Quorum sensing and remote synchronization in networks of Kuramoto oscillators: a biological interpretation

TL;DR

This paper demonstrates the emergence of quorum sensing and remote synchronization in biologically plausible networks of Kuramoto oscillators, providing insights into their roles in cell proliferation and potential pathological conditions.

Contribution

It introduces a model showing how quorum sensing and remote synchronization occur in Kuramoto oscillator networks, linking these phenomena to biological processes and pathologies.

Findings

Remote synchronization involves distinct synchronized groups separated by non-synchronized paths.

Quorum sensing emerges based on graph edge density.

Remote synchronization may be linked to pathological cell proliferation.

Abstract

Non-linear oscillator networks have revealed properties as the remote synchronization and the quorum sensing. The remote synchronization, defined as the synchronization of nodes not directly connected by any sequence of synchronized nodes, was found firstly in networks of amplitude oscillators and recently in bipartite delayed networks of phase oscillators. The quorum sensing, a biological information scheme discovered in cell aggregates, has been investigated in amplitude oscillators coupled by a common medium. Implications of such findings are important in technology and biology. We show both of them in non-bipartite, biologically plausible networks of Kuramoto oscillators. The quorum sensing emerges using the graph edge density, while the remote synchronization is obtained by means of an oscillator acting as a pacemaker. In the remote synchronization two distinct groups of well inter and infra-synchronized nodes, separated by non-synchronized paths, appear clearly. Our biological interpretation is that the remote synchronization, bypassing the normal quorum sensing mechanism, is responsible of the pathological cell proliferation. This approach seems suitable to study the quorum sensing alterations due to genetic mutation or to the environmental action before the actual mass replication begins.