3. CONTROL SYSTEMS AND RHYTHMIC PHENOMENA IN CELLS 19 



of the Krebs cycle enzymes and the synthesis of the enzymes glutamine syn- 

 thetase and ornithine transcaibamylase. But is this couphng so specific 

 and well-defined that we can suggest exphcit equations which demonstrate 

 how the synthesis of these enzymes individually varies with the activity of the 

 Krebs cycle ? That is to say, is this coupling strong in the sense that the level of 

 glutamine synthetase is controlled in a specific manner by the amount of ATP 

 generated by the Krebs cycle, and that the level of ornithine transcarbamylase 

 is also controlled by this variable but in a different way, since the enzymes can 

 vary independently of one another? Of course ATP can and does function 

 as a specific control substance in the synthesis of enzymes involved in purine 

 biosynthesis, as shown by Magasanik (1958). In this context the metabolite 

 acts as a feedback repressor in exactly the same manner as other end-products 

 of biosynthetic sequences. But regarded as a general cellular energy source, 

 it is clear that the coupling which certainly exists between ATP and the biosyn- 

 thetic activities of the cell is non-specific. When ATP is limiting in a cell, it 

 is limiting for all synthetic processes; not all equally, perhaps, but again not in 

 a manner showing sufficient specificity to allow of selective control over the 

 synthesis of different protein species. Only if there is some other independent 

 and specific control mechanism working in a cell can a general metaboHte 

 such as ATP be used to select specific epigenetic states. Flickinger (1962) has 

 proposed such a theory for cell differentiation which demands the existence of 

 a clock-like mechanism operating at the level of gene activities as the highly- 

 specific and deterministic component of the system. This theory, which 

 suggests in some detail what competence may mean in biochemical terms, will 

 be discussed in Chapter 8. 



In general, then, it is necessary to recognize that there are two types of 

 interaction between variables in cells, and these we have chosen to call strong 

 (or specific) and weak (non-specific) in analogy with the terminology of 

 physics. The strong interactions can be given an explicit mathematical repre- 

 sentation and they form the basis of a completely deterministic (non-statistical) 

 model of molecular control mechanisms in cells. The weak interactions are not 

 represented explicitly in the control equations, because they do not form an 

 integral part of the control circuits. However, they must be recognized as an 

 essential part of the system, since otherwise we would not have a model of a 

 whole cell; we would just have some equations describing the dynamics of 

 part of the cell. The control variables which are regarded in the present theory 

 as the essential epigenetic variables are mRNA, protein, and certain meta- 

 bolites. These species are really immersed in a very complex biochemical 

 space about whose dynamic properties we have very little detailed information. 

 However, this space and its effect on the control variables must be represented 

 somehow, and in fact this weak interaction forms an integral part of the 

 statistical mechanics to be constructed in Chapter 5. In effect the cell is divided 

 in this analysis into a deterministic part, described by the variables of control 

 and their equations, and a probabilistic part, the rest of the cell, upon which the 

 synthesis of the control variables depends. From the point of view of the 

 dynamics of the deterministic epigenetic control system, the "rest of the cell" 



