Tracking Ca2+ Dynamics in NOD Mouse Islets During Spontaneous Diabetes Development

The mechanisms accounting for the functional changes of α- and β-cells over the course of type 1 diabetes (T1D) development are largely unknown. Permitted by our established technology of high spatiotemporal resolution imaging of cytosolic Ca2+ ([Ca2+]c) dynamics on fresh pancreas tissue slices, we tracked the [Ca2+]c dynamic changes, as the assessment of function, in islet α- and β-cells of female nonobese diabetic (NOD) mice during the development of spontaneous diabetes. We showed that, during the phases of islet inflammation, 8 mmol/L glucose-induced synchronized short [Ca2+]c events in β-cells were diminished, whereas long [Ca2+]c events were gradually more triggerable at substimulatory 4 and 6 mmol/L glucose. In the islet destruction phase, the synchronized short [Ca2+]c events in a subset of β-cells resumed at high glucose condition, while the long [Ca2+]c events were significantly elevated already at substimulatory glucose concentrations. In the α-cells, the glucose sensitivity of the [Ca2+]c events persisted throughout the course of T1D development. At the late islet destruction phase, the α-cell [Ca2+]c events exhibited patterns of synchronicity. Our work has uncovered windows of functional recovery in β-cells and potential α-cells functional synchronization in NOD mice over the course of T1D development.

ARTICLE HIGHLIGHTS

In NOD mice β-cells, 8 mmol/L glucose-induced synchronized short [Ca2+]c events diminish in the early phases of islet inflammation, and long Ca2+ events became more sensitive to substimulatory 4 and 6 mmol/L glucose. In the late islet destruction phase, the synchronized short [Ca2+]c events in a subset of β-cells resumed at 8 mmol/L glucose, while the long Ca2+ events were significantly elevated at substimulatory glucose concentrations. In the α-cells, the glucose sensitivity of the [Ca2+]c events persisted throughout the course of type 1 diabetes development. α-Cell [Ca2+]c events occasionally synchronize in the islets with severe β-cell destruction.

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.

Physiological levels of adrenaline fail to stop pancreatic beta cell activity at unphysiologically high glucose levels

Adrenaline inhibits insulin secretion from pancreatic beta cells to allow an organism to cover immediate energy needs by unlocking internal nutrient reserves. The stimulation of α2-adrenergic receptors on the plasma membrane of beta cells reduces their excitability and insulin secretion mostly through diminished cAMP production and downstream desensitization of late step(s) of exocytotic machinery to cytosolic Ca2+ concentration ([Ca2+]c). In most studies unphysiologically high adrenaline concentrations have been used to evaluate the role of adrenergic stimulation in pancreatic endocrine cells. Here we report the effect of physiological adrenaline levels on [Ca2+]c dynamics in beta cell collectives in mice pancreatic tissue slice preparation. We used confocal microscopy with a high spatial and temporal resolution to evaluate glucose-stimulated [Ca2+]c events and their sensitivity to adrenaline. We investigated glucose concentrations from 8-20 mM to assess the concentration of adrenaline that completely abolishes [Ca2+]c events. We show that 8 mM glucose stimulation of beta cell collectives is readily inhibited by the concentration of adrenaline available under physiological conditions, and that sequent stimulation with 12 mM glucose or forskolin in high nM range overrides this inhibition. Accordingly, 12 mM glucose stimulation required at least an order of magnitude higher adrenaline concentration above the physiological level to inhibit the activity. To conclude, higher glucose concentrations stimulate beta cell activity in a non-linear manner and beyond levels that could be inhibited with physiologically available plasma adrenaline concentration.

The microdynamics shaping the relationship between democracy and corruption

Physics has a long tradition of laying rigorous quantitative foundations for social phenomena. Here, we up the ante for physics' forays into the territory of social sciences by (i) empirically documenting a tipping point in the relationship between democratic norms and corruption suppression, and then (ii) demonstrating how such a tipping point emerges from a micro-scale mechanistic model of spin dynamics in a complex network. Specifically, the tipping point in the relationship between democratic norms and corruption suppression is such that democratization has little effect on suppressing corruption below a critical threshold, but a large effect above the threshold. The micro-scale model of spin dynamics underpins this phenomenon by reinterpreting spins in terms of unbiased (i.e. altruistic) and biased (i.e. parochial) other-regarding behaviour, as well as the corresponding voting preferences. Under weak democratic norms, dense social connections of parochialists enable coercing enough opportunist voters to vote in favour of perpetuating parochial in-group bias. Society may, however, strengthen democratic norms in a rapid turn of events during which opportunists adopt altruism and vote to subdue bias. The emerging model outcome at the societal scale thus mirrors the data, implying that democracy either perpetuates or suppresses corruption depending on the prevailing democratic norms.

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).

β Cells Operate Collectively to Help Maintain Glucose Homeostasis

Residing in the islets of Langerhans in the pancreas, β cells contribute to glucose homeostasis by managing the body's insulin supply. Although it has been acknowledged that healthy β cells engage in heavy cell-to-cell communication to perform their homeostatic function, the exact role and effects of such communication remain partly understood. We offer a novel, to our knowledge, perspective on the subject in the form of 1) a dynamical network model that faithfully mimics fast calcium oscillations in response to above-threshold glucose stimulation and 2) empirical data analysis that reveals a qualitative shift in the cross-correlation structure of measured signals below and above the threshold glucose concentration. Combined together, these results point to a glucose-induced transition in β-cell activity thanks to increasing coordination through gap-junctional signaling and paracrine interactions. Our data and the model further suggest how the conservation of entire cell-cell conductance, observed in coupled but not uncoupled β cells, emerges as a collective phenomenon. An overall implication is that improving the ability to monitor β-cell signaling should offer means to better understand the pathogenesis of diabetes mellitus.

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.

Collective Behavior of Social Bots Is Encoded in Their Temporal Twitter Activity

Computational propaganda deploys social or political bots to try to shape, steer, and manipulate online public discussions and influence decisions. Collective behavior of populations of social bots has not been yet widely studied, although understanding of collective patterns arising from interactions between bots would aid social bot detection. In this study, we show that there are significant differences in collective behavior between population of bots and population of humans as detected from their Twitter activity. Using a large dataset of tweets we have collected during the UK-EU referendum campaign, we separated users into population of bots and population of humans based on the length of sequences of their high-frequency tweeting activity. We show that, while pairwise correlations between users are weak, they co-exist with collective correlated states; however the statistics of correlations and co-spiking probability differ in both populations. Our results demonstrate that populations of social bots and human users in social media exhibit collective properties similar to the ones found in social and biological systems placed near a critical point.

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.

Superlinear and sublinear urban scaling in geographical networks modeling cities

Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y(N) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y(N)∝N(β) with β>1, if Y(N) represents a creative productivity and the indicator scales sublinearly (β<1) if Y(N) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.

Functional connectivity in islets of Langerhans from mouse pancreas tissue slices

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

Scale-free networks embedded in fractal space

The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to γ = 2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture.