Progressive glucose stimulation of islet beta cells reveals a transition from segregated to integrated modular functional connectivity patterns

Sex-dependent intra-islet structural rearrangements affecting alpha-to-beta cell interactions lead to adaptive enhancements of Ca2+ dynamics in prediabetic beta cells

AIMS/HYPOTHESIS

Prediabetic pancreatic beta cells can adapt their function to maintain normoglycaemia for a limited period of time, after which diabetes mellitus will manifest upon beta cell exhaustion. Understanding sex-specific beta cell compensatory mechanisms and their failure in prediabetes (impaired glucose tolerance) is crucial for early disease diagnosis and individualised treatment. Our aims were as follows: (1) to determine the key time points of the progression from beta cells' functional adaptations to their failure in vivo; and (2) to mechanistically explain in vivo sex-specific beta cell compensatory mechanisms and their failure in prediabetes.

METHODS

Islets from male and female transgenic Ins1CreERT2-GCaMP3 mice were transplanted into the anterior chamber of the eye of 10- to 12-week-old sex-matched C57BL/6J mice. Recipient mice were fed either a control diet (CD) or western diet (WD) for a maximum of 4 months. Metabolic variables were evaluated monthly. Beta cell cytoplasmic free calcium concentration ([Ca2+]i) dynamics were monitored in vivo longitudinally by image fluorescence of the GCaMP3 reporter islets. Global islet beta cell [Ca2+]i dynamics in line with single beta cell [Ca2+]i analysis were used for beta cell coordination studies. The glucagon receptor antagonist L-168,049 (4 mmol/l) was applied topically to the transplanted eyes to evaluate in vivo the effect of glucagon on beta cell [Ca2+]idynamics. Human islets from non-diabetic women and men were cultured for 24 h in either a control medium or high-fat/high-glucose medium in the presence or absence of the glucagon receptor antagonist L-168,049. [Ca2+]i dynamics of human islets were evaluated in vitro after 1 h exposure to Fura-10.

RESULTS

Mice fed a WD for 1 month displayed increased beta cell [Ca2+]i dynamics linked to enhanced insulin secretion as a functional compensatory mechanism in prediabetes. Recruitment of inactive beta cells in WD-fed mice explained the improved beta cell function adaptation observed in vivo; this occurred in a sex-specific manner. Mechanistically, this was attributable to an intra-islet structural rearrangement involving alpha cells. These sex-dependent cytoarchitecture reorganisations, observed in both mice and humans, induced enhanced paracrine input from adjacent alpha cells, adjusting the glucose setpoint and amplifying the insulin secretion pathway. When WD feeding was prolonged, female mice maintained the adaptive mechanism due to their intrinsically high proportion of alpha cells. In males, [Ca2+]i dynamics progressively declined subsequent to glucose stimulation while insulin secretion continue to increase, suggesting uncoordinated beta cell function as an early sign of diabetes.

CONCLUSIONS/INTERPRETATION

We identified increased coordination of [Ca2+]i dynamics as a beta cell functional adaptation mechanisms in prediabetes. Importantly, we uncovered the mechanisms by which sex-dependent beta cell [Ca2+]i dynamics coordination is orchestrated by an intra-islet structure reorganisation increasing the paracrine input from alpha cells on beta cell function. Moreover, we identified reduced [Ca2+]i dynamics coordination in response to glucose as an early sign of diabetes preceding beta cell secretory dysfunction, with males being more vulnerable. Alterations in coordination capacity of [Ca2+]i dynamics may thus serve as an early marker for beta cell failure in prediabetes.

Network representation of multicellular activity in pancreatic islets: Technical considerations for functional connectivity analysis

Within the islets of Langerhans, beta cells orchestrate synchronized insulin secretion, a pivotal aspect of metabolic homeostasis. Despite the inherent heterogeneity and multimodal activity of individual cells, intercellular coupling acts as a homogenizing force, enabling coordinated responses through the propagation of intercellular waves. Disruptions in this coordination are implicated in irregular insulin secretion, a hallmark of diabetes. Recently, innovative approaches, such as integrating multicellular calcium imaging with network analysis, have emerged for a quantitative assessment of the cellular activity in islets. However, different groups use distinct experimental preparations, microscopic techniques, apply different methods to process the measured signals and use various methods to derive functional connectivity patterns. This makes comparisons between findings and their integration into a bigger picture difficult and has led to disputes in functional connectivity interpretations. To address these issues, we present here a systematic analysis of how different approaches influence the network representation of islet activity. Our findings show that the choice of methods used to construct networks is not crucial, although care is needed when combining data from different islets. Conversely, the conclusions drawn from network analysis can be heavily affected by the pre-processing of the time series, the type of the oscillatory component in the signals, and by the experimental preparation. Our tutorial-like investigation aims to resolve interpretational issues, reconcile conflicting views, advance functional implications, and encourage researchers to adopt connectivity analysis. As we conclude, we outline challenges for future research, emphasizing the broader applicability of our conclusions to other tissues exhibiting complex multicellular dynamics.

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.

β-cell intrinsic dynamics rather than gap junction structure dictates subpopulations in the islet functional network

Diabetes is caused by the inability of electrically coupled, functionally heterogeneous β-cells within the pancreatic islet to provide adequate insulin secretion. Functional networks have been used to represent synchronized oscillatory [Ca2+] dynamics and to study β-cell subpopulations, which play an important role in driving islet function. The mechanism by which highly synchronized β-cell subpopulations drive islet function is unclear. We used experimental and computational techniques to investigate the relationship between functional networks, structural (gap junction) networks, and intrinsic β-cell dynamics in slow and fast oscillating islets. Highly synchronized subpopulations in the functional network were differentiated by intrinsic dynamics, including metabolic activity and KATP channel conductance, more than structural coupling. Consistent with this, intrinsic dynamics were more predictive of high synchronization in the islet functional network as compared to high levels of structural coupling. Finally, dysfunction of gap junctions, which can occur in diabetes, caused decreases in the efficiency and clustering of the functional network. These results indicate that intrinsic dynamics rather than structure drive connections in the functional network and highly synchronized subpopulations, but gap junctions are still essential for overall network efficiency. These findings deepen our interpretation of functional networks and the formation of functional subpopulations in dynamic tissues such as the islet.

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.

The effect of forskolin and the role of Epac2A during activation, activity, and deactivation of beta cell networks

Beta cells couple stimulation by glucose with insulin secretion and impairments in this coupling play a central role in diabetes mellitus. Cyclic adenosine monophosphate (cAMP) amplifies stimulus-secretion coupling via protein kinase A and guanine nucleotide exchange protein 2 (Epac2A). With the present research, we aimed to clarify the influence of cAMP-elevating diterpene forskolin on cytoplasmic calcium dynamics and intercellular network activity, which are two of the crucial elements of normal beta cell stimulus-secretion coupling, and the role of Epac2A under normal and stimulated conditions. To this end, we performed functional multicellular calcium imaging of beta cells in mouse pancreas tissue slices after stimulation with glucose and forskolin in wild-type and Epac2A knock-out mice. Forskolin evoked calcium signals in otherwise substimulatory glucose and beta cells from Epac2A knock-out mice displayed a faster activation. During the plateau phase, beta cells from Epac2A knock-out mice displayed a slightly higher active time in response to glucose compared with wild-type littermates, and stimulation with forskolin increased the active time via an increase in oscillation frequency and a decrease in oscillation duration in both Epac2A knock-out and wild-type mice. Functional network properties during stimulation with glucose did not differ in Epac2A knock-out mice, but the presence of Epac2A was crucial for the protective effect of stimulation with forskolin in preventing a decline in beta cell functional connectivity with time. Finally, stimulation with forskolin prolonged beta cell activity during deactivation, especially in Epac2A knock-out mice.

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

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

High-resolution analysis of the cytosolic Ca2+ events in β cell collectives in situ

The release of peptide hormones is predominantly regulated by a transient increase in cytosolic Ca2+ concentration ([Ca2+]c). To trigger exocytosis, Ca2+ ions enter the cytosol from intracellular Ca2+ stores or from the extracellular space. The molecular events of late stages of exocytosis, and their dependence on [Ca2+]c, were extensively described in isolated single cells from various endocrine glands. Notably, less work has been done on endocrine cells in situ to address the heterogeneity of [Ca2+]c events contributing to a collective functional response of a gland. For this, β cell collectives in a pancreatic islet are particularly well suited as they are the smallest, experimentally manageable functional unit, where [Ca2+]c dynamics can be simultaneously assessed on both cellular and collective level. Here, we measured [Ca2+]c transients across all relevant timescales, from a subsecond to a minute time range, using high-resolution imaging with a low-affinity Ca2+ sensor. We quantified the recordings with a novel computational framework for automatic image segmentation and [Ca2+]c event identification. Our results demonstrate that under physiological conditions the duration of [Ca2+]c events is variable, and segregated into three reproducible modes, subsecond, second, and tens of seconds time range, and are a result of a progressive temporal summation of the shortest events. Using pharmacological tools we show that activation of intracellular Ca2+ receptors is both sufficient and necessary for glucose-dependent [Ca2+]c oscillations in β cell collectives, and that a subset of [Ca2+]c events could be triggered even in the absence of Ca2+ influx across the plasma membrane. In aggregate, our experimental and analytical platform was able to readily address the involvement of intracellular Ca2+ receptors in shaping the heterogeneity of [Ca2+]c responses in collectives of endocrine cells in situ.NEW & NOTEWORTHY Physiological glucose or ryanodine stimulation of β cell collectives generates a large number of [Ca2+]c events, which can be rapidly assessed with our newly developed automatic image segmentation and [Ca2+]c event identification pipeline. The event durations segregate into three reproducible modes produced by a progressive temporal summation. Using pharmacological tools, we show that activation of ryanodine intracellular Ca2+ receptors is both sufficient and necessary for glucose-dependent [Ca2+]c oscillations in β cell collectives.

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.

Cell Networks in Endocrine/Neuroendocrine Gland Function

Reproduction, growth, stress, and metabolism are determined by endocrine/neuroendocrine systems that regulate circulating hormone concentrations. All these systems generate rhythms and changes in hormone pulsatility observed in a variety of pathophysiological states. Thus, the output of endocrine/neuroendocrine systems must be regulated within a narrow window of effective hormone concentrations but must also maintain a capacity for plasticity to respond to changing physiological demands. Remarkably most endocrinologists still have a "textbook" view of endocrine gland organization which has emanated from 20^th century histological studies on thin 2D tissue sections. However, 21^st -century technological advances, including in-depth 3D imaging of specific cell types have vastly changed our knowledge. We now know that various levels of multicellular organization can be found across different glands, that organizational motifs can vary between species and can be modified to enhance or decrease hormonal release. This article focuses on how the organization of cells regulates hormone output using three endocrine/neuroendocrine glands that present different levels of organization and complexity: the adrenal medulla, with a single neuroendocrine cell type; the anterior pituitary, with multiple intermingled cell types; and the pancreas with multiple intermingled cell types organized into distinct functional units. We give an overview of recent methodologies that allow the study of the different components within endocrine systems, particularly their temporal and spatial relationships. We believe the emerging findings about network organization, and its impact on hormone secretion, are crucial to understanding how homeostatic regulation of endocrine axes is carried out within endocrine organs themselves. © 2022 American Physiological Society. Compr Physiol 12:3371-3415, 2022.

Comparative analysis of reconstructed architectures from mice and human islets

Intra-islet communication via electrical, paracrine and autocrine signals, is highly dependent on the organization of cells within the islets and is key for an adequate response to changes in blood glucose and other stimuli. In spite of the fact that relevant structural differences between mouse and human islet architectures have been described, the functional implications of these differences remain only partially understood. In this work, aiming to contribute to a better understanding of the relationship between structural and functional properties of pancreatic islets, we reconstructed human and mice islets in order to perform a structural comparison based on both morphologic and network-derived metrics. According to our results, human islets constitute a more efficient network from a connectivity viewpoint, mainly due to the higher proportion of heterotypic contacts between islet cells in comparison to mice islets.

pH-Dependence of Glucose-Dependent Activity of Beta Cell Networks in Acute Mouse Pancreatic Tissue Slice

Extracellular pH has the potential to affect various aspects of the pancreatic beta cell function. To explain this effect, a number of mechanisms was proposed involving both extracellular and intracellular targets and pathways. Here, we focus on reassessing the influence of extracellular pH on glucose-dependent beta cell activation and collective activity in physiological conditions. To this end we employed mouse pancreatic tissue slices to perform high-temporally resolved functional imaging of cytosolic Ca²⁺ oscillations. We investigated the effect of either physiological H⁺ excess or depletion on the activation properties as well as on the collective activity of beta cell in an islet. Our results indicate that lowered pH invokes activation of a subset of beta cells in substimulatory glucose concentrations, enhances the average activity of beta cells, and alters the beta cell network properties in an islet. The enhanced average activity of beta cells was determined indirectly utilizing cytosolic Ca²⁺ imaging, while direct measuring of insulin secretion confirmed that this enhanced activity is accompanied by a higher insulin release. Furthermore, reduced functional connectivity and higher functional segregation at lower pH, both signs of a reduced intercellular communication, do not necessary result in an impaired insulin release.

Autopoietic Influence Hierarchies in Pancreatic β Cells

β cells are biologically essential for humans and other vertebrates. Because their functionality arises from cell-cell interactions, they are also a model system for collective organization among cells. There are currently two contradictory pictures of this organization: the hub-cell idea pointing at leaders who coordinate the others, and the electrophysiological theory describing all cells as equal. We use new data and computational modeling to reconcile these pictures. We find via a network representation of interacting β cells that leaders emerge naturally (confirming the hub-cell idea), yet all cells can take the hub role following a perturbation (in line with electrophysiology).

In Vitro Disease Models of the Endocrine Pancreas

The ethical constraints and shortcomings of animal models, combined with the demand to study disease pathogenesis under controlled conditions, are giving rise to a new field at the interface of tissue engineering and pathophysiology, which focuses on the development of in vitro models of disease. In vitro models are defined as synthetic experimental systems that contain living human cells and mimic tissue- and organ-level physiology in vitro by taking advantage of recent advances in tissue engineering and microfabrication. This review provides an overview of in vitro models and focuses specifically on in vitro disease models of the endocrine pancreas and diabetes. First, we briefly review the anatomy, physiology, and pathophysiology of the human pancreas, with an emphasis on islets of Langerhans and beta cell dysfunction. We then discuss different types of in vitro models and fundamental elements that should be considered when developing an in vitro disease model. Finally, we review the current state and breakthroughs in the field of pancreatic in vitro models and conclude with some challenges that need to be addressed in the future development of in vitro models.

Glucose-dependent activation, activity, and deactivation of beta cell networks in acute mouse pancreas tissue slices

Many details of glucose-stimulated intracellular calcium changes in β cells during activation, activity, and deactivation, as well as their concentration-dependence, remain to be analyzed. Classical physiological experiments indicated that in islets, functional differences between individual cells are largely attenuated, but recent findings suggest considerable intercellular heterogeneity, with some cells possibly coordinating the collective responses. To address the above with an emphasis on heterogeneity and describing the relations between classical physiological and functional network properties, we performed functional multicellular calcium imaging in mouse pancreas tissue slices over a wide range of glucose concentrations. During activation, delays to activation of cells and any-cell-to-first-responder delays are shortened, and the sizes of simultaneously responding clusters increased with increasing glucose concentrations. Exactly the opposite characterized deactivation. The frequency of fast calcium oscillations during activity increased with increasing glucose up to 12 mM glucose concentration, beyond which oscillation duration became longer, resulting in a homogenous increase in active time. In terms of functional connectivity, islets progressed from a very segregated network to a single large functional unit with increasing glucose concentration. A comparison between classical physiological and network parameters revealed that the first-responders during activation had longer active times during plateau and the most active cells during the plateau tended to deactivate later. Cells with the most functional connections tended to activate sooner, have longer active times, and deactivate later. Our findings provide a common ground for recent differing views on β cell heterogeneity and an important baseline for future studies of stimulus-secretion and intercellular coupling.NEW & NOTEWORTHY We assessed concentration-dependence in coupled β cells, degree of functional heterogeneity, and uncovered possible specialized subpopulations during the different phases of the response to glucose at the level of many individual cells. To this aim, we combined acute mouse pancreas tissue slices with functional multicellular calcium imaging over a wide range from threshold (7 mM) and physiological (8 and 9 mM) to supraphysiological (12 and 16 mM) glucose concentrations, classical physiological, and advanced network analyses.

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.

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.

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.

Dynamic Uni- and Multicellular Patterns Encode Biphasic Activity in Pancreatic Islets

Biphasic secretion is an autonomous feature of many endocrine micro-organs to fulfill physiological demands. The biphasic activity of islet β-cells maintains glucose homeostasis and is altered in type 2 diabetes. Nevertheless, underlying cellular or multicellular functional organizations are only partially understood. High-resolution noninvasive multielectrode array recordings permit simultaneous analysis of recruitment, of single-cell, and of coupling activity within entire islets in long-time experiments. Using this unbiased approach, we addressed the organizational modes of both first and second phase in mouse and human islets under physiological and pathophysiological conditions. Our data provide a new uni- and multicellular model of islet β-cell activation: during the first phase, small but highly active β-cell clusters are dominant, whereas during the second phase, electrical coupling generates large functional clusters via multicellular slow potentials to favor an economic sustained activity. Postprandial levels of glucagon-like peptide 1 favor coupling only in the second phase, whereas aging and glucotoxicity alter coupled activity in both phases. In summary, biphasic activity is encoded upstream of vesicle pools at the micro-organ level by multicellular electrical signals and their dynamic synchronization between β-cells. The profound alteration of the electrical organization of islets in pathophysiological conditions may contribute to functional deficits in type 2 diabetes.

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.

Random Matrix Analysis of Ca2+ Signals in β-Cell Collectives

Even within small organs like pancreatic islets, different endocrine cell types and subtypes form a heterogeneous collective to sense the chemical composition of the extracellular solution and compute an adequate hormonal output. Erroneous cellular processing and hormonal output due to challenged heterogeneity result in various disorders with diabetes mellitus as a flagship metabolic disease. Here we attempt to address the aforementioned functional heterogeneity with comparing pairwise cell-cell cross-correlations obtained from simultaneous measurements of cytosolic calcium responses in hundreds of islet cells in an optical plane to statistical properties of correlations predicted by the random matrix theory (RMT). We find that the bulk of the empirical eigenvalue spectrum is almost completely described by RMT prediction, however, the deviating eigenvalues that exist below and above RMT spectral edges suggest that there are local and extended modes driving the correlations. We also show that empirical nearest neighbor spacing of eigenvalues follows universal RMT properties regardless of glucose stimulation, but that number variance displays clear separation from RMT prediction and can differentiate between empirical spectra obtained under non-stimulated and stimulated conditions. We suggest that RMT approach provides a sensitive tool to assess the functional cell heterogeneity and its effects on the spatio-temporal dynamics of a collective of beta cells in pancreatic islets in physiological resting and stimulatory conditions, beyond the current limitations of molecular and cellular biology.

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

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

Translational assessment of a genetic engineering methodology to improve islet function for transplantation

Background

The functional quality of insulin-secreting islet beta cells is a major factor determining the outcome of clinical transplantations for diabetes. It is therefore of importance to develop methodological strategies aiming at optimizing islet cell function prior to transplantation. In this study we propose a synthetic biology approach to genetically engineer cellular signalling pathways in islet cells.

Methods

We established a novel procedure to modify islet beta cell function by combining adenovirus-mediated transduction with reaggregation of islet cells into pseudoislets. As a proof-of-concept for the genetic engineering of islets prior to transplantation, this methodology was applied to increase the expression of the V1b receptor specifically in insulin-secreting beta cells. The functional outcomes were assessed in vitro and in vivo following transplantation into the anterior chamber of the eye.

Findings

Pseudoislets produced from mouse dissociated islet cells displayed basic functions similar to intact native islets in terms of glucose induced intracellular signalling and insulin release, and after transplantation were properly vascularized and contributed to blood glucose homeostasis. The synthetic amplification of the V1b receptor signalling in beta cells successfully modulated pseudoislet function in vitro. Finally, in vivo responses of these pseudoislet grafts to vasopressin allowed evaluation of the potential benefits of this approach in regenerative medicine.

Interpretation

These results are promising first steps towards the generation of high-quality islets and suggest synthetic biology as an important tool in future clinical islet transplantations. Moreover, the presented methodology might serve as a useful research strategy to dissect cellular signalling mechanisms of relevance for optimal islet function.

Leader β-cells coordinate Ca2+ dynamics across pancreatic islets in vivo

Pancreatic β-cells form highly connected networks within isolated islets. Whether this behaviour pertains to the situation in vivo, after innervation and during continuous perfusion with blood, is unclear. In the present study, we used the recombinant Ca2+ sensor GCaMP6 to assess glucose-regulated connectivity in living zebrafish Danio rerio, and in murine or human islets transplanted into the anterior eye chamber. In each setting, Ca2+ waves emanated from temporally defined leader β-cells, and three-dimensional connectivity across the islet increased with glucose stimulation. Photoablation of zebrafish leader cells disrupted pan-islet signalling, identifying these as likely pacemakers. Correspondingly, in engrafted mouse islets, connectivity was sustained during prolonged glucose exposure, and super-connected 'hub' cells were identified. Granger causality analysis revealed a controlling role for temporally defined leaders, and transcriptomic analyses revealed a discrete hub cell fingerprint. We thus define a population of regulatory β-cells within coordinated islet networks in vivo. This population may drive Ca2+ dynamics and pulsatile insulin secretion.

Mathematical Modelling of Endocrine Systems

Hormone rhythms are ubiquitous and essential to sustain normal physiological functions. Combined mathematical modelling and experimental approaches have shown that these rhythms result from regulatory processes occurring at multiple levels of organisation and require continuous dynamic equilibration, particularly in response to stimuli. We review how such an interdisciplinary approach has been successfully applied to unravel complex regulatory mechanisms in the metabolic, stress, and reproductive axes. We discuss how this strategy is likely to be instrumental for making progress in emerging areas such as chronobiology and network physiology. Ultimately, we envisage that the insight provided by mathematical models could lead to novel experimental tools able to continuously adapt parameters to gradual physiological changes and the design of clinical interventions to restore normal endocrine function.

Causality Analysis and Cell Network Modeling of Spatial Calcium Signaling Patterns in Liver Lobules

Dynamics as well as localization of Ca²⁺ transients plays a vital role in liver function under homeostatic conditions, repair, and disease. In response to circulating hormonal stimuli, hepatocytes exhibit intracellular Ca²⁺ responses that propagate through liver lobules in a wave-like fashion. Although intracellular processes that control cell autonomous Ca²⁺ spiking behavior have been studied extensively, the intra- and inter-cellular signaling factors that regulate lobular scale spatial patterns and wave-like propagation of Ca²⁺ remain to be determined. To address this need, we acquired images of cytosolic Ca²⁺ transients in 1300 hepatocytes situated across several mouse liver lobules over a period of 1600 s. We analyzed this time series data using correlation network analysis, causal network analysis, and computational modeling, to characterize the spatial distribution of heterogeneity in intracellular Ca²⁺ signaling components as well as intercellular interactions that control lobular scale Ca²⁺ waves. Our causal network analysis revealed that hepatocytes are causally linked to multiple other co-localized hepatocytes, but these influences are not necessarily aligned uni-directionally along the sinusoids. Our computational model-based analysis showed that spatial gradients of intracellular Ca²⁺ signaling components as well as intercellular molecular exchange are required for lobular scale propagation of Ca²⁺ waves. Additionally, our analysis suggested that causal influences of hepatocytes on Ca²⁺ responses of multiple neighbors lead to robustness of Ca²⁺ wave propagation through liver lobules.

Secretagogin protects Pdx1 from proteasomal degradation to control a transcriptional program required for β cell specification

OBJECTIVE

Specification of endocrine cell lineages in the developing pancreas relies on extrinsic signals from non-pancreatic tissues, which initiate a cell-autonomous sequence of transcription factor activation and repression switches. The steps in this pathway share reliance on activity-dependent Ca²⁺ signals. However, the mechanisms by which phasic Ca²⁺ surges become converted into a dynamic, cell-state-specific and physiologically meaningful code made up by transcription factors constellations remain essentially unknown.

METHODS

We used high-resolution histochemistry to explore the coincident expression of secretagogin and transcription factors driving β cell differentiation. Secretagogin promoter activity was tested in response to genetically manipulating Pax6 and Pax4 expression. Secretagogin null mice were produced with their pancreatic islets morphologically and functionally characterized during fetal development. A proteomic approach was utilized to identify the Ca²⁺-dependent interaction of secretagogin with subunits of the 26S proteasome and verified in vitro by focusing on Pdx1 retention.

RESULTS

Here, we show that secretagogin, a Ca²⁺ sensor protein that controls α and β cell turnover in adult, is in fact expressed in endocrine pancreas from the inception of lineage segregation in a Pax4-and Pax6-dependent fashion. By genetically and pharmacologically manipulating secretagogin expression and interactome engagement in vitro, we find secretagogin to gate excitation-driven Ca²⁺ signals for β cell differentiation and insulin production. Accordingly, secretagogin^-/- fetuses retain a non-committed pool of endocrine progenitors that co-express both insulin and glucagon. We identify the Ca²⁺-dependent interaction of secretagogin with subunits of the 26S proteasome complex to prevent Pdx1 degradation through proteasome inactivation. This coincides with retained Nkx6.1, Pax4 and insulin transcription in prospective β cells.

CONCLUSIONS

In sum, secretagogin scales the temporal availability of a Ca²⁺-dependent transcription factor network to define β cell identity.

Insulin secretion kinetics from single islets reveals distinct subpopulations

Type II diabetes progresses with inadequate insulin secretion and prolonged elevated circulating glucose levels. Also, pancreatic islets isolated for transplantation or tissue engineering can be exposed to glucose over extended timeframe. We hypothesized that isolated pancreatic islets can secrete insulin over a prolonged period of time when incubated in glucose solution and that not all islets release insulin in unison. Insulin secretion kinetics was examined and modeled from single mouse islets in response to chronic glucose exposure (2.8-20 mM). Results with single islets were compared to those from pools of islets. Kinetic analysis of 58 single islets over 72 h in response to elevated glucose revealed distinct insulin secretion profiles: slow-, fast-, and constant-rate secretors, with slow-secretors being most prominent (ca., 50%). Variations in the temporal response to glucose therefore exist. During short-term (<4 h) exposure to elevated glucose few islets are responding with sustained insulin release. The model allowed studying the influence of islet size, revealing no clear effect. At high-glucose concentrations, when secretion is normalized to islet volume, the tendency is that smaller islets secrete more insulin. At high-glucose concentrations, insulin secretion from single islets is representative of islet populations, while under low-glucose conditions pooled islets did not behave as single ones. The characterization of insulin secretion over prolonged periods complements studies on insulin secretion performed over short timeframe. Further investigation of these differences in secretion profiles may resolve open-ended questions on pre-diabetic conditions and transplanted islets performance. This study deliberates the importance of size of islets in insulin secretion. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:1059-1068, 2018.

Collective Sensing of β-Cells Generates the Metabolic Code

Major part of a pancreatic islet is composed of β-cells that secrete insulin, a key hormone regulating influx of nutrients into all cells in a vertebrate organism to support nutrition, housekeeping or energy storage. β-cells constantly communicate with each other using both direct, short-range interactions through gap junctions, and paracrine long-range signaling. However, how these cell interactions shape collective sensing and cell behavior in islets that leads to insulin release is unknown. When stimulated by specific ligands, primarily glucose, β-cells collectively respond with expression of a series of transient Ca²⁺ changes on several temporal scales. Here we reanalyze a set of Ca²⁺ spike trains recorded in acute rodent pancreatic tissue slice under physiological conditions. We found strongly correlated states of co-spiking cells coexisting with mostly weak pairwise correlations widespread across the islet. Furthermore, the collective Ca²⁺ spiking activity in islet shows on-off intermittency with scaling of spiking amplitudes, and stimulus dependent autoassociative memory features. We use a simple spin glass-like model for the functional network of a β-cell collective to describe these findings and argue that Ca²⁺ spike trains produced by collective sensing of β-cells constitute part of the islet metabolic code that regulates insulin release and limits the islet size.

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.

Spatially Organized β-Cell Subpopulations Control Electrical Dynamics across Islets of Langerhans

Understanding how heterogeneous cells within a multicellular system interact and affect overall function is difficult without a means of perturbing individual cells or subpopulations. Here we apply optogenetics to understand how subpopulations of β-cells control the overall [Ca²⁺]_i response and insulin secretion dynamics of the islets of Langerhans. We spatiotemporally perturbed electrical activity in β-cells of channelrhodopsin2-expressing islets, mapped the [Ca²⁺]_i response, and correlated this with the cellular metabolic activity and an in silico electrophysiology model. We discovered organized regions of metabolic activity across the islet, and these affect the way in which β-cells electrically interact. Specific regions acted as pacemakers by initiating calcium wave propagation. Our findings reveal the functional architecture of the islet, and show how distinct subpopulations of cells can disproportionality affect function. These results also suggest ways in which other neuroendocrine systems can be regulated, and demonstrate how optogenetic tools can discern their functional architecture.

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.

SNAP-25b-deficiency increases insulin secretion and changes spatiotemporal profile of Ca2+oscillations in β cell networks

SNAP-25 is a protein of the core SNARE complex mediating stimulus-dependent release of insulin from pancreatic β cells. The protein exists as two alternatively spliced isoforms, SNAP-25a and SNAP-25b, differing in 9 out of 206 amino acids, yet their specific roles in pancreatic β cells remain unclear. We explored the effect of SNAP-25b-deficiency on glucose-stimulated insulin release in islets and found increased secretion both in vivo and in vitro. However, slow photo-release of caged Ca²⁺ in β cells within pancreatic slices showed no significant differences in Ca²⁺-sensitivity, amplitude or rate of exocytosis between SNAP-25b-deficient and wild-type littermates. Therefore, we next investigated if Ca²⁺ handling was affected in glucose-stimulated β cells using intracellular Ca²⁺-imaging and found premature activation and delayed termination of [Ca²⁺]_i elevations. These findings were accompanied by less synchronized Ca²⁺-oscillations and hence more segregated functional β cell networks in SNAP-25b-deficient mice. Islet gross morphology and architecture were maintained in mutant mice, although sex specific compensatory changes were observed. Thus, our study proposes that SNAP-25b in pancreatic β cells, except for participating in the core SNARE complex, is necessary for accurate regulation of Ca²⁺-dynamics.

A chaotic bursting-spiking transition in a pancreatic beta-cells system: Observation of an interior glucose-induced crisis

Nonlinear systems are commonly able to display abrupt qualitative changes (or transitions) in the dynamics. A particular type of these transitions occurs when the size of a chaotic attractor suddenly changes. In this article, we present such a transition through the observation of a chaotic interior crisis in the Deng bursting-spiking model for the glucose-induced electrical activity of pancreatic β-cells. To this chaos-chaos transition corresponds precisely the change between the bursting and spiking dynamics, which are central and key dynamical regimes that the Deng model is able to perform. We provide a description of the crisis mechanism at the bursting-spiking transition point in terms of time series variations and based on certain amplitudes of invariant intervals associated with return maps. Using symbolic dynamics, we are able to accurately compute the points of a curve representing the transition between the bursting and spiking regimes in a biophysical meaningfully parameter space. The analysis of the chaotic interior crisis is complemented by means of topological invariants with the computation of the topological entropy and the maximum Lyapunov exponent. Considering very recent developments in the literature, we construct analytical solutions triggering the bursting-spiking transition in the Deng model. This study provides an illustration of how an integrated approach, involving numerical evidences and theoretical reasoning within the theory of dynamical systems, can directly enhance our understanding of biophysically motivated models.

Depression Disorder Classification of fMRI Data Using Sparse Low-Rank Functional Brain Network and Graph-Based Features

Study of functional brain network (FBN) based on functional magnetic resonance imaging (fMRI) has proved successful in depression disorder classification. One popular approach to construct FBN is Pearson correlation. However, it only captures pairwise relationship between brain regions, while it ignores the influence of other brain regions. Another common issue existing in many depression disorder classification methods is applying only single local feature extracted from constructed FBN. To address these issues, we develop a new method to classify fMRI data of patients with depression and healthy controls. First, we construct the FBN using a sparse low-rank model, which considers the relationship between two brain regions given all the other brain regions. Moreover, it can automatically remove weak relationship and retain the modular structure of FBN. Secondly, FBN are effectively measured by eight graph-based features from different aspects. Tested on fMRI data of 31 patients with depression and 29 healthy controls, our method achieves 95% accuracy, 96.77% sensitivity, and 93.10% specificity, which outperforms the Pearson correlation FBN and sparse FBN. In addition, the combination of graph-based features in our method further improves classification performance. Moreover, we explore the discriminative brain regions that contribute to depression disorder classification, which can help understand the pathogenesis of depression disorder.

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.

Statistical approaches and software for clustering islet cell functional heterogeneity

Worldwide efforts are underway to replace or repair lost or dysfunctional pancreatic β-cells to cure diabetes. However, it is unclear what the final product of these efforts should be, as β-cells are thought to be heterogeneous. To enable the analysis of β-cell heterogeneity in an unbiased and quantitative way, we developed model-free and model-based statistical clustering approaches, and created new software called TraceCluster. Using an example data set, we illustrate the utility of these approaches by clustering dynamic intracellular Ca(2+) responses to high glucose in ∼300 simultaneously imaged single islet cells. Using feature extraction from the Ca(2+) traces on this reference data set, we identified 2 distinct populations of cells with β-like responses to glucose. To the best of our knowledge, this report represents the first unbiased cluster-based analysis of human β-cell functional heterogeneity of simultaneous recordings. We hope that the approaches and tools described here will be helpful for those studying heterogeneity in primary islet cells, as well as excitable cells derived from embryonic stem cells or induced pluripotent cells.

The Analysis of Intracellular and Intercellular Calcium Signaling in Human Anterior Lens Capsule Epithelial Cells with Regard to Different Types and Stages of the Cataract

In this work we investigated how modifications of the Ca²⁺ homeostasis in anterior lens epithelial cells (LECs) are associated with different types of cataract (cortical or nuclear) and how the progression of the cataract (mild or moderate) affects the Ca²⁺ signaling. We systematically analyzed different aspects of intra- and inter-cellular Ca²⁺ signaling in the human LECs, which are attached to surgically isolated lens capsule (LC), obtained during cataract surgery. We monitored the temporal and spatial changes in intracellular Ca²⁺ concentration after stimulation with acetylcholine by means of Fura-2 fluorescence captured with an inverted microscope. In our analysis we compared the features of Ca²⁺ signals in individual cells, synchronized activations, spatio-temporal grouping and the nature of intercellular communication between LECs. The latter was assessed by using the methodologies of the complex network theory. Our results point out that at the level of individual cells there are no significant differences when comparing the features of the signals with regard either to the type or the stage of the cataract. On the other hand, noticeable differences are observed at the multicellular level, despite inter-capsule variability. LCs associated with more developed cataracts were found to exhibit a slower collective response to stimulation, a less pronounced spatio-temporal clustering of LECs with similar signaling characteristics. The reconstructed intercellular networks were found to be sparser and more segregated than in LCs associated with mild cataracts. Moreover, we show that spontaneously active LECs often operate in localized groups with quite well aligned Ca²⁺ activity. The presence of spontaneous activity was also found to affect the stimulated Ca²⁺ responses of individual cells. Our findings indicate that the cataract progression entails the impairment of intercellular signaling thereby suggesting the functional importance of altered Ca²⁺ signaling of LECs in cataractogenesis.

Membrane Potential and Calcium Dynamics in Beta Cells from Mouse Pancreas Tissue Slices: Theory, Experimentation, and Analysis

Beta cells in the pancreatic islets of Langerhans are precise biological sensors for glucose and play a central role in balancing the organism between catabolic and anabolic needs. A hallmark of the beta cell response to glucose are oscillatory changes of membrane potential that are tightly coupled with oscillatory changes in intracellular calcium concentration which, in turn, elicit oscillations of insulin secretion. Both membrane potential and calcium changes spread from one beta cell to the other in a wave-like manner. In order to assess the properties of the abovementioned responses to physiological and pathological stimuli, the main challenge remains how to effectively measure membrane potential and calcium changes at the same time with high spatial and temporal resolution, and also in as many cells as possible. To date, the most wide-spread approach has employed the electrophysiological patch-clamp method to monitor membrane potential changes. Inherently, this technique has many advantages, such as a direct contact with the cell and a high temporal resolution. However, it allows one to assess information from a single cell only. In some instances, this technique has been used in conjunction with CCD camera-based imaging, offering the opportunity to simultaneously monitor membrane potential and calcium changes, but not in the same cells and not with a reliable cellular or subcellular spatial resolution. Recently, a novel family of highly-sensitive membrane potential reporter dyes in combination with high temporal and spatial confocal calcium imaging allows for simultaneously detecting membrane potential and calcium changes in many cells at a time. Since the signals yielded from both types of reporter dyes are inherently noisy, we have developed complex methods of data denoising that permit for visualization and pixel-wise analysis of signals. Combining the experimental approach of high-resolution imaging with the advanced analysis of noisy data enables novel physiological insights and reassessment of current concepts in unprecedented detail.

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

Coordinated insulin secretion is controlled by electrical coupling of pancreatic β-cells due to connexin-36 gap junctions. Gap junction coupling not only synchronizes the heterogeneous β-cell population, but can also modify the electrical behavior of the cells. These phenomena have been widely studied with mathematical models based on data from mouse β-cells. However, it is now known that human β-cell electrophysiology shows important differences to its rodent counterpart, and although human pancreatic islets express connexin-36 and show evidence of β-cell coupling, these aspects have been little investigated in human β-cells. Here we investigate theoretically, the gap junction coupling strength required for synchronizing electrical activity in a small cluster of cells simulated with a recent mathematical model of human β-cell electrophysiology. We find a lower limit for the coupling strength of approximately 20 pS (i.e., normalized to cell size, ∼2 pS pF(-1)) below which spiking electrical activity is asynchronous. To confront this theoretical lower bound with data, we use our model to estimate from an experimental patch clamp recording that the coupling strength is approximately 100-200 pS (10-20 pS pF(-1)), similar to previous estimates in mouse β-cells. We then investigate the role of gap junction coupling in synchronizing and modifying other forms of electrical activity in human β-cell clusters. We find that electrical coupling can prolong the period of rapid bursting electrical activity, and synchronize metabolically driven slow bursting, in particular when the metabolic oscillators are in phase. Our results show that realistic coupling conductances are sufficient to promote synchrony in small clusters of human β-cells as observed experimentally, and provide motivation for further detailed studies of electrical coupling in human pancreatic islets.

The relationship between node degree and dissipation rate in networks of diffusively coupled oscillators and its significance for pancreatic beta cells

Self-sustained oscillatory dynamics is a motion along a stable limit cycle in the phase space, and it arises in a wide variety of mechanical, electrical, and biological systems. Typically, oscillations are due to a balance between energy dissipation and generation. Their stability depends on the properties of the attractor, in particular, its dissipative characteristics, which in turn determine the flexibility of a given dynamical system. In a network of oscillators, the coupling additionally contributes to the dissipation, and hence affects the robustness of the oscillatory solution. Here, we therefore investigate how a heterogeneous network structure affects the dissipation rate of individual oscillators. First, we show that in a network of diffusively coupled oscillators, the dissipation is a linearly decreasing function of the node degree, and we demonstrate this numerically by calculating the average divergence of coupled Hopf oscillators. Subsequently, we use recordings of intracellular calcium dynamics in pancreatic beta cells in mouse acute tissue slices and the corresponding functional connectivity networks for an experimental verification of the presented theory. We use methods of nonlinear time series analysis to reconstruct the phase space and calculate the sum of Lyapunov exponents. Our analysis reveals a clear tendency of cells with a higher degree, that is, more interconnected cells, having more negative values of divergence, thus confirming our theoretical predictions. We discuss these findings in the context of energetic aspects of signaling in beta cells and potential risks for pathological changes in the tissue.