TWO INHIBITORS ACTING ON A SINGLE ENZYME 489 



Both inhibitors competitive {a = /3 = y = oo): if each inhibitor prevents 

 the substrate from binding to the enzyme, it is likely that they will inter- 

 fere with each other. 



(S)' + 1 + (I,)' 4- (I,)' 



(I.)' + ihr 



(S)' + 1 + (I,)' + (I,)' 



(10-3) 

 (10-4) 



Both inhibitors noncompetitive (/? = y = 1): there would be two extreme 

 situations — either the inhibitors react at a similar locus and would thus 

 interfere completely with each other's binding (a = go), or the inhibitors 

 may react at different loci independently (u = 1). 



Binding of inhibitors at the same site {a = oo): 



F„(S)' 



[(S)' -J- 1] [1 ^ (I:)' + (I2)'] 

 (Ii)' + (I2)' 



1 + (I,)' 4- (I,)' 



Binding of inhibitors at different sites (u — \] 



F,,„(S)' 



[(S)' 4 1] [1 + (I,)' + (T,)' + (I,)' (T,)'] 

 dJ' + (I,)' + {\,)'{l,)' 



1 -^ da)' + (I2)' + (Ii)'(I. 



(10-5) 



(10-6) 



(10-7) 

 (10-8) 



One inhihitor (I^) is competitive and the other (I2) is noncompetitive {a = 

 y = 1, /? = oc): the inhibitors may or may not interfere with each other's 

 binding but it is most likely that they will not since they presumably react 

 at different loci. 



[(S)' + di)' + 1] [(!,)' + 1] 



(I,)' + (i,)'[(S)' + a,y 4- 1] 

 [(S)' + (hr + 1] [(!,)' + 1] 



;io-9) 



(10-10) 



Similar expressions can be easily derived for cases in which the inhibitions 

 are partially competitive, partially noncompetitive, mixed, uncompetitive, 

 or of other types. 



It would be expected that the inhibition observed with two inhibitors 

 would not be the sum of the individual inhibitions when the inhibitors are 



