22 TEMPORAL ORGANIZATION IN CELLS 



early cosmologists; and hence there is an overwhelming tendency for men to 

 think in circles. 



However that may be, the occurrence of periodicities in the dynamic 

 motion of complex systems is of the greatest analytical importance, as Poincare 

 discovered in his studies of non-linear planetary motions: "Ce qui nous rend 

 ces solutions periodiques si precieuses, c'est qu'elles sont, pour ainsi dire, la 

 seule breche par ou nous puissions penetrer dans une place jusqu'ici reputee 

 inabordable." The same opening may give us an entrance into a general 

 dynamics of cellular activity, hitherto an almost inaccessible field of study. 

 It is of interest to note that Volterra's (1931) work on prey-predator systems 

 was also grounded in the analytic study of oscillating motions, the observa- 

 tional background for his work being the most obtrusive feature of population 

 dynamics : fluctuations in population numbers. There are not many ecologists 

 who would defend the assumptions which Volterra made with regard to the 

 details of prey-predator interactions and their importance in general ecological 

 regulation. It would seem that the emphasis in this field is now more on the 

 question of available food supply and physiological control of reproduction 

 and migration, an emphasis which in fact fits more readily the point of view 

 of control by feed-back processes. Nevertheless, the procedure followed in 

 the present study owes much to the methodology of Volterra as well as Poincare, 

 and also to more recent extensions of their work, especially Kerner's (1957, 

 1959) very interesting papers on the statistical mechanics of Volterra systems. 

 The accessibility of periodic phenomena to experimental and theoretical study 

 allows one to proceed with a rationally directed programme of investigation 

 which can draw heavily upon the classical procedures of observational and 

 analytical science. 



