SPECIFICITY AND INHIBITION OF FUMARASE 161 



one group is in its acid form so that it can serve as a proton donor and the other 

 group is in the basic form so that it can serve as a proton acceptor. The enzyme- 

 malate complex is cocked to catalyze the reverse reaction. Thus, we believe that 

 the enzyme works essentially by an acid-base catalysis, but the reaction occurs 

 rapidly in neutral solutions because the acidic and basic groups are located at 

 exactly the right positions in space. This sort of picture helps us to understand 

 many things about the fumarase reaction. For example, the activity is low in 

 strongly acidic solutions because the group which has to serve as a proton ac- 

 ceptor spends a very small fraction of the time in the basic form. A single opti- 

 cal isomer of malate is obtained because group R' determines the side on which 

 the hydroxy 1 group is added. Similarly, the mechanism helps us understand 

 why monodeuteromalate is formed when the reaction is carried out in deuterium 

 oxide and why no deuterium is found in the fumarate. 



Competitive Inhibition of Fumarase 



The inhibition constant Ki for a competitive inhibitor / is obtained by use of 

 the equation 



, = Vs (10) 



1 -1- Ks[\ + {i)/K:y{s) 



In contrast with the Michaelis constant, which is not to be interpreted as an 

 equilibrium constant, the inhibition constant may be interpreted as a dissocia- 

 tion constant for the enzyme-inhibitor complex. However, Ki may depend 

 strongly upon the pH (Massey, 1953). If the active site may be considered to 

 be a dibasic acid, the dissociation of the enzyme-inhibitor complex may be 

 represented by 



EI E 



KbEi It 11 KbE 



EHI . ' ^ I + EH (11) 



11 11 Ka, 



KaEi EH J EHo 



where KaEi = (H+) {EHI)/{EHJ), K^ei = (H+) {EI)/{EHI), K,e = (H+) 

 {EH)/\EH-i), and Ki,e = (H+) (E)/(EH). It is assumed that the inhibitor does 

 not ionize in the region under investigation, although provision could readily 

 be made for such ionization if necessary. The inhibition constant which is ob- 

 tained by use of the equation (10) is given by 



^I — ^I' H , /XT + 



1 + {B.+)/KaE + K,,/{ -R+) (12) 



1 + (u'-)/K„Er + K,Ei/(n^) 



where K/ is the dissociation constant for the complex with a particular ionized 



