Key features of turing systems are determined purely by network topology

Diego, Xavier; Marcon, Luciano, 1983-; Müller, Patrick; Sharpe, James

doi:http://dx.doi.org/10.1103/PhysRevX.8.021071

Key features of turing systems are determined purely by network topology

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Diego X, Marcon L, Müller P, Sharpe J. Key features of turing systems are determined purely by network topology. Phys Rev X. 2018;8(2):021071. DOI: 10.1103/PhysRevX.8.021071

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 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.