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In 1952, Alan Turing, a British mathematician best known for his work on code-breaking and artificial intelligence, was convicted of engaging in homosexual acts and sentenced to chemical castration. Amid that personal drama, he still found the time to publish a visionary paper on the mathematics of regularly repeating patterns in nature, which could be applied to the stripes on tigers and zebra fish, the spots on leopards and the spacing in rows of alligator teeth, to name a few.
Now, more than 60 years later, biologists are uncovering evidence of the patterning mechanisms that Turing proposed in his paper, prompting a resurgence of interest in them, with the potential to shed light on such developmental questions as how genes ultimately make a hand. “That structure is there,” said Jeremy Green, a developmental biologist at King’s College London. “We just need to put the chemistry onto the mathematics to get the biology.”
For the work that led to his 1952 paper, Turing wanted to understand the underlying mechanism that produces natural patterns. He proposed that patterns such as spots form as a result of the interactions between two chemicals that spread throughout a system much like gas atoms in a box do, with one crucial difference. Instead of diffusing evenly like a gas, the chemicals, which Turing called “morphogens,” diffuse at different rates. One serves as an activator to express a unique characteristic, like a tiger’s stripe, and the other acts as an inhibitor, kicking in periodically to shut down the activator’s expression.
To explain Turing’s idea, James Murray, emeritus professor of mathematical biology at the University of Oxford and an applied mathematician at Princeton, imagined a field of dry grass dotted with grasshoppers. If the grass were set on fire at several random points and no moisture were present to inhibit the flames, Murray said, the fires would char the entire field. If this scenario played out like a Turing mechanism, however, the heat from the encroaching flames would cause some of the fleeing grasshoppers to sweat, dampening the grass around them and thereby creating periodic unburned spots in the otherwise burned field.
The notion was intriguing but speculative. Turing died two years after the publishing of his paper, which languished in relative obscurity for decades. “He didn’t actually apply it to any real biological problem,” Murray said. “It was mainly a boon for mathematicians looking for analytical problems.”
Although there was an explosion of theoretical work and computer modeling in the 1970s that successfully reproduced patterns like spots and stripes using Turing mechanisms, molecular biology was nowhere near the point where researchers could identify the specific molecules acting as activators and inhibitors.
The latest research suggests that Turing-type mechanisms may be responsible for the spacing between hair follicles in mice and feather buds on a bird’s skin, the ridges that form on a mouse’s palate and the digits on a mouse’s paw.