Key features of turing systems are determined purely by network topology

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dc.contributor.author	Diego, Xavier
dc.contributor.author	Marcon, Luciano, 1983-
dc.contributor.author	Müller, Patrick
dc.contributor.author	Sharpe, James
dc.date	2018
dc.identifier.citation	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
dc.identifier.citation	2160-3308
dc.identifier.citation	http://dx.doi.org/10.1103/PhysRevX.8.021071
dc.identifier.uri	http://hdl.handle.net/10230/43059
dc.format	application/pdf
dc.language.iso	eng
dc.publisher	American Physical Society
dc.relation	Phys Rev X. 2018; 8(2):021071
dc.relation	info:eu-repo/grantAgreement/EC/H2020/670555
dc.relation	info:eu-repo/grantAgreement/EC/FP7/601062
dc.relation	info:eu-repo/grantAgreement/EC/H2020/637840
dc.rights	© Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
dc.rights	https://creativecommons.org/licenses/by/4.0/
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Biological physics complex systems
dc.subject	Nonlinear dynamics
dc.title	Key features of turing systems are determined purely by network topology
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/publishedVersion
dc.description.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.
dc.description.abstract	This research was supported by the ERC advanced grant SIMBIONT (670555) and the Ministerio de Economía y Competitividad (through Centro de Excelencia Severo Ochoa 2013-2017, SEV-2012-0208). X. D. acknowledges support by the ERC-FP7 Grant Swarmorgan (601062). J. S. ackowledges support from ICREA. P. M. and L. M. were supported by ERC Starting Grant QUANTPATTERN (637840).

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