Physical Review X (Jun 2018)

Key Features of Turing Systems are Determined Purely by Network Topology

  • Xavier Diego,
  • Luciano Marcon,
  • Patrick Müller,
  • James Sharpe

DOI
https://doi.org/10.1103/PhysRevX.8.021071
Journal volume & issue
Vol. 8, no. 2
p. 021071

Abstract

Read online Read online

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 explaining how network topology determines fundamental system properties and constraints has not been 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.