108 3. KINETICS OF ENZYME INHIBITION 



The advantage of cp is that it is an additive function; if an inhibitor com- 

 bines with two or more intermediates in an enzyme reaction or there are 

 two or more noninteracting inhibitors, the total cp can be expressed as the 

 sum of the individual 9?'s: 



n 



notal == S 9'i (3-119) 



» = l 



when there are n different contributions to the inhibition. The fractional 

 inhibition, of course, is not additive. In certain complex inhibitions the 

 treatment may thus be simplified, as in the inhibition of urease by thiourea 

 which is complicated by inhibition by hydrogen ion and high concentrations 

 of urea, as well as buffer effects. There is no particular advantage in using 

 the inhibition index for simple inhibitions. 



Possible Heterogeneity of Active Centers 



It is generally assumed that enzyme molecules in a population are iden- 

 tical with respect to the molecular structure of their active centers and 

 that the affinities for substrate and inhibitor do not vary from molecule 

 to molecule. Heterogeneity however is not unlikely, at least in certain in- 

 stances, since protein molecules may not be as rigidly uniform as more 

 simple substances. Pauling et at. (1944) in their studies on hapten inhibition 

 of antisera found that the results could be adequately explained on the 

 basis of a statistical distribution of inhibitor constants among the antibody 

 molecules. It is not suggested that this is evidence for heterogeneity of en- 

 zymes but the theoretical approach made to antibody group variation can 

 be applied to enzyme inhibition if necessary. The distribution function is 

 of the form: 



1 



7^= exp 



^\/ n 



(In K,IK,^) 



(3-120) 



where K^ is the inhibitor constant for a particular enzyme, K^ is the aver- 

 age inhibitor constant as determined experimentally, and o is the hetero- 

 geneity index. It is possible for different values of o to calculate the proba- 

 bility of a particular enzyme having its Kj^ within a certain range. In the 

 tabulation below 84% of the enzyme active centers will have K-& within 

 the range given. If cr = 2, 84% of the active centers will have X/s 

 distributed throughout a range such that the highest Ki is approx- 

 imately fifty-seven fold greater than the lowest and the difference in 

 binding energy of the inhibitor to the enzyme is 2.4 kcal/mole be- 

 tween these extremes in the given range; 16% of the active centers 



