Non-negative Least Squares Approach to Quantification of ¹H Nuclear Magnetic Resonance Spectra of Human Urine

Because of its quantitative character and capability for high-throughput screening, ¹H nuclear magnetic resonance (NMR) spectroscopy is used extensively in the profiling of biofluids such as urine and blood plasma. However, the narrow frequency bandwidth of ¹H NMR spectroscopy leads to a severe overlap of the spectra of components present in the complex mixtures such as biofluids. Therefore, ¹H NMR-based metabolomics analysis is focused on targeted studies related to concentrations of the small number of metabolites. Here, we propose a library-based approach to quantify proportions of overlapping metabolites from ¹H NMR mixture spectra. The method boils down to the linear non-negative least squares (NNLS) problem, whereas proportions of the pure components contained in the library stand for the unknowns. The method is validated on an estimation of the proportions of (i) the 78 pure spectra, presumably related to type 2 diabetes mellitus (T2DM), from their synthetic linear mixture; (ii) metabolites present in 62 ¹H NMR spectra of urine of subjects with T2DM and 62 ¹H NMR spectra of urine of control subjects. In both cases, the in-house library of 210 pure component ¹H NMR spectra represented the design matrix in the related NNLS problem. The proposed method pinpoints 63 metabolites that in a statistically significant way discriminate the T2DM group from the control group and 46 metabolites discriminating control from the T2DM group. For several T2DM-discriminative metabolites, we prove their presence by independent analytical determination or by pointing out the corresponding findings in the published literature.