# Patterns Turing spotted

07 Aug 2006Did you know that Alan Turing tried to solve the problem of biological form? That following D'Arcy Thompson, he laid the groundwork for an important branch of what has become evo-devo?

Well, Nature News has a story about it, in the context of a bunch of mathematical biologists who have been trying to fit the model to the ontogeny of cat spots:

Turing supposed that coat patterns could be produced by two chemicals, which he called 'morphogens', interacting on the more or less two-dimensional space of the hide. If one morphogen causes hair to turn black, for example, and another causes it to remain pale, then differences in the rates at which these chemicals diffuse through the coat, along with various reactions between the two, would determine the patterns.

Turing called them 'reaction-diffusion equations'. By tweaking the variables of diffusion speed and other behaviours of the morphogens, researchers have been able to use these equations to replicate familiar coat patterns.

For the past couple of decades, people have been trying to fiddle with the parameters of this model to account for various biological patterns, from the positions of leaves on stems of plants to the coat patterns of mammals. The trigger for the story here was the innovation of two distinct stages to account for infant and adult cat coat patterns:

"The pattern of the jaguar was the hardest part," says [researcher Sy-Sang] Liaw, who reports the work in Physical Review E2. "People who try to do the pattern with one stage only will never get it. You have to separate it into two stages."

The interesting part to me is how Turing got interested in the problem. The Slashdot discussion of the topic includes a comment quoting from the topic introduction in the *Collected Works of Alan Turing*:

For Turing, however, the fundamental problem of biology had always been to account for pattern and form, and the dramatic progress that was being made at that time in genetics did not alter his view. And because he believed that the solution was to be found in physics and chemistry it was to these subjects and the sort of mathematics that could be applied to them that he turned. In my view, he was right, but even someone who disagrees must be impressed by the way in which he went directly to what he saw as the most important problem and set out to attack it with the tools that he judged appropriate to the task, rather than those which were easiest to hand or which others were already using.

You can find one of the relevant papers, "The chemical basis of morphogenesis" at the Turing Archive. Another site has a strangely addictive Java script that yields random biological patterns based on the reaction-diffusion model.

#### References:

Turing A. 1952. The chemical basis of morphogenesis. Phil Trans Roy Soc Lond B 237:37. Turing Archive

Liu RT, Liaw SS, Maini PK. 2006. Two-stage Turing model for generating pigment patterns on the leopard and the jaguar. Phys Rev E 74:011914. DOI link