Alan Turing's leopard science

’After another long time, what with standing half in the shade and half out of it, and what with the slippery-slidy shadows of the trees falling on them, the Giraffe grew blotchy, and the Zebra grew stripy, and the Eland and the Koodoo grew darker, with little wavy grey lines on their backs like bark on a tree trunk .’

Rudyard Kipling, ’Just so stories’, 1902

Kipling’s story of how the animals of Africa obtained their distinctive marking patterns is a fine example of Lamarckism - the inheritance of environmentally acquired characteristics. But the explanation that his contemporary biologists would have offered, invoking Darwinian adaptation driven by the markings’ ability to camouflage their hosts, was arguably little more than a ’Just so story’ too.

Although it explained why a marking pattern would spread and persist in a population, it could say nothing about how such a pattern came to be, either in evolutionary terms or during the embryonic development of a particular zebra, giraffe or koodoo.

It cannot be down to genetic painting-by-numbers: the markings on two animals of the same species are recognisably alike, but not identical. So how do the melanin pigments of animal pelts get distributed across the embryonic epidermis in these characteristically blotchy ways?

Today’s favoured explanation is based on a mechanism proposed in 1952 by the British mathematician Alan Turing. He is best known for his work on artificial intelligence and his wartime code-cracking at Bletchley Park; but his paper on ’The chemical basis of morphogenesis’¹ was something else. It attempted to explain how a spherical ball of cells ends up as a shape in which different cells, tissues and appendages are assigned to different locations.

Turing proposed a set of differential equations which explained how that initial spherical symmetry could be broken. The equations describe a reaction-diffusion system, where some autocatalytic reaction can amplify random chemical inhomogeneities while the competing process of molecular diffusion tends to smooth them out. Turing’s calculations showed that patterning could emerge from this system.

In 1972, Hans Meinhardt and Alfred Gierer in Germany clarified the essential ingredients of Turing’s model. They showed that the chemical patterns are due to competition between an autocatalytic ’activator’ molecule, and an inhibitor molecule that suppresses the activator.

If the inhibitor diffuses more rapidly than the activator, high concentrations of activator develop close to their source while being suppressed by the inhibitor over longer distances. This gives rise to isolated islands of activator, producing patterns of regularly sized and spaced spots and stripes.

But it wasn’t clear whether this system was anything more than a pretty mathematical fiction until 1990, when a team led by Patrick De Kepper at the University of Bordeaux, France, identified the first chemical Turing pattern, using a reaction that, when well mixed, oscillated between yellow and blue states. This was closely related to the Belousov-Zhabotinsky reaction, known since the 1960s to generate travelling chemical waves.

So are patterns in the living world really made this way? Theoretical activator-inhibitor systems have now been able to provide very convincing mimics of a wide range of animal markings, from the reticulated mesh of the giraffe’s pelt to the crescent-shaped rosettes of the leopard and jaguar, the spots of the ladybird and the stripes of the zebrafish. It all looks plausible enough, but the clinching proof - the identification of the diffusing chemicals responsible for pigmentation - has remained elusive.

Biomolecules called transforming growth factor b proteins seem to act as diffusing chemical morphogens of the sort Turing envisaged in fly and vertebrate embryogenesis, signalling the developmental fate of cells as they diffuse through the embryo. But there wasn’t any direct evidence of such morphogens acting as the agents of activator-inhibitor patterns, as they did in Turing’s original model.

Not, that is, until now. Thomas Schlake and colleagues at the Max Planck Institute of Immunobiology in Freiburg have finally discovered activator and inhibitor molecules at work in biological patterning.

They have found that the follicles of mouse hair are positioned in the epidermis by the protein products of two classes of genes, called WNT and DKK. The former appears to take the role of activator, inducing follicle formation, while several variants of DKK proteins act as inhibitors.²

Hair and feather positioning has long been suspected as an example of a Turing pattern - the equidistant, roughly hexagonally packed patterns are just what would be expected. Schlake and colleagues have made that case by looking at how over-expression of WNT and DKK alters the follicle patterns on mutant mice, showing that these match the predictions based on an activator-inhibitor model. It is probably the best reason yet to think that Turing’s intuition was sound.