Diversity of coupled oscillators can enhance their synchronization

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.

Random heterogeneity outperforms design in network synchronization

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.

Synchronizing Chaos with Imperfections

Previous research on nonlinear oscillator networks has shown that chaos synchronization is attainable for identical oscillators but deteriorates in the presence of parameter mismatches. Here, we identify regimes for which the opposite occurs and show that oscillator heterogeneity can synchronize chaos for conditions under which identical oscillators cannot. This effect is not limited to small mismatches and is observed for random oscillator heterogeneity on both homogeneous and heterogeneous network structures. The results are demonstrated experimentally using networks of Chua's oscillators and are further supported by numerical simulations and theoretical analysis. In particular, we propose a general mechanism based on heterogeneity-induced mode mixing that provides insights into the observed phenomenon. Since individual differences are ubiquitous and often unavoidable in real systems, it follows that such imperfections can be an unexpected source of synchronization stability.

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.