14 TEMPORAL ORGANIZATION IN CELLS 



the time required for a metabolic response to a small stimulus. If the stimulus 

 is large and prolonged, however, there will be an initial rapid response by the 

 metabolic system and then a slower and probably more extensive response in 

 metabolic variables due to changes in macromolecular concentrations. During 

 this second-level response the "parameters" of the metabolic system are 

 changing, the time period of observation has been increased over that required 

 for the primary metabolic response, and the process must be regarded, in our 

 terms, as a response by the epigenetic system of the cell. The quantities which 

 were parameters for the time scale of response in the metabolic system have 

 become variables in the longer-term process: the "environment" of the 

 metabolic system has become part of a larger system whose environment now 

 consists of whatever quantities can be treated as constants over the time periods 

 required for observable changes in macromolecular concentrations. Further- 

 more, the initial response of the metabohc system can, and usually does, initiate 

 the slower change in macromolecular concentrations by such processes as 

 feed-back repression and end-product inhibition. The complex readjustment 

 of metabolite and macromolecular levels to the new conditions is brought 

 about by interactions between the different molecular species, and the whole 

 process can only be regarded as a response by a higher-order system consisting 

 of metabolites and macromolecules : the epigenetic system. This latter system 

 can thus be said to contain within it the metabolic system. 



Using the notion of relaxation time further, it is possible to define the 

 genetic system of a single cell, such as a bacterium or a protozoon, but for 

 metazoon organisms there is no genetic system of a single cell. In the latter case 

 the genetic system only operates at the level of the whole organism; while the 

 epigenetic system is much more extensive than the intracellular activities which 

 we have been considering, including intercellular and intertissue events as well. 

 Since we make no attempt to analyse these higher-order phenomena in the 

 present work, it seems inadvisable to attempt to delineate the activities which 

 might be dynamically distinguishable on the basis of relaxation times in 

 embryological and genetic process. Let us note only some general properties 

 of systems defined hierarchically in terms of this notion. 



Relations Between Systems 



We have observed that the epigenetic system contains the metabolic system 

 in the sense that all the variables of the latter system are included in the defini- 

 tion of the former. If it were not possible to consider the metabolic system as 

 being in a steady state relative to rates of change of epigenetic variables, then 

 the epigenetic system would necessarily have a much more complex dynamic 

 representation than the metabolic, since it would consist of many more vari- 

 ables and their equations of motion. However, the steady state assumption 

 allows us to reduce the variables of the metabolic system to epigenetic variables 

 when our interest is in epigenetic processes, because the epigenetic variables, as 

 controlling parameters of the metabolic system, actually define its steady state. 

 Thus it is possible to eliminate all metabolic variables from the dynamic 



