SPECIFICITY AND INHIBITION OF FUMARASE 



159 



Thus, once theoretical curves have been drawn through the plots for Vp , 

 Vm and Km we are no longer at liberty to draw an independent theoretical curve 

 through the points for Kp . The theoretical line in the Kh- plot of Fig. 1 may be 

 considered to come from the other three plots. 



The Michaelis constant is represented by equation (4) which has five param- 

 eters, but two of these parameters, the ionization constants for the enzyme- 

 substrate complex, are determinable from the pH variation of the maximum 

 velocity. Since Ks has nothing to do with the pH dependence, the nature of 

 this dependence is represented by two additional parameters, KaE and K^e . 

 The values of K„e and K^e may be obtained from a plot of Vs/Ks versus pH 

 since 



Ks 



Vs' Kg' 



(9) 



1 + (U+)/KaE + K,E/{il+) 



We now have an opportunity to test the theory since the same values of K^e 

 and KbE should be obtained whether we are studying the forward reaction or 

 the reverse reaction. Such a plot is shown in Fig. 2. The correction terms 

 [1 + (H+)/i^^f] and [1 + {B.+)/Khm] are required at low pH values to allow 

 the secondary ionizations of the substrates in the case of the fumarase reaction. 

 The equilibrium constant for the over-all reaction under the conditions used is 

 4.4. The values of pK„E and pKhs are calculated from this bell-shaped plot. 



The pK values for the active site of fumarase obtained in this way are sum- 

 marized in Table I (Frieden and Alberty, 1955). It is of interest to note that the 



Km Khm 



4.4 Kp Khf 



Fig. 2. Plot of Ve [1 + (H+)/A'^H/4.4 Ke (•) and F.^[l + (H+)/Khm)/Khm 

 (O) versus pH at 25° for 0.01 M /;-/.?-(hydroxymethyl)-aminomethane acetate buffers 

 (Frieden and Alberty, 1955). The curve has been calculated using equation (9). 



