5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 79 



The suggestion here is that the interactions between biochemical oscillators 

 might be found to produce some kind of ordered relationships between the 

 frequencies of the individual oscillators which could be described by a mini- 

 mum principle on a potential function. The emphasis of such a principle would 

 be on relationships in time rather than relationships in space. The physical 

 theorem of minimum potential energy is essentially a space-ordering principle, 

 whereas the type of order we have in mind for oscillating control systems is in 

 the time dimension. This would lead us directly into the analysis of temporal 

 organization in cells. In Chapter 7 we will show how the statistical mechanics 

 can be used to get information about this aspect of the epigenetic system. 

 But before doing this it is necessary to examine quite critically the dynamic 

 basis of our original differential equations, and to try to reach some conclusions 

 about the sizes of the molecular populations involved and the rates of the 

 different processes which underly the dynamics. Only thus can we give the 

 theory a quantitative foundation. 



