INHIBITION CONSTANTS AND INTERACTION ENERGY 269 



where x = I -{- [{S)IKJ, the difference in binding energy is given by: 



^^ 



AF, - JF, = 1.422 log — !- (6-105) 



K i 



2 



AF, - AF, = 1.422 log i^^l Sj ~ '.'\'' (6-106) 



(I2) (1 - i2)*i 



If 50% inhibition is taken for both inhibitors: 



AF, - AF, = 1.422 log lAi- (6-107) 



(^2)0. 5 



where (I)o5 is the concentration of inhibitor inhibiting 50%. If the same 

 concentration is used for each inhibitor, (I^) = (Ig), and: 



AF, - AF, = 1.422 log '"SI ~ \'l (6-108) 



n(i - ^2) 



Knowing the concentration of each inhibitor and the degree of inhibition, 

 is thus possible to calculate the difference in interaction energy; the ac- 

 curacy of the experimental values will determine the reliability of the 

 energy difference — with reasonable care it is possible to determine the 

 value of AF^ — JF2 to an accuracy of 0.01 kcal/mole or better. 



If the two inhibitors are reasonably alike in properties and size, this 

 difference in binding energy will be independent of factors such as changes 

 in water structure or effects of the ionic atmosphere. If one inhibitor is 

 R-A and the other R-B, the difference in binding energy may be related 

 to the different interactions of the groups A and B provided these groups 

 are similar. For example, if A is a nonpolar group and B is an ionic group, 

 the energy difference will not be an accurate expression of the binding 

 difference because AF for the ionic group will include terms that do not 

 occur in that for the nonpolar group. How^ever, such factors are corrected 

 for in expressions for the interaction energy (Eq. 6-90) and hence the expe- 

 rimentally determined zJi^i — AF2 may be equated with such a correct- 



Although this procedure is the most reliable for the estimation of inter- 

 action energies of single groups or parts of inhibitor molecules, some pre- 

 cautions must be observed in the interpretation. When a group is altered, 

 or replaced by another group, or when a group is added, the changes are 

 not necessarily localized to the region of the group but may extend to 

 adjacent parts of the molecule. Thus the placing of a group on a benzene 

 ring not only changes that position on the ring but alters the electronic 

 distribution and polarizability of the ring. The binding energy difference 

 for cp and cp-A will not be due entirely to the forces exerted by the group A 



