12 TEMPORAL ORGANIZATION IN CELLS 



metabolic system, wherein certain metabolites undergo continuous periodic 

 changes in concentration. Spangler and Snell (1961) have shown, for example, 

 that oscillations can arise when two enzymes are coupled together by reciprocal 

 feed back inhibition. The existence of metabolic oscillators complicates the 

 analysis of temporal organization in cells, because it is necessary to consider 

 what effect these oscillators will have on the dynamics of the epigenetic system. 

 Again, the answer depends upon the relaxation times of the two systems, but 

 our estimates of lO^^-lO^ sec for the relaxation time of the metabolic system 

 will probably be too small if oscillations form an important aspect of its 

 dynamics. The reason for this is that non-linear oscillators, and metabolic 

 oscillators will certainly not be Hnear, can show rather complicated types of 

 interaction which give rise to subharmonic phenomena. (These will be discussed 

 in considerable detail in Chapter 7.) Thus even if the period of a metabolic 

 oscillator is 1 or 2 min, in which case it will be outside the dynamic range of 

 the epigenetic system, as we will soon see, the phenomenon of frequency 

 demultiphcation could give rise to oscillations with periods anywhere from 

 5 to 30 min or larger. The upper values come close to the time range of dynamic 

 activities in the epigenetic system, so that a metabolite which oscillates relatively 

 slowly could form a significant dynamic element in epigenetic processes. 



This observation should put us on our guard in two ways: first, a rigid 

 distinction between different systems in the cell cannot be achieved ; secondly, 

 the use of a temporal criterion for attempting such a distinction implies a 

 purely dynamic attitude to activities in the cell ; that is to say, if a variable 

 shows a "slow" rate of change, then it forms a part of the dynamic system 

 whose relaxation time is of the same order of magnitude, and the nature of 

 the variable is immaterial. We have used the term metabolic system to define 

 a particular set of activities in cells, not a particular class of molecule, so 

 that there is no contradiction if a "small" molecule enters into the dynamic 

 description of the epigenetic system. Again, the slow changes in oxidation- 

 reduction potential between animal and vegetal poles which have been observed 

 in fertilized eggs after activation, taking several hours to complete a cycle 

 of change (Brown, 1934), are to be regarded as epigenetic phenomena. Thus 

 it is not necessary to know in any detail the molecular formulation of a process 

 in order to classify it in a particular system according to a temporal criterion. 

 It is a fact, however, that there is a natural time boundary which occurs 

 between enzyme catalysed metabolic transformations and macromolecular 

 synthesis, and this forms the essential molecular basis for the distinctions 

 proposed in this work. It is difficult to avoid the use of essentially taxonomic 

 terms like small molecule and macromolecule in discussing cellular processes, 

 although, strictly speaking, relaxation times have nothing to do with molecular 

 species and relate solely to rates of change of state in the system, of whatever 

 nature they may be. 



Returning to the question of oscillatory phenomena in the metabolic 

 system, we will assume that if these occur then their frequencies are small 

 enough that they fall outside the dynamic range of the epigenetic system so 

 that a steady state approximation can be used. But we must be prepared to 



