The NMR chemical shift pH measurement revisited: analysis of error and modeling of a pH dependent reference

A standard differential calculus-based propagation of error treatment is applied to the traditional chemical-exchange Henderson-Hasselbalch NMR pH model in which the reference shift is pH independent. It is seen naturally from this analysis that (i) the error minimum in derived pH occurs in the region where pH and indicator pKa are equal and that (ii) the dynamic range, or difference between the limiting chemical shifts of acid and base forms of indicator species, determines the insensitivity of the technique to propagation of errors. To extend the useful pH range and utility of NMR pH determination methodology, a more general model is developed in which the internal reference species is also considered as having a pH-dependent chemical shift. Data from standard solution pH titrations are fitted to both models and parameters are estimated for the normally observed family of ionizable phosphorus metabolites (ATP, inorganic phosphate, phosphoethanolamine and phosphocholine) and the xenometabolite 2-deoxyglucose-6-phosphate with either phosphocreatine, the alpha-phosphate of ATP, or H2O taken as the 31P or 1H chemical shift internal reference species as well as with an external reference.