8. APPLICATIONS AND PREDICTIONS 145 



Other rhythmic systems. The latter are genuinely periodic : they cycle through 

 the same state at regular intervals. There is no evidence that embryological 

 competence in general is cyclic in this sense. In Curtis's work, competence 

 appears to occur once only after a certain period of time from commencement 

 of aggregation. After the cell has become competent and has responded 

 to a particular stimulus, it changes its state and proceeds to develop new 

 competences. And if it is not induced, there is no evidence that it will become 

 competent again after the same period of time, although this possibility is not 

 ruled out by Curtis's studies either. In Holtfreter's work, however, the obser- 

 vations definitely indicate an absence of cyclic behaviour in the development 

 of competence, ahhough there is here the complicating question of cell survival 

 in salt solution. The blastula ectoderm cells may not have sufficient nutrient 

 store to go through many complete endogeneous cycles of activity so that the 

 "clock" decays after a single cycle. Ebert and Wilt (1960) have reported a 

 cyclic emergence of competence with respect to the infectivity of chick embryo 

 cells to Rous sarcoma virus, but this is one of the few suggestions of clock-like 

 activity in developing systems. Another is the rhythm of cell division in 

 regenerating liver cells. It would seem that the irreversibility of embryonic 

 development is such that differentiating cells have no time to go through more 

 than one endogenous cycle of activities before they are shifted into a new oscil- 

 latory mode, if indeed oscillatory behaviour in the control systems underlies the 

 timing mechanisms in competence. This makes such systems inaccessible to 

 analysis by means of the statistical mechanics developed in this study, which 

 demands quasi-stationarity at least in the oscillating variables. That is to say, 

 in order to apply the statistical theory to cell behaviour the oscillators must go 

 through many complete cycles before a significant change occurs in the micro- 

 scopic parameters, so that they are always at, or near, the equilibrium condition 

 defined by equation (33). Otherwise the parameter 6 and other functions such 

 as the mean frequency of oscillations have no meaning. 



It would be of considerable interest and importance to be able to describe 

 the developmental process in terms of a higher-order invariant which was based 

 upon changes in steady state quantities /?, and ^,- for example. An extended 

 theory of this kind would be of great value not only for the study of diflferen- 

 tiation, but it is actually required for an adequate description of circadian 

 organization in cells since, in general, circadian behaviour occurs in growing, 

 not just in resting, cells. This would lead us into a hierarchy of invariant theories 

 such as was suggested in Chapter 6. There does not seem to be any reason why 

 such a theory could not be developed for the analysis of temporal organization 

 in embryonic and other non-stationary (relative to the present theory) systems. 

 But it must be conceded that the theory advanced in this study certainly falls 

 short of this goal. We can only suggest that oscillatory phenomena, such as 

 those observed by Gross and Jackson, should be a universal feature of macro- 

 molecular dynamics in developing cells, and that competence may be under- 

 stood in terms of the interaction of non-linear biochemical oscillations. The 

 duration of various competences should therefore be altered by experimental 

 procedures which affect the sizes of epigenetic oscillations in the manner of the 



