224 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



The potential energy of two neutral nonpolar molecules was given by 

 London as: 



(6-33) 



a is the molecular polarizability (for convenience we shall drop the sub- 

 script in Uq), Ji is Planck's constant (6.624 xlO"^' erg-sec), v^ is the fre- 

 quency of the electrical oscillator responsible for the polarizability, and 

 the subscripts 1 and 2 refer to the two molecules interacting. London sim- 

 plified the equation by equating Jir^ to the ionization potential of the mol- 

 ecule. Thus Eq. 6-33 may be rewritten as: 



<p = - ^^^ ^^ (6-34) 



where / is the ionization potential. Since a = 3RI4:7tN: 



27RiR2 lili 



327t2N'^(^» /i + /j 



(6-35) 



Since molar refractions and ionization potentials are experimental quanti- 

 ties, this equation may be used to calculate interaction energies for any 

 specified distance between the molecules. 1\\ terms of kcal/mole: 



w = — 1.5 — ; — -^ ;— kcal/mole (6-36) 



d' I, + U 



<p = - 0.236 ^?^ , ^'^\ kcal/mole (6-37) 



d' h + h 



when a is in units of lO"-"* ml/molecule, R is in ml/mole, / is in kcal/mole, 

 and d is in A. When / is in electron volts (ev) each equation must be mul- 

 tiplied by 23.06. Pauling and Pressman (1945) assumed an average ioni- 

 zation energy of 14 ev and applied the equation: 



(p = - 38.1 Jh^ kcal/mole (6-38) 



d^ 



to protein interactions. 



The London treatment gives values for the interaction energy that are 

 less than the experimental values. An improvement was made by Slater 

 and Kirkwood (1931), who introduced the factor Z, the number of elec- 

 trons in the outer shells of the molecule (the bonding and unbonded elec- 



