74 TEMPORAL ORGANIZATION IN CELLS 



surroundings except when this exchange occurs reversibly if we are going to 

 apply thermodynamic-Hke theorems to its behaviour. This means that a cell 

 cannot be growing or differentiating but must be simply maintaining itself in a 

 given microscopic state; and any changes in 6 must occur very slowly by an 

 interaction between the cell and its environment so that changes of talandic 

 state in the cell are reversible in the thermodynamic sense. When these condi- 

 tions are satisfied, then we can use the apparatus of the present theory to calcu- 

 late, for example, changes of talandic free energy in the epigenetic system. 



In Chapter 8 we will suggest what type of experimental procedure might 

 cause slow changes of 6 in cells without altering the microscopic state of the 

 system (i.e. the steady state values), and how these changes may be observed 

 macroscopically without destroying the cells. Let us note here that the theory 

 imposes no restrictions upon the frequencies of the epigenetic oscillators or 

 upon the relationships of different component frequencies to one another in 

 time, which gives us an important dimension of freedom for studying the 

 temporal organization of the system. Time structure is, in fact, the emphasis of 

 this study, the time structure which occurs in the epigenetic system for a given 

 set of mean values of the macromolecular species. 



The necessity of assuming that a cell is not growing or differentiating is 

 admittedly a severe restriction which would seem to negate the possibility of 

 applying the present theory embryology. The most that we can do in this 

 direction is to attempt some applications, more qualitative than quantitative, 

 to certain developmental phenomena which appear to be closely connected 

 with the oscillatory behaviour of our feed-back control systems, and to make 

 some suggestions about the basis of temporal organization in embryonic cells. 

 A more adequate treatment of this question would be obtained by extending 

 the theory analytically to cover irreversible processes in a manner analogous to 

 the procedures of Onsager, Prigogine, de Groot and others in irreversible 

 thermodynamics. A second alternative is to re-define the system in terms of new 

 variables so that the equilibrium condition is no longer defined by constant 

 macromolecular populations in the cell, but by some relative measure of these 

 populations such as specific population numbers (e.g. the ratio of a species of 

 mRNA to the total mRNA population of a cell, and similarly for protein). 

 This would mean that the system is at equilibrium so long as it is in a steady 

 state, either of growth or of maintenance; but differentiation would again 

 represent an irreversible process. Such an extension would certainly be a 

 useful generalization of the theory and it is being examined. However, it 

 involves a number of difficulties whose solution is not yet apparent, and 

 the more general approach of obtaining a comprehensive time-dependent 

 thermodynamics may prove to be the most satisfactory way of handling 

 the recurring problem of irreversibility in invariant theories of natural pro- 

 cesses. This latter course involves a profound reorganization and recon- 

 struction of physical theory, and it may be that an adequate description of 

 biological process must await for the formulation of such a powerful 

 phenomenological theory. However, there seem to be certain areas of 

 biology which are accessible to more specific and less comprehensive analysis 



