104 3. KINETICS OF ENZYME INHIBITION 



the endogenous rate and the effect of the inhibitor upon it. An example of 

 the use of this equation is given by Euler (1942) in a study of competitive 

 inhibition of dehydrogenases. 



EXPRESSION AND INTERPRETATION OF INHIBITION 



Recording of the inhibition merely as the fractional inhibition i or the 

 per cent inhibition is never illuminating with respect to the mechanism of 

 the inhibition. Even the determination of a constant characteristic of the 

 inhibition, such as K^, is not generally indicative of the manner in which 

 the inhibitor exerts its action. Various ways of expressing inhibition will 

 be discussed in this section and a few aspects of the molecular interpreta- 

 tion of inhibition kinetics will be mentioned. 



The Ratio K^IK/ for Competitive Inhibition 



The degree of inhibition in a competitive system does not depend only 

 on K^ but on the ratio of the substrate and inhibitor constants, i.e., the 

 relative affinities for the enzyme. This may be seen by transposing the rate 

 Eq. 3-12 for competitive inhibition to: 



--^~ (S)H-A-.f(I)(i../^., '^•"°' 



wherein the deviation from uninhibited Michaelis-Menten behavior is given 

 by the term (I) [KJK^). In deriving Eq. 3-12 an equilibrium system was 

 assumed but in general it is more correct to use K^JK^. Now, although it 

 is K„,IKi that determines the inhibition at any inhibitor concentration, 

 this ratio does not necessarily provide a measure of the relative affinities. 

 It is often of interest to calculate the relative binding energies of substrate 

 and inhibitor but this can be done only from KJK^. When the proper 

 reciprocal plots are made, the iiC/s derived are true dissociation constants, 

 but the KJs may not be. Uncritical comparison of K^ with K,,^ leads to 

 no valid conclusions about molecular events or the energetics of the reac- 

 tion. It is quite simple to determine K„JK^, either by determining each 

 constant separately or directly (see Chapter 5), but in few studies of inhi- 

 bition is one certain of the more important ratio. Sometimes it is not too 

 difficult to determine the individual rate constants if K„, = {k_-^ + J<:2)IK 

 or adjust the conditions so that K„j = K^. For example, if one can reduce 

 A', by some means, it is possible by extrapolation to arrive at k^-^jk^, as was 

 done by Thorn (1953) for the malonate inhibition of succinic dehydrogenase. 

 The F,„ was varied by using different concentrations of the dye acceptor, 

 methylene blue, and this was plotted against KJK^\ the intercept on the 



