How does a cell know what to become?

In 1952 Alan Turing showed mathematically that two substances reacting together and diffusing through a tissue can turn a uniform field into a regular pattern. A homogeneous equilibrium goes unstable under random disturbance, and in the case he found most interesting what appears is a set of stationary waves. Their natural spacing, what he called the chemical wavelength, is set by the reaction and diffusion rates rather than by the size of the tissue; a finite tissue makes do with the nearest spacing that fits.

It was a purely theoretical result, published in a paper about morphogenesis, and it stayed theoretical for a long time because nobody could point to the substances.

A 2012 study started from mice lacking Gli3, which already grow extra digits, and removed distal Hox genes in stages on top of that. Each step made the polydactyly worse: more digits, thinner and more densely packed. With computer modelling, the authors read that as a Turing-type mechanism whose wavelength the dose of those genes modulates.

On that account the digits are stripes, their spacing is a wavelength, and the genes tune it rather than specifying each one. The paper argues for it rather than demonstrating it, and notes that the mutant digits resemble the endoskeleton of a fish fin, which would make five fingers a modification of an older mechanism.

Alongside self-organisation, cells read gradients of signalling molecules to know roughly where they are, and switch on different genes at different concentrations. Wolpert named that positional information in 1969, and it has been the other half of the subject since.

Both mechanisms operate, and Green and Sharpe propose three distinct ways they could work together, which they present as a hypothesis. In the limb, the leading model is a self-organising digit network modulated by morphogen gradients.

For most Turing-like patterns proposed in animals, the interacting molecules are candidates rather than demonstrations: hair follicles and feather buds alone have several rival proposals. Digits are among the cases that have gone furthest: a 2014 paper proposes a network of Bmp, Sox9 and Wnt, arrived at by combining experiments with a two-dimensional simulation that reproduces Sox9 expression in normal limbs and in perturbed ones.

A model that fits a pattern is much easier to produce than a demonstration that particular molecules produce it. A 2020 review holds that resemblance between simulated and real patterns is not enough, and that how often living systems use the mechanism remains unclear; a 2021 review calls its role in development firmly established. The digit network has since grown from three components to five, and when the 2020 review was written some of the added interactions were still untested.

Early analyses found Turing systems sensitive to noise and to their starting conditions, and development is not: digits form in the same stereotyped pattern in individual after individual.

What makes the outcome robust is an open question, and it is the part that any engineering account of development has to answer. Later modelling has found network designs that form patterns across a wide range of their parameters, which answers part of the old objection without showing that development uses them. The 2014 digit model gets its reproducibility from a combination of growth, morphogen gradients and the self-organising network.