450 THE BIOCHEMISTRY OF B VITAMINS 



simultaneously in order to study the enzyme system; otherwise, one of 

 the factors may combine with the enzyme completely before the other 

 has a chance to combine with the apoenzyme. This problem exists particu- 

 larly with isolated and nongrowing systems. 



Effect of Substrate on Velocity of Inhibited Enzymatic Reactions. 17 - 18 

 In some instances, determination of the rate of a biological process involv- 

 ing an inhibited enzyme system has advantages over the inhibition index 

 method both in ease of obtaining experimental data and in its interpreta- 

 tion. This is true particularly for biological systems in which concentra- 

 tions of inhibitor and substrate sufficiently high to approach enzyme 

 saturation cannot be employed. Such rate studies are frequently employed 

 in the elucidation of the mechanisms of inhibition of isolated enzyme 

 systems. The equations which may be applied to a general system of this 

 type are analogous to those previously indicated in the derivation of the 

 inhibition index. Under these conditions of suboptimal substrate concen- 

 trations the possibility of the combination of the inhibitor with the 

 enzyme-substrate complex as well as with the free enzyme must be 

 considered. Thus, 



E +Szi=±ES — >P+E 

 E + I ^=± EI 



ES + I =^= ESI 



where the symbols represent the quantities previously indicated in the 

 inhibition index method, and ESI represents the enzyme-substrate- 

 inhibitor complex. By the Law of Mass Action, equations (1) and (2) 

 apply to the dissociation of the enzyme-substrate complex and to the 

 dissociation of the enzyme-inhibitor complex. Similarly, the dissociation 

 constant, K S j, of the enzyme-substrate-inhibitor complex can be obtained. 



[ES][I] 



-[ESiY = SI (10) 



The total enzyme concentration, [E t ], may be represented as follows: 



[E t ] = [E]+[EI} + [ES} + [ESI] (11) 



Solving equation (1) for [E], equation (2) for [EI], and equation (10) 

 for [ESI] and substituting these values in equation (11), one obtains: 



_, K s [ES]. Ks[ES)[I) . wq] . [ES][I] f . 



Et= ~TsT + k,[S] +[ES]+ ~IGr (12) 



The velocity of the enzymatic reaction is proportional to f ES] , so that 

 r=k[ES], where r is the rate and k is the rate constant of the reaction. 

 The maximum rate, R, of the enzymatic reaction is similarly proportional 

 to the total enzyme concentration since [ES] becomes equal to [E t ] 



