252 



6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



The best presentation of the modern concepts of ion-solvent interactions 

 is to be found in the symposium published in the Discussions of the Fa- 

 raday Society in 1957 (No. 24). The work of Platzman and Franck (1954), 

 Brady (1958) and George (1959) may also be mentioned as particularly 

 pertinent to the problems of ionic hydration in the interactions of proteins 

 with inorganic ions and small molecules. 



Calculation of Hydration Energy from Interaction Energies 



It is interesting to calculate the hydration energy of an ion on the basis 

 of the interaction equations proposed in order to illustrate the complexi- 

 ties of such systems and to obtain a rough estimation of the relative con- 

 tributions of the various types of interaction. We shall consider the po- 

 tential energy of an ion surrounded by its primary hydration layer; the 

 specific calculations will refer to the K"^ ion for which a primary hydration 

 number of six is assumed. There are the following contributions to the total 

 potential energy. 



lon-dipole interaction: 



57.4 



nZi/-i,„ 



cos Q 



— 63.1 kcal/mole 



Ion-induced dipole interaction: 



Ve 



111 



d^ 



13.8 kcal/mole 



Dispersion (ion- water and water- water): 





6.03 kcal/mole 



Dipole-dipole interaction (water- water): 



= + 14.4 



«/', 



2V2c?. 



+ 4.24 kcal/mole 



Total interaction energy: 



78.69 kcal/mole 



The primary hydration number n = 6, z^ = \, //„, = 1.83 debyes, a^ = 

 0.87, a^ = 1.44, Z = 8, = Oo, and d, = 2.891 A. The value of d, was 

 obtained by summing the ionic radius of K+ and the van der Waals' ra- 

 dius of water; f/g is the distance of the water dipole center from the mole- 

 cular center (0.274 A). Two further energy terms must be included to 



