Glucose Oscillations Can Activate an Endogenous Oscillator in Pancreatic Islets

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.

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.

Risk for Imbalanced Blood Glucose Pattern: Construct Analysis and Nursing Diagnosis Proposal

To identify a clinical judgment of susceptibility referring to the development of glycemic fluctuations in adults with Diabetes Mellitus undergoing treatment. Theoretical study with construct analysis. The exploration of the phenomena of glycemic variations provided clues for the description of the blood glucose pattern construct and the proposal of a new risk Nursing diagnosis as a judgment of susceptibility to the balance of this pattern. The risk factors for "Risk for Imbalanced Blood Glucose Pattern" are cognitive dysfunction; excessive alcohol consumption; excessive daily exercise; inadequate follow through with treatment regimen; increased frequency of self-monitoring of blood glucose; inadequate knowledge of disease process; inadequate management of amount of food; inadequate regularity of meal consumption; obesity; overweight; smoking; underweight. The elaboration of "Risk for Imbalanced Blood Glucose Pattern" Nursing diagnosis contributes to the advancement in the Nursing classifications and to the elaboration of planning actions and specific interventions.

Classification of bursting patterns: A tale of two ducks

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s and is still ongoing. As a by-product, it establishes analytical and numerical foundations for studying complex temporal behaviors in multiple timescale models of cellular activity. In this review, we first present the seminal works of Rinzel and Izhikevich in classifying bursting patterns of excitable systems. We recall a complementary mathematical classification approach by Bertram and colleagues, and then by Golubitsky and colleagues, which, together with the Rinzel-Izhikevich proposals, provide the state-of-the-art foundations to these classifications. Beyond classical approaches, we review a recent bursting example that falls outside the previous classification systems. Generalizing this example leads us to propose an extended classification, which requires the analysis of both fast and slow subsystems of an underlying slow-fast model and allows the dissection of a larger class of bursters. Namely, we provide a general framework for bursting systems with both subthreshold and superthreshold oscillations. A new class of bursters with at least 2 slow variables is then added, which we denote folded-node bursters, to convey the idea that the bursts are initiated or annihilated via a folded-node singularity. Key to this mechanism are so-called canard or duck orbits, organizing the underpinning excitability structure. We describe the 2 main families of folded-node bursters, depending upon the phase (active/spiking or silent/nonspiking) of the bursting cycle during which folded-node dynamics occurs. We classify both families and give examples of minimal systems displaying these novel bursting patterns. Finally, we provide a biophysical example by reinterpreting a generic conductance-based episodic burster as a folded-node burster, showing that the associated framework can explain its subthreshold oscillations over a larger parameter region than the fast subsystem approach.

Bursting is ubiquitous in cellular excitable rhythms and comes in a plethora of patterns, both experimentally recorded and reproduced through models. As these different patterns may reflect different coding or information properties, it is therefore crucial to develop modeling frameworks that can both capture them and understand their characteristics. In this review, we propose a comprehensive account of the main bursting classification systems that have been developed over the past 40 years, together with recent developments allowing us to extend these classifications. Based upon bifurcation theory and heavily reliant on timescale separation, these schemes take full advantage of the fast subsystem analysis, obtained when slow variables are frozen and considered as bifurcation parameters. We complement this classical view by showing that nontrivial slow subsystem may also encode key informations important to classify bursting rhythms, due to the presence of so-called folded-node singularities. We provide minimal idealized models as well as one generic conductance-based example displaying bursting oscillations that require our extended classification in order to be fully characterized. We also highlight examples of biological data that could be suitably revisited with the lenses of this extended classifications and could lead to new models of complex cellular activity.

The physiological role of β-cell heterogeneity in pancreatic islet function

Endocrine cells within the pancreatic islets of Langerhans are heterogeneous in terms of transcriptional profile, protein expression and the regulation of hormone release. Even though this heterogeneity has long been appreciated, only within the past 5 years have detailed molecular analyses led to an improved understanding of its basis. Although we are beginning to recognize why some subpopulations of endocrine cells are phenotypically different to others, arguably the most important consideration is how this heterogeneity affects the regulation of hormone release to control the homeostasis of glucose and other energy-rich nutrients. The focus of this Review is the description of how endocrine cell heterogeneity (and principally that of insulin-secreting β-cells) affects the regulation of hormone secretion within the islets of Langerhans. This discussion includes an overview of the functional characteristics of the different islet cell subpopulations and describes how they can communicate to influence islet function under basal and glucose-stimulated conditions. We further discuss how changes to the specific islet cell subpopulations or their numbers might underlie islet dysfunction in type 2 diabetes mellitus. We conclude with a discussion of several key open questions regarding the physiological role of islet cell heterogeneity.

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.

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.

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.

NMDA receptor inhibition increases, synchronizes, and stabilizes the collective pancreatic beta cell activity: Insights through multilayer network analysis

NMDA receptors promote repolarization in pancreatic beta cells and thereby reduce glucose-stimulated insulin secretion. Therefore, NMDA receptors are a potential therapeutic target for diabetes. While the mechanism of NMDA receptor inhibition in beta cells is rather well understood at the molecular level, its possible effects on the collective cellular activity have not been addressed to date, even though proper insulin secretion patterns result from well-synchronized beta cell behavior. The latter is enabled by strong intercellular connectivity, which governs propagating calcium waves across the islets and makes the heterogeneous beta cell population work in synchrony. Since a disrupted collective activity is an important and possibly early contributor to impaired insulin secretion and glucose intolerance, it is of utmost importance to understand possible effects of NMDA receptor inhibition on beta cell functional connectivity. To address this issue, we combined confocal functional multicellular calcium imaging in mouse tissue slices with network science approaches. Our results revealed that NMDA receptor inhibition increases, synchronizes, and stabilizes beta cell activity without affecting the velocity or size of calcium waves. To explore intercellular interactions more precisely, we made use of the multilayer network formalism by regarding each calcium wave as an individual network layer, with weighted directed connections portraying the intercellular propagation. NMDA receptor inhibition stabilized both the role of wave initiators and the course of waves. The findings obtained with the experimental antagonist of NMDA receptors, MK-801, were additionally validated with dextrorphan, the active metabolite of the approved drug dextromethorphan, as well as with experiments on NMDA receptor KO mice. In sum, our results provide additional and new evidence for a possible role of NMDA receptor inhibition in treatment of type 2 diabetes and introduce the multilayer network paradigm as a general strategy to examine effects of drugs on connectivity in multicellular systems.

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.

Integrated multiscale mathematical modeling of insulin secretion reveals the role of islet network integrity for proper oscillatory glucose-dose response

The integrated multiscale mathematical model we present in this paper is built on two of our previous ones: a model of electrical oscillation in β-cells connected to neighboring cells within a three-dimensional (3D) network, and a model of glucose-induced β-cell intracellular insulin granule trafficking and insulin secretion. In order to couple these two models, we assume that the rate at which primed and release-ready insulin granules fuse at the cell membrane increases with the intracellular calcium concentration. Moreover, by assuming that the fraction of free K_ATP-channels decreases with increasing glucose concentration, we take into account the effect of glucose dose on membrane potential and, indirectly via the effect on the potential, on intracellular calcium. Numerical analysis of our new model shows that a single step increase in glucose concentration yields the experimentally observed characteristic biphasic insulin release. We find that the biphasic response is typically oscillatory in nature for low and moderate glucose concentrations. The plateau fraction (the time that the β-cells spend in their active firing phase) increases with increasing glucose dose, as does the total insulin secretion. At high glucose concentrations, the oscillations tend to vanish due to a constantly elevated membrane potential of the β-cells. Our results also demonstrate how insulin secretion characteristics in various glucose protocols depend on the degree of β-cell loss, highlighting the potential impact from disease. In particular, both the secretory capacity (average insulin secretion rate per β-cell) and the oscillatory response diminish as the islet cell network becomes compromised.

Synchronization of pancreatic islets by periodic or non-periodic muscarinic agonist pulse trains

Pulsatile insulin secretion into the portal vein from the many pancreatic islets of Langerhans is critical for efficient glucose homeostasis. The islets are themselves endogenous oscillators, but since they are not physically coupled it is not obvious how their oscillations are synchronized across the pancreas. It has been proposed that synchronization of islets is achieved through periodic activity of intrapancreatic ganglia, and indeed there are data supporting this proposal. Postganglionic nerves are cholinergic, and their product, acetylcholine, can influence islet β-cells through actions on M₃ muscarinic receptors which are coupled to G_q type G-proteins. In addition, the neurons secrete several peptide hormones that act on β-cell receptors. The data supporting synchronization via intrapancreatic ganglia are, however, limited. In particular, it has not been shown that trains of muscarinic pulses are effective at synchronizing islets in vitro. Also, if as has been suggested, there is a ganglionic pacemaker driving islets to a preferred frequency, no neural circuitry for this pacemaker has been identified. In this study, both points are addressed using a microfluidic system that allows for the pulsed application of the muscarinic agonist carbachol. We find that murine islets are entrained and synchronized over a wide range of frequencies when the carbachol pulsing is periodic, adding support to the hypothesis that ganglia can synchronize islets in vivo. We also find that islet synchronization is very effective even if the carbachol pulses are applied at random times. This suggests that a neural pacemaker is not needed; all that is required is that islets receive occasional coordinated input from postganglionic neurons. The endogenous rhythmic activity of the islets then sets the frequency of the islet population rhythm, while the input from ganglia acts only to keep the islet oscillators in phase.

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.

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.

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.