4. THE DYNAMICS OF THE EPIGENETIC SYSTEM 



41 



the case will the control circuit be sensitive to the level of 7V/,„ in the cell and 

 regulate the pool size according to cellular demands for the metabolite. If 

 the limiting factor were another enzyme in the sequence, say F,, which was 

 insensitive to repression by M„„ then pool size would be fixed by 7, and no 

 adaptive feed-back regulation would occur. 



However, it now appears probable (Vogel, 1961 ; Gorini, Gundersen, and 

 Burger, 1961) that in fact the end-product, M,„, can repress several or all of 

 the loci in the sequence so that under different cellular conditions different 

 enzymes may be limiting in the reaction sequence and hence controlling the 

 level of the metabolite Af,„. Then the closed control loop can differ with 

 differing cell states; but the important observation is that there must be some 

 closed circuit of control if the level of A/,„ is to be regulated by the enzyme 



© 



X, 



X, 



® ® 



® 



M 



C 



M, 



Mm 

 Figure 6. 



sequence producing the metabolite. Assume that this circuit is in fact the one 

 shown in Fig. 6. 



Using again the simplest possible kinetic assumptions, the rate of produc- 

 tion of Ml will be given by an equation of the form 



dMi 



CiYi 



k2Y2Mi 

 ' K2 + M1 



Here Ci Yi is the rate of synthesis of Mi by the enzyme present in concentra- 

 tion Yi, while the second term is the expression for the catalytic action of the 

 next enzyme in the sequence, present in concentration Y2, on Mi with K2 as 

 Michaelis constant and k2 as rate constant. The corresponding expression for 

 M2 will be 



dM2^ k2Y2Mi k,Y^M2 



dt K2-\-Mi Ki + M2 

 The third step in the sequence removes M2 at the rate given by the second term 



