808 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



and substitution of this in Eq. 15-63 gives: 



It must be remembered that AFf^ is in cal/mole in Eq. 15-63 and in kcal/ 

 mole in Eq. 15-64. A plot of log k against IjD should then give a straight 

 line of slope — "lliz^z^ld and an intercept on the log k axis of log RTjNh — 

 z1i''*p^/2.303KT. If the dielectric constant of the medium is changed from 

 D^ to D,^, the change of the rate constant is given by: 



log-^ =214^ 



1 1 



(15-66) 



The change in the rate constant is thus related only to the electrostatic 

 interactions. The problem arises again of the proper dielectric constants 

 to use. Bulk dielectric constants have been generally used in the past but 

 for the same reasons as given in the section on equilibrium constants, it is 

 likely that the correction for short-range interactions should be applied. 



An important result of plotting log k against 1 \D is that the electrostatic 

 interaction energy may be separated from the nonelectrostatic, since one 

 is derivable from the slope and the other from the intercept. Some idea of 

 the distance of separation in the activated complex may also be obtained 

 if Zi and z<^ are known or can be estimated. From the variation of the free 

 energy of activation with the temperature, the enthalpy and entropy of 

 activation may be calculated, and these quantities will relate to either the 

 electrostatic or nonelectrostatic interactions, depending on whether AF"^^ 

 or Ji^*(,s is used. A similar separation of the free energy of formation of 

 the EI complex into AF ^^ and AF ^^^^ may be made by plotting log K^ 

 against 1/Z). 



It must be emphasized that AF ^^ or Ji^?, may include terms other than 

 those arising from the simple electrostatic interaction of ionic groups. The 

 complex may involve the association or dissociation of a proton and the 

 energy for this will appear in the over-all free energy change. Charged 

 groups on the enzyme or the inhibitor may be moved closer together or 

 farther apart and these energy terms will be dependent on the dielectric 

 constant also. Furthermore, even in interactions of simple ions, the forces 

 arising from induced dipoles may be appreciable in some cases, although 

 in general they are probably less than 1 % of the ion-ion interaction energy 

 (see Table 6-15). When more complex inhibitors are considered, one may 

 have a situation in which AF ^^ or zli^*, is itself made up of several terms, 

 each with a different numerical coefficient. In some instances, energy 

 terms dependent on l/D- may occur, as in induced dipole interactions, and 

 this may produce some deviation from linearity in the plots. The energy 

 values therefore cannot be directly applied to single simple interactions in 



