Key features of Turing systems are determined purely by network topology

TL;DR

This paper develops a general theory linking the topology of Turing networks to key system properties, explaining how network structure influences diffusion constraints, robustness, and phase relations in pattern formation.

Contribution

It introduces the first comprehensive theory showing how Turing network topology determines fundamental properties of pattern formation systems.

Findings

Topology constrains diffusion rate restrictions

Network structure influences system robustness

Phase relations are dictated by network topology

Abstract

Turing's theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the mechanisms of pattern selection are well understood in small networks. However, a general set of rules governing how network topology determines fundamental system properties and constraints has not be found. Here we provide a first general theory of Turing network topology, which proves why three key features of a Turing system are directly determined by the topology: the type of restrictions that apply to the diffusion rates, the robustness of the system, and the phase relations of the molecular species.