Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions

TL;DR

This study explores how inhomogeneous chemostatted species influence glycolytic wave patterns in a reaction-diffusion system, revealing complex dynamic transitions and phase behaviors relevant to biological processes.

Contribution

It introduces an analytical amplitude equation linking complex Ginzburg-Landau and Lambda-omega models to understand phase dynamics in glycolytic waves with inhomogeneous influx.

Findings

Diffusion amplitude and symmetry affect pattern types and transitions.

Dynamic transitions include wave direction changes.

Analytical formulation clarifies phase behavior in the system.

Abstract

An inhomogeneous profile of chemostatted species generates a rich variety of patterns in glycolytic waves depicted in a Selkov reaction-diffusion framework here. A key role played by diffusion amplitude and symmetry in the chemostatted species profile in dictating the fate of local spatial dynamics involving periodic, quasiperiodic, and chaotic patterns and transitions among them are investigated systematically. More importantly, various dynamic transitions, including wave propagation direction changes, are illustrated in interesting situations. Besides numerical results, our analytical formulation of the amplitude equation connecting complex Ginzburg-Landau and Lambda-omega representation shed light on the phase dynamics of the system. This systematic study of the glycolytic reaction-diffusion wave is in line with previous experimental results in the open spatial reactors and will provide knowledge about the dynamics that shape and control biological information processing and related phenomena.