5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 59 



mitted to the smaller ones. At the same time, the common pools exert something 

 of a damping effect upon oscillators with large amplitudes, for during periods 

 of depletion in the pools their own synthesis is discouraged, while at periods 

 of abundance their synthesis is encouraged. Thus the general result of this 

 weak interaction between components through common pools is a general 

 "smoothing" of oscillatory motions, components with oscillations much 

 larger than'the mean amplitude tending to be damped, and components with 

 small amplitudes tending to be excited. There may also be an effect upon the 

 phasing of the oscillators, the general tendency being for large oscillators to 

 induce^an antiphase relation in small oscillators, since the synthetic phases 

 of the latter will be encouraged during degradative phases of the former due to 

 larger pool sizes, and vice versa. 



It is evident that the notion of weak interaction is introduced to cover an 

 area of comparative ignorance about the microscopic details of the complex 

 interplay which must occur between the staggering variety of biochemical 

 processes taking place in the living cell. This we discussed in Chapter 3. What 

 we observe now, however, is that this ignorance is taken account of explicitly 

 in our theory by means of the introduction of probabilistic procedures. We 

 do not know all the details of biochemical interaction; if we did we would have 

 a perfectly well-defined machine. But we have assumed that current knowledge 

 about molecular control mechanisms gives us enough microscopic detail to 

 write down, in a very approximate manner, some equations which describe the 

 dynamics of part of the cell. This deterministic part is, however, immersed in a 

 "noisy" biochemical space, and so its motion will be disturbed in a random 

 manner. It is therefore essential that we study this motion by statistical 

 methods. We thus have two areas of ignorance to deal with: an ignorance 

 about the initial conditions of the control variables ; and an ignorance about the 

 dynamic details of the space in which the control systems operate and which 

 support their existence. Faced with such a situation, we must adopt a proba- 

 bilistic attitude to the dynamics, and this is intrinsic to the statistical mechanics. 

 The dynamic behaviour of metabolic pools in cells with oscillating control 

 circuits of the type considered in this study is complicated by the fact that the 

 sizes of pools consisting of the feed-back metabolites, M,-, will themselves 

 oscillate. This is an immediate consequence of equation (13), wherein we see 

 that Mi will have essentially the same dynamic behaviour as 7, over time 

 periods of epigenetic phenomena. Over shorter time-periods M,- will also 

 exhibit any dynamic behaviour which arises from interactions in the metabolic 

 system, as discussed in Chapter 2; but relative to epigenetic processes this is 

 to be regarded as noise, according to our assumptions with respect to relaxation 

 times in the two systems. It is thus predicted by the present analysis that 

 metabolic pools of cellular metabolites which act as specific feed-back re- 

 pressors will vary in size with a fairly well-defined periodicity. Some evidence 

 that this may indeed be the case is presented in Chapter 6. 



However, the pools which are predicted to have oscillatory behaviour of 

 this kind are not those which are directly coupled to macromolecular synthesis, 

 viz., activated nucleotides and activated amino acids. These latter pools will 



