Symmetry breaking and computer simulation

Alan Turing's 1952 paper 'The Chemical Basis of Morphogenesis' — his last before committing suicide in 1954 — might not appear on everyone's list of Milestones as it fails to answer any specific question in developmental biology. However, by showing that patterns could be generated by simple chemical reactions, together with diffusion, it marked a change in how the processes of development were viewed. It also contains the first applications of computer modelling in biology.

Turing attempted to discover how the symmetry of a homogeneous mass of identical cells could be broken to form a particular pattern of two or more spatially distinct cell types. He saw that, if the differentiated state was more thermodynamically stable than the homogeneous state, then any small deviations from complete homogeneity, such as were produced by the stochastic fluctuations that occur all the time, would be amplified and homogeneity would be lost.

To set up this kind of instability, Turing investigated a hypothetical situation in which cells produced two or three different 'morphogens' — freely-diffusing molecules that controlled their own production and the cells' subsequent development. In the two-morphogen case, the first diffused slowly and enhanced morphogen production, and the second diffused more quickly and was inhibitory. This scheme could be applied to a ring of cells using “relatively elementary mathematics”.

Turing also had, at his disposal, Manchester University's newly installed Ferranti Mark I, the first ever commercially available computer. With this he showed that depending on the values assigned to the model's parameters, six different classes of self-organizing pattern could result, some reminiscent of biological structures. The most evocative had standing waves of morphogen around the ring, reminding Turing of the distribution of tentacles around a hydra or the distribution of petals in a flower.

By considering a sphere of cells, Turing also modelled the blastula stage of embryo development, a point at which some embryos begin patterning. Here, the equations predicted a single, randomly positioned area of maximum morphogen concentration, which could be identified with the vegetal pole formed by amphibian and sea-urchin embryos.

Although no event in embryogenesis has been found that relies on the exact scheme that Turing outlined, reaction–diffusion models of the Turing type have been widely explored. Most notably, Alfred Gierer and Hans Meinhardt showed that the more general case of local self-enhancement coupled with longer-range inhibition was not only sufficient but, in fact, necessary for pattern formation to occur. Many processes in both animals and plants depend on such Turing–Gierer–Meinhardt mechanisms.

That is not to say that Turing's original proposal wouldn't work. In the early 1990s, purely chemical systems producing Turing patterns were developed and 5 years later, a natural Turing pattern was found on the skin of an angelfish. However, the significance of Turing's paper is not in what it says — although anyone trying to present highly mathematical arguments to a non-mathematical audience should read it as an object lesson on how it should be done — but rather for its demonstration that development could be approached in a quantitatively rigorous fashion.