254 2. ANALOGS OF ENZYME REACTION COMPONENTS 



It is obvious that a statement that the inhibition was a certain value at 

 (I)/(S) = 0.3 would be of little significance. 



When a series of analogs is tested, quantitative expression of the relative 

 affinities of the enzyme for the various analogs is desirable when possible. 

 The term affinity implies no units and has a vague meaning, having been 

 used in a variety of ways. A common method of expressing the affinity 

 is to equate it tolIK^ in the case of an inhibitor, and to HKg for a substrate. 

 The ratio of the affinities of an inhibitor and a substrate is thus often ex- 

 pressed as KJKi. If K, = 1 mM, and K, = 0.001 mM, it would be stated 

 that the affinity of the enzyme for the inhibitor is 1000 times that for the 

 substrate. This may sound dramatic but is misleading in a way. It would 

 seem that affinity might be better expressed in terms of binding energies. 

 The ratio of the free energies of binding of inhibitor and substrate is 

 given by: 



AF, vKs 



(2-9) 



In the hypothetical case above, AFJAF^ = 2, and the inhibitor is bound 

 twice as tightly as the substrate, which is a more reasonable way of desig- 

 nating the relative affinities. 



One might consider three types of AF for the binding of an inhibitor to 

 an enzyme. There is the true AF corresponding to the true K^^ and an ap- 

 parent AF corresponding to the apparent experimental K^. In addition 

 there is the theoretical AF corresponding to the interaction energy of the 

 enzyme and inhibitor in a vacuum, uncomplicated by solvent and ions. In 

 order to compare different analogs with respect to their affinities for the 

 enzyme, it is actually this last AF one would wish in most cases, but it is 

 impossible to obtain. Lacking this, one must use the true AF values, but, 

 as pointed out above, true K/s are not often available. It may be quite 

 misleading to compare calculated AF values for a series of analogs if these 

 analogs have different p-ff^'s and the experimental pH is in the region of 

 these p-fi'./s. The differences in the AF's may reflect mainly the different 

 degrees of ionization rather than the differences in binding energies of the 

 inhibitory forms. In several instances in this chapter, I have calculated the 

 AF values for such series of analogs and it must be remembered that the 

 validity of comparing these values is sometimes questionable. It is some- 

 times impossible to calculate even an apparent AF and one must be satisfied 

 with values that are relative to some chosen compound; these will be called 

 relative AF values. Although the AF itself may not be meaningful, occa- 

 sionally the difference of the AF values for two inhibitors will be significant 

 in attributing interaction energies to certain groups, as discussed in Chapter 

 1-6 (page 268), since all of the other factors involving the solvent and ionic 

 atmosphere may remain relatively constant for the inhibitors. The relative 

 binding energies may be calculated in some cases even though the K^'a 



