Formation of antiwaves in gap-junction-coupled chains of neurons

TL;DR

This paper demonstrates the formation of antiwaves and stable phase-shifted activity patterns in gap-junction-coupled neuron chains, using phase models derived from Wang-Buszaki neuron networks, with implications for biological neural systems.

Contribution

It introduces the concept of stable intermediate phase shifts in coupled neuron chains and analyzes their stability and dependence on coupling function Fourier components.

Findings

Stable phase-shifted states can produce wave-like activity patterns.

Higher order Fourier terms influence solution stability and basin of attraction.

Models are potentially applicable to spinal and cortical neural systems.

Abstract

Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call these phase shifts intermediate stable phaselocked states. These phase shifts can produce a large variety of wave-like activity patterns in one-dimensional chains and two-dimensional arrays of neurons, which can be studied by reducing the system of equations to a phase model. The 2\pi periodic coupling functions of these models are characterized by prominent higher order terms in their Fourier expansion, which can be varied by changing model parameters. We study how the relative contribution of the odd and even terms affect what solutions are possible, the basin of attraction of those solutions and their stability. These models may be applicable to the spinal central pattern generators of the dogfish and also to the developing neocortex of the neonatal rat.