Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

TL;DR

This paper demonstrates that spatiotemporal patterns can naturally emerge in electrically-coupled smooth muscle cells without external forcing, using a reaction-diffusion model and bifurcation analysis.

Contribution

It shows spontaneous pattern formation in coupled muscle cells through a reaction-diffusion model, without relying on external stimuli or forcing.

Findings

Patterns occur without external forcing.

Bifurcation analysis explains excitability types.

Traveling waves are characterized in the system.

Abstract

Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that spatiotemporal patterns in electrically-coupled smooth muscle cells occur even in the absence of forcing. We study a reaction-diffusion system with the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling -- in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and use travelling wave coordinates to analyse travelling waves.