Mathematical Models for Interacting Groups in Nuclear Magnetic Resonance Titration Curves

Mathematical models were developed for the interpretation of nuclear magnetic resonance titration curves of chemical shift vs. pH with emphasis on the case of two interacting titrating groups. The equations were applied by means of computer curvé fitting to data obtained for the imidazole C-2 and C-4 proton resonances of L-histidine, N-acetyl-L-histidine, L-histidine methyl ester, and several L-histidine dipeptides. Inflections are observed in these titration curves due to the effects of the neighboring titrating amino and carboxyl groups. The curve-fitting procedure provided accurate values for the ionization constants of the imidazole and the interacting titrating groups, even when the pK values were sufficiently close that the inflections had merged to produce an asymmetric curve. Application of these procedures to the titration curves of L-histidyl-L-histidine indicated that the asymmetry noted in the high pH region of one of the curves is due to the effect of an adjacent amino group and not to an interaction between the two imidazole rings.