Mathematical modeling of gap junction coupling and electrical activity in human β-cells

Exendin-4 affects calcium signalling predominantly during activation and activity of beta cell networks in acute mouse pancreas tissue slices

Tight control of beta cell stimulus-secretion coupling is crucial for maintaining homeostasis of energy-rich nutrients. While glucose serves as a primary regulator of this process, incretins augment beta cell function, partly by enhancing cytosolic [Ca2+] dynamics. However, the details of how precisely they affect beta cell recruitment during activation, their active time, and functional connectivity during plateau activity, and how they influence beta cell deactivation remain to be described. Performing functional multicellular Ca2+ imaging in acute mouse pancreas tissue slices enabled us to systematically assess the effects of the GLP-1 receptor agonist exendin-4 (Ex-4) simultaneously in many coupled beta cells with high resolution. In otherwise substimulatory glucose, Ex-4 was able to recruit approximately a quarter of beta cells into an active state. Costimulation with Ex-4 and stimulatory glucose shortened the activation delays and accelerated beta cell activation dynamics. More specifically, active time increased faster, and the time required to reach half-maximal activation was effectively halved in the presence of Ex-4. Moreover, the active time and regularity of [Ca2+]IC oscillations increased, especially during the first part of beta cell response. In contrast, subsequent addition of Ex-4 to already active cells did not significantly enhance beta cell activity. Network analyses further confirmed increased connectivity during activation and activity in the presence of Ex-4, with hub cell roles remaining rather stable in both control experiments and experiments with Ex-4. Interestingly, Ex-4 demonstrated a biphasic effect on deactivation, slightly prolonging beta cell activity at physiological concentrations and shortening deactivation delays at supraphysiological concentrations. In sum, costimulation by Ex-4 and glucose increases [Ca2+]IC during beta cell activation and activity, indicating that the effect of incretins may, to an important extent, be explained by enhanced [Ca2+]IC signals. During deactivation, previous incretin stimulation does not critically prolong cellular activity, which corroborates their low risk of hypoglycemia.

Deconstructing the integrated oscillator model for pancreatic β-cells

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

Both electrical and metabolic coupling shape the collective multimodal activity and functional connectivity patterns in beta cell collectives: A computational model perspective

Pancreatic beta cells are coupled excitable oscillators that synchronize their activity via different communication pathways. Their oscillatory activity manifests itself on multiple timescales and consists of bursting electrical activity, subsequent oscillations in the intracellular Ca^{2+}, as well as oscillations in metabolism and exocytosis. The coordination of the intricate activity on the multicellular level plays a key role in the regulation of physiological pulsatile insulin secretion and is incompletely understood. In this paper, we investigate theoretically the principles that give rise to the synchronized activity of beta cell populations by building up a phenomenological multicellular model that incorporates the basic features of beta cell dynamics. Specifically, the model is composed of coupled slow and fast oscillatory units that reflect metabolic processes and electrical activity, respectively. Using a realistic description of the intercellular interactions, we study how the combination of electrical and metabolic coupling generates collective rhythmicity and shapes functional beta cell networks. It turns out that while electrical coupling solely can synchronize the responses, the addition of metabolic interactions further enhances coordination, the spatial range of interactions increases the number of connections in the functional beta cell networks, and ensures a better consistency with experimental findings. Moreover, our computational results provide additional insights into the relationship between beta cell heterogeneity, their activity profiles, and functional connectivity, supplementing thereby recent experimental results on endocrine networks.

The simplified Kirchhoff network model (SKNM): a cell-based reaction-diffusion model of excitable tissue

Cell-based models of excitable tissues offer the advantage of cell-level precision, which cannot be achieved using traditional homogenized electrophysiological models. However, this enhanced accuracy comes at the cost of increased computational demands, necessitating the development of efficient cell-based models. The widely-accepted bidomain model serves as the standard in computational cardiac electrophysiology, and under certain anisotropy ratio conditions, it is well known that it can be reduced to the simpler monodomain model. Recently, the Kirchhoff Network Model (KNM) was developed as a cell-based counterpart to the bidomain model. In this paper, we aim to demonstrate that KNM can be simplified using the same steps employed to derive the monodomain model from the bidomain model. We present the cell-based Simplified Kirchhoff Network Model (SKNM), which produces results closely aligned with those of KNM while requiring significantly less computational resources.

Multilevel synchronization of human β-cells networks

β-cells within the endocrine pancreas are fundamental for glucose, lipid and protein homeostasis. Gap junctions between cells constitute the primary coupling mechanism through which cells synchronize their electrical and metabolic activities. This evidence is still only partially investigated through models and numerical simulations. In this contribution, we explore the effect of combined electrical and metabolic coupling in β-cell clusters using a detailed biophysical model. We add heterogeneity and stochasticity to realistically reproduce β-cell dynamics and study networks mimicking arrangements of β-cells within human pancreatic islets. Model simulations are performed over different couplings and heterogeneities, analyzing emerging synchronization at the membrane potential, calcium, and metabolites levels. To describe network synchronization, we use the formalism of multiplex networks and investigate functional network properties and multiplex synchronization motifs over the structural, electrical, and metabolic layers. Our results show that metabolic coupling can support slow wave propagation in human islets, that combined electrical and metabolic synchronization is realized in small aggregates, and that metabolic long-range correlation is more pronounced with respect to the electrical one.

A Supportive Role of Mesenchymal Stem Cells on Insulin-Producing Langerhans Islets with a Specific Emphasis on The Secretome

Type 1 Diabetes (T1D) is a chronic autoimmune disease characterized by a gradual destruction of insulin-producing β-cells in the endocrine pancreas due to innate and specific immune responses, leading to impaired glucose homeostasis. T1D patients usually require regular insulin injections after meals to maintain normal serum glucose levels. In severe cases, pancreas or Langerhans islet transplantation can assist in reaching a sufficient β-mass to normalize glucose homeostasis. The latter procedure is limited because of low donor availability, high islet loss, and immune rejection. There is still a need to develop new technologies to improve islet survival and implantation and to keep the islets functional. Mesenchymal stem cells (MSCs) are multipotent non-hematopoietic progenitor cells with high plasticity that can support human pancreatic islet function both in vitro and in vivo and islet co-transplantation with MSCs is more effective than islet transplantation alone in attenuating diabetes progression. The beneficial effect of MSCs on islet function is due to a combined effect on angiogenesis, suppression of immune responses, and secretion of growth factors essential for islet survival and function. In this review, various aspects of MSCs related to islet function and diabetes are described.

Functional characteristics of hub and wave-initiator cells in β cell networks

Islets of Langerhans operate as multicellular networks in which several hundred β cells work in synchrony to produce secretory pulses of insulin, a hormone crucial for controlling metabolic homeostasis. Their collective rhythmic activity is facilitated by gap junctional coupling and affected by their functional heterogeneity, but the details of this robust and coordinated behavior are still not fully understood. Recent advances in multicellular imaging and optogenetic and photopharmacological strategies, as well as in network science, have led to the discovery of specialized β cell subpopulations that were suggested to critically determine the collective dynamics in the islets. In particular hubs, i.e., β cells with many functional connections, are believed to significantly enhance communication capacities of the intercellular network and facilitate an efficient spreading of intercellular Ca2+ waves, whereas wave-initiator cells trigger intercellular signals in their cohorts. Here, we determined Ca2+ signaling characteristics of these two β cell subpopulations and the relationship between them by means of functional multicellular Ca2+ imaging in mouse pancreatic tissue slices in combination with methods of complex network theory. We constructed network layers based on individual Ca2+ waves to identify wave initiators, and functional correlation-based networks to detect hubs. We found that both cell types exhibit a higher-than-average active time under both physiological and supraphysiological glucose concentrations, but also that they differ significantly in many other functional characteristics. Specifically, Ca2+ oscillations in hubs are more regular, and their role appears to be much more stable over time than for initiator cells. Moreover, in contrast to wave initiators, hubs transmit intercellular signals faster than other cells, which implies a stronger intercellular coupling. Our research indicates that hubs and wave-initiator cell subpopulations are both natural features of healthy pancreatic islets, but their functional roles in principle do not overlap and should thus not be considered equal.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

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

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

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.

The effects of beta-cell mass and function, intercellular coupling, and islet synchrony on [Formula: see text] dynamics

Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a substantial loss of [Formula: see text]-cell mass and alteration of [Formula: see text]-cell function in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. The mechanisms for deficiency in [Formula: see text]-cell mass and function during the hyperglycemia development and T2D pathogenesis are complex. To study the relative contribution of [Formula: see text]-cell mass to [Formula: see text]-cell function in T2D, we make use of a comprehensive electrophysiological model of human [Formula: see text]-cell clusters. We find that defect in [Formula: see text]-cell mass causes a functional decline in single [Formula: see text]-cell, impairment in intra-islet synchrony, and changes in the form of oscillatory patterns of membrane potential and intracellular [Formula: see text] concentration, which can lead to changes in insulin secretion dynamics and in insulin levels. The model demonstrates a good correspondence between suppression of synchronizing electrical activity and published experimental measurements. We then compare the role of gap junction-mediated electrical coupling with both [Formula: see text]-cell synchronization and metabolic coupling in the behavior of [Formula: see text] concentration dynamics within human islets. Our results indicate that inter-[Formula: see text]-cellular electrical coupling depicts a more important factor in shaping the physiological regulation of islet function and in human T2D. We further predict that varying the whole-cell conductance of delayed rectifier [Formula: see text] channels modifies oscillatory activity patterns of [Formula: see text]-cell population lacking intercellular coupling, which significantly affect [Formula: see text] concentration and insulin secretion.

Assessing Different Temporal Scales of Calcium Dynamics in Networks of Beta Cell Populations

Beta cells within the pancreatic islets of Langerhans respond to stimulation with coherent oscillations of membrane potential and intracellular calcium concentration that presumably drive the pulsatile exocytosis of insulin. Their rhythmic activity is multimodal, resulting from networked feedback interactions of various oscillatory subsystems, such as the glycolytic, mitochondrial, and electrical/calcium components. How these oscillatory modules interact and affect the collective cellular activity, which is a prerequisite for proper hormone release, is incompletely understood. In the present work, we combined advanced confocal Ca2+ imaging in fresh mouse pancreas tissue slices with time series analysis and network science approaches to unveil the glucose-dependent characteristics of different oscillatory components on both the intra- and inter-cellular level. Our results reveal an interrelationship between the metabolically driven low-frequency component and the electrically driven high-frequency component, with the latter exhibiting the highest bursting rates around the peaks of the slow component and the lowest around the nadirs. Moreover, the activity, as well as the average synchronicity of the fast component, considerably increased with increasing stimulatory glucose concentration, whereas the stimulation level did not affect any of these parameters in the slow component domain. Remarkably, in both dynamical components, the average correlation decreased similarly with intercellular distance, which implies that intercellular communication affects the synchronicity of both types of oscillations. To explore the intra-islet synchronization patterns in more detail, we constructed functional connectivity maps. The subsequent comparison of network characteristics of different oscillatory components showed more locally clustered and segregated networks of fast oscillatory activity, while the slow oscillations were more global, resulting in several long-range connections and a more cohesive structure. Besides the structural differences, we found a relatively weak relationship between the fast and slow network layer, which suggests that different synchronization mechanisms shape the collective cellular activity in islets, a finding which has to be kept in mind in future studies employing different oscillations for constructing networks.

Biophysics and Modeling of Mechanotransduction in Neurons: A Review

Mechanosensing is a key feature through which organisms can receive inputs from the environment and convert them into specific functional and behavioral outputs. Mechanosensation occurs in many cells and tissues, regulating a plethora of molecular processes based on the distribution of forces and stresses both at the cell membrane and at the intracellular organelles levels, through complex interactions between cells’ microstructures, cytoskeleton, and extracellular matrix. Although several primary and secondary mechanisms have been shown to contribute to mechanosensation, a fundamental pathway in simple organisms and mammals involves the presence of specialized sensory neurons and the presence of different types of mechanosensitive ion channels on the neuronal cell membrane. In this contribution, we present a review of the main ion channels which have been proven to be significantly involved in mechanotransduction in neurons. Further, we discuss recent studies focused on the biological mechanisms and modeling of mechanosensitive ion channels’ gating, and on mechanotransduction modeling at different scales and levels of details.

Mata A, Godínez-Fernández JR. Reconstructing human pancreatic islet architectures using computational optimization

We outline a general methodology based on computational optimization and experimental data to reconstruct human pancreatic islet architectures. By using the nuclei coordinates of islet cells obtained through DAPI staining, cell types identified by immunostaining, and cell size distributions estimated from capacitance measurements, reconstructed islets composed of non-overlapping spherical cells were obtained through an iterative optimization procedure. In all cases, the reconstructed architectures included >99% of the experimental identified cells, each of them having a radius within the experimentally reported ranges. Given the wide use of mathematical modeling for the study of pancreatic cells, and recently, of cell-cell interactions within the pancreatic islets, the methodology here proposed, also capable of identifying cell-to-cell contacts, is aimed to provide with a framework for modeling and analyzing experimentally-based pancreatic islet architectures.

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

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

Biophysical modeling of C. elegans neurons: Single ion currents and whole-cell dynamics of AWCon and RMD

C. elegans neuronal system constitutes the ideal framework for studying simple, yet realistic, neuronal activity, since the whole nervous system is fully characterized with respect to the exact number of neurons and the neuronal connections. Most recent efforts are devoted to investigate and clarify the signal processing and functional connectivity, which are at the basis of sensing mechanisms, signal transmission, and motor control. In this framework, a refined modelof whole neuron dynamics constitutes a key ingredient to describe the electrophysiological processes, both at thecellular and at the network scale. In this work, we present Hodgkin-Huxley-based models of ion channels dynamics black, built on data available both from C. elegans and from other organisms, expressing homologous channels. We combine these channel models to simulate the electrical activity oftwo among the most studied neurons in C. elegans, which display prototypical dynamics of neuronal activation, the chemosensory AWCON and the motor neuron RMD. Our model properly describes the regenerative responses of the two cells. We analyze in detail the role of ion currents, both in wild type and in in silico knockout neurons. Moreover, we specifically investigate the behavior of RMD, identifying a heterogeneous dynamical response which includes bistable regimes and sustained oscillations. We are able to assess the critical role of T-type calcium currents, carried by CCA-1 channels, and leakage currents in the regulation of RMD response. Overall, our results provide new insights in the activity of key C. elegans neurons. The developed mathematical framework constitute a basis for single-cell and neuronal networks analyses, opening new scenarios in the in silico modeling of C. elegans neuronal system.

Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

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.

Investigation of the role of ion channels in human pancreatic β-cell hubs: A mathematical modeling study

In many cellular networks, the structure of the network follows a scale-free organization, where a limited number of cells are strongly coupled to other cells. These cells are called hub cells and their critical roles are well accepted. Despite their importance, there have been only a few studies investigating the characteristic features of these cells. In this paper, a computational approach is proposed to study the possible role of different ion channels in distinguishing between the hub and non-hub cells. The results show that the P/Q-type and T-type calcium channels may have an especial role in the β-cell hubs because the high-level expressions of these channels make a pancreatic β-cell more potent to force other coupled cells to follow it. In addition, in order to consider the variation of the coupling strength with voltage, a novel mathematical model is proposed for the gap junction coupling between the pancreatic β-cells. The proposed approach is validated based on the data from the literature.

Beta-cell hubs maintain Ca2+ oscillations in human and mouse islet simulations

Islet β-cells are responsible for secreting all circulating insulin in response to rising plasma glucose concentrations. These cells are a phenotypically diverse population that express great functional heterogeneity. In mice, certain β-cells (termed 'hubs') have been shown to be crucial for dictating the islet response to high glucose, with inhibition of these hub cells abolishing the coordinated Ca2+ oscillations necessary for driving insulin secretion. These β-cell hubs were found to be highly metabolic and susceptible to pro-inflammatory and glucolipotoxic insults. In this study, we explored the importance of hub cells in human by constructing mathematical models of Ca2+ activity in human islets. Our simulations revealed that hubs dictate the coordinated Ca2+ response in both mouse and human islets; silencing a small proportion of hubs abolished whole-islet Ca2+ activity. We also observed that if hubs are assumed to be preferentially gap junction coupled, then the simulations better adhere to the available experimental data. Our simulations of 16 size-matched mouse and human islet architectures revealed that there are species differences in the role of hubs; Ca2+ activity in human islets was more vulnerable to hub inhibition than mouse islets. These simulation results not only substantiate the existence of β-cell hubs, but also suggest that hubs may be favorably coupled in the electrical and metabolic network of the islet, and that targeted destruction of these cells would greatly impair human islet function.

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.

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

Key points

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

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

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

Abstract

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

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

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

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

Gap-junction coupling and ATP-sensitive potassium channels in human β-cell clusters: Effects on emergent dynamics

The importance of gap-junction coupling between β cells in pancreatic islets is well established in mouse. Such ultrastructural connections synchronize cellular activity, confine biological heterogeneity, and enhance insulin pulsatility. Dysfunction of coupling has been associated with diabetes and altered β-cell function. However, the role of gap junctions between human β cells is still largely unexplored. By using patch-clamp recordings of β cells from human donors, we previously estimated electrical properties of these channels by mathematical modeling of pairs of human β cells. In this work we revise our estimate by modeling triplet configurations and larger heterogeneous clusters. We find that a coupling conductance in the range 0.005-0.020 nS/pF can reproduce experiments in almost all the simulated arrangements. We finally explore the consequence of gap-junction coupling of this magnitude between β cells with mutant variants of the ATP-sensitive potassium channels involved in some metabolic disorders and diabetic conditions, translating studies performed on rodents to the human case. Our results are finally discussed from the perspective of therapeutic strategies. In summary, modeling of more realistic clusters with more than two β cells slightly lowers our previous estimate of gap-junction conductance and gives rise to patterns that more closely resemble experimental traces.

Decreases in Gap Junction Coupling Recovers Ca2+ and Insulin Secretion in Neonatal Diabetes Mellitus, Dependent on Beta Cell Heterogeneity and Noise

Diabetes is caused by dysfunction to β-cells in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. Gap junction-mediated electrical coupling between β-cells in the islet plays a major role in coordinating a pulsatile secretory response at elevated glucose and suppressing insulin secretion at basal glucose. Previously, we demonstrated that a critical number of inexcitable cells can rapidly suppress the overall islet response, as a result of gap junction coupling. This was demonstrated in a murine model of Neonatal Diabetes Mellitus (NDM) involving expression of ATP-insensitive K_ATP channels, and by a multi-cellular computational model of islet electrical activity. Here we examined the mechanisms by which gap junction coupling contributes to islet dysfunction in NDM. We first verified the computational model against [Ca²⁺] and insulin secretion measurements in islets expressing ATP-insensitive K_ATP channels under different levels of gap junction coupling. We then applied this model to predict how different K_ATP channel mutations found in NDM suppress [Ca²⁺], and the role of gap junction coupling in this suppression. We further extended the model to account for stochastic noise and insulin secretion dynamics. We found experimentally and in the islet model that reductions in gap junction coupling allow progressively greater glucose-stimulated [Ca²⁺] and insulin secretion following expression of ATP-insensitive K_ATP channels. The model demonstrated good correspondence between suppression of [Ca²⁺] and clinical presentation of different NDM mutations. Significant recoveries in [Ca²⁺] and insulin secretion were predicted for many mutations upon reductions in gap junction coupling, where stochastic noise played a significant role in the recoveries. These findings provide new understanding how the islet functions as a multicellular system and for the role of gap junction channels in exacerbating the effects of decreased cellular excitability. They further suggest novel therapeutic options for NDM and other monogenic forms of diabetes.

Diabetes is a disease reaching a global epidemic, which results from dysfunction to the islets of Langerhans in the pancreas and their ability to secrete the hormone insulin to regulate glucose homeostasis. Islets are multicellular structures that show extensive coupling between heterogeneous cellular units; and central to the causes of diabetes is a dysfunction to these cellular units and their interactions. Understanding the inter-relationship between structure and function is challenging in biological systems, but is crucial to the cause of disease and discovering therapeutic targets. With the goal of further characterizing the islet of Langerhans and its excitable behavior, we examined the role of important channels in the islet where dysfunction is linked to or causes diabetes. Advances in our ability to computationally model perturbations in physiological systems has allowed for the testing of hypothesis quickly, in systems that are not experimentally accessible. Using an experimentally validated model and modeling human mutations, we discover that monogenic forms of diabetes may be remedied by a reduction in electrical coupling between cells; either alone or in conjunction with pharmacological intervention. Knowledge of biological systems in general is also helped by these findings, in that small changes to cellular elements may lead to major disruptions in the overall system. This may then be overcome by allowing the system components to function independently in the presence of dysfunction to individual cells.