Biological Evidence for Turing Patterns

Mouse hair development patterns follow Turing's predictions

In the 1950s, computer science pioneer Alan Turing suggested an elegantly simple mechanism for how biological patterns such as scales, feathers, and hair might form. Now, more than fifty years later, biologists have used a computer model and transgenic mice to confirm mathematical predictions of the Turing model of pattern formation within a specific biological system: mouse hair development.


“It’s the most convincing biological (as contrasted with chemical) experiment to date that claims to support the Turing mechanism,” says Irving Epstein, PhD, a chemistry professor at Brandeis University. The work appeared online in the journal Science in November 2006.


Turing’s 1952 proposition goes like this: Two molecules—an activator that enhances its own production, and an inhibitor that slows the production of the activator—diffuse and react. If the inhibitor diffuses sufficiently faster than the activator, repetitive patterns may spontaneously emerge.


Normal mice have well-spaced hair follicles (left). But a moderate suppression of WNT signaling changes the pattern to follicle clumps (right). Courtesy of Thomas Schlake, Max Planck Institute of Immunobiology.Evenly spaced mouse hair is just the type of pattern that a Turing mechanism might create. That’s one reason biologist Thomas Schlake, PhD, at the Max Planck Institute of Immunobiology started searching for key molecules involved in mouse hair follicle formation that might fit Turing’s predicted pair. He found them in the signaling molecule WNT and its inhibitor DKK.


Schlake and his colleagues created a computer model describing the pair’s Turing behavior and then asked the model to predict what would happen if something went wrong—if WNT or DKK appeared in too great or too small a burst. Experiments with transgenic mice verified their computational predictions. Mice that strongly overexpress DKK, suppressing WNT signaling, look like they are balding. And mice that moderately over-express DKK form clumps of hair instead of regularly spaced follicles.


Schlake thinks it’s likely that other inhibitor/activator pairs (Turing called them morphogens) form the base of other natural patterns.


Of course, stripping complex developmental pathways down to the actions of one Turing pair is a strong simplification of the real world, he adds. Mouse hair follicle placement doesn’t solely depend on the behavior of two interacting molecules. Leagues of other signaling molecules stabilize and refine the process.


Yet it is that very power to simplify and predict outcomes from a small number of key variables that is the hallmark of a good model, Epstein says. He is not surprised that 50 years after Turing proposed his model, biologists are just now providing detailed molecular evidence for it. “Turing,” he says, “was a very smart man.”


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