Key features of Turing systems are determined purely 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.

19 pages, 6 figure, supplementary material (29 pages, 19 figures)

References in corpus (2)

• Turing patterns in network-organized activator-inhibitor systems
• Feedbacks, Receptor Clustering, and Receptor Restriction to Single Cells yield large Turing Spaces for Ligand-receptor based Turing Models

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