698 14. EFFECTS OF pH ON ENZYME INHIBITION 



vicinal groups up to at least 12 A from the active center can produce 

 significant effects. Some might consider the ionization of the vicinal group, 

 in its effect upon K^, as an ionization of the enzyme-inhibitor complex 

 However, it would seem more usual to consider the EI complex as made 

 up of the inhibitor and the active center, and it is probably preferable to 

 consider ionizing groups outside of the active center as separate from the 

 EI complex. Experimentally, nevertheless, it is sometimes not easy to dis- 

 tinguish between ionizations in the active center and ionizations of groups 

 that are close by, unless a definite jog instead of a change in slope is evi- 

 dent in the piiTZ-pH plot. Such jogs have not been recognized or treated 

 in the enzymes so far subjected to this analysis, but if one examines the 

 experimental points closely, definite jogs are often observed, usually be- 

 tween 0.1 and 0.4 ])K- units in magnitude and thus indicate vicinal groups 

 between 8 and 12 A distant from the active center. 



We have considered the effects of a single vicinal group on the K^ but 

 actually there are probably several ionizing groups within an effective dis- 

 tance of the active center on most enzyme proteins. Averaging data from a 

 number of proteins for which the total number of ionizing groups and the 

 molecular size are known, it may be calculated that a typical protein mol- 

 ecule possesses an ionizing group for each 25 A^ area of the surface. The 

 area of the protein surface within 12 A of the active center may be esti 

 mated as approximately 500 A- (since most enzyme proteins are not spher- 

 ical, only rough estimates need be made) and hence will contain on the 

 average about twenty ionizing groups. Now, only a fraction of these groups 

 will ionize over the pH range of interest. Usually not over 25% of the total 

 groups will have piiC^'s between 5 and 9 and thus we can assume that 

 around five groups are so situated that they can produce a significant ef- 

 fect on the p^,. This will clearly vary with the amino acid composition of 

 the enzyme protein but the calculation shows that usually more than one 

 ionizable group must be expected. If two or more groups have the same 

 pi^a, their individual effects will sum; thus three interacting vicinal groups 

 at a distance of 10 A could change the p^, by as much as one unit. The 

 progressive effects on the p/ii , of several vicinal groups with different pJ^^'s, 

 when the pH is varied, may be complex. 



Another ai^proach to the effects of protein ionizing groups on the K^ is 

 to neglect the interactions of specific groups with the EI complex and con- 

 sider only the total net charge on the enzyme. The total interaction energy 

 of the protein charge with the EI complex is, of course, the sum of the 

 energies from the individual groups, i.e., Ji^^^,,,, = i^]^" AF i where AF^ 

 is the interaction energy due to the ?'th group and there are n such groups. 

 Although single groups beyond 15 A from the active center do not affect 

 the K^ markedly, there are so many ionizing groups on most proteins that 

 the summed effect may be appreciable. The effects of the total protein 



