Synchronization patterns on networks of pancreatic β-cell models

This paper presents the emergence of collective behaviors, such as complete and cluster synchronization, in a network of a-cells coupled through gap-junction channels. Usually, the interaction between adjacent a-cells is dominated by ionic currents through the gap-junctions channel. Whereas in a spatially distributed set of beta cells, the current flow is not necessarily uniform, and the interactions between them change. Motivated by this, we propose a structure for a pancreatic islet where there are different levels of connection. In the first instance, we present a model made up of small densely connected substructures, called compact units. Next, we model the entire islet as a network formed by compact units coupled with different strengths in the gap-junctions channel, and we established the conditions required to achieve complete synchronization in the model. Besides, individually the a-cells present two different modes of operation: the active state where the electrical behavior is characterized by presenting oscillations, known as, square-bursting; and the inhibited state, where its electrical behavior does not produce oscillation. If we extend these behaviors to compact units, we can form weighted networks with different dynamical behaviors. Therefore, we propose the heterogeneous islet model in which compact units have different dynamics (square-bursting behavior or inhibited behavior), and we derived conditions for the emergence of cluster synchronization in the islet using Lyapunov stability theory. Finally, to illustrate our theoretical results, we present numerical simulations. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This paper discusses the emergence of collective behaviors in a network of a-cells coupled through gap-junction channels, presenting a pancreatic islet structure with different levels of connection and proposing a heterogeneous islet model with different dynamics in compact units. The conditions for achieving synchronization in the model and the emergence of cluster synchronization in the islet are established using Lyapunov stability theory. Numerical simulations are presented to illustrate the theoretical results.