© Job Boot

“I’ll take spots, then,” said the Leopard, “but don’t make ’em too vulgar-big. I wouldn’t look like Giraffe – not for ever so.”

– ‘How The Leopard Got His Spots’, from Rudyard Kipling’s Just So Stories (1902)

High up in the Centre for Genomic Regulation in Barcelona is an office papered with brightly coloured pictures of embryonic mouse paws. Each one shows neat stripes of developing bones fanning out inside blob-like budding limbs – something the room’s decorator, systems biologist James Sharpe, is convinced can be explained by Turing’s model.

Turing’s idea is simple, so one can easily imagine how it could explain the patterns we see in nature. And that’s part of the problem, because a simple likeness isn’t proof that a system is at work – it’s like seeing the face of Jesus in a piece of toast. Telling biological Just So Stories about how things have come to be is a dangerous game, yet this kind of thinking was used to justify the French flag model too.

In Sharpe’s view it was the chicken’s fault. “If studies of limb development had started with a mouse,” he says, “the whole history would have been very different.”

In his opinion there was a built-in bias right from the start that digits were fundamentally different from each other, requiring specific individual instructions for each one (provided by precise morphogen ‘coordinates’, according to the French flag model). This was one of the primary arguments made against a role for Turing patterns being involved in limb development – they can only ever generate the same thing, such as a stripe or a spot, again and again.

So how could a Turing system create the three distinctive digits of a chick’s limb? Surely each one must be told to grow in a certain way by an underlying gradient ‘map’? But a chick only has three fingers. “If they had 20, you would see that wasn’t the case,” says Sharpe, wiggling his fingers towards me by way of demonstration. “They’d all look much more similar to each other.”

I look down at my own hand and see his point. I have four fingers and a thumb, and each finger doesn’t seem to have particularly unique identity of its own. Sure, there are subtle differences in size, yet they’re basically the same. According to Sharpe, the best evidence that they aren’t that different comes from one of the most obvious but incorrect assumptions about the body: that people always have five fingers.

In reality the number of fingers and toes is one of the least robust things about the way we’re made. “We don’t always have five,” he says, “and it’s surprisingly common to have more.” In fact, it’s thought that up to one in 500 children is born with extra digits on their hands or feet. And while the French flag model can’t account for this, Turing patterns can.

By definition Turing systems are self-organising, creating consistent patterns with specific properties depending on the parameters. In the case of a stripy pattern, this means that the same set-up will always create stripes with the same distance (or wavelength, as mathematicians call it) between them. If you disrupt the pattern, for example by removing a chunk, the system will attempt to fill in the missing bits in a highly characteristic way. And while Turing systems are good at generating repeating patterns with a consistent wavelength, such as regular-sized fingers, they’re less good at counting how many they’ve made, hence the bonus digits.

Importantly, a particular Turing system can only make the same thing over and over again. But look closely at the body and there are many examples of repeating structures. In many animals, including ourselves, the fingers and toes are more or less all the same. But, according to the flag model, structures created in response to different levels of morphogen would all have to be different. How to explain the fact that the same thing can be ‘read’ out from a higher and lower morphogen level?

Sharpe maintains that the concept of an underlying molecular ‘road map’ just doesn’t hold up. “I don’t think it’s an exaggeration to say that for a long time a lot of the developmental biology community has thought that you have these seas of gradients washing over a whole organ. And because they’re going in different directions, every part of the organ has a different coordinate.”

In 2012 – the centenary of Turing’s birth and 60 years since his ‘chemical morphogenesis’ paper – Sharpe showed that this idea (at least in the limb) was wrong.

The proof was neatly demonstrated in a paper by Sharpe and Maria Ros at the University of Cantabria in Spain, published in Science. Ros used genetic engineering techniques to systematically remove members of a particular family of genes from mice. Their targets were the Hox genes, which play a fundamental role in organising the body plan of a developing embryo, including patterning mouse paws and human hands.

Getting rid of any of these crucial regulators might be expected to have some fairly major effects, but what the researchers saw was positively freakish. As they knocked out more and more of the 39 Hox genes found in mice, the resulting animals had more and more fingers on their paws, going up to 15 in the animals missing the most genes.

Importantly, as more Hox genes were cut and more fingers appeared, the spacing between them got smaller. So the increased number of fingers wasn’t due to larger paws, but to smaller and smaller stripes fitting into the same space – a classic hallmark of a Turing system, which had never been observed before in mouse limbs. When Sharpe crunched the numbers, Turing’s equations could account for the extra fingers Ros and her team were seeing.

That’s great for the near-identical digits of a mouse, I say, but it doesn’t explain why the chick’s three digits are so different. Sharpe scribbles on a piece of paper, drawing a Venn diagram of two scruffy overlapping circles. One is labelled “PI” for positional information à la Wolpert, the other “SO” for self-organising systems such as Turing patterns. Tapping at them with his pen, he says, “The answer is not that Turing is right and Wolpert was wrong, but that there’s a combination at work.”

Wolpert himself has conceded, to a certain extent, that a Turing system could be capable of patterning fingers. But it can’t, by definition, impart the differences between them. Morphogen gradients must work on top of this established pattern to give the digits their individual characteristics, from thumb to pinky, marrying together Wolpert’s positional information idea with Turing’s self-organising one.