274 6. INTERACTIONS OF INHIBITOES WITH ENZYMES 



factors in his expressions for the ion-solvent interactions. His expression 

 for the association constant of an ion pair must therefore be considered as 

 very approximate. 



K = 2.524 X 10-3 «V 



where a = the ionic diameter in A and h — e^JciDkT. A much more complex, 

 but probably more accurate, treatment has been given by Levine and Wrig- 

 ley (1957) for the interaction energy of two univalent ions in water at 

 small separations. The region around an ion is divided into two portions: 

 a primary hydration shell and the rest of the water (which is assumed to 

 be a continuous dielectric medium). The dipole moments that are induced 

 in the hydration water molecules by the ion are calculated and taken into 

 account. The energy of two hydrated ions in a vacuum is calculated and 

 then to this is added the energy required to introduce the dielectric med- 

 ium. The deviation from the simple coulombic expression is given by 

 a correction factor, 9?^: 



y- = {e^idD) + cp, (6-111) 



The correction factor takes the form: 



-=^+^+^ (6-112, 



where the C's are complex functions of the ionic polarizability, dielectric 

 constant, and other factors. Calculations were made for potassium fluoride 

 and it was found that at ion separations of 6-8 A (contact of hydration shells) 

 9?c was about + 8% of the coulombic term. It is also interesting that the 

 effective dielectric constant for the hydrated ions was found to be close 

 to 2.5. 



INTERACTIONS OF HAPTENS WITH ANTIBODIES 



Much of the quantitative work on antibody-hapten binding reported 

 during the past 15 years, especially by Pauling, Pressman, and their asso- 

 ciates, can be applied to interactions of inhibitors with enzymes. In both 

 cases one is dealing with the binding of relatively small molecules to pro- 

 teins, the same types of interaction forces are involved, there are similar 

 orientation factors, and in both there is usually a specifically patterned 

 site on the protein where the binding occurs. The energies for the interac- 

 tions of various simple groups with proteins have been derived from hapten 

 inhibition studies and these values are useful in estimating energy contri- 

 butions from enzyme inhibitor groups, as well as providing an experimental 

 test of the theoretical interaction equations derived above. 



