34 EMBRYOGENESIS IN PLANTS 



a homogeneous manner, a regular, patternised distribution of specific 

 metabolites may eventually result, affording the basis for the inception 

 of a morphological or histological pattern, (see below). 



Turing's Diffusion Reaction Theory of Morphogenesis. This theory 

 is based on a consideration of the diffusibilities and reaction rates 

 of substances which may be involved in growth and morphogenesis. 

 Considerable mathematical knowledge is essential to follow the theory 

 in detail; but its main features can be indicated to, and appreciated 

 by, the non-mathematical biologist without too much difficulty. 

 The theory introduces no new hypotheses: on the contrary, it 

 makes use of well-known laws of physical chemistry, and, as Turing 

 has shown, these seem likely to be sufficient to account for many 

 of the facts of morphogenesis. The underlying point of view, in fact, 

 is closely akin to that expressed by D'Arcy Thompson in Growth and 

 Form. It will be appreciated that a theory, based essentially on laws 

 of physical chemistry that must apply to every growing system, is of the 

 kind that may well account for the general occurrence of certain 

 organisational features in plants. An essential feature of the theory is 

 that it deals with the inception of a morphogenetic pattern as a whole; 

 but it is not inconsistent with epigenetic development when other 

 organs or parts have already been formed. Not least, it is compatible 

 with the concepts of physiological genetics. 



An indication of the theory may be given by assuming that two 

 interacting, pattern-forming substances, or morphogens, X and Y, are 

 essential metaboUtes in a morphogenetic process ; a third substance C, 

 which is in the nature of an evocator and catalyst, is also involved, a 

 pattern only appearing if its concentration is sufficiently great. It is 

 necessary to assume: (i) that both X and Y are diffusible, and at 

 different rates ; and (ii) that there is a number of reactions involving 

 X, Y and the catalyst C: these reactions do not merely use up the 

 substances X and Y, but also tend to produce them from other meta- 

 bolic substances (which might be called 'fuel substances') which are 

 assumed to be abundantly present in the growing region, i.e. to some 

 extent the morphogens are autocatalytic. If a pattern is to be produced, 

 there is a number of conditions relating the diffusibilities and marginal 

 reaction rates which must be satisfied. (By marginal reaction rate is 

 meant the amount by which the reaction rate changes per unit change of 

 concentration.) If we assume that the appropriate conditions are 

 satisfied, and that the concentration of the catalyst-evocator is initially 

 at a low value, but is slowly increasing, the phenomena observed will 

 be as follows : 



(i) Initially there is a state of homogeneity: both X and Y are 

 uniformly distributed (i.e. in the embryonic tissue in which a pattern 



