COMBINATION WITH MOLECULES OF INHIBITORS 95 



The Active Centers Have Different Intrinsic Affinities for the Inhibitor 



If the enzyme possesses more than one substrate site and the inhibitor 

 is bound with different affinities at or near these sites, the inhibition for 

 each site is given by the simple equation: 



but the total inhibition of the enzyme is not the sum of these separate 

 inhibitions, i.e., i 7^ i-^ + t'.^ -|- ... + r„. The inhibition is obtained by di- 

 viding the sum of the inhibitor-bound sites of each type by the total number 

 of sites on the enzyme: 



1 



/(,(I) , n,{l) ^ , n,{l) 



(I) + K, (I) + K, ' (I) + K, 



(3-93) 



if there are p types of sites with different iiC/s, if n^, n.^ ... n^ are the num- 

 bers of sites of each type per molecule, and where n = n^ + n.^, + ... + n^. 

 For competitive inhibition the K/s are simply multiplied by 1 + [(S)/^J 

 if the Kg is the same for each site. If there are only two different types of 

 sites (p = 2) and if they are in equal number on the enzyme, (I)o 5 = K^^K^^, 

 so that this may also introduce an error in equating (I)o 5 with K^. In this 

 case also, the over-all inhibition will be one-half the sum of the individual 

 inhibitions for the two sites. 



The Active Centers Are Not Independent 



When the enzyme possesses more than one active center, each with the 

 same affinity for the inhibitor, so situated that the binding of inhibitor 

 alters the affinity of adjacent groups for the inhibitor, the kinetics of inhi- 

 bition deviate from those where the sites are independent. Let us first 

 consider the situation in which there are two interactive centers on the 

 enzyme. The problem is not inherently different from that for the disso- 

 ciation of dicarboxylic acids, where association of an H+ with one carboxy- 

 late ion leads to a change in the K^ of the second group. 



In the case of dibasic acids the macroscopic dissociation constants, ob- 

 tained from titration data, always differ by a factor of 4 or more; i.e., 

 K^ jK^^ = 4 when there is no interaction between groups and more than 

 4 if there is interaction. This is a statistical factor and is due to the fact that 

 the first hydrogen ion may dissociate from, either carboxylic group and 

 the second hydrogen ion may associate with either carboxylate ion. How- 

 ever, this factor does not enter into enzyme formulations since (E,) is 

 not the concentration of enzyme molecules but of active centers, whereas 

 for dicarboxylic acids the concentration of acid refers to the entire molecule 

 and not the individual groups. Thus the dissociation constants used here 



