A PROBABILISTIC MODEL FOR MORPHOGENESIS* 



Murray Eden 



Laboratory of Technical Development, National Heart Institute, 

 National Institutes of Health, Bethesda 14, Maryland 



Abstract — A program has been outlined for establishing relationships between the form of an 

 organism and the minimal information content of the germ cell from which the organism was 

 derived. A simple two-dimensional model has been chosen in order to explore the feasibility 

 of such a program. A suitable information measure has been defined for this model and 

 computations of information have been made for small aggregates of cells, as well as estimates 

 for larger aggregates. 



An arbitrary growth process has been formulated which is analogous to an assignment of 

 virtually no information to the germ cell. The properties of this growth process have been 

 studied and suggest that even such minimal information content in the germ cell is sufficient to 

 specify the over-all form of the organism with high probability after a certain number of 

 divisions have taken place. Possible ways of extending the model and increasing its embryo- 

 logical relevance have been suggested. 



One of the problems that has been touched in this symposium is the particularly 

 elusive subject that has been with biology since its beginnings as a science; 

 that is, the general relationship between function and form and between growth 

 and form. In the particular terms of discourse of this symposium the question 

 might be phrased in this way: 'What is the minimal amount of information 

 that is required in a fertilized egg, so that after a certain number of divisions 

 and a certain length of time the egg will have developed into an organism that 

 is recognizable as being a member of a certain species?' 



A number of workers have estimated the information content of biological 

 objects. Dancoff and Quastler (1) computed values of information content 

 relative to four different models; on the basis of atomic orientation, molecular 

 structure, chromosome volume and a genotype catalogue. These authors were 

 careful to specify the limitations of their computations. They write, 'We have 

 arrived, by very tentative methods, to the result that the essential complexity 

 of a single cell and of a whole man are both not more than 10^^ nor less than 

 10^ bits; this is an extremely coarse estimate, but is better than no estimate 

 at all.' LiNSCHiTZ estimated the 'physical entropy' of a bacterial cell as being 

 10^^ bits (2) and Yockey (3) has computed the information content of DNA 

 based on its molecular size and on a postulated cryptographic relation between 

 proteins and nucleic acids. Most of the values obtained have been very large, 

 and one would presume that they are large enough to describe adequately 

 the observable properties of a living organism, it may be that the growing 

 organism requires a lot less information in the germ cell than is indicated by 



* The work presented here was begun during the tenure of an United States Public Health 

 Service Special Fellowship in the Department of Mathematics, Princeton University, Princeton, 

 New Jersey. 



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