3. CONTROL SYSTEMS AND RHYTHMIC PHENOMENA IN CELLS 17 



organization of cells, provides the detailed structure necessary for an under- 

 standing of cellular control mechanisms, and also gives an entrance to theo- 

 retical analysis. Before the detailed nature of these cycles was understood, the 

 only structure which could be built into a theory of cellular control was that 

 of weak, competitive interaction, between biosynthetic pathways. By weak 

 interaction is meant competition for precursors or substrates common to two 

 or more synthetic or metabolic systems. In contrast to this we will use the term 

 strong interaction to mean the specific effects of small molecules on the cata- 

 lytic or other surface properties of macromolecular species. It is these strong 

 interactions which have recently been recognized to form the basis of control 

 mechanisms in living cells. Theories of control formulated in terms of weak 

 interactions tended to fall into two groups, accordingly as they focused upon 

 interactions in the metabolic system or in the epigenetic system. Thus the 

 theoretical studies by Waddington (1956, 1957) and Kacser (1957), for example, 

 emphasized metabolic interactions, and they showed how competition for 

 common precursors between alternative metabolic pathways could explain 

 how one molecular species can attain a high steady state level and a competitor 

 a low level, starting from the same values. Many other properties of open 

 metabolic systems were shown in these studies to have relevance to the be- 

 haviour of biological systems in general, such as the buffering capacity of 

 complex metabolic networks against environmental disturbances (Kacser, 

 1957); but these are not so directly related to the problem of control of bio- 

 synthetic activity. 



The question of how to generate "switching" circuits in metabolic systems, 

 whereby one or another of two alternative products is eliminated and only one 

 survives, has always been a significant one in these kinetic studies, and refer- 

 ence is often made to the equations obtained by Denbigh, Hicks, and Page 

 (1948) wherein such behaviour occurs. The major feature of these equations 

 is the presence of autocatalytic terms modelled upon the self-activating proper- 

 ties of such enzymes as trypsin and pepsin, and a type of "strong" interaction 

 or coupling between different autocatalytic processes. The range of possible 

 behaviour in such systems includes not only switching from one state to 

 another under different initial conditions, but also the occurrence of continuing 

 oscillations. The system showing oscillations is, in fact, a Lotka-Volterra 

 oscillator of prey-predator type. The difficulty with these kinetic schemes, 

 interesting as they are, has always been to justify them biochemically, for the 

 type of bimolecular coupling between autocatalytic species required to give 

 rise to the novel behaviour is rather unusual in known biochemical reactions. 

 Nevertheless the range of possible "strong" interactions between enzymes in 

 particular, and macromolecules in general, has been greatly extended by the 

 recent discoveries in molecular biology regarding the nature of activation 

 and inhibition. Suddenly there is an enormously open field for the study 

 of various types of dynamic behaviour in what we have called the metabolic 

 system. 



However, the evidence now seems to indicate that the discontinuous switch- 

 ing from one state to another such as occurs in microorganisms in response to 



