On the Hill plot of NMR data for titration of proteins residues

The Hill plots of NMR titration data for protein residues disclose more clearly than the usual titration curves the presence of multiple weak perturbations originating from other titratable groups, and should be used whenever the conventional curve fitting is poor. For a quantitative interpretation, we derive here expressions for the Hill equation and the Hill coefficient when the titration of the observed group is perturbed by more than one titratable group. When the generalized Hill equation is fitted to the data, values of the interaction parameters between the observed group and the others are extracted provided that there are no mutual interactions between the latter groups. The method is applied to the titration data of two histidyl residues of L-arginine phosphotransferase (E.C. 2.7.3.3.) in the transition state analogue complex (enzyme-Mg2+-ADP-NO3(-)-L-Arg). From the Hill plots, interactions with three titratable groups are disclosed for both residues, and the fitting with the Hill equation reveals that they experience perturbations from the same three groups. Microscopic pK values are obtained for all the involved groups, indicating large changes (up to 3 pH units) upon protonation of the interacting groups. As compared to the conventional fitting procedure, the use and fitting of Hill plots yields from NMR data more information on the neighbourhood of enzyme residues and on the changes intervening therein through the steps involved in the catalysis.