28 TEMPORAL ORGANIZATION IN CELLS 



If we had assumed that 7?, had a specific site on the template T, which did not 

 combine with precursors A/, then we would have had a non-competitive 

 representation of the effect of i?, on the concentration of the complex r,vi,-. 

 Without deriving this result, let us note that the expression is 



The difference between these two expressions is important if we are considering 

 both [Aj] and [Rj] as variables in the system. However, we are going to assume 

 that the concentration of activated precursors for mRNA synthesis, [Aj], is 

 effectively constant in the system, or at least that its pattern of variation is a 

 random one. In this case there is no difference between the two expressions 

 from the point of view of the functional representation of [/?,]. Let us therefore 

 use the competitive form of the expression, remembering that the constants 

 do not necessarily have the usual meaning that they have in enzyme kinetics. 

 The treatment of surface adsorption given above, and throughout this 

 study, is the classical one which is to be found in any text on enzymology. 

 New notions about the effect of adsorbed molecules on the conformation and 

 activity of macromolecules, particularly the concept of allosteric effects in 

 proteins introduced by Monod and Jacob (1961), may lead to new formulations 

 of surface reactions of macromolecules. But here we use the older and simpler 

 treatment which leads to expressions very similar to those obtained by Szilard 

 (1960) in his very interesting study of control processes in cells. 



The Characteristics of the Feed-back Signal 



We want now to obtain a relation between [Rj], the concentration of re- 

 pressor, and [Mj], the concentration of the feed-back metabolite. There are 

 two parts to this question. One relates to what we may call the characteristics 

 of the metabolite pool containing A/,. (We will restrict our attention to the case 

 where M, is the end product of a reaction sequence, after which it feeds into 

 some metabolic pool whence it is drawn for various cellular reactions.) Only 

 a fraction of the total concentration of metabolite feeds back to exert a repres- 

 sive function on the synthesis of mRNA, the rest of it entering a metabolic 

 pool. When Af,- is relatively small, very little of it will "spill over" from the 

 pool and the locus L, will be largely derepressed ; and as A/,- increases, more of 

 it will serve a repressive function. The kinetics of this process could easily be 

 quite complicated, however, and would depend upon the nature of the meta- 

 bolic pool. Cowie and McClure (1959), and more recently Britten and McClure 

 (1962), have studied the properties of metabolic pools in microorganisms 

 and their results suggest that metabolites which are in the "internal" pools, 

 which are those intimately associated with biosynthetic processes, are not in 

 a free state but may be bound loosely or firmly to proteins. Thus we have 

 again a surface adsorption phenomenon to deal with. 



However, practically no information is at present available about the actual 

 kinetics of the process whereby metabolites are stored in and released from 



