Bayesian estimation of the number of protonation sites for urinary metabolites from NMR spectroscopic data

Lifeng Ye, Maria De Iorio, Timothy M. D. Ebbels

To aid the development of better algorithms for [Formula: see text]H NMR data analysis, such as alignment or peak-fitting, it is important to characterise and model chemical shift changes caused by variation in pH. The number of protonation sites, a key parameter in the theoretical relationship between pH and chemical shift, is traditionally estimated from the molecular structure, which is often unknown in untargeted metabolomics applications. We aim to use observed NMR chemical shift titration data to estimate the number of protonation sites for a range of urinary metabolites. A pool of urine from healthy subjects was titrated in the range pH 2-12, standard [Formula: see text]H NMR spectra were acquired and positions of 51 peaks (corresponding to 32 identified metabolites) were recorded. A theoretical model of chemical shift was fit to the data using a Bayesian statistical framework, using model selection procedures in a Markov Chain Monte Carlo algorithm to estimate the number of protonation sites for each molecule. The estimated number of protonation sites was found to be correct for 41 out of 51 peaks. In some cases, the number of sites was incorrectly estimated, due to very close pKa values or a limited amount of data in the required pH range. Given appropriate data, it is possible to estimate the number of protonation sites for many metabolites typically observed in [Formula: see text]H NMR metabolomics without knowledge of the molecular structure. This approach may be a valuable resource for the development of future automated metabolite alignment, annotation and peak fitting algorithms.