TWO INHIBITORS ACTING ON A SINGLE ENZYME 491 



explain such interactions. Simple electrostatic forces must be involved 

 where the inhibitors are charged as in the following examples: 



Negative interaction: 

 (cX) > « > 1) 



Positive interaction: 

 (a < 1) 



Furthermore, if Rg is an acidic or basic group, the binding of a charged in- 

 hibitor molecule on 7?^ could alter the p/ii^ of R2 and hence the fraction of 

 these groups that is dissociated. Steric factors could also operate, especi- 

 ally when the first molecule bound extends spatially in such a way as to 

 interfere with the attachment of the second inhibitor, but positive inter- 

 action could conceivably result if a greater area of interaction were pro- 

 vided for dipolar and dispersion forces. One must also consider the possi- 

 bility of inductive effects through the protein structure or an actual change 

 in the configuration of the local protein structure. Finally, the direct reac- 

 tion of the unbound inhibitors with one another — I^ + I2 :;:^ I1I2 — can 

 complicate the kinetics considerably, particularly when the inhibitor com- 

 plex Ijlg is also an inhibitor. Indeed, when \yy<i is a more potent inhibitor 

 than either I^ or Ig, the inhibition in the presence of both inhibitors may be 

 greater than predicted on the basis of their individual actions. 

 When the inhibitors react with one another: 



I, +1, — IJ, K, (10-12) 



the concentration of Ijl, may be calculated from the quadratic equation: 



(IJ,)^ - (IJ,)[(I:), + (I,), + K,\ 4- {\,)A^^)t = (10-13) 



and from this the concentrations of the uncomplexecl inhibitors may be ob- 

 tained. If Ij, I2, and Ijlg are all inhibitory, and each inhibits noncompeti- 

 tively, the total inhibition is given by: 



(I.)' + (I.)' + (IJ.)' (^^^^^ 



1 + (I,)' + (I,)' -f (IJ,)' 



If Ijlg were not formed, the iniiibition would be given by Eq. 10-6; the 

 concentrations of Ij and Ig would be in this case the total concentrations. 

 Whether the multiple inhibition will be greater or less than in the situation 



