208 6. INTERACTIONS OF INHIBITORS WITH ENZYMES 



when d is in A. This electrostatic interaction between ions is the most 

 important, but not the only, contribution to the total energy; this will be 

 apparent in the following sections. The interaction between ions in solu- 

 tion depends on the dielectric constant in the region of the ions, the hydra- 

 tion of the ions, and the ionic atmosphere, and will be much less than cal- 

 culated above (see page 249). 



lon-Dipole Interactions 



An electrical dipole results when two equal charges, q^, of opposite sign 

 are held at a distance, I, apart and the magnitude of this dipole is given by: 



Dipole moment = /< = qj, (6-6) 



The electrostatic interaction between a dipole and an ion is the sum of the 

 interactions of the ion with each of the charges on the dipole. From Fig. 6-3 

 it is seen that the potential energy is given by: 



QdQ 

 D 



1 1 



di di 



(6-7) 



When the dipolar distance, /, is less than the distance, d, between the ion 

 and the center of the dipole, as is usually the case, this equation may be 

 rewritten in the approximate form: 



q/ii cos 6 

 d'D 





(6-8) 



The term in brackets approaches unity as the distance of the ion from the 

 dipole increases: it is 0.91 when djl = 2, 0.96 when djl = 3, and 0.98 when 

 djl = 4. Thus the further approximation may often be used with minor 

 error since I is often 1-2 A and the interaction distances 5-10 A: 



?/< cos 6 

 <P = ~^^^ (6-9) 



The dependency of the potential energy on orientation is also shown in 

 Fig. 6.3. If the dipole were rapidly and uniformly rotating, the time average 

 of the potential energy would be zero. However, due to the field of the ion, 

 the dipole will be statistically oriented towards the position of maximal 

 attraction or minimal potential energy. The degree of orientation will de- 

 pend on the relative magnitudes of the interaction energy and the thermal 

 rotational energy kT. This is the orientation polarization of a permanent 

 dipole in an electric field whereby a statistical dipole is produced with a 

 moment: 



Tc = -J^^— (6-10) 



