44 TEMPORAL ORGANIZATION IN CELLS 



behaves in the manner of a constitutive mutant, wherein the normal control 

 mechanism for some protein has been lost and the protein is always present in 

 maximal amounts.) Thus the case of parallel repression, as it is called, in the 

 enzymes of a biosynthetic sequence definitely leads to oscillatory behaviour 

 in the end-product, M„„ on the basis of our assumptions, but different com- 

 ponents may be controlling the overall dynamic activity of the sequence in 

 different cell states. This produces a kind of degeneracy in the epigenetic 

 states of the system, which can be handled without difficulty in the mathematical 

 treatment. 



If there are enzymes in a biosynthetic sequence whose genetic loci do not 

 respond to any feed-back repression signal, then such loci simply are not 

 controlled by the catalytic activities of the enzyme sequence (still assuming 

 no linkage in the group Lj, L2, . ■ ., L„). If such loci exist then they must be 

 continuously active at a rate which is affected only by the availability of pre- 

 cursors for synthesis. It must be assumed that such loci occurring as part of a 

 reaction sequence as in Fig. 6 must be producing enzyme in quantities which 

 are not rate-Umiting, since otherwise there can be no control at all by a feed- 

 back signal. An uncontrolled locus of this kind might serve a cut-off function 

 in the sense that it determines the maximum level at which M,„ can be produced 

 • — i.e. when the metabolic sequence is operating at its maximum ("de- 

 repressed") level, the limiting step is determined by the enzyme produced by the 

 "free" locus. In such a condition the dynamics of the system is very simple: a 

 constant steady state occurs, and there is no need to investigate the dynamic 

 consequences offeed-back control mechanisms since none is operating. Situ- 

 ations of this kind very probably occur in cells under optimal conditions for 

 growth, as in bacterial cells during exponential growth. Then cellular dynamics 

 are at their most irreversible, and many of the subtler control mechanisms may 

 be cut out by saturation effects. It is as well to emphasize at this point that 

 the major concern of the present study is not with "saturation dynamics" of 

 this kind, but with the dynamics of control systems operating much closer to a 

 stationary state, as when cells are simply maintaining themselves or are adapt- 

 ing slowly to new environmental conditions. 



The case where the loci Li, L2, . . ., L,„ are linked in sequence on the chromo- 

 some, as occurs apparently in the case of Salmonella (Demerec and Hartman, 

 1959) introduces another possibility. Such a group of finked genes can be 

 simultaneously controlled from an operator locus adjacent to Li . However, the 

 activities of the loci cannot then be controlled individually, and in this case it is 

 possible that the concentration of enzyme, Y^, is not the rate-limiting variable 

 in the metabolic sequence. Another enzyme, say 7/, could be the rate-limiting 

 factor under all possible states of the system; or different enzymes could be 

 limiting under different conditions, as discussed previously in connection with 

 multiple repression. However, the existence of a single operator site for the 

 whole sequence seems to imply that we can regard the linked group of genes as 

 a single unit for the purposes of control. If enzyme 7/ is limiting the production 

 of A/„„ then 7/ is controlling the amount of repression exercised on the linked 

 group through the operon and hence on the locus L/. We thus have again a 



