Structural stability, morphogenesis and epigenetic landscape

The paper " Une théorie dynamique de la morphgenèse " , written by René Thom in 1966 and appeared in 1967 in Towards a theoretical Biology I, published by Conrad Hal Waddington, can be considered as the princeps paper of the catastrophe theory. In this paper Thom declares that embryology and, in particular, Waddington's notions of epigenetic landscape and chreod have been one of his sources in conceiving catastrophe theory. Moreover, Thom tries and shows that embryology, and in particular the problem of cellular differentiation as it was introduced by Max Delbrück in 1949, can be a field of application of Thom's catastrophe theory, i.e. a mathematical theory of morphogenesis, based on the study of the property of structural stability by topology and differential analysis. In the collection of René Thom's works Modèles mathématiques de la Morphogenèse, published in 1980, the French version of this paper is augmented by a correspondence between Conrad Hal Waddington and René Thom (five letters, from the 25th of January till the 23th of February 1967). In my commentary from this correspondence and from other unpublished letters, I will consider two Waddington's criticisms to the first version of Thom's paper and the debate between the two scientists that followed these Waddington's criticisms. The first commentary concerns the paternity of the notion of cellular differentiation. The second criticism concerns the use of alternative steady states instead of time extended chreods. A first interpretation of this lack of agreement between the two scientists can be based on the taking into account of their cultural differences. To use the expression introduced by Evelyn Fox Keller in " Making Sense of Life " , they do not share the same epistemological culture and they do not have the same explanatory needs. René Thom himself introduces this correspondence as an example of the difficulties in communication between a mathematician and a biologist because of the differences in their exigencies of mathematical rigour. However, following some Waddington's remarks on the peculiarity of the variable " time " in biology, I suggest another interpretation of their disagreement. This second interpretation is based on the Waddington's unsatisfied need of representing, thanks to the metaphor of epigenetic landscape, different time scales in the process of the organism development.