Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling

TL;DR

This paper introduces a new mechanism for spatiotemporal oscillations in extended systems, arising from membrane-bulk coupling of different dimensions, with potential biological implications.

Contribution

It demonstrates that membrane-bulk coupling can induce self-sustained oscillations without local bulk instabilities, supported by analytical and numerical analysis.

Findings

Coupling a passive bulk with a membrane induces oscillations.

Oscillations exhibit in-phase and anti-phase synchronization.

Mechanism applicable to biological systems like cells.

Abstract

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and anti-phase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.