A new dimension to Turing patterns

TL;DR

This paper explores three-dimensional Turing patterns through reaction-diffusion systems, analyzing morphology, stability, and robustness, and raises questions about their potential role in neuronal growth signaling.

Contribution

It introduces a study of 3D Turing patterns in generic and Gray-Scott models, including effects of morphogen sources and implications for neuronal signaling.

Findings

3D Turing patterns exhibit complex morphologies and stability.

Adding morphogen sources affects pattern robustness and connectivity.

Potential link between Turing patterns and neuronal growth signaling.

Abstract

It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signaling mechanism for neuronal growth.