Investigating the role of islet cytoarchitecture in its oscillation using a new beta-cell cluster model

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.

A primer on modelling pancreatic islets: from models of coupled β-cells to multicellular islet models

Pancreatic islets are mini-organs composed of hundreds or thousands of ɑ, β and δ-cells, which, respectively, secrete glucagon, insulin and somatostatin, key hormones for the regulation of blood glucose. In pancreatic islets, hormone secretion is tightly regulated by both internal and external mechanisms, including electrical communication and paracrine signaling between islet cells. Given its complexity, the experimental study of pancreatic islets has been complemented with computational modeling as a tool to gain a better understanding about how all the mechanisms involved at different levels of organization interact. In this review, we describe how multicellular models of pancreatic cells have evolved from the early models of electrically coupled β-cells to models in which experimentally derived architectures and both electrical and paracrine signals have been considered.

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.

Determinants and dynamics of pancreatic islet architecture

The islets of Langerhans are highly organized structures that have species-specific, three-dimensional tissue architecture. Islet architecture is critical for proper hormone secretion in response to nutritional stimuli. Islet architecture is disrupted in all types of diabetes mellitus and in cadaveric islets for transplantation during isolation, culture, and perfusion, limiting patient outcomes. Moreover, recapitulating native islet architecture remains a key challenge for in vitro generation of islets from stem cells. In this review, we discuss work that has led to the current understanding of determinants of pancreatic islet architecture, and how this architecture is maintained or disrupted during tissue remodeling in response to normal and pathological metabolic changes. We further discuss both empirical and modeling data that highlight the importance of islet architecture for islet function.

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.

Reduced synchroneity of intra-islet Ca2+ oscillations in vivo in Robo-deficient β cells

The spatial architecture of the islets of Langerhans is hypothesized to facilitate synchronized insulin secretion among β cells, yet testing this in vivo in the intact pancreas is challenging. Robo βKO mice, in which the genes Robo1 and Robo2 are deleted selectively in β cells, provide a unique model of altered islet spatial architecture without loss of β cell differentiation or islet damage from diabetes. Combining Robo βKO mice with intravital microscopy, we show here that Robo βKO islets have reduced synchronized intra-islet Ca2+ oscillations among β cells in vivo. We provide evidence that this loss is not due to a β cell-intrinsic function of Robo, mis-expression or mis-localization of Cx36 gap junctions, or changes in islet vascularization or innervation, suggesting that the islet architecture itself is required for synchronized Ca2+ oscillations. These results have implications for understanding structure-function relationships in the islets during progression to diabetes as well as engineering islets from stem cells.

Flipping the switch on the hub cell: Islet desynchronization through cell silencing

Pancreatic β cells, responsible for secreting insulin into the bloodstream and maintaining glucose homeostasis, are organized in the islets of Langerhans as clusters of electrically coupled cells. Gap junctions, connecting neighboring cells, coordinate the behavior of the islet, leading to the synchronized oscillations in the intracellular calcium and insulin secretion in healthy islets. Recent experimental work has shown that silencing special hub cells can lead to a disruption in the coordinated behavior, calling into question the democratic paradigm of islet insulin secretion with more or less equal input from each β cell. Islets were shown to have scale-free functional connectivity and a hub cell whose silencing would lead to a loss of functional connectivity and activity in the islet. A mechanistic model representing the electrical and calcium dynamics of β cells during insulin secretion was applied to a network of cells connected by gap junctions to test the hypothesis of hub cells. Functional connectivity networks were built from the simulated calcium traces, with some networks classified as scale-free, confirming experimental results. Potential hub cells were identified using previously defined centrality measures, but silencing them was unable to desynchronize the islet. Instead, switch cells, which were able to turn off the activity of the islet but were not highly functionally connected, were found via systematically silencing each cell in the network.

Microwell Scaffolds Using Collagen-IV and Laminin-111 Lead to Improved Insulin Secretion of Human Islets

IMPACT STATEMENT

This research deals with finding a proper bioengineering strategy to improve the outcome of islets transplantation for treatment of type 1 diabetes. It is focused on the mimicking of islet extracellular matrix niche in microwell islet delivery devices to improve their endocrine function.

How Heterogeneity in Glucokinase and Gap-Junction Coupling Determines the Islet [Ca2+] Response

Understanding how cell subpopulations in a tissue impact overall system function is challenging. There is extensive heterogeneity among insulin-secreting β-cells within islets of Langerhans, including their insulin secretory response and gene expression profile, and this heterogeneity can be altered in diabetes. Several studies have identified variations in nutrient sensing between β-cells, including glucokinase (GK) levels, mitochondrial function, or expression of genes important for glucose metabolism. Subpopulations of β-cells with defined electrical properties can disproportionately influence islet-wide free-calcium activity ([Ca2+]) and insulin secretion via gap-junction electrical coupling. However, it is poorly understood how subpopulations of β-cells with altered glucose metabolism may impact islet function. To address this, we utilized a multicellular computational model of the islet in which a population of cells deficient in GK activity and glucose metabolism was imposed on the islet or in which β-cells were heterogeneous in glucose metabolism and GK kinetics were altered. This included simulating GK gene (GCK) mutations that cause monogenic diabetes. We combined these approaches with experimental models in which gck was genetically deleted in a population of cells or GK was pharmacologically inhibited. In each case, we modulated gap-junction electrical coupling. Both the simulated islet and the experimental system required 30-50% of the cells to have near-normal glucose metabolism, fewer than cells with normal KATP conductance. Below this number, the islet lacked any glucose-stimulated [Ca2+] elevations. In the absence of electrical coupling, the change in [Ca2+] was more gradual. As such, electrical coupling allows a large minority of cells with normal glucose metabolism to promote glucose-stimulated [Ca2+]. If insufficient numbers of cells are present, which we predict can be caused by a subset of GCK mutations that cause monogenic diabetes, electrical coupling exacerbates [Ca2+] suppression. This demonstrates precisely how metabolically heterogeneous β-cell populations interact to impact islet function.

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.

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.

Fibronectin and Collagen IV Microcontact Printing Improves Insulin Secretion by INS1E Cells

IMPACT STATEMENT

This research deals with finding a proper bioengineering strategy for the creation of improved β-cell replacement therapy in type 1 diabetes. It specifically deals with the microenvironment of β-cells and its relationship to their endocrine function.

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.

Critical and Supercritical Spatiotemporal Calcium Dynamics in Beta Cells

A coordinated functioning of beta cells within pancreatic islets is mediated by oscillatory membrane depolarization and subsequent changes in cytoplasmic calcium concentration. While gap junctions allow for intraislet information exchange, beta cells within islets form complex syncytia that are intrinsically nonlinear and highly heterogeneous. To study spatiotemporal calcium dynamics within these syncytia, we make use of computational modeling and confocal high-speed functional multicellular imaging. We show that model predictions are in good agreement with experimental data, especially if a high degree of heterogeneity in the intercellular coupling term is assumed. In particular, during the first few minutes after stimulation, the probability distribution of calcium wave sizes is characterized by a power law, thus indicating critical behavior. After this period, the dynamics changes qualitatively such that the number of global intercellular calcium events increases to the point where the behavior becomes supercritical. To better mimic normal in vivo conditions, we compare the described behavior during supraphysiological non-oscillatory stimulation with the behavior during exposure to a slightly lower and oscillatory glucose challenge. In the case of this protocol, we observe only critical behavior in both experiment and model. Our results indicate that the loss of oscillatory changes, along with the rise in plasma glucose observed in diabetes, could be associated with a switch to supercritical calcium dynamics and loss of beta cell functionality.

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.

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.

The Different Faces of the Pancreatic Islet

Type 1 diabetes (T1D) patients who receive pancreatic islet transplant experience significant improvement in their quality-of-life. This comes primarily through improved control of blood sugar levels, restored awareness of hypoglycemia, and prevention of serious and potentially life-threatening diabetes-associated complications, such as kidney failure, heart and vascular disease, stroke, nerve damage, and blindness. Therefore, beta cell replacement through transplantation of isolated islets is an important option in the treatment of T1D. However, lasting success of this promising therapy depends on durable survival and efficacy of the transplanted islets, which are directly influenced by the islet isolation procedures. Thus, isolating pancreatic islets with consistent and reliable quality is critical in the clinical application of islet transplantation.Quality of isolated islets is important in pre-clinical studies as well, as efforts to advance and improve clinical outcomes of islet transplant therapy have relied heavily on animal models ranging from rodents, to pigs, to nonhuman primates. As a result, pancreatic islets have been isolated from these and other species and used in a variety of in vitro or in vivo applications for this and other research purposes. Protocols for islet isolation have been somewhat similar across species, especially, in mammals. However, given the increasing evidence about the distinct structural and functional features of human and mouse islets, using similar methods of islet isolation may contribute to inconsistencies in the islet quality, immunogenicity, and experimental outcomes. This may also contribute to the discrepancies commonly observed between pre-clinical findings and clinical outcomes. Therefore, it is prudent to consider the particular features of pancreatic islets from different species when optimizing islet isolation protocols.In this chapter, we explore the structural and functional features of pancreatic islets from mice, pigs, nonhuman primates, and humans because of their prevalent use in nonclinical, preclinical, and clinical applications.

Heterogeneity and nearest-neighbor coupling can explain small-worldness and wave properties in pancreatic islets

Many multicellular systems consist of coupled cells that work as a syncytium. The pancreatic islet of Langerhans is a well-studied example of such a microorgan. The islets are responsible for secretion of glucose-regulating hormones, mainly glucagon and insulin, which are released in distinct pulses. In order to observe pulsatile insulin secretion from the β-cells within the islets, the cellular responses must be synchronized. It is now well established that gap junctions provide the electrical nearest-neighbor coupling that allows excitation waves to spread across islets to synchronize the β-cell population. Surprisingly, functional coupling analysis of calcium responses in β-cells shows small-world properties, i.e., a high degree of local coupling with a few long-range "short-cut" connections that reduce the average path-length greatly. Here, we investigate how such long-range functional coupling can appear as a result of heterogeneity, nearest-neighbor coupling, and wave propagation. Heterogeneity is also able to explain a set of experimentally observed synchronization and wave properties without introducing all-or-none cell coupling and percolation theory. Our theoretical results highlight how local biological coupling can give rise to functional small-world properties via heterogeneity and wave propagation.

Design Principles of Pancreatic Islets: Glucose-Dependent Coordination of Hormone Pulses

Pancreatic islets are functional units involved in glucose homeostasis. The multicellular system comprises three main cell types; β and α cells reciprocally decrease and increase blood glucose by producing insulin and glucagon pulses, while the role of δ cells is less clear. Although their spatial organization and the paracrine/autocrine interactions between them have been extensively studied, the functional implications of the design principles are still lacking. In this study, we formulated a mathematical model that integrates the pulsatility of hormone secretion and the interactions and organization of islet cells and examined the effects of different cellular compositions and organizations in mouse and human islets. A common feature of both species was that islet cells produced synchronous hormone pulses under low- and high-glucose conditions, while they produced asynchronous hormone pulses under normal glucose conditions. However, the synchronous coordination of insulin and glucagon pulses at low glucose was more pronounced in human islets that had more α cells. When β cells were selectively removed to mimic diabetic conditions, the anti-synchronicity of insulin and glucagon pulses was deteriorated at high glucose, but it could be partially recovered when the re-aggregation of remaining cells was considered. Finally, the third cell type, δ cells, which introduced additional complexity in the multicellular system, prevented the excessive synchronization of hormone pulses. Our computational study suggests that controllable synchronization is a design principle of pancreatic islets.

Development, growth and maintenance of β-cell mass: models are also part of the story

Pancreatic β-cells in the islets of Langerhans play a crucial role in regulating glucose homeostasis in the circulation. Loss of β-cell mass or function due to environmental, genetic and immunological factors leads to the manifestation of diabetes mellitus. The mechanisms regulating the dynamics of pancreatic β-cell mass during normal development and diabetes progression are complex. To fully unravel such complexity, experimental and clinical approaches need to be combined with mathematical and computational models. In the natural sciences, mathematical and computational models have aided the identification of key mechanisms underlying the behavior of systems comprising multiple interacting components. A number of mathematical and computational models have been proposed to explain the development, growth and death of pancreatic β-cells. In this review, we discuss some of these models and how their predictions provide novel insight into the mechanisms controlling β-cell mass during normal development and diabetes progression. Lastly, we discuss a handful of the major open questions in the field.

Time-stepping techniques to enable the simulation of bursting behavior in a physiologically realistic computational islet

Physiologically realistic simulations of computational islets of beta cells require the long-time solution of several thousands of coupled ordinary differential equations (ODEs), resulting from the combination of several ODEs in each cell and realistic numbers of several hundreds of cells in an islet. For a reliable and accurate solution of complex nonlinear models up to the desired final times on the scale of several bursting periods, an appropriate ODE solver designed for stiff problems is eventually a necessity, since other solvers may not be able to handle the problem or are exceedingly inefficient. But stiff solvers are potentially significantly harder to use, since their algorithms require at least an approximation of the Jacobian matrix. For sophisticated models, systems of several complex ODEs in each cell, it is practically unworkable to differentiate these intricate nonlinear systems analytically and to manually program the resulting Jacobian matrix in computer code. This paper demonstrates that automatic differentiation can be used to obtain code for the Jacobian directly from code for the ODE system, which allows a full accounting for the sophisticated model equations. This technique is also feasible in source-code languages Fortran and C, and the conclusions apply to a wide range of systems of coupled, nonlinear reaction equations. However, when we combine an appropriately supplied Jacobian with slightly modified memory management in the ODE solver, simulations on the realistic scale of one thousand cells in the islet become possible that are several orders of magnitude faster than the original solver in the software Matlab, a language that is particularly user friendly for programming complicated model equations. We use the efficient simulator to analyze electrical bursting and show non-monotonic average burst period between fast and slow cells for increasing coupling strengths. We also find that interestingly, the arrangement of the connected fast and slow heterogeneous cells impacts the peak bursting period monotonically.

Phase transitions in the multi-cellular regulatory behavior of pancreatic islet excitability

The pancreatic islets of Langerhans are multicellular micro-organs integral to maintaining glucose homeostasis through secretion of the hormone insulin. β-cells within the islet exist as a highly coupled electrical network which coordinates electrical activity and insulin release at high glucose, but leads to global suppression at basal glucose. Despite its importance, how network dynamics generate this emergent binary on/off behavior remains to be elucidated. Previous work has suggested that a small threshold of quiescent cells is able to suppress the entire network. By modeling the islet as a Boolean network, we predicted a phase-transition between globally active and inactive states would emerge near this threshold number of cells, indicative of critical behavior. This was tested using islets with an inducible-expression mutation which renders defined numbers of cells electrically inactive, together with pharmacological modulation of electrical activity. This was combined with real-time imaging of intracellular free-calcium activity [Ca²⁺]_i and measurement of physiological parameters in mice. As the number of inexcitable cells was increased beyond ∼15%, a phase-transition in islet activity occurred, switching from globally active wild-type behavior to global quiescence. This phase-transition was also seen in insulin secretion and blood glucose, indicating physiological impact. This behavior was reproduced in a multicellular dynamical model suggesting critical behavior in the islet may obey general properties of coupled heterogeneous networks. This study represents the first detailed explanation for how the islet facilitates inhibitory activity in spite of a heterogeneous cell population, as well as the role this plays in diabetes and its reversal. We further explain how islets utilize this critical behavior to leverage cellular heterogeneity and coordinate a robust insulin response with high dynamic range. These findings also give new insight into emergent multicellular dynamics in general which are applicable to many coupled physiological systems, specifically where inhibitory dynamics result from coupled networks.

As science has successfully broken down the elements of many biological systems, the network dynamics of large-scale cellular interactions has emerged as a new frontier. One way to understand how dynamical elements within large networks behave collectively is via mathematical modeling. Diabetes, which is of increasing international concern, is commonly caused by a deterioration of these complex dynamics in a highly coupled micro-organ called the islet of Langerhans. Therefore, if we are to understand diabetes and how to treat it, we must understand how coupling affects ensemble dynamics. While the role of network connectivity in islet excitation under stimulatory conditions has been well studied, how connectivity also suppresses activity under fasting conditions remains to be elucidated. Here we use two network models of islet connectivity to investigate this process. Using genetically altered islets and pharmacological treatments, we show how suppression of islet activity is solely dependent on a threshold number of inactive cells. We found that the islet exhibits critical behavior in the threshold region, rapidly transitioning from global activity to inactivity. We therefore propose how the islet and multicellular systems in general can generate a robust stimulated response from a heterogeneous cell population.

Dimensionality and size scaling of coordinated Ca(2+) dynamics in MIN6 β-cell clusters

Pancreatic islets of Langerhans regulate blood glucose homeostasis by the secretion of the hormone insulin. Like many neuroendocrine cells, the coupling between insulin-secreting β-cells in the islet is critical for the dynamics of hormone secretion. We have examined how this coupling architecture regulates the electrical dynamics that underlie insulin secretion by utilizing a microwell-based aggregation method to generate clusters of a β-cell line with defined sizes and dimensions. We measured the dynamics of free-calcium activity ([Ca(2+)]i) and insulin secretion and compared these measurements with a percolating network model. We observed that the coupling dimension was critical for regulating [Ca(2+)]i dynamics and insulin secretion. Three-dimensional coupling led to size-invariant suppression of [Ca(2+)]i at low glucose and robust synchronized [Ca(2+)]i oscillations at elevated glucose, whereas two-dimensional coupling showed poor suppression and less robust synchronization, with significant size-dependence. The dimension- and size-scaling of [Ca(2+)]i at high and low glucose could be accurately described with the percolating network model, using similar network connectivity. As such this could explain the fundamentally different behavior and size-scaling observed under each coupling dimension. This study highlights the dependence of proper β-cell function on the coupling architecture that will be important for developing therapeutic treatments for diabetes such as islet transplantation techniques. Furthermore, this will be vital to gain a better understanding of the general features by which cellular interactions regulate coupled multicellular systems.

Scaffold architecture controls insulinoma clustering, viability, and insulin production

Recently, in vitro diagnostic tools have shifted focus toward personalized medicine by incorporating patient cells into traditional test beds. These cell-based platforms commonly utilize two-dimensional substrates that lack the ability to support three-dimensional cell structures seen in vivo. As monolayer cell cultures have previously been shown to function differently than cells in vivo, the results of such in vitro tests may not accurately reflect cell response in vivo. It is therefore of interest to determine the relationships between substrate architecture, cell structure, and cell function in 3D cell-based platforms. To investigate the effect of substrate architecture on insulinoma organization and function, insulinomas were seeded onto 2D gelatin substrates and 3D fibrous gelatin scaffolds with three distinct fiber diameters and fiber densities. Cell viability and clustering was assessed at culture days 3, 5, and 7 with baseline insulin secretion and glucose-stimulated insulin production measured at day 7. Small, closely spaced gelatin fibers promoted the formation of large, rounded insulinoma clusters, whereas monolayer organization and large fibers prevented cell clustering and reduced glucose-stimulated insulin production. Taken together, these data show that scaffold properties can be used to control the organization and function of insulin-producing cells and may be useful as a 3D test bed for diabetes drug development.

Phase transitions in pancreatic islet cellular networks and implications for type-1 diabetes

In many aspects the onset of a chronic disease resembles a phase transition in a complex dynamic system: Quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. In this study we examine a special case, the onset of type-1 diabetes (T1D), a disease that results from loss of the insulin-producing pancreatic islet β cells. Within each islet, the β cells are electrically coupled to each other via gap-junctional channels. This intercellular coupling enables the β cells to synchronize their insulin release, thereby generating the multiscale temporal rhythms in blood insulin that are critical to maintaining blood glucose homeostasis. Using percolation theory we show how normal islet function is intrinsically linked to network connectivity. In particular, the critical amount of β-cell death at which the islet cellular network loses site percolation is consistent with laboratory and clinical observations of the threshold loss of β cells that causes islet functional failure. In addition, numerical simulations confirm that the islet cellular network needs to be percolated for β cells to synchronize. Furthermore, the interplay between site percolation and bond strength predicts the existence of a transient phase of islet functional recovery after onset of T1D and introduction of treatment, potentially explaining the honeymoon phenomenon. Based on these results, we hypothesize that the onset of T1D may be the result of a phase transition of the islet β-cell network.

Functional connectivity in islets of Langerhans from mouse pancreas tissue slices

We propose a network representation of electrically coupled beta cells in islets of Langerhans. Beta cells are functionally connected on the basis of correlations between calcium dynamics of individual cells, obtained by means of confocal laser-scanning calcium imaging in islets from acute mouse pancreas tissue slices. Obtained functional networks are analyzed in the light of known structural and physiological properties of islets. Focusing on the temporal evolution of the network under stimulation with glucose, we show that the dynamics are more correlated under stimulation than under non-stimulated conditions and that the highest overall correlation, largely independent of Euclidean distances between cells, is observed in the activation and deactivation phases when cells are driven by the external stimulus. Moreover, we find that the range of interactions in networks during activity shows a clear dependence on the Euclidean distance, lending support to previous observations that beta cells are synchronized via calcium waves spreading throughout islets. Most interestingly, the functional connectivity patterns between beta cells exhibit small-world properties, suggesting that beta cells do not form a homogeneous geometric network but are connected in a functionally more efficient way. Presented results provide support for the existing knowledge of beta cell physiology from a network perspective and shed important new light on the functional organization of beta cell syncitia whose structural topology is probably not as trivial as believed so far.

Size-controlled insulin-secreting cell clusters

The search for an effective cure for type I diabetes from the transplantation of encapsulated pancreatic β-cell clusters has so far produced sub-optimal clinical outcomes. Previous efforts have not controlled the size of transplanted clusters, a parameter implicated in affecting long-term viability and the secretion of therapeutically sufficient insulin. Here we demonstrate a method based on covalent attachment of patterned laminin for fabricating uniformly size-controlled insulin-secreting cell clusters. We show that cluster size within the range 40-120μm in diameter affects a variety of therapeutically relevant cellular responses including insulin expression, content and secretion. Our studies elucidate two size-dependent phenomena: (1) as the cluster size increases from 40μm to 60μm, glucose stimulation results in a greater amount of insulin produced per cell; and (2) as the cluster size increases beyond 60μm, sustained glucose stimulation results in a greater amount of insulin secreted per cell. Our study describes a method for producing uniformly sized insulin-secreting cell clusters, and since larger cluster sizes risk nutrient availability limitations, our data suggest that 100-120μm clusters may provide optimal viability and efficacy for encapsulated β-cell transplants as a treatment for type I diabetes and that further in vivo evaluation is warranted.

Mathematical modeling of insulin secretion and the role of glucose-dependent mobilization, docking, priming and fusion of insulin granules

In this paper we develop a new mathematical model of glucose-induced insulin secretion from pancreatic islet β-cells, and we use this model to investigate the rate limiting factors. We assume that insulin granules reside in different pools inside each β-cell, and that all β-cells respond homogeneously to glucose with the same recruitment thresholds. Consistent with recent experimental observations, our model also accounts for the fusion of newcomer granules that are not pre-docked at the plasma membrane. In response to a single step increase in glucose concentration, our model reproduces the characteristic biphasic insulin release observed in multiple experimental systems, including perfused pancreata and isolated islets of rodent or human origin. From our model analysis we note that first-phase insulin secretion depends on rapid depletion of the primed, release-ready granule pools, while the second phase relies on granule mobilization from the reserve. Moreover, newcomers have the potential to contribute significantly to the second phase. When the glucose protocol consists of multiple changes in sequence (a so-called glucose staircase), our model predicts insulin spikes of increasing height, as has been seen experimentally. This increase stems from the glucose-dependent increase in the fusion rate of insulin granules at the plasma membrane of single β-cells. In contrast, previous mathematical models reproduced the staircase experiment by assuming heterogeneous β-cell activation. In light of experimental data indicating limited heterogeneous activation for β-cells within intact islets, our findings suggest that a graded, dose-dependent cell response to glucose may contribute to insulin secretion patterns observed in multiple experiments, and thus regulate in vivo insulin release. In addition, the strength of insulin granule mobilization, priming and fusion are critical limiting factors in determining the total amount of insulin release.

Functional imaging of glucose-evoked rat islet activities using transient intrinsic optical signals

We demonstrate intrinsic optical signal (IOS) imaging of intact rat islet, which consists of many endocrine cells working together. A near-infrared digital microscope was employed for optical monitoring of islet activities evoked by glucose stimulation. Dynamic NIR images revealed transient IOS responses in the islet activated by low-dose (2.75mM) and high-dose (5.5mM) glucose stimuli. Comparative experiments and quantitative analysis indicated that both glucose metabolism and calcium/insulin dynamics might contribute to the observed IOS responses. Further investigation of the IOS imaging technology may provide a high resolution method for ex vivo functional examination of the islet, which is important for advanced study of diabetes associated islet dysfunctions and for improved quality control of donor islets for transplantation.

Intrinsic optical signal imaging of glucose-stimulated insulin secreting β-cells

Simultaneous monitoring of many functioning β-cells is essential for understanding β-cell dysfunction as an early event in the progression to diabetes. Intrinsic optical signal (IOS) imaging has been shown to allow high resolution detection of stimulus-evoked physiological responses in the retina and other neural tissues. In this paper, we demonstrate the feasibility of using IOS imaging for functional examination of insulin secreting INS-1 cells, a popular model for investigating diabetes associated β-cell dysfunction. Our experiments indicate that IOS imaging permits simultaneous monitoring of glucose-stimulated physiological responses in multiple cells with high spatial (sub-cellular) and temporal (sub-second) resolution. Rapid IOS image sequences revealed transient optical responses that had time courses tightly correlated with the glucose stimulation.

Patterning of mono- and multilayered pancreatic beta-cell clusters

Cluster-size dependent behavior of pancreatic beta-cells has direct implications in islet transplantation therapy for type I diabetes treatment. Control over the cluster size enables evaluation of cluster-size-dependent function, ultimately leading to the production of beta-cell clusters with improved transplant efficacy. This work for the first time demonstrates the use of microcontact-printing-based cell patterning of discrete two- and three-dimensional clusters of pancreatic beta-cells. Both single and multiple cell layers are confined to a 2D area by attaching to patterns of covalently linked laminin and not adhering to surrounding polyethylene glycol. Cell clusters were successfully formed within 24 h for printed patterns in the range 40-120 microm, and simple modulation of the initial cell seeding density leads to the formation of multiple cell layers. Semiquantitative fluorescence microscopy, X-ray photoelectron spectroscopy, and Fourier transform infrared spectroscopy were used to extensively characterize the surface chemistry. This technique offers exceptional control over cell cluster shape and size, and not only provides an effective tool to study the cluster-size-dependent behavior of pancreatic beta-cells but also has potential applicability to numerous other cell lines.

The hyperbolic effect of density and strength of inter beta-cell coupling on islet bursting: a theoretical investigation

BACKGROUND

Insulin, the principal regulating hormone of blood glucose, is released through the bursting of the pancreatic islets. Increasing evidence indicates the importance of islet morphostructure in its function, and the need of a quantitative investigation. Recently we have studied this problem from the perspective of islet bursting of insulin, utilizing a new 3D hexagonal closest packing (HCP) model of islet structure that we have developed. Quantitative non-linear dependence of islet function on its structure was found. In this study, we further investigate two key structural measures: the number of neighboring cells that each beta-cell is coupled to, nc, and the coupling strength, gc.

RESULTS

BETA-cell clusters of different sizes with number of beta-cells nbeta ranging from 1-343, nc from 0-12, and gc from 0-1000 pS, were simulated. Three functional measures of islet bursting characteristics--fraction of bursting beta-cells fb, synchronization index lambda, and bursting period Tb, were quantified. The results revealed a hyperbolic dependence on the combined effect of nc and gc. From this we propose to define a dimensionless cluster coupling index or CCI, as a composite measure for islet morphostructural integrity. We show that the robustness of islet oscillatory bursting depends on CCI, with all three functional measures fb, lambda and Tb increasing monotonically with CCI when it is small, and plateau around CCI = 1.

CONCLUSION

CCI is a good islet function predictor. It has the potential of linking islet structure and function, and providing insight to identify therapeutic targets for the preservation and restoration of islet beta-cell mass and function.