2. SYSTEM AND ENVIRONMENT 1 1 



different. We must now try to estimate very roughly the relaxation times of 

 the systems which are of most significance to the present analysis. Only order 

 of magnitude estimates will be made at this point. In Chapter 6 a much more 

 detailed consideration of the epigenetic relaxation time will be undertaken, 

 for it is of great importance to the applicability of the statistical theory which 

 is developed in Chapter 5. 



The Metabolic System 



In the metabolic system of cells, the major processes determining rates of 

 change are the diffusion, interaction and transformation by enzyme catalysis 

 of "small" molecules (not macromolecules). Included in this system are 

 interactions between small molecules and macromolecules, such as the pro- 

 cesses occurring in enzyme inhibition and activation. Macromolecular 

 synthesis is excluded from the activities constituting this system, so that macro- 

 molecular concentrations are regarded as constants or very slowly changing 

 environmental parameters of the metabolic system. This is the usual assump- 

 tion made in kinetic studies of open metabolic systems, and that it is a 

 reasonable one from the point of view of relaxation times will soon be 

 evident. 



One of the major determinants of how rapidly steady states can be reached 

 in the metabolic system, is the turnover rate of substrate molecules by the 

 enzymes of intermediary metabolism. This falls largely in the range of 10-10"* 

 molecules 'sec. (cf. Eigen and Hammes, 1963). The detailed studies of Chance 

 and Hess (1959), Hess and Chance (1961), on changes in the pattern of glucose 

 metabolism in ascites tumour cells following different disturbances show that 

 very extensive changes in metabolic steady state occur in a matter of 1 or 2 

 min in response to large stimuli. For example, the level of glucose-6-phosphate 

 rises from a very low value (~005 /LtM/g cells) to a new steady state value of 

 about 0-8 /LiM/g cells in about 1 min after the addition of 7-5 mM of glucose to 

 the system. As for the interaction between small molecules and macromolecules, 

 enzyme studies show that steady states are reached in a very few seconds after 

 a change in inhibitor concentration, for example. Even when the response of 

 a whole cell to a new environment is involved, such as occurs when an inducer 

 is removed from a bacterial culture, it has been reported (Monod, 1962) 

 that a new steady state between inducer and repressor molecules (the latter 

 assumed to be a macromolecule) is reached in less than 15 sec. Since the 

 relaxation time is defined for considerably smaller disturbances than the ones 

 we have mentioned, it seems reasonable to suggest that the relaxation time of the 

 metabolic system will fall in the range 10"i-102 sec. 



This estimate depends upon observations made on what appear to be 

 genuinely steady state systems; i.e. systems which approach a particular 

 metabolic state and remain there provided no further parametric changes occur. 

 However, there is a class of dynamic process which this analysis ignores, and 

 which is, in fact, of central importance to our whole approach to the dynamic 

 organization of cells. This is the possibility of oscillatory behaviour in the 



