162 ROBERT A. ALBERTY 



form of the enzyme 



„ _ {I){EH) (13) 



^" ~~jEHiy 



Thus the experimentally-determined dissociation constant Ki depends not only 

 upon the affinity of the inhibitor for a particular ionized form of the enzymatic 

 site, but also upon the effect of the bound inhibitor on the ionization constants 

 of the two dissociable groups. As shown by ]\lassey's data (1953) different in- 

 hibitors have very different effects on the ionization constants of the two 

 groups in fumarase. In other words, inhibitors with the same K/ value might 

 have quite different Ki values at a given pH. Thus, if inhibitions are arranged 

 in the order of their inhibition constants at an arbitrarily chosen pH and a 

 structural interpretation of the data is developed, very likely some agonizing 

 reappraisals would be required when additional studies are made at another 

 pH value. 



By comparison of equations (3), (4) and (12) it is seen that the calculation of 

 KaEi and KbEi may be facilitated by plotting KjVs/Ks versus pH since a sym- 

 metrical bell-shaped plot should be obtained. Preliminary data on the competi- 

 tive inhibition of fumarase bears out this expectation (Frieden, 1955). The 

 best inhibitor that has been found for the fumarase reaction is me^o-tartrate 

 (Frieden, 1955). 



In order to illustrate the nature of the pH variation of Ki which is permitted 

 by equation (12), plots of log (Ki/K/) versus pH are given for two hypothetical 

 cases in Fig. 4. The plot on the left might be considered to be that expected for 

 an anionic inhibitor which causes the pK values for both groups in the enzyme 

 to be increased one unit. The plot on the right illustrates the case in which one 

 pK value {pKasi) is decreased one unit and the other (pKbEi) increased one unit 

 by the bound inhibitor. When this occurs the apparent inhibition constant will 

 not have a value at any pH which is equal to K/. The direction of the electro- 

 static effect of an ionic inhibitor on the ionization constant of a neighboring 

 group may be predicted (Kirkwood and Westheimer, 1938a.) (Westheimer and 

 Kirkwood, 1938b.) but other effects, such as the formation of hydrogen bonds 

 (Laskowski and Scheraga, 1954), may be involved. 



Another aspect of the effect of bound inhibitor upon the ionization constants 

 of groups in the enzymatic site is that acid will be produced or consumed in the 

 reaction. The number, AX, of equivalents of acid produced per mole of enzyma- 

 tic sites in the dissociation reaction is given by (Alberty, 1955) 



1 + 2{i{-^)/KaEi _ 1 + 2(ii^)/K,E (14) 



^ 1 -f- {U+)/KaEI + KbEl/{il+) 1 + (B.+)/KaE + i^6E/(H+) 



This equation is different from that derived by Wyman (1948) but actually in- 

 volves the same dependence on hydrogen ion concentration. This is the equation 



