270 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



on the enzyme but also to changes in the benzene ring and its interaction 

 with the enzyme. Also it is possible that adding a group to a molecule may 

 sterically prevent the rest of the molecule from approaching the enzyme 

 surface as closely as before; the difference in binding energy will then not 

 reflect only interactions of the added group. 



DETERMINATION OF THE EQUILIBRIUM DISTANCE d^ 



FROM K, 



The interaction energy derived from iiC , may be used to estimate the equi- 

 librium distance between the inhibitor and the enzyme. This applies, of 

 course, to specific groups whose interaction can be ascertained and not 

 usually to the entire inhibitor molecule and the total interaction energy. 

 When (fg is made up of several contributions, with different dependencies 

 on separation distance d^, calculation of the equilibrium distance is difficult 

 and graphical methods must be used. If ionic interaction is considered, it 

 might be thought that one could simply use the expression d^ = SOSz^Zg/?'?-^ 

 obtained from Eq. 6-56. In the first place, one must decide upon what val- 

 ue of D to use. Since D cannot be taken as unity (as in a vacuum) or as 

 74.1, the bulk dielectric constant, Init depends upon the separation distance, 

 its value cannot be assigned without knowing d^. Thus an equation such 

 as 6-75 must be used which results in a quadratic expression for d^. In ad- 

 dition, the effect of the ionic atmosphere, which also depends on the distance, 

 should be included, according to Eq. 6-89 or 6-90. Finally, the contribu- 

 tions to (fg from induced dipole and dispersion interactions should be 

 included. 



One of the most important interactions in inhibitions is that between 

 an amino group and a carboxyl group in the ionized state. Let us assume 

 that the value of AF for this interaction has been determined experimen- 

 tally for a particular inhibitor and we wish to calculate the equilibrium sep- 

 aration distance between these ionic groups. The expression for the total 

 potential energy may be written as: 



305 e"<'-o-'^e> lll(ai -}- a,)e'<<%-V ll^^/Ya,a^ ^^, ^^^^ 



" — (b-iuy) 



Ion-ion Ion-induced dipole Dispersion 



using the equations derived in the previous sections. The following values 

 may be used: a^ for the carboxyl group = 1.87, a.^ for the amino group 

 = 2.14; Zi for the carboxyl group = 16, and Zg for the amino group = 8, 

 whence V-Z = 11.3 since ^f Z = Z^Z,;, and D = M, — 7. With regard to r^ 

 and K, it is difficult to decide upon whether the distance of closest approach 

 should involve the primary hydration layers or not. Calculations will be 



