6. THE RELAXATION TIME OF THE EPIGENETIC SYSTEM 93 



Another aspect of these studies which is of great interest is the fact that the 

 periodic fluctuations in DNAase activity were observed not in single cells but 

 in a population of cells from developing tissue of lily anthers. The dynamic 

 behaviour of these cells must therefore be quite strongly synchronized. This 

 indicates that time structure in developing organisms can be generated at a 

 level higher than the single cell, as indeed one might have expected from the 

 embryological phenomena of competence and individuation in tissues. It may 

 thus be necessary to extend the ideas developed in this study to include inter- 

 actions between cells as well as within them, an extension which could readily 

 be realized by using the theoretical construct known as the grand canonical 

 ensemble. The possibility that time structure of the type considered here may 

 extend beyond the single cell in embryological systems has very important 

 implications not only theoretically but experimentally as well, since it makes 

 possible dynamic studies on developing cell populations rather than on single 

 cells. 



Hotta and Stern (1961) have also made observations on the dynamic be- 

 haviour of other enzymes involved in nucleotide metabolism besides DNAase. 

 In general they do not show the same kind of periodicity as that observed in the 

 case of DNAase, their behaviour being more directly related to the mitotic 

 cycle. For example, thymidine kinase activity increases dramatically in lily 

 microspores just prior to DNA synthesis. However, the time-course of vari- 

 ation of this enzyme in differentiating microspores is not a smooth one, a 

 number of smaller peaks of activity preceding the main ones. Thus even in this 

 case there may be an indication of an oscillating control mechanism underlying 

 the time structure involved in the mitotic cycle. 



The second set of experiments to be considered comes from recent work by 

 Tanzer and Gross (1963) and by Jackson, (personal communication) on 

 the dynamics of the proline pool in embryonic chick cells and in the skin of the 

 young guinea-pig. Somewhat to their surprise, these workers have all observed 

 very marked fluctuations in the specific activity of radioactive proline both 

 in the free state and in collagen, with periods of 1 to 4 h, following the adminis- 

 tration of labelled amino acid to the experimental animals. More detailed 

 investigations are required before it can be categorically stated that what is 

 being observed by these workers is an endogenous metabolic oscillator with a 

 period in the range of 1-4 h; but the variations have a very marked periodicity 

 which is too definite to be ascribed to random fluctuations in the experimental 

 procedure. This is further reinforced by the fact that it is possible to eliminate 

 the variations by either flooding the embryos with cold proline after exposure 

 to hot metabolite, or by administering cortisone with the labelled amino acid. 



The first observation is an extremely interesting one in relation to the 

 present theory, which off'ers an interpretation of it. As discussed in the last 

 chapter, one of the immediate consequences of our assumptions regarding the 

 dynamic behaviour of cellular control circuits is that the size of a metabolic 

 pool should show periodic variations whenever the cell is producing the 

 metabolite endogenously by a biosynthetic sequence which is regulated by 

 feed-back repression. If we assume that the cells of the chick are synthesizing 



