684 14. EFFECTS OF pH ON ENZYME INHIBITION 



SO that a plot of ])K/ against pH would provide curves, the slopes and 

 inflections of which would lead to information on the ionizing groups. 



However, it has been made clear that the experimentally determined 

 K^' is not always related to K, in this simple way. Since the p.K'./s of sub- 

 strates and inhibitors are generally known, or can be determined more 

 readily by other means, the Dixon method is usually designed to provide 

 information on the ionizing groups at the active site, either when the en- 

 zyme in free on when it is complexed with substrate or inhibitor. It is 

 particularly in these cases in which the enzyme ionizes, that K/ is often 

 not completely given by equations of the type 14-107. One difficulty is 

 that K/ can mean different things depending on what graphical method 

 is used for its determination. To take a simple example, if one determined 

 Ki from the intercept of a type F plot (where (I) (1 — i)li is plotted against 

 (S)), for cases of noncompetitive inhiliition on the active form of the enzyme, 

 one would obtain the true K^ (Eqs. 14-91 and 14-94); if this were plotted 

 against pH the slope would be zero and there would be no inflections, so that 

 a lack of ionizing groups on the enzyme might be deduced. If the inhibition 

 were on the inactive form of the enzyme, ///i , or //,/ii , would be obtained, 

 and a plot of piiT / against pH would jjrovide information on the ionization 

 constant of the enzyme. One must conclude that the equations for K/ 

 and i)K/ given above are not generally correct. The expressions for K/ 

 in terms of A', are given in Table 14-1 for most of the inhibitions discussed 

 in this chapter; the relationship is seldom as simple as in Eq. 14-107. 



The types of curves obtained by plotting pA/ against pH and the inter- 

 pretation of such curves must now be examined. Only certain types of 

 inhibition will be discussed to illustrate the problems involved. Actually, 

 the situation is not quite as bad as it would appear from inspection of 

 Table 14-1 since even the more complicated expressions for K/ generally 

 plot out in a simple manner. The real difficulty lies in the interpretation of 

 the inflections. Most of the possible expressions for K/ , as found in Table 

 14-1, are plotted as pAj'-pH curves in Fig. 14-10. The fundamental mean- 

 ings attached to the slopes and inflections are just as valid as in Dixon's 

 rules, e.g., each inflection indicates the pA^ of some group, but there are 

 three complications unforeseen in the earlier work. 



In the first place, some curves do not show any inflection despite the 

 operation of an ionizing group. This would be true for those expressions 

 for K,' in Table 14-1 that do not involve any pH or pH functions (and which 

 are not jjlotted because they are simply straight horizontal lines) but it 

 is also true for inhibition on the inactive form of the enzyme when K/ 

 is determined from plots of type A or D (numbers 9, 13, and 14). 



In the second jilace, the directions of the inflections do not correlate 

 with the location of the ionizing group, as specified in Dixon's rules for 

 pA/-pH plots. An inflection that is concave upwards in the pA/-pH 



