VAEIATION OF ENZYME ACTIVITY WITH ]^H 661 



ionizing groups. If the enzyme ionizes in two steps and KJ = f^^^'K^, 

 the same procedure of setting d{f/J')ld{B.) = gives: 



pH„,, = l/2(pZ„' +pZ„") (14-39) 



where pK^' and pK^" refer to the two dissociations of the enzyme. 



The more complete scheme shown in Eq. 14-34 may be treated similarly 

 and setting the derivative of the denominator of Eq. 14-35 equal to zero 



leads to: 



1 



pHoBj 2 



pKa' + vKa - log 



[(S)/«iS] + K, 



(14-40) 



The v^opt ii^ ^l^is case will depend on (S) and on the factors, a and /5, that 

 express the effects of H and S on each other's binding. If a = /5 = 1 — i.e,. 

 there is no interaction in the binding of H and S — the equation reduces 

 to 14-39 as expected. 



The pH optimum for a-chymotrypsin is 8.3 but the presence of increas- 

 ing amounts of methanol leads to a progressive fall in this value to 7.8 

 (Stein and Laidler, 1959). This is shown in Fig. 14-1 for methanol concen- 

 trations between and 20%. It may be noticed that the shift in V^opi 

 is associated with a depression of the rate. The action of methanol had been 

 previously treated (Barnard and Laidler, 1952) as a dielectric constant ef- 

 fect, but in the more recent report it is felt that the dielectric constant de- 

 crease, at least in the lower methanol concentrations, is not sufficient to 

 produce the changes observed. Instead, Stein and Laidler postulate that 

 the methanol may bind to the enzyme and interfere with hydrogen bond- 

 ing at the active site and thus affect the interaction of the enzyme and 

 substrate. These results demonstrate that the pH optima for enzymes may 

 vary with the conditions of the experiment and that the inhibition of a reac- 

 tion may shift pH^^,. 



Dixon's Treatment of the Variation of Kg' with the pH 



A method for utilizing the data obtained from the variation of the pH 

 for the localization of the ionizing groups was developed by Dixon (1953 a). 

 This will be discussed briefly at this point and applied more rigorously to 

 inhibition in a later section. The experimentally determined or apparent 

 substrate constant (not the Michaelis constant) may be expressed as: 



^, (E,)(S,) /.(E)/,(S) fj, ^ ,-.,,. 



^' = "mr ^ T/;xEsr = 7:7 ^' ^''"''^ 



where here the pH functions designate the appropriate functions for E, S, 

 and ES. From this one may write: 



pif/ = pZ, - log/, - log/, + log/,, (14-42) 



