Fifty years after Alan M. Turing - An extraordinary theory of morphogenesis

The publication of `The Chemical Basis of Morphogenesis' by ALAN M. TURING in 1952 was a milestone for the development of mathematical biology and for many (biological) disciplines leaning on it. TURING provided an original solution to the problem of morphogenesis, by adapting a system of coupled differential equations to describe both chemical reaction and diffusion of morphogenetic substances in an initially homogeneous configuration. FOURIER'S analysis of the `ring problem' in heat conduction, and the theory of spherical harmonies and their solution by (normalized) LEGENDRE's associated functions form the mathematical backbone of TURING's work on morphogenesis. TURING was up to more than providing a mathematical description of initial stages of embryonic development. Rather he was eager to unveil the mathematical foundations of living, biological organization. An investigation of the archival material of unpublished letters and manuscripts indicates that TURING was clearly determined to provide an argument for the generation of `order-from-disorder'. Unfortunately, during his lifetime TURING remained unable to demonstrate the use of his model beyond the level of early embryonic stages. In the posthumously-published manuscripts several indications are found for further adaptation and improvement of TURING'S model to handle more accurately the reaction-diffusion processes in small organisms.