Fig. 3

Importance of metabolite concentrations in determining chemical shifts and vice versa. The importance of the concentrations of the metabolites listed on the y-axis in determining the chemical shifts of the metabolites listed on the x-axis is shown by the colored boxes (red lowest, violet highest). The same color codes describe the importance of the knowledge of the chemical shifts of the metabolites listed on the x-axis in predicting the concentrations of the metabolites listed on the y-axis. ANOVA decomposition (Methods) of the models predicting concentrations and pH yielded the most important variables for the construction of the models themselves, as well as their relative importance for the best fitting accuracy. For instance, as depicted, chemical shifts values of 3-aminoisobutyrate H7 protons (last column) were needed for predicting the concentration of very few metabolites, and their significance was always very low (< 2), except for predicting pH (≈9). Conversely, the chemical shift of the l-histidine H5 proton (first column) is needed for the prediction of almost all metabolite concentrations as well as of pH, and appears always as a very important (20–100) variable. The 10 most frequently employed ¹H NMR signals for model construction are from the l-histidine H5, creatinine H3 and H7, glycine, citrate H3,6, l-threonine H4 and H6, 3-methylhistidine H5, and glycolate H2 protons. The chemical shift ranges of these signals are large (Supplementary Table 1), and it appears that their variations are able to reflect the majority of the metabolite concentration (and pH) changes in the artificial urine mixtures. These relationships could reasonably be translated into chemical interactions. For instance, the imidazole signals of l-histidine and, similarly, of 3-methylhistidine are very sensitive to any pH and/or ionic change, justifying why they are almost always important variables for predicting pH and the concentration of ions. Five spin systems (dashed box) from three metabolites—two doublets of doublets of citrate, two singlets of creatinine and one singlet of glycine—are easily identifiable, very sensitive to the concentrations of the mixture components, and differently sensitive to the concentrations of different components, ensuring the broadest coverage of the concentration space. These spin systems are thus chosen as navigator signals, as they guide the search of the point in the concentration space that corresponds to that particular mixture