INTRODUCTION AND THEORETICAL CONSIDERATIONS 449 



substrate, enzyme-substrate complex and the product of the enzyme 

 system. The following equation can be derived in a manner analogous 

 to equation (3) : 



[7] Kj[EJ] 



[Co] K C [E a Co] K) 



where K r and K c are the dissociation constants for the apoenzyme-in- 

 hibitor complex and for the complete enzyme, respectively. By the Law 

 of Mass Action: 



[S] [E a Co] .. 



[E a CoS] =Ks (8) 



where K g is the dissociation constant of the enzyme-substrate complex. 

 The total apoenzyme concentration, [E a ] becomes 



[E a J = [E a ] + [EJ] + [E a Co] + [E a Co S] (9) 



In the application of these equations to the determination of the effect 

 of the concentrations of inhibitor and coenzyme on the degree of inhibi- 

 tion of a biological system, the rate of the reaction in which the final 

 product, P, is formed would be expected to govern the rate of the biologi- 

 cal process. The effect of any change in substrate concentrations, resulting 

 from the lack of the complete enzyme in optimal concentration, would 

 be a function of time under the experimental conditions. For a defined 

 degree of inhibition after a constant experimental period, the rate of the 

 reaction is limited in the manner previously indicated for substrate 

 inhibition. Consequently, the concentration of the enzyme-substrate com- 

 plex, [E a CoS] , must be reduced to a defined amount at the outset of the 

 biological process in order to attain a defined inhibition. Since [S] is not 

 a variable at the outset of the experiment, it is apparent from equation 

 (8) that the concentration of E a Co must be reduced initially to a defined 

 amount. Since the concentration of [E a ] becomes negligible, in comparison 

 with [EJ], with increasing concentrations of inhibitor and coenzyme, and 

 since the total enzyme concentration is considered to be constant, it fol- 

 lows from equation (9) that EJ must then become a defined concentra- 

 tion initially in order for a defined inhibition to be obtained. 



Since both E n C and EJ must initially be defined quantities for a defined 

 inhibition, it follows from equation (7) that the ratio of inhibitor to 

 coenzyme necessary for a defined inhibition is constant. Consequently, 

 the inhibition index may be applied to such a system. 



The problem of the reverse rate of reaction being so slow that equilib- 

 rium conditions are not attained becomes a reality for reactions of many 

 apoenzymes with their coenzymes or analogues of the coenzymes. In such 

 cases, it is essential that both the inhibitor and coenzyme be added 



