Being dead for sixty years hasn’t stopped Alan Turing’s giant contributions to science. While Turing is primarily famous for laying the foundations for computing (and cracking the Enigma Code) this work refers to a different sort of digit – an explanation of how fingers and toes form.

Aside from his work on computing, artificial intelligence and code breaking, Turing also proposed a theory for how identical embryonic cells could self-organize into the complex shapes and patterning we see in nature. 

Turing demonstrated that remarkable features could be the product of just two chemicals, which he called morphogens. In Turing’s model one morphogen acted as an activator, the other as an inhibitor. Both diffuse away from the cell. On a leopard's fur, concentrations reduce with distance, but they do not do so evenly. While the inhibitor shows a linear decline, the activator declines exponentially from a higher starting point. Where the concentration of activator is higher than inhibitor cells can change color, creating dark spots on a light background.

The elegance of Turing's theory saw it win near universal support as an explanation for not just spots but other colouring such as zebra stripes and many plant features. Earlier this year experimental evidence for Turing’s explanation was published for the first time using synthetic cell-like structures. 

However, support for the idea that Turing’s mechanism explains features such as fingers and toes has waned in recent decades. In 2012 Professor James Sharpe of the Spanish Center for Genomic Regulation produced a paper demonstrating that Hox genes, which control the overall body plan of embryos in animals operate on a Turing system.

Now Sharpe and his colleagues have followed up with evidence in Science that the process of digits emerging from the limb bud, “is controlled by a self-organizing Turing mechanism, whereby diffusible molecules interact to produce a periodic pattern of digital and interdigital fates.”

Sharpe has identified the BMP and WNT signaling pathways as being essential, and linked by the transcription factor Sox9. Predictions on how these pathways would respond to inhibiting factors were confirmed using limb bud tissue in a Petri dish, producing the beginnings of embryonic fingers. The paper claims, “By combining experiments and modeling, we reveal evidence that a Turing network...drives digit specification.”

For all their elegance, Turing systems are less precise than other methods to control cell formation, so this work explains why polydactylism (extra fingers or toes) is relatively common.

The implications however, are deeper than our extremities. The dominant theory on the formation of internal organs has been that the cells that make them up are instructed on how to develop based on their locations within the body. Sharpe's work suggests that self-organizing processes may have a larger role to play than has been accepted. Resolving this question is crucial to the hope of being able to grow organs in the lab.