5. THE STATISTICAL MECHANICS OF THE EPIGENETIC SYSTEM 73 



of cell structure imposes rigid boundaries to an exchange of oscillatory motion 

 between different parts of the cell, so that it is not meaningful to define para- 

 meters for the whole cell interior. 



It should be borne in mind, however, that there are communication channels 

 in the cell from chromosomes to cell organelles and back again. That is to say, 

 there is some kind of two-way traffic of signals in cells which is essential for their 

 functional coordination, and it is the dynamics of these communication 

 channels that we are studying. Choline esterase (located in the nuclei and 

 microsomes of animal cells) may be quite strictly isolated physically from 

 deoxyribonuclease (located in mitochondria and lysosomes; see, e.g. de Duve, 

 Wattiaux, and Baudhuin (1962)), but according to current theory both must 

 have messenger RNA's which are synthesized on centrally located DNA 

 templates (nuclear DNA) from activated nucleotides drawn from a pool, and 

 both are proteins synthesized from common pools of activated amino acids. 

 The exact nature of the feed-back signals which serve to inform the genetic loci 

 of the metabolic state produced by the activity of these enzymes remains un- 

 determined; but it seems safe to say that the control circuit is somehow closed 

 by a return communication channel. These general metabolic processes 

 provide the common biochemical "space" in which interactions must occur 

 between components, so that weak coupling does exist throughout the cell. 

 This would seem to provide a sufficient basis for the introduction of general cell 

 parameters and functions. To attempt the use of general parameters on a 

 classical thermodynamic basis using physical energy as the fundamental 

 invariant would be much more difficult to justify, for there does appear to be a 

 compartmentalization with respect to energy distribution in cells which would 

 defy the use of the usual thermodynamic parameters of state over the whole cell 

 interior. The application of irreversible thermodynamics to this context is 

 certainly more promising. However, the difficulty in this field is to obtain 

 useful and valid macroscopic principles which hold for systems operating far 

 from thermodynamic equihbrium. The fundamental result of minimum 

 entropy production in steady state systems (Prigogine, 1947) has been shown 

 by a number of authors (e.g. Denbigh, 1951) to hold strictly only in the 

 immediate vicinity of equilibrium, where the Onsager relations are valid. 

 There would seem to be a real difficulty in extending this theory to processes 

 which are as highly irreversible as macromolecular synthesis in cells, although 

 Prigogine and Balescu (1955, 1956) have obtained a very interesting result 

 which will be discussed in the next chapter. 



It is evident that a considerable advantage is gained by starting with the 

 assumption that the system to be studied is highly irreversible and constructing 

 a new thermodynamics on this basis. It is then possible to obtain macro- 

 scopic laws which are analogues of the classical ones, such as a maximum 

 entropy theorem. However, there is inevitably a restriction imposed by an 

 analysis which depends upon an assumption of stationarity, such as underlies 

 time-independent thermodynamics. In the context of our present study, this 

 restriction is that all components must have well-defined, constant steady state 

 values, and that the whole system must be closed to an exchange of G with its 



