804 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



of all the components of the medium, or should the concentrations be 

 adjusted so that they are the same as in the aqueous medium? Although 

 the details are generally not given, it would appear that the former pro- 

 cedure has usually been followed. Such changes in concentrations and ionic 

 strength might have important effects on the reaction studied. 



Effect of Dielectric Constant on the Binding of the Inhibitor to the Enzyme 



Lowering the dielectric constant of the medium will increase the electri- 

 cal interactions between the enzyme and the inhibitor, and if the binding is 

 mainly dependent on ionic and dipolar interactions, the affinity for the in- 

 hibitor will increase. A simple approach to the effect of the dielectric 

 constant on the inhibitor constant K^ will be outlined. Let us assume that 

 the inhibitor is bound to the enzyme by ion-ion forces only. We may then 

 combine Eqs. 6-54 and 6-87 to give: 



log Z, = 214 ^ (15-58) 



where Zj and Zg ^i"© ^^e number of charges on the enzyme and inhibitor 

 respectively, d^ is the equilibrium interaction distance, and D is the di- 

 electric constant. A plot of log K^ against IjD should give a straight line 

 with a slope of ^l^iZyZ^jdg. If the inhibition is determined at two different 

 dielectric constants, we may write: 



log -^ = 214 -^ 

 Ki„ de 



1 1 



(15-59) 



The bulk dielectric constants have been used almost exclusively in the 

 studies reported on both chemical and enzymic equilibria, but it is probable 

 that microscopic dielectric constants would be more appropriate. Let us 

 calculate the predicted change in the K^ when the dielectric constant is 

 changed from that of pure water to that of 30% dioxane; we shall assume 

 that K^^ = 1 mM, D^ = 74.1, D^ = 48.6, z^ = l,z^= - I, and d, = 6 A. 

 Application of Eq. 15-59 leads to a value of K^ of 0.56 niM using the bulk 

 dielectric constants. If we assume that the microscopic dielectric constant 

 for a separation of 6 A is given by 29 (from Eq. 6-72) in pure water and 

 that the dielectric constant in the dioxane mixture is reduced proportionally, 

 D.y = 19. Using these values, K^ is found to be 0.226 niM. Thus it is quite 

 important whether one uses the bulk dielectric constants or attempts to 

 make some correction for the short-range interactions usually occurring in 

 ionic associations. 



The general validity of Eq. 15-58 and the decision as to which form of 

 dielectric constant to use may be tested by using the accurate data obtained 



