ISOBOLOGRAMS 183 



or in the form: 



which is similar to the Eq. 5-7 for single-curve plots, but neglects the K^ 

 term on the right side, thus indicating the error introduced by this ap- 

 proximate method. 



The difficulty lies usually in relating this ratio to the ratio of the true 

 dissociation constants, since neither K„^ nor K/ may be such. The calcu- 

 lated inhibition constant K/ will equal K^ in simple systems where no other 

 components are involved, but it has already been pointed out that K^' may 

 include the concentrations and constants of activators, coenzymes, hy- 

 drogen ions, and other possible components when determined by the stan- 

 dard methods without recognizing the role such components may play 

 in the reaction. One common source of error appears when the rate and 

 inhibition depend on pH, for, as will be shown in greater detail in Chapter 14, 

 the Ki found for a particular pH will generally not correspond to the K^ 

 for the EI complex. If the pH is not varied and the (H+) factor is not tak- 

 en into consideration in, the calculation of K^, considerable error can arise. 

 The best example of the determination of a true KJK^ ratio is probably 

 that of Thorn (1953) for the inhibition of succinic dehydrogenase by mal- 

 onate. It was found here that K„JK^ varied from 4.7 to 60 depending on 

 the nature and concentration of the hydrogen acceptors used, since ^2 is 

 dependent on these; extrapolation to A'a ^ l^d to a value of near 3 for 

 KJKi. Such a low value indicates that succinate and malonate are bound 

 to comparable degrees (about 0.67 kcal/mole difference in binding energy) 

 whereas earlier values (which were really K„JK^) would have indicated a 

 2-3 kcal/mole difference in binding. Interpretation of the spatial relations 

 of the cationic sites on the succinic dehydrogenase is correspondingly 

 modified. 



ISOBOLOGRAMS 



A method of plotting that has not been used for enzyme inhibition but 

 was developed for the study of drug antagonism (Loewe and Muischnek, 

 1926) involves the construction of isobols or curves of constant activity 

 on a graph that has substrate and inhibitor concentrations as the abscissa 

 and ordinate. A specific degree of inhibition is chosen and the various pairs 

 of (S) and (I) giving this inhibition are plotted so that each point on an 

 isobol represents the same activity of the enzyme (igoc, = same + PoXyj = 

 stroke, effect, or activity). It is, of course, only of interest when substrate 

 concentration affects the inhibition, as in competitive cases or where the 

 inhibitor reacts with the substrate. Isobols plotted in the usual way and 



