Chapter 5 



THE STATISTICAL MECHANICS OF THE EPIGENETIC 



SYSTEM 



The Necessity for a Statistical Theory 



Classical statistical mechanics was developed to deal with the dynamic 

 properties of gases. The very large numbers of molecules and their microscopic 

 dimensions make it impossible to obtain detailed information about the motion 

 of the individual molecules making up the gas, and so it was necessary to 

 develop a procedure which takes account of this ignorance while making full 

 use of whatever information is available about the state of the gas. If one had 

 complete knowledge about the initial conditions of every molecule in the gas, 

 then in theory it would be possible to predict on the basis of Newtonian 

 mechanics exactly where each molecule would be after a given period of time. 

 However, lacking this microscopic detail, it was postulated that all possible 

 initial conditions (i.e. microscopic states) compatible with the known macro- 

 scopic state of the gas (e.g. its temperature, pressure, etc.) would be regarded 

 as equally probable, since there is no way of distinguishing between them. 

 This is a basic postulate of statistical mechanics, and it is through it that 

 probabiHstic procedures are introduced into a theory which would otherwise 

 be completely deterministic (non-statistical). 



The reasons for constructing a statistical mechanics to study the dynamics 

 of cellular control systems are not altogether the same as those which led to 

 the original formulation of the theory. The variables of the epigenetic system 

 which are analogous to position and momentum, the microscopic quantities 

 of gas dynamics, are populations of messenger RNA and protein molecules. 

 These are real observables which in physics would be regarded as macroscopic 

 quantities, and they can be measured by biochemical techniques. In the 

 present theory these quantities are considered to be microscopic only in the 

 sense that they are used to define the molecular components whose interactions 

 are regarded as giving rise to higher-order or macroscopic properties of cells. 

 The quantities Xi and Y/ of the present theory are independently observable, 

 and it is quite possible that in the future techniques will be developed which 

 will enable one to make quantitative measurements on molecular species in 

 single, living cells. Optical methods such as microspectrophotometry and 

 microfluorometry are extremely promising technical developments which 

 would seem to offer some chance of making continuous observations on the 

 motion (in the sense of changing concentrations) of one or a few molecular 

 species /// vivo. Nevertheless there would appear to remain a real barrier to the 

 simultaneous observation of hundreds of different molecular species in a 



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