40 TEMPORAL ORGANIZATION IN CELLS 



On the other hand it is possible to regard the variables X2 and Y^ as epi- 

 genetic quantities which are not necessarily in a steady state. Depending 

 upon the mean value of the variable ^i, the variable X^, and hence Y2, can be 

 either increasing or decreasing. These quantities could thus be regarded as 

 part of the cell which is undergoing differentiation. If many epigenetic 

 components are coupled by feed-back repression to the component {Xi^ Y2), 

 then the stability of this component will depend upon the mean levels of many 

 variables. It is thus possible that some components are in a steady state while 

 others are changing irreversibly, either increasing or decreasing. The direction 

 of this change will be determined by the epigenetic state as defined by the 

 components which constitute the closed-loop, self-regulating control systems 

 of the cell. In this way the epigenetic system of the cell can be divided into 

 autonomous and dependent parts in a manner which is very suggestive of the 

 "generative mass" (Weiss and Kavanau, 1957) or reproductive part as 

 compared with the "differentiated mass" of the cell. However, it should be 

 emphasized that the dependent variables do not enter into the thermodynamic 

 description of the epigenetic system to be constructed in the next chapter 

 because there is no general integral for the system of equations (21). Once 

 again we are up against the intrinsic limitations of a classical-type dynamic 

 analysis which could be rectified by a more general theory. 



A second deficiency in the simple system described by n independently- 

 operating control components relates to the exact converse of the one discussed 

 above: there appear to be enzymes whose metabolic products do not act as 

 feed-back signals for the control of mRNA synthesis. It would seem that only 

 those metabolites which are located at strategic points of the metabolic path- 

 ways in cells function as repressors. Just how the cell has determined where 

 these strategic points are located in the interlocking complex of metabolic 

 paths, is probably as much a question of evolutionary history as of metabolic 

 logic; but one of these key positions seems very often to be the end-product 

 of a metabolic sequence (Magasanik, 1958; Umbarger, 1961). It is these 

 end-products which have relatively long life-times in the metabolic system 

 (long compared with the unstable intermediates which often occur in the 

 metabolic sequences), and which constitute the branch-points in the metabolic 

 pathways, so the advantage of selecting them as control substances is quite 

 clear. However, these key metabolites do not repress only the genetic locus 

 responsible for producing the enzyme which occurs last in the sequence 

 and so produces the metabolite; they feed back to control enzymes occurring 

 at the beginning of the metabolic sequence. What we seem to have here, 

 then, is a situation like that represented in Fig. 6. Here the loci L,, Z,2, . . ., L,„ 

 (which are first assumed not to be closely linked and so cannot all be controlled 

 by a single operon in the manner suggested by Jacob et al. (I960)) produce en- 

 zymes involved in a metabolic sequence which produces the end-product, M,„. 

 Assume, to begin with, that M„, feeds back only to the locus Lj. Assume further 

 that the controlling step in the whole sequence is the first one, i.e. the produc- 

 tion of the first intermediate in concentration Mj. This means that Y^ is the 

 rate-limiting factor in the enzyme sequence, and it is clear that only if this is 



