446 THE BIOCHEMISTRY OF B VITAMINS 



where Ki is the dissociation constant of the enzyme-inhibitor complex. 

 By dividing equation 2 by equation 1, one obtains 



m ki[ei) ( 



[S] K S [ES] K J 



If [E t ] represents the total enzyme concentration, both free and com- 

 bined, by definition 



[E t ] = [E]+[EI)+[ES] (4) 



In the application of the above equations to biological systems, certain 

 experimental conditions designed to limit some of the variables greatly 

 simplify the problem. In order to study the effect of an inhibitor on an 

 entire biological system, conditions must be such that an observable effect 

 on the rate of a biological process will result from the interaction of the 

 inhibitor with an enzyme; this specific enzymatic reaction then becomes 

 the limiting reaction of the biological process. In an isolated enzyme 

 system, the observable effect may be a decrease in the rate of formation 

 of a product. The observable effect on bacterial cells or any isolated 

 culture of cells such as tissue cultures may be a decreased growth rate or 

 complete inhibition of growth; or the effect observed in an animal or 

 embryo may be on the rate of growth, time of survival or time necessary 

 for the development of certain deficiency symptoms. Hence, any observ- 

 able effect resulting from a decreased rate of reaction of an inhibited 

 enzyme system can be used to determine the effect of an inhibitor on a 

 specific enzyme system. One method of studying the mode of action of 

 an inhibitor is to determine the relationship between the concentration 

 of inhibitor and the concentration of substrate necessary to obtain a 

 defined observable effect within a constant period of time. Other experi- 

 mental conditions of the biological system are not allowed to vary. For 

 example, in bacterial studies, the concentrations of inhibitor just neces- 

 sary to attain a defined inhibition of growth, e.g., maximum or half- 

 maximum inhibition, are determined with variable concentrations of 

 substrate under conditions of a defined medium, constant size of inoculum, 

 and a defined time and temperature of incubation. 



The quantitative response of biological systems under such conditions 

 is dependent upon the rate, r, of the limiting reaction, which can be 

 expressed as follows: 



r = k[ES] (5) 



where k is the rate constant for the reaction. Under the defined experi- 

 mental conditions, the variables which may affect [ES] and in turn the 

 rate of the reaction are the concentrations of the inhibitor and substrate 

 as well as the total enzyme concentration, [E t ]. The inhibitor and sub- 



