COMPETITIVE DISPLACEMENT BY SUBSTRATE 



613 



This equation is plotted for different concentrations of added substrate 

 in Fig. 13-3 and the general form of the curves is seen to be similar to 

 that found for dilution (Fig. 13-1). Actually the reversal rates are quite 

 comparable in the two cases when the final inhibition reached is the same, 

 as would be expected since dissociation of EI is the determining factor in 

 each. 



TIME 



Fig. 13-3. Rates of displacement of the enzyme-bound inhibitor by the sub- 

 strate in competitive inhibition (Eq. 13-1.5). K^ = I mM, K^ = 3 mM, A,-_i = 0.1, 

 and (I) = 5 mil/. Curve A: (S') = 1; curve B: (S') = 5; curve C: (S') = 20; 



curve D: (S') = 100. 



A more generalized treatment results from the integration of Eq. 12-33 

 after rewriting it in terms of the dissociation rate constants and setting 

 the inhibition at zero time as ?„. 



('''a 



if) exp - 



(!') + (S') 



[ (r)M-_, + (S')M-_i J 



(13-16) 



This equation is of the same form as Eq. 13-8 except for the exponential 

 factor. An equation with the same exponential factor was derived by Gold- 

 stein (1944) for the displacement of physostigmine from cholinesterase by 

 acetylcholine. However, the rest of his equation differs from that presented 



