Alan Turing Predicted That Sharks and Birds Share a Surprising Feature

Alan Turing described this pattern decades ago.

Patterns are everywhere in nature, from the colors of Jupiter to a zebrafish’s stripes. Patterns even show up across very different animals. Scientists have long known that mammals’ hairs and birds’ feathers follow a particular pattern of arrangement, and new research published in Science Advances shows that shark scales follow the same pattern.

In the paper, published November 7, a team of researchers identified how sharks’ denticles — the tiny, V-shaped scales that cover their bodies — follow the pattern identified by Alan Turing’s reaction-diffusion theory. This theory, which the codebreaking mathematician published in 1952, outlines how molecules in biological systems can give rise to particular patterns. These patterns, scientists have since found, can accurately describe the development of hair follicles and feather patterning. Now sharks join the list of animals whose appendages Turing predicted.

Gareth Fraser, Ph.D., an assistant professor of evolutionary developmental biology at the University of Florida, worked on the research while at the University of Sheffield in the UK. He first noticed something interesting in chickens’ DNA while examining the way they develop their feathers.

“We found these very nice lines of gene expression that pattern where these spots appear that eventually grow into feathers,” Fraser said. “We thought maybe the shark does a similar thing, and we found two rows on the dorsal surface, which start the whole process.”

Through genetic analysis and a genetic inhibition experiment in the small-spotted catshark (Scyliorhinus canicula), scientists inhibited some genes from being expressed in shark embryos — similar genes as those that control the feather development process in chicks. When they did this, they found they could prevent certain rows of scales from developing, which supports the idea that chickens’ and sharks’ appendages are controlled by a similar set of genetic information.

But they also wanted to find out if the shark scales’ patterns fit Turing’s math.

“We teamed up with a mathematician to figure out what the pattern is and whether we can model it. We found that shark skin denticles are precisely patterned through a set of equations that Alan Turing — the mathematician, computer scientist, and the code breaker — came up with,” said Fraser. He and his colleagues found that Turing’s reaction-diffusion equations matched what they observed on the sharks’ denticles, shown in the video of a CT scan above.

A CT scan of a small-spotted catshark hatchling's head shows its arrangement of denticles.

Rory Cooper

Rory Cooper, a Ph.D. student at the University of Sheffield and the paper’s first author, explained that since sharks belong to an extremely old branch of vertebrate evolution, studying shark skin can give scientists a better idea of what vertebrates’ skin appendages — like hair and scales — looked like very early on.

“We wanted to learn about the developmental processes that control how these diverse structures are patterned, and therefore the processes which facilitate their various functions,” he said.

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