806 15. EFFECTS OF VARIOUS FACTORS ON INHIBITION 



for other than ion-ion interactions, the slopes of the log K^ — IjD curves 

 would have different values. If dispersion forces play a significant role in 

 the binding, these relationships will be modified as described later. 



It is well to remember that as the dielectric constant is reduced, at 

 first there is relatively little effect on K^, but because of the exponential 

 relationship, iii, will decrease progressively more rapidly. Thus a decrease in 

 the microscopic dielectric constant from 29 to 19, as in the example above, 

 reduces Kj by a factor of 4.43, but a further fall in the dielectric constant 

 to 5 would decrease K^ by a factor of 801,000. In most enzyme work, how- 

 ever, the dielectric constant cannot be reduced far enough to bring about 

 these very marked changes in ion association. 



In cases of competitive inhibition involving electrostatic interactions 

 of both the substrate and the inhibitor with the enzyme, a decrease in the 

 dielectric constant will increase the binding of both and the inhibition 

 will not increase as much as in noncompetitive inhibition. It might be 

 thought that equal changes in K^ and K, would lead to no change in the 

 inhibition in competitive systems, but this is not true. Equation 3-13 may 

 be written as: 



^'^ ^'^ (15-60) 



(I) + A^[l + (S)/AJ (I) + K, + (8){K,IK,) 



If K^ and K^ are decreased equally, the inhibition will become greater be- 

 cause the third term in the denominator will remain unchanged but K^ will 

 be less. Thus a decrease in the dielectric constant would be expected to 

 increase competitive inhibition even though the affinities of the enzyme 

 for the substrate and the inhibitor are simultaneously increased to the 

 same degree. However, this increase in the inhibition will not be as great 

 as in a noncompetitive situation. For example, if a noncompetitive inhi- 

 bition is 33% with (I) = 1 mM and K, = 2 mM, a change of K, to 0.2 

 niM will raise the inhibition to 83.3%, whereas a competitive inhibition of 

 33% with (I) = 1 mM, K, = 1 mM, (S) = 5 mM, and K, = 5 mM will 

 be increased to 47.6% if K^ and K, are both reduced to one-tenth their 

 original values. 



Sometimes additional factors must be taken into account. The inhibition 

 of succinic dehydrogenase by malonate would be an example of the type of 

 competitive inhibition discussed above, since a decreased dielectric constant 

 would increase the affinity of the enzyme for both succinate and malonate. 

 However, the energy required to bend the succinate molecule into the form 

 necessary for binding may be appreciably greater when the dielectric con- 

 stant is lowered because there will be greater repulsion between the carbox- 

 ylate groups. This factor is not important for malonate. Thus one would 

 expect that the affinity for malonate would be increased more than for suc- 

 cinate when the dielectric constant is reduced. In other w^ords, every change 



