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

Critical transitions in pancreatic islets

Calcium signals in pancreatic β cell collectives show a sharp transition from uncorrelated to correlated state resembling a phase transition as the slowly increasing glucose concentration crosses the tipping point. However, the exact nature or the order of this phase transition is not well understood. Using confocal microscopy to record the collective calcium activation of β cells in an intact islet under changing glucose concentration in an increasing and then decreasing way, we first show that in, addition to the sharp transition, the coordinated calcium response exhibits a hysteresis indicating a critical, first-order transition. A network model of β cells combining link selection and coordination mechanisms capture the observed hysteresis loop and the critical nature of the transition. Our results point towards an understanding of the role of islets as tipping elements in the pancreas that, interconnected by perfusion, diffusion, and innervation, cause the tipping dynamics and abrupt insulin release.

Exploration and identification of diabetes targets in nursing: CDH1 and DVL1

Diabetes is a chronic disease caused by absolute or relative insufficiency of insulin secretion and impaired insulin utilization. CDH1 and DVL1 role in diabetes and its nursing care is unclear. The diabetes dataset GSE21321 and GSE19790 profiles were downloaded from the gene expression omnibus (GEO) database. Perform differentially expressed genes (DEGs) screening, weighted gene co-expression network analysis (WGCNA), protein-protein interaction (PPI) network construction and analysis, functional enrichment analysis, gene set enrichment analysis (GSEA), immune infiltration analysis, and Comparative Toxicogenomics Database (CTD) analysis. Gene expression heat map was drawn. TargetScan was used to screen the miRNA that regulates central DEGs. 1983 DEGs were obtained. According to Gene Ontology (GO) analysis, they were mainly enriched in signal regulation, catenin complexes, and signal receptor binding. In Kyoto Encyclopedia of Gene and Genome (KEGG) analysis, they were mainly concentrated in the Rap1 signaling pathway, cAMP signaling pathway, and Hippo signaling pathway. The DEGs are mainly enriched in cell signaling, Wnt signaling vesicles, growth factor activity, and the interaction between neural active ligands and receptors. In the enrichment project of Metascape, BMP signaling pathways and cell population proliferation can be seen in the GO enrichment project. The soft threshold power in WGCNA is set to 5. A total of 15 modules were generated. Core gene expression heatmap showed that core genes (CTNNB1, CDH1, DVL1) were highly expressed in diabetes samples. CTD analysis showed thatCTNNB1, CDH1, DVL1were associated with weight gain, inflammation, and necrosis. CDH1 and DVL1 are highly expressed in diabetes and may become molecular targets for diabetes and its care.

Critical transitions in pancreatic islets

Calcium signals in pancreatic β cells collectives show a sharp transition from uncorrelated to correlated state resembling a phase transition as the slowly increasing glucose concentration crosses the tipping point. However, the exact nature or the order of this phase transition is not well understood. Using confocal microscopy to record the collective calcium activation of β cells in an intact islet under changing glucose concentration in increasing and then decreasing way, we first show that in addition to the sharp transition, the coordinated calcium response exhibits a hysteresis indicating a critical, first order transition. A network model of β cells combining link selection and coordination mechanisms capture the observed hysteresis loop and the critical nature of the transition. Our results point towards the understanding the role of islets as tipping elements in the pancreas that interconnected by perfusion, diffusion and innervation cause the tipping dynamics and abrupt insulin release.

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.

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.

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.

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.

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.

Role of topology in complex functional networks of beta cells

The activity of pancreatic β cells can be described by biological networks of coupled nonlinear oscillators that, via electrochemical synchronization, release insulin in response to augmented glucose levels. In this work, we analyze the emergent behavior of regular and percolated β-cells clusters through a stochastic mathematical model where "functional" networks arise. We show that the emergence and robustness of the synchronized dynamics depend both on intrinsic and extrinsic parameters. In particular, cellular noise level, glucose concentration, network spatial architecture, and cell-to-cell coupling strength are the key factors for the generation of a rhythmic and robust activity. Their role in the functional network topology associated with β-cells clusters is analyzed and discussed.

Autophagy mediates phase transitions from cell death to life

Autophagy is a lysosomal degradation pathway, which is critical for maintaining normal cellular functions. Despite considerable advances in defining the specific molecular mechanism governing the autophagy pathway during the last decades, we are still far from understanding the underlying principle of the autophagy machinery and its complex role in human disease. As an alternative attempt to reinvigorate the search for the principle of the autophagy pathway, we in this study make use of the computer-aided analysis, complementing current molecular-level studies of autophagy. Specifically, we propose a hypothesis that autophagy mediates cellular phase transitions and demonstrate that the autophagic phase transitions are essential to the maintenance of normal cellular functions and critical in the fate of a cell, i.e., cell death or survival. This study should provide valuable insight into how interactions of sub-cellular components such as genes and protein modules/complexes regulate autophagy and then impact on the dynamic behaviors of living cells as a whole, bridging the microscopic molecular-level studies and the macroscopic cellular-level and physiological approaches.

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.

Electrical coupling in ensembles of nonexcitable cells: modeling the spatial map of single cell potentials

We analyze the coupling of model nonexcitable (non-neural) cells assuming that the cell membrane potential is the basic individual property. We obtain this potential on the basis of the inward and outward rectifying voltage-gated channels characteristic of cell membranes. We concentrate on the electrical coupling of a cell ensemble rather than on the biochemical and mechanical characteristics of the individual cells, obtain the map of single cell potentials using simple assumptions, and suggest procedures to collectively modify this spatial map. The response of the cell ensemble to an external perturbation and the consequences of cell isolation, heterogeneity, and ensemble size are also analyzed. The results suggest that simple coupling mechanisms can be significant for the biophysical chemistry of model biomolecular ensembles. In particular, the spatiotemporal map of single cell potentials should be relevant for the uptake and distribution of charged nanoparticles over model cell ensembles and the collective properties of droplet networks incorporating protein ion channels inserted in lipid bilayers.

Critical transitions in chronic disease: transferring concepts from ecology to systems medicine

Ecosystems and biological systems are known to be inherently complex and to exhibit nonlinear dynamics. Diseases such as microbiome dysregulation or depression can be seen as complex systems as well and were shown to exhibit patterns of nonlinearity in their response to perturbations. These nonlinearities can be revealed by a sudden shift in system states, for instance from health to disease. The identification and characterization of early warning signals which could predict upcoming critical transitions is of primordial interest as prevention of disease onset is a major aim in health care. In this review, we focus on recent evidence for critical transitions in diseases and discuss the potential of such studies for therapeutic applications.

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.