92 TEMPORAL ORGANIZATION IN CELLS 



certain molecular species of cells, which is to say changes of microscopic state. 

 They do not actually tell us how rapidly changes occur in the macroscopic state 

 of the whole epigenetic system, defined in the present study by quantities such as 

 d, G, and S. These microscopic and macroscopic variables are certainly closely 

 related in their rates of change, but it is possible that even after a particular 

 epigenetic component has settled down to a mean value, the whole system may 

 not have reached equilibrium as defined by the relations (33). This equilibrium 

 is reached only as a result of interactions between components, and thus it is a 

 condition which is characteristic of the whole system rather than of any 

 of its parts. We have therefore taken a value for the relaxation time of the 

 epigenetic system which is larger than the time required for small changes to 

 occur in the sizes of the macromolecular populations in the cells of higher 

 organisms. 



Experimental Evidence 



We would like to turn now briefly to two sets of experimental observations 

 which may actually provide some confirmation for the fundamental assump- 

 tions underlying the present analysis, and for the order-of-magnitude estimates 

 which led us to suggest that epigenetic oscillations should have periods of 2-8 h 

 or so. Stern (1961), studying the developmental process in the lily anther, has 

 observed a very pronounced periodic variation in the activity of the enzyme 

 deoxyribonuclease (DNAase). Enzyme activities were studied as a function 

 of bud length, and it was found that the enzyme appeared in pulses which had 

 a duration of from 4 to 6 h. This period is very short compared with the 25 

 days required for the growth of microspores from the tetrad stage to postmitotic 

 DNA synthesis in the anthers, so that the periodicity cannot be correlated with 

 meiotic or mitotic activity. Furthermore, the changes in enzyme activity 

 appear to involve synthesis of new enzyme, since a simple activation mechanism 

 was ruled out. This direct observation of a strongly pronounced rhythmic 

 variation in the activity of a particular enzyme in diff"erentiating cells of a 

 higher plant was quite unexpected, and Stern could find no explanation for it 

 except to suggest that it is in some way a mechanism for its morphogenetic 

 development. In the context of the present study, however, these results could 

 be interpreted as providing the first evidence for our assumptions regarding the 

 fundamental dynamic behaviour of cellular control mechanisms. One very 

 interesting feature of these rhythms in DNAase activity is the fact that the 

 activity does not oscillate in a continuous manner such as is shown by the oscil- 

 lator in Fig. 4. On the contrary, the oscillation is a discontinuous one in the 

 sense that DNAase activity is not detectable at all during parts of the 

 cycles. The oscillations which we have considered so far do not show such 

 behaviour. However, in Chapter 8 we will see how such a "statistical" 

 discontinuity can arise in a weakly interacting system of a particular kind. 

 Stern's observations are the first that seem to bear directly upon the question 

 of whether or not oscillations are an intrinsic part of the dynamic organization 

 of cells. 



