a sparse population continue or cease to oscillate. Furthermore, we provide an overview of the pathway leading to the onset of synchronized oscillations. We also address the effects of spatial inhomogeneities (e.g., the formation of spatial clusters) on the collective dynamics, and also review the emergence of travelling waves of glycolytic activity. Finally, we briefly review the approaches used in numerical modelling of synchronized cell populations.

Hubs, diversity, and synchronization in FitzHugh-Nagumo oscillator networks: Resonance effects and biophysical implications

Using the FitzHugh-Nagumo equations to represent the oscillatory electrical behavior of β-cells, we develop a coupled oscillator network model with cubic lattice topology, showing that the emergence of pacemakers or hubs in the system can be viewed as a natural consequence of oscillator population diversity. The optimal hub to nonhub ratio is determined by the position of the diversity-induced resonance maximum for a given set of FitzHugh-Nagumo equation parameters and is predicted by the model to be in a range that is fully consistent with experimental observations. The model also suggests that hubs in a β-cell network should have the ability to "switch on" and "off" their pacemaker function. As a consequence, their relative amount in the population can vary in order to ensure an optimal oscillatory performance of the network in response to environmental changes, such as variations of an external stimulus.

Pancreatic β-cell heterogeneity in health and diabetes: classes, sources, and subtypes

Pancreatic β-cells perform glucose-stimulated insulin secretion, a process at the center of type 2 diabetes etiology. Efforts to understand how β-cells behave in healthy and stressful conditions have revealed a wide degree of morphological, functional, and transcriptional heterogeneity. Sources of heterogeneity include β-cell topography, developmental origin, maturation state, and stress response. Advances in sequencing and imaging technologies have led to the identification of β-cell subtypes, which play distinct roles in the islet niche. This review examines β-cell heterogeneity from morphological, functional, and transcriptional perspectives, and considers the relevance of topography, maturation, development, and stress response. It also discusses how these factors have been used to identify β-cell subtypes, and how heterogeneity is impacted by diabetes. We examine open questions in the field and discuss recent technological innovations that could advance understanding of β-cell heterogeneity in health and disease.

Intercellular communication induces glycolytic synchronization waves between individually oscillating cells

Many organs have internal structures with spatially differentiated and sometimes temporally synchronized groups of cells. The mechanisms leading to such differentiation and coordination are not well understood. Here we design a diffusion-limited microfluidic system to mimic a multicellular organ structure with peripheral blood flow and test whether a group of individually oscillating yeast cells could form subpopulations of spatially differentiated and temporally synchronized cells. Upon substrate addition, the dynamic response at single-cell level shows glycolytic oscillations, leading to wave fronts traveling through the monolayered population and to synchronized communities at well-defined positions in the cell chamber. A detailed mechanistic model with the architectural structure of the flow chamber incorporated successfully predicts the spatial-temporal experimental data, and allows for a molecular understanding of the observed phenomena. The intricate interplay of intracellular biochemical reaction networks leading to the oscillations, combined with intercellular communication via metabolic intermediates and fluid dynamics of the reaction chamber, is responsible for the generation of the subpopulations of synchronized cells. This mechanism, as analyzed from the model simulations, is experimentally tested using different concentrations of cyanide stress solutions. The results are reproducible and stable, despite cellular heterogeneity, and the spontaneous community development is reminiscent of a zoned cell differentiation often observed in multicellular organs.

Bax inhibitor-1 deficiency leads to obesity by increasing Ca2+-dependent insulin secretion

Abstract

Transmembrane BAX inhibitor motif containing 6 (TMBIM6), also known as Bax inhibitor-1, is an evolutionarily conserved protein involved in endoplasmic reticulum (ER) function. TMBIM6 is an ER Ca²⁺ leak channel and its deficiency enhances susceptibility to ER stress due to inhibition of the ER stress sensor IRE1α. It was previously shown that TMBIM6 overexpression improves glucose metabolism and that TMBIM6 knockout mice develop obesity. We here examined the metabolic alterations underlying the obese phenotype and subjected TMBIM6 knockout mice to indirect calorimetry and euglycemic-hyperinsulinemic tests with stable isotope dilution to gauge tissue-specific insulin sensitivity. This demonstrated no changes in heat production, food intake, activity or hepatic and peripheral insulin sensitivity. TMBIM6 knockout mice, however, featured a higher glucose-stimulated insulin secretion in vivo as assessed by the hyperglycemic clamp test and hepatic steatosis. This coincided with profound changes in glucose-mediated Ca²⁺ regulation in isolated pancreatic β cells and increased levels of IRE1α levels but no differences in downstream effects of IRE1α like increased Xbp1 mRNA splicing or Ire1-dependent decay of insulin mRNA in the pancreas. We therefore conclude that lack of TMBIM6 does not affect insulin sensitivity but leads to hyperinsulinemia, which serves to explain the weight gain. TMBIM6-mediated metabolic alterations are mainly caused by its role as a Ca²⁺ release channel in the ER.

Key messages

TMBIM6^−/− leads to obesity and hepatic steatosis.

Food intake and energy expenditure are not changed in TMBIM6^−/− mice.

No changes in insulin resistance in TMBIM6^−/− mice.

Increased insulin secretion caused by altered calcium dynamics in β cells.

Metabolic regulation of calcium signaling in beta cells

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

Heterogeneity and Delayed Activation as Hallmarks of Self-Organization and Criticality in Excitable Tissue

Self-organized critical dynamics is assumed to be an attractive mode of functioning for several real-life systems and entails an emergent activity in which the extent of observables follows a power-law distribution. The hallmarks of criticality have recently been observed in a plethora of biological systems, including beta cell populations within pancreatic islets of Langerhans. In the present study, we systematically explored the mechanisms that drive the critical and supercritical behavior in networks of coupled beta cells under different circumstances by means of experimental and computational approaches. Experimentally, we employed high-speed functional multicellular calcium imaging of fluorescently labeled acute mouse pancreas tissue slices to record calcium signals in a large number of beta cells simultaneously, and with a high spatiotemporal resolution. Our experimental results revealed that the cellular responses to stimulation with glucose are biphasic and glucose-dependent. Under physiological as well as under supraphysiological levels of stimulation, an initial activation phase was followed by a supercritical plateau phase with a high number of global intercellular calcium waves. However, the activation phase displayed fingerprints of critical behavior under lower stimulation levels, with a progressive recruitment of cells and a power-law distribution of calcium wave sizes. On the other hand, the activation phase provoked by pathophysiologically high glucose concentrations, differed considerably and was more rapid, less continuous, and supercritical. To gain a deeper insight into the experimentally observed complex dynamical patterns, we built up a phenomenological model of coupled excitable cells and explored empirically the model’s necessities that ensured a good overlap between computational and experimental results. It turned out that such a good agreement between experimental and computational findings was attained when both heterogeneous and stimulus-dependent time lags, variability in excitability levels, as well as a heterogeneous cell-cell coupling were included into the model. Most importantly, since our phenomenological approach involved only a few parameters, it naturally lends itself not only for determining key mechanisms of self-organized criticality at the tissue level, but also points out various features for comprehensive and realistic modeling of different excitable systems in nature.

Computational modeling of the effect of temperature variations on human pancreatic β-cell activity

The effect of temperature variations on the pancreatic β-cell activity and the role of different model compartments in temperature sensing have been investigated using a computational modeling approach. The results of our study show that temperature variations by several degrees can change the dynamical states of the β-cell system. In addition, temperature variations can alter the characteristic features of the membrane voltage, which correlates with insulin secretion. Simulation results show that the ion channels such as the L-type calcium, the hERG potassium, sodium channels and the glycolysis pathway are the possible sites for sensing temperature variation. Results indicate that for a small temperature change, even though the frequency and amplitude of electrical activity are altered, the area under the membrane potential curve remains almost unchanged, which implies the existence of a thermoregulatory mechanism for preserving the amount of insulin secretion. Furthermore, the computational analysis shows that the β-cell electrical activity exhibits a bursting pattern in physiological temperature (37 °C) while in vitro studies reported almost the spiking activity at lower temperatures. Since hormone-secreting systems work more efficient in bursting mode, we propose that the pancreatic β-cell works better in the physiological temperature compared with the reference temperature (33 °C).

Gap-junction coupling can prolong beta-cell burst period by an order of magnitude via phantom bursting

Pancreatic β-cells show multiple intrinsic modes of oscillation with bursting electrical activity playing a crucial role. Bursting is seen both in experimentally isolated β-cells as well as in electrically coupled cells in the pancreatic islets, but the burst period is typically an order of magnitude greater in coupled cells. This difference has previously been attributed to noisier dynamics, or perturbed electrophysiological properties, in isolated β-cells. Here, we show that diffusive coupling alone can extend the period more than ten-fold in bursting oscillators modeled with a so-called phantom burster model and analyze this result with slow-fast bifurcation analysis of an electrically coupled pair of cells. Our results should be applicable to other scenarios where coupling of bursting units, e.g., neurons, may increase the oscillation period drastically.

Closing in on the Mechanisms of Pulsatile Insulin Secretion

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

TRPM5 in the battle against diabetes and obesity

TRPM5 is a non-selective monovalent cation channel activated by increases in intracellular Ca²⁺ . It has a distinct expression pattern: expression is detected in chemosensitive tissues from solitary chemosensory cells to the taste receptor cells and in pancreatic β-cells. The role of TRPM5 has been investigated with the use of knockout mouse models. Trpm5^-/- mice have a lack of type II taste perception and show reduced glucose-induced insulin secretion. Expression levels of TRPM5 are reduced in obese, leptin-signalling-deficient mice, and mutations in TRPM5 have been associated with type II diabetes and metabolic syndrome. In this review, we aim to give an overview of the activation, selectivity, modulation and physiological roles of TRPM5.

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

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

Emergence of localized patterns in globally coupled networks of relaxation oscillators with heterogeneous connectivity

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

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.

Heterogeneity in the Beta-Cell Population: a Guided Search Into Its Significance in Pancreas and in Implants

PURPOSE OF REVIEW

Intercellular differences in function have since long been noticed in the pancreatic beta-cell population. Heterogeneity in cellular glucose responsiveness is considered of physiological and pathological relevance. The present review updates evidence for the physiologic significance of beta-cell heterogeneity in the pancreas. It also briefly discusses what this role would imply for beta-cell implants in diabetes.

RECENT FINDINGS

Over the past 3 years, functionally different beta cells have been related to mechanisms that may underlie their heterogeneity in the pancreas, such as the stage in their life cycle and the degree of their clustering to islets with varying vascularization. Markers were identified for detecting these subpopulations in tissues. The existence of a functional heterogeneity in the pancreatic beta-cell population is further supported. Views on its origin and methods for its analysis in pancreas and implants will help guide the search into its significance in beta-cell biology, pathology, and therapy.

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.

The Pancreatic β-Cell: A Bioenergetic Perspective

The pancreatic β-cell secretes insulin in response to elevated plasma glucose. This review applies an external bioenergetic critique to the central processes of glucose-stimulated insulin secretion, including glycolytic and mitochondrial metabolism, the cytosolic adenine nucleotide pool, and its interaction with plasma membrane ion channels. The control mechanisms responsible for the unique responsiveness of the cell to glucose availability are discussed from bioenergetic and metabolic control standpoints. The concept of coupling factor facilitation of secretion is critiqued, and an attempt is made to unravel the bioenergetic basis of the oscillatory mechanisms controlling secretion. The need to consider the physiological constraints operating in the intact cell is emphasized throughout. The aim is to provide a coherent pathway through an extensive, complex, and sometimes bewildering literature, particularly for those unfamiliar with the field.

Phase modulation of insulin pulses enhances glucose regulation and enables inter-islet synchronization

Insulin is secreted in a pulsatile manner from multiple micro-organs called the islets of Langerhans. The amplitude and phase (shape) of insulin secretion are modulated by numerous factors including glucose. The role of phase modulation in glucose homeostasis is not well understood compared to the obvious contribution of amplitude modulation. In the present study, we measured Ca²⁺ oscillations in islets as a proxy for insulin pulses, and we observed their frequency and shape changes under constant/alternating glucose stimuli. Here we asked how the phase modulation of insulin pulses contributes to glucose regulation. To directly answer this question, we developed a phenomenological oscillator model that drastically simplifies insulin secretion, but precisely incorporates the observed phase modulation of insulin pulses in response to glucose stimuli. Then, we mathematically modeled how insulin pulses regulate the glucose concentration in the body. The model of insulin oscillation and glucose regulation describes the glucose-insulin feedback loop. The data-based model demonstrates that the existence of phase modulation narrows the range within which the glucose concentration is maintained through the suppression/enhancement of insulin secretion in conjunction with the amplitude modulation of this secretion. The phase modulation is the response of islets to glucose perturbations. When multiple islets are exposed to the same glucose stimuli, they can be entrained to generate synchronous insulin pulses. Thus, we conclude that the phase modulation of insulin pulses is essential for glucose regulation and inter-islet synchronization.

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.

Modeling of glucose-induced cAMP oscillations in pancreatic β cells: cAMP rocks when metabolism rolls

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.

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.

Regulation of Glucokinase by Intracellular Calcium Levels in Pancreatic β Cells

Glucokinase (GCK) controls the rate of glucose metabolism in pancreatic β cells, and its activity is rate-limiting for insulin secretion. Posttranslational GCK activation can be stimulated through either G protein-coupled receptors or receptor tyrosine kinase signaling pathways, suggesting a common mechanism. Here we show that inhibiting Ca(2+) release from the endoplasmic reticulum (ER) decouples GCK activation from receptor stimulation. Furthermore, pharmacological release of ER Ca(2+) stimulates activation of a GCK optical biosensor and potentiates glucose metabolism, implicating rises in cytoplasmic Ca(2+) as a critical regulatory mechanism. To explore the potential for glucose-stimulated GCK activation, the GCK biosensor was optimized using circularly permuted mCerulean3 proteins. This new sensor sensitively reports activation in response to insulin, glucagon-like peptide 1, and agents that raise cAMP levels. Transient, glucose-stimulated GCK activation was observed in βTC3 and MIN6 cells. An ER-localized channelrhodopsin was used to manipulate the cytoplasmic Ca(2+) concentration in cells expressing the optimized FRET-GCK sensor. This permitted quantification of the relationship between cytoplasmic Ca(2+) concentrations and GCK activation. Half-maximal activation of the FRET-GCK sensor was estimated to occur at ∼400 nm Ca(2+). When expressed in islets, fluctuations in GCK activation were observed in response to glucose, and we estimated that posttranslational activation of GCK enhances glucose metabolism by ∼35%. These results suggest a mechanism for integrative control over GCK activation and, therefore, glucose metabolism and insulin secretion through regulation of cytoplasmic Ca(2+) levels.

Mathematical Modeling of Interacting Glucose-Sensing Mechanisms and Electrical Activity Underlying Glucagon-Like Peptide 1 Secretion

Intestinal L-cells sense glucose and other nutrients, and in response release glucagon-like peptide 1 (GLP-1), peptide YY and other hormones with anti-diabetic and weight-reducing effects. The stimulus-secretion pathway in L-cells is still poorly understood, although it is known that GLP-1 secreting cells use sodium-glucose co-transporters (SGLT) and ATP-sensitive K+-channels (K(ATP)-channels) to sense intestinal glucose levels. Electrical activity then transduces glucose sensing to Ca2+-stimulated exocytosis. This particular glucose-sensing arrangement with glucose triggering both a depolarizing SGLT current as well as leading to closure of the hyperpolarizing K(ATP) current is of more general interest for our understanding of glucose-sensing cells. To dissect the interactions of these two glucose-sensing mechanisms, we build a mathematical model of electrical activity underlying GLP-1 secretion. Two sets of model parameters are presented: one set represents primary mouse colonic L-cells; the other set is based on data from the GLP-1 secreting GLUTag cell line. The model is then used to obtain insight into the differences in glucose-sensing between primary L-cells and GLUTag cells. Our results illuminate how the two glucose-sensing mechanisms interact, and suggest that the depolarizing effect of SGLT currents is modulated by K(ATP)-channel activity. Based on our simulations, we propose that primary L-cells encode the glucose signal as changes in action potential amplitude, whereas GLUTag cells rely mainly on frequency modulation. The model should be useful for further basic, pharmacological and theoretical investigations of the cellular signals underlying endogenous GLP-1 and peptide YY release.

Type 2 Diabetes-Associated K+ Channel TALK-1 Modulates β-Cell Electrical Excitability, Second-Phase Insulin Secretion, and Glucose Homeostasis

Two-pore domain K+ (K2P) channels play an important role in tuning β-cell glucose-stimulated insulin secretion (GSIS). The K2P channel TWIK-related alkaline pH-activated K2P (TALK)-1 is linked to type 2 diabetes risk through a coding sequence polymorphism (rs1535500); however, its physiological function has remained elusive. Here, we show that TALK-1 channels are expressed in mouse and human β-cells, where they serve as key regulators of electrical excitability and GSIS. We find that the rs1535500 polymorphism, which results in an alanine-to-glutamate substitution in the C-terminus of human TALK-1, increases channel activity. Genetic ablation of TALK-1 results in β-cell membrane potential depolarization, increased islet Ca2+ influx, and enhanced second-phase GSIS. Moreover, mice lacking TALK-1 channels are resistant to high-fat diet-induced elevations in fasting glycemia. These findings reveal TALK-1 channels as important modulators of second-phase insulin secretion and suggest a clinically relevant mechanism for rs1535500, which may increase type 2 diabetes risk by limiting GSIS.

Mathematical modelling of local calcium and regulated exocytosis during inhibition and stimulation of glucagon secretion from pancreatic alpha-cells

Glucagon secretion from pancreatic alpha-cells is dysregulated in diabetes. Despite decades of investigations of the control of glucagon release by glucose and hormones, the underlying mechanisms are still debated. Recently, mathematical models have been applied to investigate the modification of electrical activity in alpha-cells as a result of glucose application. However, recent studies have shown that paracrine effects such as inhibition of glucagon secretion by glucagon-like peptide 1 (GLP-1) or stimulation of release by adrenaline involve cAMP-mediated effects downstream of electrical activity. In particular, depending of the intracellular cAMP concentration, specific types of Ca(2+) channels are inhibited or activated, which interacts with mobilization of secretory granules. To investigate these aspects of alpha-cell function theoretically, we carefully developed a mathematical model of Ca(2+) levels near open or closed Ca(2+) channels of various types, which was linked to a description of Ca(2+) below the plasma membrane, in the bulk cytosol and in the endoplasmic reticulum. We investigated how the various subcellular Ca(2+) compartments contribute to control of glucagon-exocytosis in response to glucose, GLP-1 or adrenaline. Our studies refine previous modelling studies of alpha-cell function, and provide deeper insight into the control of glucagon secretion.

Representative Sinusoids for Hepatic Four-Scale Pharmacokinetics Simulations

The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the body. The corresponding biochemical processes are typically subject to spatial variations at different length scales. Zonal enzyme expression along sinusoids leads to zonated metabolization already in the healthy state. Pathological states of the liver may involve liver cells affected in a zonated manner or heterogeneously across the whole organ. This spatial heterogeneity, however, cannot be described by most computational models which usually consider the liver as a homogeneous, well-stirred organ.

The goal of this article is to present a methodology to extend whole-body pharmacokinetics models by a detailed liver model, combining different modeling approaches from the literature. This approach results in an integrated four-scale model, from single cells via sinusoids and the organ to the whole organism, capable of mechanistically representing metabolization inhomogeneity in livers at different spatial scales. Moreover, the model shows circulatory mixing effects due to a delayed recirculation through the surrounding organism.

To show that this approach is generally applicable for different physiological processes, we show three applications as proofs of concept, covering a range of species, compounds, and diseased states: clearance of midazolam in steatotic human livers, clearance of caffeine in mouse livers regenerating from necrosis, and a parameter study on the impact of different cell entities on insulin uptake in mouse livers.

The examples illustrate how variations only discernible at the local scale influence substance distribution in the plasma at the whole-body level. In particular, our results show that simultaneously considering variations at all relevant spatial scales may be necessary to understand their impact on observations at the organism scale.

Measurement of the entrainment window of islets of Langerhans by microfluidic delivery of a chirped glucose waveform

Within single islets of Langerhans, the endocrine portion of the pancreas, intracellular metabolites, as well as insulin secretion, oscillate with a period of ∼5 min. In vivo, pulsatile insulin oscillations are also observed with periods ranging from 5-15 minutes. In order for oscillations of insulin to be observed in vivo, the majority of islets in the pancreas must synchronize their output. It is known that populations of islets can be synchronized via entrainment of the individual islets to low amplitude glucose oscillations that have periods close to islets' natural period. However, the range of glucose periods and amplitudes that can entrain islets has not been rigorously examined. To find the range of glucose periods that can entrain islets, a microfluidic system was utilized to produce and deliver a chirped glucose waveform to populations of islets while their individual intracellular [Ca(2+)] ([Ca(2+)]i) oscillations were imaged. Waveforms with amplitudes of 0.5, 1, and 1.5 mM above a median value of 11 mM were applied while the period was swept from 20-2 min. Oscillations of [Ca(2+)]i resonated the strongest when the period of the glucose wave was within 2 min of the natural period of the islets, typically close to 5 min. Some examples of 1 : 2 and 2 : 1 entrainment were observed during exposure to long and short glucose periods, respectively. These results shed light on the dynamic nature of islet behavior and may help to understand dynamics observed in vivo.