The Chemical Basis of Morphogenesis

The Turing Pattern. First edition of the rare true author's-presentation offprint of Turing's last major published work - the paper in which he showed how chemical diffusion through living tissue can break symmetry and organise itself into stable spatial pattern, founding the mathematical theory of biological pattern formation and standing now, of everything Turing wrote, as the most-cited. The present copy carries the ink ownership inscription of the plant morphologist Otto L. Stein. Loosely inserted is a typed letter of 28 August 1956 from R. A. Brooker - Turing's successor at the Manchester Computing Machine Laboratory - answering the request for a reprint that Stein had posted, more than two years earlier, to Turing himself. Provenance: Otto Ludwig Stein (1925-2014), German-born American botanist, with his ink ownership inscription at the upper right corner of the front wrapper and, loosely inserted, the typed letter of R. A. Brooker to him of 28 August 1956. Stein took his doctorate at the University of Minnesota in 1954 and worked, at Brookhaven National Laboratory, on precisely the problem Turing's paper had named - the rates at which leaves are initiated at a growing shoot-tip, the phyllotaxis Turing had singled out as a target. He came to Turing's theory through the Manchester botanist C. W. Wardlaw, who had worked with Turing on an unpublished joint paper on plant morphogenesis - the typescript survives in the King's College Turing Archive - and who carried the theory to botanists in two New Phytologist commentaries of 1953 and 1955. Stein duly wrote to Turing for a copy of the paper - but his postcard reached Manchester after Turing's death at Wilmslow on 7 June 1954, and lay unanswered until R. A. ('Tony') Brooker, whom Turing had brought to Manchester to take over the running of the Ferranti, replied for the dead man. Brooker's letter, typed on the printed laboratory stationery of F. C. Williams, is plain and exact: he has received the postcard 'addressed to Dr. A. M. Turing, who died some two years ago', and encloses 'a copy of the reprint requested'. The letter records a working botanist's request for the paper, the author two years dead, answered out of the laboratory's reserve by his successor, and ties this copy to the work the paper had set in motion. The question the paper attacks had held Turing since he read D'Arcy Wentworth Thompson's On Growth and Form as a young man: how does biological matter, growing from a nearly uniform egg, decide where to put a limb, a stripe, a whorl of leaves? He came to Manchester in 1948 as deputy director of the Royal Society Computing Machine Laboratory, and when the Ferranti Mark I was delivered there in February 1951 he had at last the machine on which to attack it. He told Mike Woodger at the National Physical Laboratory that one of the machine's first jobs would be 'to do something about "chemical embryology"' (Hodges, Alan Turing: The Enigma, p. 436), and worked at it through 1951, often at night. He told Robin Gandy the theory was meant 'to defeat the Argument from Design': where the biology of the day spoke vaguely of 'morphogenetic fields' endowing tissue with an invisible pattern, and where Michael Polanyi held that embryonic form admitted no mechanical explanation at all, Turing proposed to treat the field as nothing more than a distribution of chemical concentrations and to ask what such a distribution could do on its own. His answer is the paper's lasting contribution. Pattern, he showed, can arise from the interaction of diffusing, reacting chemical substances - he called them morphogens - by a mechanism that runs flatly against intuition. Diffusion alone smooths differences away and should erase any pattern; but Turing proved that in a system of two such substances reacting together, one diffusing faster than the other, the uniform state becomes unstable, so that the smallest random disturbance grows into a fixed, regular spatial pattern of concentration. He w.…