6. THE RELAXATION TIME OF THE EPIGENETIC SYSTEM 95 



value, then a new steady state is defined and there will be a certain time lag 

 before the statistical properties of the system settle down to new equilibrium 

 values, thus giving new values to the macroscopic variables. The relaxation 

 time gives us some idea of how long this will be. It is usually assumed that a 

 period of at least 10 times the relaxation time is necessary for a system to move 

 to a new equilibrium state after a change in parameter values. For cells of a 

 higher organism this means some 40 h or more for equilibration in the epi- 

 genetic system, according to our estimates. Now it may happen that the micro- 

 scopic parameters of the epigenetic system such as a,-, A:,-, bi, etc., are undergoing 

 a process of change either continuously or discontinuously in discrete steps. 

 This is what happens in a cell during adaptation or differentiation. If the 

 changes in the microscopic parameters are slow enough, then it is possible to 

 regard the epigenetic system as being always very close to equilibrium so that 

 it is possible to speak of its state in terms of the macroscopic variables 6, G, 

 etc. Under such conditions we may look upon the whole process of change as 

 one in which the epigenetic system is driven very slowly through a sequence of 

 quasi-equilibrium states by the parameters which are themselves responding 

 to environmental forces. 



However, it must be emphasized that the rate of parametric change must 

 be very slow if this type of analysis is to be valid, significant changes in the 

 parameters occurring only during a period of some 2-3 days in the case of cells 

 of a higher organism. Some processes such as regeneration and wound-healing, 

 which generally take several days or weeks (Needham, 1952), would seem to 

 provide a time-table which might allow such a procedure to be applied, and 

 even certain aspects of embryonic development may be amenable to this type 

 of analysis. The usual description of the developmental process is, in fact, one 

 which divides this extremely complex pattern of events into a step-wise series 

 of inductions and responses. Needham's (1950) series of cones is a geometrical 

 representation of this analytical procedure, it being suggested that develop- 

 ment can be resolved into a sequence of equilibrium states alternating with 

 non-equihbrium ones produced by the action of an inducer. If such an analysis 

 is valid for embryological phenomena, then the present theory could be applied 

 to this field of study providing always that certain time relations hold between 

 parametric change and the relaxation time of the epigenetic system in develop- 

 ing cells. 



It seems advisable at present to proceed with great caution in the application 

 of the " stationary" theory developed in this study to non-stationary processes, 

 although this is certainly a very important, indeed the dominant, class of 

 biological processes. Where the theory cannot be applied to epigenetic 

 phenomena in cells it will be necessary to employ another theory which is 

 constructed to deal specifically with the class of irreversible processes which 

 are being considered. Thus for many embryological phenomena and for studies 

 on rapidly growing cells or tissues, it will probably be necessary to conduct an 

 analysis which explicitly incorporates the irreversible features of these processes 

 into its structure, in the same way that the present theory of cellular control 

 mechanism specifically assumes thermodynamic irreversibility and proceeds 



