90 TEMPORAL ORGANIZATION IN CELLS 



to equilibrium is proportional to the magnitude of the perturbation, and we 

 can write 



-f = ^^'> 



k being a constant. This gives us the relation 



Ap = {Ap),e-" 



The relaxation time of the system is now defined as the time required for the 

 disturbance to be reduced to 1/e of its original value. This value is / = Xjk, 

 at which time Ap = (zJp)o/e. We are thus led to enquire into the nature of the 

 rate constant k and the factors which determine its size. 



The forces which cause p to return to an equilibrium value from non- 

 equilibrium ones, are just those forces that bring about an even distribution of 

 G throughout all parts of the epigenetic system, producing the equilibrium 

 relationships 



CiXi{x,-pd = d = 



As discussed in the last chapter, this even distribution of talandic energy 

 throughout the system, results from interactions between all components 

 which arise from the existence of common metabolic pools for macromolecular 

 synthesis. The rate at which G is transferred from one component or group of 

 components to another, will therefore depend upon such factors as the sizes 

 of these pools and the rate of metabolic exchange between pools and macro- 

 molecules — i.e. the turnover values for proteins and nucleic acids. A recent 

 study by A. L. Koch (1962) contains much that is of interest in this context, 

 for his analysis is applied to a steady state system of the type we are considering 

 and is directed towards the question of interaction between different macro- 

 molecular species coupled through common pools. Although Koch's primary 

 interest is the evaluation of true macromolecular turnover rates from tracer 

 kinetic data, he demonstrates certain properties of pool-coupled synthetic 

 systems which are relevant to our present problem. Thus it is shown that when 

 metabolic pools are small and turning over rapidly, then there will usually be a 

 much stronger interaction between components than when these pools are 

 large. This certainly agrees with what one would expect. A second result is 

 that coupling between components through metabolic pools will in general be 

 appreciable unless rather special relations hold between the rates of the various 

 reactions for entry of metabolites into pools and the synthesis and degradation 

 of different macromolecular species. Thus, for example, it is shown by Koch 

 that interaction is small if macromolecular synthetic rates are much smaller 

 than the rates of degradation and metabolite supply, so that a particular ratio 

 in his equations is very small compared with 1. A third conclusion from 

 Koch's study is more in the nature of a caution about the interpretation of 

 tracer kinetic data. The possibility of recycling, i.e. the reincorporation of a 



