490 10. EFFECTS OF MORE THAN ONE INHIBITOR 



used separately and the equations above provide an estimate of the 

 deviations to be expected. Thus when both inhiliitors are noncompetitive 

 and bind at the same site, the sum of t'j = (Ii)7[(Ii)' + 1] and i^ = (12)'/ 

 [(I2)' + 1] which may be written as: 



.^. (I,)' + (I2)' + 2(I,)'(I,)' ,,„,,, 



''^''= 1 + (I.)' + (I.)' + (I,)U)' ^''-''^ 



would always be greater than ?'i 2 as given by Eq. 10-6. So that if {l^}' — 1 

 and (I2)' = 0.4, the sum of the individual inhibitions would be i^ -{- {2 = 

 0.786 while the inhibition produced by the two acting together would be 

 I'l 2 = 0.583. 



Graphical Analysis of Multiple Inhibition 



The determination of inhibition constants by the plotting methods out- 

 lined in Chapter 5 presents no proljlem when two or more known inhibitors 

 are used since measurements with single inhibitors can be made. However, 

 in the presence of an unrecognized inhibitor, such as an added ion or buf- 

 fer, or an impurity in the enzyme preparation, the calculated K, may not 

 be the true dissociation constant of the tested inhibitor. For example, the 

 1/v, — 1/(S) plot for two competitive iidiibitors will give a straight line 

 with a slope of 



K. r, , (i>) , (I. 



A , A , 



1 



and if the presence of Ig is not suspected, the calculation of K, will be in 

 error by an amount depending on the magnitude of (I2)|K^ . Determination 

 of the type of inhibition will not be disturbed by a second inhibitor 

 as long as this inhibitor remains at a constant concentration, except 

 for the special case where the two inhibitors react with one another 

 (see below). 



Types of Interaction between Inhibitors 



In the treatment above it was assumed that I^ and L, either completely 

 interfere with each other's binding (as when both react with the same active 

 site on the enzyme and El^Ia is impossible) or are bound independently (as 

 when they react with sites sufficiently far apart to preclude significant 

 intermolecular forces). However, intermediate situations can occur, the 

 binding of the second inhibitor molecule to the enzyme being either reduced 

 (negative interaction) or facilitated (positive interaction) by the presence 

 of the other inhibitor molecule. Several mechanisms may be visualized to 



