866 16. SPECIFICITY OF INHIBITION 



For the enzymes to be inhibited to specified degrees by a certain concen- 

 tration of the inhibitor, the ratio of the inhibitor constants is given by: 



Ki„ iA\ — io) 

 -~ = ~ 4 (16-3) 



A few selected results are shown in Table 16-1, from which it may be seen 

 that the requirements for differential sensitivity of the two enzymes depend 

 not only on the specificity, a, but on the absolute values of the inhibitions. 

 It may also be noted that a very large difference between inhibitor constants 

 is required if a high specificity is to be achieved; for example, to inhibit 

 El almost completely without inhibiting E2 appreciably, Kj must be about 

 ten-thousand times as large as ^^ , or the pK/s must differ by approximately 

 four units. Finally, it is seen that if Ej is to be inhibited only 50% without 

 significantly affecting E2, Kj must be about a hundred times as large as 

 Kj , so that even to get a low inhibition specifically requires an appreciable 

 difference in the affinities of the inhibitor for the two enzymes (actually 

 around 2.83 kcal/mole). Conversely, it is evident that if the K^s do not 

 differ by more than a factor of 10, it is impossible to obtain any i^ractically 

 useful degree of specificity. These considerations serve to set some kind of 

 limits to the specificity one may achieve in the simplest type of enzyme 

 inhibition. 



The Maximal Specificity for an Inhibitor and Two Enzymes 



The specificity will vary with the concentration of the inhibitor so that 

 it is frequently useful to know the concentration which will give the max- 

 imal degree of specificity. From Eqs. 16-1 and 16-2, the specificity for 

 noncompetitive inhibition is: 



(I) (I) 



(I) + K,^ (I) -1- K, 

 Differentiating and setting equal to zero: 



da K,- K. 



(16-4) 



= (16-5) 



d{l) [(I) + Z, J^ [(I) + K^J 

 so that the inhibitor concentration for maximal specificity is given by: 



ah=,na. = V1[~K~ (16-6) 



Substituting this value of (I) back in Eq. 16-4 gives the maximal speci- 

 ficity that may be obtained: 



V X,. + V K,, 



