# CRG: New theory deepens understanding of Turing patterns in biology

News from CRG

Alan Turing sought to explain how patterns in nature arise with his 1952 theory on morphogenesis. The stripes of a zebra, the arrangement of fingers and the radial whorls in the head of a sunflower, he proposed, are all determined through a unique interaction between molecules spreading out through space and chemically interacting with each other. Turing’s famous theory can be applied to various fields, from biology to astrophysics.

Many biological patterns have been proposed to arise according to Turing’s rules, but scientists have not yet been able to provide a definitive proof that these biological patterns are governed by Turing´s theory. Theoretical analysis also seemed to predict that Turing systems are intrinsically very fragile, unlikely for a mechanism that governs patterns in nature.

CRG alumni scientists Xavier Diego, James Sharpe and colleagues now at EMBL’s new site in Barcelona, analysed computational evidence that Turing systems can be much more flexible than previously thought. Following this hint, the scientists expanded Turing’s original theory by using graph theory: a branch of mathematics that studies the properties of networks and makes it easier to work with complex, realistic systems. This led to the realization that network topology –the structure of the feedback between the networks' components– is what determines many fundamental properties of a Turing system. Their new topological theory provides a unifying view of many crucial properties for Turing systems that were previously not well understood and explicitly defines what is required to make a successful Turing system.

Reference article:

Diego, X., et al. Key features of Turing systems are determined purely by network topology. *Physical Review X*, published online 20 June 2018. DOI: 10.1103/PhysRevX.8.021071

More information:

CRG website