1 52 TEMPORAL ORGANIZATION IN CELLS 



irreversible in the sense of the present theory, so that the steady state quantities 

 Pi and qi undergo permanent change. Thus once again we see the inadequacy 

 of the present statistical theory for deahng with developmental phenomena. 



Conclusion 



Perhaps the most important contribution which this study can make to the 

 development of theoretical biology is the demonstration that invariant 

 theories with the same basic structure as classical statistical mechanics can 

 be constructed on a totally new molecular foundation, one which is much 

 more appropriate to the analysis of cellular function and behaviour than is the 

 molecular theory underlying physics and classical thermodynamics. Further- 

 more the major macroscopic quantities which have emerged from this in- 

 vestigation, talandic energy and talandic temperature, can be intimately 

 related to the organizational properties of biological systems whose basic 

 dynamic features arise from the operation of a certain class of molecular 

 control systems. This is because, as we have seen repeatedly, ^ is a direct 

 measure of the degree of non-linearity in the dynamics of the epigenetic 

 system. Since the higher-order time structure which can emerge in the epi- 

 genetic system, depending upon such phenomena as entrainment, subharmonic 

 resonance, and other relations between coupled oscillators, require the occur- 

 rence of sufficient non-hnearity in the dynamics of the molecular control units, 

 it emerges that B, and hence also G, is closely related to the organizational 

 potential of the epigenetic system in the time domain. Thus a cell which is in 

 a state of relatively high talandic temperature can have a much more complex 

 time structure than one which has a very low talandic temperature, wherein 

 the dynamics are approaching linearity. 



We might even go so far as to say that a cell with its epigenetic system in an 

 elevated G-state has a considerable adaptive advantage over one in a very low 

 G-state, when the cells are exposed to an environment with periodicities such 

 as occur generally on this planet. This follows again from the observation that 

 considerable non-linearity is required for the cell to be able to generate stable, 

 ordered relationships between its constituent biochemical activities in time 

 and thus achieve an adapted relation to a periodic environment. However, 

 an argument of this kind would have to be developed on a rigorous basis, 

 involving an exact definition of the environmental periodicity, and proceeding 

 by the demonstration that at elevated G-levels the epigenetic system need 

 perform much less talandic work in order to achieve an adapted state than 

 when the system is in a state of very low 6. This will not be attempted here. 

 What we wish to suggest is that the arguments and ideas which have arisen in 

 this statistical study of interacting cellular control systems may serve to give 

 analytical precision to the notion of temporal organization in cells; and that 

 the macroscopic variables of the theory may be used to develop a quantitative 

 basis for the measurement of such general properties of cells as their organiza- 

 tional and adaptive potential. 



Our investigation has been largely exploratory but enough information 

 about the statistical behaviour of the interacting control systems assumed 



