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How the leopard got his spots: Turing's theory

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In Rudyard Kipling’s ‘Just So Stories’ is a tale entitled “How the leopard got his spots”. For a variety of reasons I do not enjoy much of Kipling’s work, and I find this particular story excruciatingly awful. (Perhaps I should have written scrutiatingly in acknowledgement of Kipling’s 17 uses of sclusively in his 2,400-word piece.) However, we can dismiss Kipling’s fanciful explanation because we now more or less understand the truth about how the leopards got his spots, thanks mainly to innovative work by Alan Turing (1912–54).

Yes, that’s the Alan Turing who was recently been brought to public attention by the cinema biopic ‘The Imitation Game’. Turing is widely acknowledged as a pioneer in the fields of computer science, mathematics, cryptanalysis, logic and philosophy. He is generally considered to be the father of theoretical computer science and artificial intelligence. He is also lauded for his pivotal code-cracking work at Bletchley Park during the 1939–45 war.

Less well known is Turing’s seminal achievement in mathematical biology, a subject on which he worked from 1952 until his premature death two years later. He published just one paper on the subject, “The chemical basis of morphogenesis”, in which he put forward a set of equations that tried to explain the patterns we see in nature, such as the leopard’s spots, the zebra’s stripes and the arrangement of a plant’s leaves and flowers.

Turing’s simple but elegant theory was that any repeating natural pattern could be created by the interaction of two components with particular characteristics. Through a mathematical principle he called “reaction–diffusion”, these two elements would spontaneously organise themselves to create stripes, spots, rings, etc.

In particular, Turing focused on the theory that developing organisms contained specific molecules — morphogens — that controlled the growing shape and structure. At the time, no one had identified any of these conjectured molecules, but biologists were sure they existed.

Turing’s hypothesis was that morphogenesis involved two components that diffused at different speeds. One component was auto-activating, meaning that it could turn on a mechanism to make more of itself. However, once it reached a certain level it would start producing the second component, an inhibitor that spread at a faster pace and built up to a level at which it switched off the activator.

Turing showed mathematically that these simple components could account for a wide range of patterns. A subtle tweaking of the parameters could alter the pattern to create spots, stripes, swirls, splodges or other markings.

Despite its simplicity and eloquence, Turing’s theory was for decades dismissed by the developmental biology community. Only in recent years has his hypothesis been experimentally confirmed. Although the reality is slightly more complicated than Turing proposed, his theory is now considered a seminal contribution to the science of pattern formation.

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