676 14. EFFECTS OF pH ON ENZYME INHIBITION 



which is usually described in terms of the ionization of the enzyme-inhi- 

 bitor complex. In all cases, the concentration of HE, and hence of HES, 

 is the same, however the situation is described. 



Case V: the enzyme and the inhibitor andjor the substrate ionize. These 

 more complex situations actually do not present any problems. If the in- 

 hibitor ionizes, the apparent K"s in the equations for the six types of inhi- 

 bition must be replaced with Ki multiplied by the appropriate pH functions. 

 Likewise, the ionization of the substrate requires only the application of its 

 functions to K,. It may only be noted that when both the enzyme and the 

 inhibitor ionize, the possibility arises that there will be a maximum in the 

 ^-13H curve, such as has been discussed for uninhibited enzymes in the 

 v-I)H curves. The pHg^; for the inhibition will not necessarily lie midway 

 between the P-K^^'s of the enzyme and inhibitor. 



Case VI: the enzyme exhibits a dibasic ionization. This also presents no 

 trouble since only the dibasic pH functions, /", for tlie enzyme have to be 

 substituted in the equations of the type derived under case IV. For example, 

 in an extension of scheme 14-52: 



HES ^ HE + P 



E ;i± HE ;^ R,E (14-74) 



HEI 



to include HoE, where the inhibitor combines only with HE, the catalytically 

 active form of the enzyme, the inhibition is given by: 



^^^ (14-75) 



(I) + A^ 



>„ ,iS)^ 



J he T^ jr 



A., 



which is comparable to Eq. 14-55. The a^jparent inhibitor constant is giv- 

 en by: 



K,' = K, 



fhe'Ks + (S) 



K, + (S) 



(14-76) 



When the pH lies between piiT,/ and Y>K^" (assuming they are sufficiently 

 far apart), K/ = K^ since here /;,/' ^ 1, but on either side of this range, 

 the ajDparent inhibitor constant will be dependent on pH. 



These expressions differ from those given by Alberty (1954), although 

 the formulations of the reactions would appear on the surface to be the 

 same. Actually, the systems are quite different. Alberty assumed that 

 the HEI complex could lose or gain protons, whicli means that EI and 



