6 TEMPORAL ORGANIZATION IN CELLS 



is nearly always regarded as a hindrance to the efficient operation of a control 

 system. The central importance of negative feed-back as a control device in the 

 organism was first brought to the attention of biologists with the publication of 

 Wiener's now classic work, "Cybernetics: or Control and Communication in 

 the Animal and the Machine " (1 948). Here the possibility of oscillatory pheno- 

 mena arising as a result of partial or complete failure in a negative feed-back 

 control circuit was predicted as a likely aberrant aspect of animal behaviour. 

 The prediction was immediately confirmed by the diagnosis of various forms 

 of ataxia as examples of such failure in the control mechanisms operating in 

 neurophysiological systems. Since this very striking insight into the essential 

 principles of biological control, the discovery of negative feed-back devices in 

 a variety of biological systems has revealed even more forcefully the univer- 

 sahty and simplicity of this control mechanism, whereby a process generates 

 conditions which discourage the continuation of that process. Only very 

 recently has it been demonstrated that specific control circuits in the molecular 

 organization of cells operate on cybernetic principles, as we have already 

 observed. This by no means implies that oscillations must therefore occur in 

 the variables which form the control circuits ; it only suggests that under certain 

 circumstances oscillations may occur. 



The position which we adopt in the present study goes much further than 

 this, however, and assumes that oscillatory behaviour in cellular control 

 circuits is extremely likely. In Chapter 3 we give our reasons for this belief; 

 and in Chapter 6 we will present some experimental evidence which is the first 

 to give direct support to this contention. Our position throughout this work is, 

 in fact, that the occurrence of genuine steady states in cell variables is very 

 unhkely, and that with high probability all or nearly all molecular populations 

 in living cells will be undergoing continuing oscillations of some kind. On the 

 theoretical side, support for this idea comes from studies on the dynamic 

 properties of general transformations defined over arbitrarily large spaces, 

 such as the work of Gontcharoff (1944), and Rubin and Sitgreaves (1954). 

 These studies show that as the space becomes more complex in the sense that 

 the total number of points increases, the probability that any trajectory ends 

 in a cycle approaches a certainty, and true "equilibrium" points become 

 extremely rare. If one is prepared to regard the cell and all its variables as 

 a very complex dynamic system, then the implication of such a result is that 

 variables in cells are very unlikely to be stationary under any conditions, even 

 when the cell is in a true resting state without growth, division, or diflferentia- 

 tion. This does not mean simply that all molecular species in cells are in a 

 dynamic state with respect to their constant degradation and replacement by 

 newly synthesized molecules; it means that there is a continuing oscillation in 

 the concentration of the species. These theoretical studies are an interesting 

 indication that the dynamics of complex systems necessarily involve oscillatory 

 motion. However, in this study we will not make use of these results explicitly, 

 but will rather consider the general implications for cell behaviour of a parti- 

 cular class of oscillations which may be expected to arise in the molecular 

 control circuits of living cells. Our approach is therefore much more specific 



