Saturday, June 23, 2012

Turing at 100

The NY Times has a piece commemorating Turing's 100th birthday anniversary today. Despite Turing's work on computers and codes, in the long run it may be one of his last papers published in August 1952, entitled (he died June 7, 1954):

The Chemical Basis of Morphogenesis, Phil Trans Royal Society London pp 37‐72, 1952

He states in the Abstract:

It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system.

The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and  or whorled leaves. A system of reactions and diffusion on a sphere is also considered.  Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. 

The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.

Frankly the paper has lasting insight which may surface again as we examine metastatic processes and intra/extra cellular signalling.

It should be noted that the pattern in the above Hemerocallis can be explained by Turing's work. For those who understand the wave equation with a nonlinear constraint then we see two waves of red, one in the center and one at the edge (see my paper on Turing coloring). It can likewise be argued that the flow of inter-cellular ligands in metastatic cancers follow a similar model (see my White Paper).

One can only imagine what would have happened if he had gotten further with the Watson and Crick paper, dated April 25, 1953.