6. THE RELAXATION TIME OF THE EPIGENETIC SYSTEM 83 



dropped sufficiently to allow continuing oscillations to be a significant dynamic 

 feature of the control system, if the time constants are such as to generate 

 oscillatory behaviour. Due to the high synthetic capacities of bacteria these 

 oscillations could have a period of a few minutes, perhaps 20-30, so that the 

 frequency might be 2-3 cycles per hour. Each cell would then have a single or 

 perhaps a small number of well-defined oscillators, if some other components 

 have relatively large messenger populations also. These might be enough to 

 give some time structure to the cell, but what its nature and function might be 

 remains thoroughly obscure. 



Before considering other cell types besides bacteria, it should be mentioned 

 that there is one process in these organisms which is in a sense cyclic, and that 

 is cell division. Bacterial populations can be synchronized by various means 

 for a limited number of cell divisions (cf. Lark, 1960) so that some 90% of the 

 cells divide at the same time. Clearly there is some kind of temporal organiza- 

 tion in the control of metabolic events. Our above calculations, rough as they 

 are, suggest that the origin of such dynamic organization is not likely to be 

 found in the dynamics of epigenetic phenomena, assuming always that bio- 

 chemical oscillations of some kind provide the fundamental mechanism for 

 ordering metabolic events in time. This is certainly not a necessary assump- 

 tion, and the regularity and repeatability of the events during cell division in 

 bacteria may depend upon a totally different causal mechanism than the bio- 

 chemical clocks which have been assumed to underly rhythmic behaviour in 

 higher cells. 



There remains the possibility, however, that oscillatory behaviour in the 

 metabolic system, generated by the process of feed-back inhibition, could 

 underly the temporal organization of events producing the division cycle in 

 bacteria. Protein and metabolite populations are certainly large enough so 

 that regular oscillations could occur in these variables in bacteria. Nevertheless 

 there remains the problem of the irreversible nature of cell division relative to 

 the steady states which serve as equilibrium states in the present theory. In 

 terms of metabolite and protein populations, cell division is not a cyclic 

 process since these quantities are doubled with each division. By using specific 

 quantities in analysing the dynamics of cell division one could represent this as 

 a genuinely periodic process, as we observed in the last chapter. However it is 

 not yet clear that the problem can be treated in this manner. Until the present 

 theory has been extended in some way to cover the dynamics of cells undergoing 

 rapid division, it is unfortunately necessary to leave bacteria out of the sub- 

 sequent discussion and concentrate our attention upon cells and cell systems 

 showing clock-like behaviour at or near the resting state. 



Let us now turn to the protozoa, where very definite periodic phenomena are 

 observed . What we see immediately as compared with bacteria is an enormous in- 

 crease in the size of the cell. Paramecium, for example, has dimensions roughly 

 1 50 ju. long by 50 /x broad. Compared with the usual bacterium which is of the 

 order of 1 /x in diameter, Paramecium will have a volume which is some 10^ 

 times that of a bacterium. We cannot conclude that all macromolecular pop- 

 ulations will necessarily be increased by the same factor, but it seems reasonable 



