226 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



Values of )',, are also given in Table 6-6. The use of this equation pro- 

 vides satisfactory values for the interaction energy in those cases of simple 

 molecules that have been investigated. The factor 5 relating v,. and v^ 

 is the effective number of dispersion electrons and values are given in 

 Table 6-6. Although Eq. 6-41 is admittedly only an approximation, it 

 will be used in the present book for calculating dispersion energies. When 

 possible, the values of h\. and Z should be used, but in cases where the 

 interaction involves many groups or the groups interacting are not known 

 (as is the situation usually in binding to enzymes), it is useful to derive 

 an expression employing the most probable values for molecules of the type 

 encountered in enzyme studies. The values of )',, for molecules composed 

 of C, 0, H, N, and S are reasonably constant (Table 6-6) and an average 

 value of 3.34 sec~^ may be assumed leading to an average value for Jn\ of 

 22.1 X 10~^^ ergs/molecule. Taking Z to be approximately the same in each 

 of the interacting molecules or groups: 



(p = - 238.6 V^-^^ kcal/mole (6-42) 



(p = -37.b\/Z — '—- kcal/mole (6-43) 



The difference between this result and Eq. 6-38 of Pauling and Pressman 

 is mainly in the V Z factor. Since Z is usually between 8 to 16 for interact- 

 ting atoms, bonds and small groups, the energies of interaction will be about 

 three to four fold greater than in the Pauling and Pressman expression. 

 The potential energy due to dispersion forces between two methyl groups 

 at a separation of 5 A from values in Table 6-6 and Eq. 6-41 is — 0.322 

 kcal/mole and from Eq. 6-43 is — 0.318 kcal'mole. Although single group 

 interactions exliibit small energies due to dis])ersion forces over several A, 

 the strong dependency on distance leads to appreciable energies when the 

 groups are in contact; also in larger molecules these dispersion forces may 

 occur over an extensive surface of contact and the total energy may be fairly 

 large. 



The London expressions for the interaction of mutually induced dipoles 

 are inaccurate for short distances where the atomic wave functions overlap 

 and at long distances due to the phenomenon of retardation. It was pointed 

 out by Casimir and Polder (1948) that the dispersion energy should fall 

 off faster than predicted by London when the distance between the atoms 

 or molecules becomes comparable to the wavelength corresponding to the 

 electronic frequencies involved (actually the chief absorption wavelength 

 of the interacting atom). The effect of the movement of a charge on another 

 charge is not instantaneous but progresses at the velocity of light. As 

 long as the mutually oscillating dipoles are close together, the interaction 



