Alan Turing’s equations explain shark skin


The mathematician’s reaction-diffusion model explains patterning across the vertebrate lineage. Nick Carne reports.


A small-spotted catshark embryo.

A small-spotted catshark embryo.

Cooper, et al.

Alan Turing’s explanation for how modern animals developed their scales, feathers and hair may have even broader application.

New research suggests the famous mathematician’s famous reaction-diffusion (RD) model also explains the development of the shark’s tooth-line skin.

That’s significant, according to zoologist Rory Cooper from the University of Sheffield, UK, because while previous research has found support for RD patterning in four-legged animals, its role in earlier-diverging lineages has not been clear.

Widely known simply as the Turing Model, RD is a theoretical construct used to explain self-regulated pattern formation in the developing animal embryo.

The model, Cooper says, explains the progression of epithelial appendages – external structures such as hair, feathers, scales, spines and teeth – over at least 450 million years, a timeframe that spans the evolution of vertebrates.

These structures, he says, all possess similar developmental positioning in relation to one another because they grow from a common foundation – the thickened areas of the epithelium known as placodes.

In their recent research, described in a paper published in Science Advances, Cooper and colleagues from the UK and the US studied the small-spotted catshark (Scyliorhinus canicula) at about 80 days post-fertilisation, using RD modelling and gene expression analysis.

The modelling showed that dorsal denticle rows acted as “initiator” rows, triggering the patterning of surrounding tooth-like skin.

The researchers compared the patterning of shark denticles to chick feathers, in which RD modelling is at play, by examining the expression of a protein called beta-catenin that is an early regulator of chick epithelial placode signalling – and determined a similarity.

The shark lateral line expressed the protein soon before denticle patterning began, a comparable timeline to feather patterning.

They then used the RD model to explain the diversity of denticle patterning in other ancient cartilaginous fishes – the thornback skate (Raja clavate) and the little skate (Leucoraja erinacea) – and suggest it may have aided the evolution of such functions as protective armour, hydrodynamic drag reduction, feeding and communication

“We propose that a diverse range of vertebrate appendages, from shark denticles to avian feathers and mammalian hair, use this ancient and conserved system, with slight genetic modulation accounting for broad variations in patterning,” the researchers conclude.

  1. https://www.britannica.com/biography/Alan-Turing
  2. http://science.sciencemag.org/content/329/5999/1616
  3. http://advances.sciencemag.org/content/4/11/eaau5484
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