MUTUAL DEPLETION SYSTEMS 67 



tance. Easson and Stedman (1936) were the first to consider this problem 

 but did not develop the kinetics extensively because they were primarily 

 concerned with the determination of enzyme concentration, a useful ap- 

 plication of the basic kinetics that will be discussed later. The detailed 

 presentation of the kinetics, with applications to cholinesterase, is due to 

 Straus and Goldstein (1943) and Goldstein (1944). 



Previously it has been assumed that (I) = (I^) but now one must write: 



(I,) = (I) -^ (EI) (3-31) 



where (EI) includes (EIS) because presence of substrate does not alter the 

 binding of inhibitor to enzyme. The value of (I) may be obtained from the 

 equilibrium expression (I)(E)/(EI) = Ki, the fractional inhibition relation- 

 ship i = (EI)/(E,), and the equation (E,) = (E) + (EI): 



(I.) - K, 



+ i(E,) (3-32) 



1 - 



and this may be rewritten with specific concentrations as: 



(I/) = ^i-^ + /(E/) (3-33) 



1 — t 



Total inhibitor = free inhibitor + combined inibitor 



Three possible situations may be distinguished: the inhibitor is mainly free, 

 or it is mainly combined, or it may occur significantly in both free and com- 

 bined forms. Straus and Goldstein designated these three situations in terms 

 of zones in the following manner: 



Zone A: inhibitor mainly free, (I/) = il(l — i). 



I = (hllian ^ 1] (3-34) 



Zone B: inhibitor free and combined, (I/) = z7(l — i) + «(E/). 



[an + (E/) + 1] -V[(I/) + (E/) + 1]^ - 4(I/)(E,') 



(3-35) 



2(E,') 



Zone C: inhibitor mainly combined, (I/) = i(E/). 



I = (I/)/(E/) (3-36) 



They were called zones because as (E/) is increased, the system will pass 

 from zone A through zone B into zone C. 



In Eq. 3-33 the designations of the form of the inhibitor do not indicate 

 ordinary concentrations but specific concentrations; the actual concentra- 



