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

Exploring pancreatic beta-cell subgroups and their connectivity

Functional pancreatic islet beta cells are essential to ensure glucose homeostasis across species from zebrafish to humans. These cells show significant heterogeneity, and emerging studies have revealed that connectivity across a hierarchical network is required for normal insulin release. Here, we discuss current thinking and areas of debate around intra-islet connectivity, cellular hierarchies and potential "controlling" beta-cell populations. We focus on methodologies, including comparisons of different cell preparations as well as in vitro and in vivo approaches to imaging and controlling the activity of human and rodent islet preparations. We also discuss the analytical approaches that can be applied to live-cell data to identify and study critical subgroups of cells with a disproportionate role in control Ca2+ dynamics and thus insulin secretion (such as "first responders", "leaders" and "hubs", as defined by Ca2+ responses to glucose stimulation). Possible mechanisms by which this hierarchy is achieved, its physiological relevance and how its loss may contribute to islet failure in diabetes mellitus are also considered. A glossary of terms and links to computational resources are provided.

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.

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

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

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

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

Multilevel synchronization of human β-cells networks

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

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.

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.

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.

SIBPA on the crest of the Adriatic Sea wave: Introduction to the SIBPA XXIV (2018 congress) special issue

The Italian Society for Pure and Applied Biophysics (SIBPA) held its XXIV National Congress in the beautiful seaside town of Ancona, Italy, on September 10-13, 2018. This special issue features a selection of contributions from the Congress in all areas of modern biophysics including molecular, cellular, applied, computational and nanoscale biophysics. SIBPA pursues its institutional tasks and carries on its successful promotion of biophysical disciplines at the national and international levels, also trough the consolidation of its partnership with Biophysical Chemistry and Elsevier.