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

Exploring nonlinear phenomena in animal vocalizations through oscillator theory

Animal vocalizations comprise a rich array of complex sounds that exhibit nonlinear phenomena (NLP), which have fascinated researchers for decades. From the melodic songs of birds to the clicks and whistles of dolphins, many species have been found to produce nonlinear vocalizations, offering a valuable perspective on the mechanisms underlying sound production and potential adaptive functions. By leveraging on the principles of oscillator theory and nonlinear dynamics, animal vocalizations, which are based on coupled oscillators, can be described and conveniently classified. We review the basic ingredients for self-sustained oscillations and how different NLP can emerge. We discuss important terms in the context of oscillator theory: attractor types, phase space, bifurcations and Arnold tongue diagrams. Through a comparative analysis of observed NLP and bifurcation diagrams, our study reviews how the tools of nonlinear dynamics can provide insights into the intricate complexity of animal vocalizations, as well as into the evolutionary pressures and adaptive strategies that have shaped the diverse communication systems of the animal kingdom.This article is part of the theme issue, 'Nonlinear phenomena in vertebrate vocalizations: mechanisms and communicative functions'.

Causal interaction of metabolic oscillations in monolayers of Hela cervical cancer cells: emergence of complex networks

A novel global cooperative phenomenon was observed in monolayers of HeLa cervical cancer cells that exhibited glycolytic oscillations but did not exhibit synchronisation or partial synchronisation. The analysis of causality of the oscillations between cell pairs in the cell-monolayer sheet revealed a hidden causal interaction network. Furthermore, the network exhibits characteristics of a broad-scale network. This suggests that key cells perform a hub-like function in the network and that the population of HeLa cells forms metabolically connected functional network rather than randomly connected one. Unlike previous work that focused on the synchronisation of glycolytic oscillations in the HeLa cells, the present study analysed the causality between the oscillating cells by Convergent Cross Mapping (CCM), which is based on the phase-space reconstruction of time-series data and is used to find causality in weakly coupled components of nonlinear dynamical systems. We believe that the framework proposed in this study is useful for investigating the hidden state of a group of cells and can accelerate studies on cellular metabolic phenomena including metabolic oscillations in [Formula: see text] cells within islets of Langerhans. It would also be applicable to systems of weakly coupled oscillators that may include hidden cooperative phenomena.

Glucokinase activity controls peripherally located subpopulations of β-cells that lead islet Ca2+ oscillations

Oscillations in insulin secretion, driven by islet Ca2+ waves, are crucial for glycemic control. Prior studies, performed with single-plane imaging, suggest that subpopulations of electrically coupled β-cells have privileged roles in leading and coordinating the propagation of Ca2+ waves. Here, we used three-dimensional (3D) light-sheet imaging to analyze the location and Ca2+ activity of single β-cells within the entire islet at >2 Hz. In contrast with single-plane studies, 3D network analysis indicates that the most highly synchronized β-cells are located at the islet center, and remain regionally but not cellularly stable between oscillations. This subpopulation, which includes 'hub cells', is insensitive to changes in fuel metabolism induced by glucokinase and pyruvate kinase activation. β-Cells that initiate the Ca2+ wave (leaders) are located at the islet periphery, and strikingly, change their identity over time via rotations in the wave axis. Glucokinase activation, which increased oscillation period, reinforced leader cells and stabilized the wave axis. Pyruvate kinase activation, despite increasing oscillation frequency, had no effect on leader cells, indicating the wave origin is patterned by fuel input. These findings emphasize the stochastic nature of the β-cell subpopulations that control Ca2+ oscillations and identify a role for glucokinase in spatially patterning 'leader' β-cells.

Glucokinase activity controls peripherally-located subpopulations of β-cells that lead islet Ca2+ oscillations

Oscillations in insulin secretion, driven by islet Ca2+ waves, are crucial for glycemic control. Prior studies, performed with single-plane imaging, suggest that subpopulations of electrically coupled β-cells have privileged roles in leading and coordinating the propagation of Ca2+ waves. Here, we used 3D light-sheet imaging to analyze the location and Ca2+ activity of single β-cells within the entire islet at >2 Hz. In contrast with single-plane studies, 3D network analysis indicates that the most highly synchronized β-cells are located at the islet center, and remain regionally but not cellularly stable between oscillations. This subpopulation, which includes 'hub cells', is insensitive to changes in fuel metabolism induced by glucokinase and pyruvate kinase activation. β-cells that initiate the Ca2+ wave ('leaders') are located at the islet periphery, and strikingly, change their identity over time via rotations in the wave axis. Glucokinase activation, which increased oscillation period, reinforced leader cells and stabilized the wave axis. Pyruvate kinase activation, despite increasing oscillation frequency, had no effect on leader cells, indicating the wave origin is patterned by fuel input. These findings emphasize the stochastic nature of the β-cell subpopulations that control Ca2+ oscillations and identify a role for glucokinase in spatially patterning 'leader' β-cells.

Study of the Synchronization and Transmission of Intracellular Signaling Oscillations in Cells Using Bispectral Analysis

The oscillation synchronization analysis in biological systems will expand our knowledge about the response of living systems to changes in environmental conditions. This knowledge can be used in medicine (diagnosis, therapy, monitoring) and agriculture (increasing productivity, resistance to adverse effects). Currently, the search is underway for an informative, accurate and sensitive method for analyzing the synchronization of oscillatory processes in cell biology. It is especially pronounced in analyzing the concentration oscillations of intracellular signaling molecules in electrically nonexcitable cells. The bispectral analysis method could be applied to assess the characteristics of synchronized oscillations of intracellular mediators. We chose endothelial cells from mouse microvessels as model cells. Concentrations of well-studied calcium and nitric oxide (NO) were selected for study in control conditions and well-described stress: heating to 40 °C and hyperglycemia. The bispectral analysis allows us to accurately evaluate the proportion of synchronized cells, their synchronization degree, and the amplitude and frequency of synchronized calcium and NO oscillations. Heating to 40 °C increased cell synchronization for calcium but decreased for NO oscillations. Hyperglycemia abolished this effect. Heating to 40 °C changed the frequencies and increased the amplitudes of synchronized oscillations of calcium concentration and the NO synthesis rate. The first part of this paper describes the principles of the bispectral analysis method and equations and modifications of the method we propose. In the second part of this paper, specific examples of the application of bispectral analysis to assess the synchronization of living cells in vitro are presented. The discussion compares the capabilities of bispectral analysis with other analytical methods in this field.

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.

Exendin-4 affects calcium signalling predominantly during activation and activity of beta cell networks in acute mouse pancreas tissue slices

Tight control of beta cell stimulus-secretion coupling is crucial for maintaining homeostasis of energy-rich nutrients. While glucose serves as a primary regulator of this process, incretins augment beta cell function, partly by enhancing cytosolic [Ca2+] dynamics. However, the details of how precisely they affect beta cell recruitment during activation, their active time, and functional connectivity during plateau activity, and how they influence beta cell deactivation remain to be described. Performing functional multicellular Ca2+ imaging in acute mouse pancreas tissue slices enabled us to systematically assess the effects of the GLP-1 receptor agonist exendin-4 (Ex-4) simultaneously in many coupled beta cells with high resolution. In otherwise substimulatory glucose, Ex-4 was able to recruit approximately a quarter of beta cells into an active state. Costimulation with Ex-4 and stimulatory glucose shortened the activation delays and accelerated beta cell activation dynamics. More specifically, active time increased faster, and the time required to reach half-maximal activation was effectively halved in the presence of Ex-4. Moreover, the active time and regularity of [Ca2+]IC oscillations increased, especially during the first part of beta cell response. In contrast, subsequent addition of Ex-4 to already active cells did not significantly enhance beta cell activity. Network analyses further confirmed increased connectivity during activation and activity in the presence of Ex-4, with hub cell roles remaining rather stable in both control experiments and experiments with Ex-4. Interestingly, Ex-4 demonstrated a biphasic effect on deactivation, slightly prolonging beta cell activity at physiological concentrations and shortening deactivation delays at supraphysiological concentrations. In sum, costimulation by Ex-4 and glucose increases [Ca2+]IC during beta cell activation and activity, indicating that the effect of incretins may, to an important extent, be explained by enhanced [Ca2+]IC signals. During deactivation, previous incretin stimulation does not critically prolong cellular activity, which corroborates their low risk of hypoglycemia.