20 TEMPORAL ORGANIZATION IN CELLS 



behaves as "noise". Even a deterministic set of control reactions with strong 

 coupling operating in the metabolic system would act as noise on the 

 epigenetic variables, defined according to the assumptions of the last chapter, 

 because the rates of metabolic processes are so much faster than those of 

 epigenetic processes. It is via this noisy space that the control components 

 interact weakly with one another. As will be seen in Chapter 5, a situation 

 of this kind is exactly suited to a statistical mechanical treatment. The approxi- 

 mation of the theory to the real system depends on how well one selects the 

 control variables, and how accurately the equations define their dynamics. It 

 is to be hoped that the analysis given in the next chapter is close enough to 

 at least produce qualitative predictions about macroscopic features of cell 

 behaviour, and to lead subsequently to quantitative ones as the equations are 

 improved. 



Oscillatory Behaviour in Control Mechanisms 



The major dynamic feature of the control processes which will be studied 

 here, is the occurrence of continuing oscillations in the concentrations of the 

 molecular species involved in the closed control loops. The appearance of such 

 oscillations is very common in feed-back control systems. Engineers call them 

 parasitic oscillations because they use up a lot of energy. They are usually 

 regarded as undesirable and the control system is nearly always designed, if 

 possible, to eliminate them. One very notable exception occurs in the design 

 of self-optimizing machines, where a constant search must be made by the 

 machine for a state which is optimal according to a prescribed criterion. In 

 this case a dynamic oscillation is essential to efficient operation of the machine, 

 and if it does not occur naturally it must be built in (Tsien, 1954). This highly- 

 suggestive observation is not quite so relevant for the operation of biological 

 systems as it might at first sight appear. The primary reason for the oscillation 

 in self-optimizing machines is to keep all moving parts in constant motion so 

 that they will not get "stuck" by stationary friction, and the machine will then 

 always be ready to respond to a change in the environmental parameters. A 

 constant oscillatory motion about the steady state also improves the perfor- 

 mance of the sensing devices which compute the optimizing function. 



This reasoning does not have such relevance for an open biochemical system 

 which is always in motion anyway, since the steady state is maintained by 

 constant synthesis and degradation of components; and there is no obvious 

 reason to believe that biochemical "sensing" devices respond better to an 

 oscillatory signal than to a stationary one. However, there is a good reason 

 why oscillations might be expected to occur in cellular control mechanisms 

 which operate by closed loop repression pathways involving DNA, RNA, 

 protein, and metabolites. A change (say an increase) in the rate of mRNA 

 synthesis at a genetic locus will take some time to have an effect upon the state 

 of the metabolic system, since the intervening steps of mRNA synthesis, 

 diffusion of mRNA to a protein-synthesizing site, synthesis of enzyme (say), 

 possible diff'usion of enzyme to a metabolic site, and then catalytic action of the 



