6. THE RELAXATION TIME OF THE EPIGENETIC SYSTEM 91 



molecule into a macromolecular species from which it arises by degradation 

 is a very real problem in the study of "true" turnover rates, and unless special 

 methods, described by Koch are employed the results of tracer experiments 

 may indicate much smaller turnover rates than in fact occur in the cell. Thus 

 current estimates of the mean life-times of macromolecular species may be 

 high. However, studies which largely avoid the usual difficulties (Swick, 1958) 

 indicate that recycling does not introduce a significant error, at least for the 

 case of arginine in liver proteins. 



In general these studies indicate that common pools give rise to a very 

 variable but nevertheless a significant feature of intracellular dynamics, with a 

 considerable "stirring" of amino acids and nucleotides occurring among 

 macromolecular species in a cell. However, this still does not give us any 

 information about the actual size of these interactions which could lead to an 

 estimate for k, and in fact in the absence of numerical estimates for this para- 

 meter the best that we can do is to make an informed guess. Let us fix our 

 ideas by considering a specific type of "small" disturbance which might be 

 used for studying the relaxation time of the epigenetic system in the cells of 

 higher organisms. Suppose that a culture of cells is kept in a steady state of 

 maintenance without growth by restricting the supply of required amino acids. 

 Now introduce a small pulse of the limiting amino acids into the culture, 

 sufficient to cause an increase in protein synthesis which might last for 20-30 

 min. The synthetic rates of the different protein species will be differently 

 affected by this stimulus, depending upon how much of the limiting amino 

 acids they contain. The pulse will also cause a disturbance in the oscillatory 

 trajectories of the species, causing those which are on that part of the trajectory 

 which is above the steady state to move further from the steady state value, 

 and those which are at values less than the steady state to move closer to it. The 

 stimulus may also have an effect upon mRNA synthesis in view of the control 

 mechanism proposed by Stent and Brenner (1961) whereby amino acids act as 

 inducers of mRNA synthesis. This pulse of amino acids will therefore cause a 

 temporary change of state in the epigenetic system, but after the small amount 

 of added residues is exhausted, the system will "relax" back to its original 

 steady state condition, the equilibrium state in our theory. How long after 

 the added amino acids have been used up will it take for about | (really Xje) 

 of the disturbance to disappear? We are going to suggest that this time will 

 be roughly the same order of magnitude as the mean period of the oscillations 

 in the system, which we have estimated to be about 4 h. Since in 4 h some 4% 

 of an "average" protein in the cell of a higher organism will have turned over, 

 and for an active enzyme the value may be considerably larger, we see that the 

 effect of the small transient disturbance should have decreased considerably 

 in this time and the system may be expected to be settling back to its undis- 

 turbed state. 



The value of 4 h for the relaxation time of the epigenetic system in the cells 

 of higher organisms is somewhat larger than the upper limit which we estimated 

 in Chapter 2 for this system on the basis of the results of Feigelson and Green- 

 gard (1962). These results give information about rates of change in the state of 



