2.2.1. Creation of a Starting Profile and Deconvolution of NMR Spectra

Metabolites present in urine were first quantified by NMR using a deconvolution process. When this approach is applied, the goal is to minimize the difference between the experimental and calculated profiles. The latter is obtained by adding signals belonging to all the mixture components, weighted by their concentrations. To obtain a reasonable starting point for the first calculation, we selected 180 metabolites previously identified and quantified by NMR, considering their chemical shifts from the Chenomx database and their reported average concentrations in urine [16].

The SYNHMET procedure is illustrated using, as an example, the region between 2.47 and 2.37 ppm. The observed NMR profile of this zone mainly consists of the superimpositions of signals belonging to eleven metabolites: 2-oxoglutarate, 3-hydroxy-3-methylglutarate, 3-hydroxybutyrate, 4-pyridoxate, carnitine, glutamine, glutaric acid monomethyl ester, levulinate, pyroglutamate, succinate, and trans-4-hydroxy-L-proline.

In the first step, all chemical shifts and concentrations were changed to minimize the difference between calculated and experimental shapes. As a result, we obtained a list of metabolite concentrations constituted by very approximate values, especially those present at low levels or have their resonances hidden by other signals. The next step used MS-derived information to improve the accuracy of these measurements.

### 2.2.2. Using the NMR/MS Correlation to Identify an MS peak(s)

The first step to incorporate the HRMS measurements involved creating a list for each metabolite containing all MS-detected peaks showing a difference lower than 5 ppm between their measured accurate masses and the monoisotopic molecular weight. After this search, all the eleven metabolites were linked to a variable number of MS-chromatographic peaks, ranging from seventeen (glutamine and 4-pyridoxate) to one (3-hydroxybutyrate). These numbers show the level of ambiguity in identifying an MS hit based only on the exact mass. We exploited the correlation between the MS intensities and the NMR concentrations obtained in the first step to assist MS identification.

Such an MS feature selection process is illustrated in Figure 1 for 2-oxoglutarate, which shows the correlations between NMR concentrations obtained in the first deconvolution round and five different chromatographic peak intensities. Despite the expected inaccuracy of these NMR concentrations, we could still identify the HC- peak at 4.57 min as 2-oxoglutarate (Figure 1e).

**Figure 1.** (**a**–**e**) Correlation plots between the relative MS intensities and 2-oxoglutarate NMR concentrations obtained after the first round for five peaks showing an exact mass compatible with the monoisotopic molecular weight of 2-oxoglutarate (monoisotopic MW = 146.021523302).

Using this procedure, we could unambiguously identify at least one MS feature for all other metabolites of this region, except for 3-hydroxybutyrate and trans-4-hydroxy-Lproline.

#### 2.2.3. HRMS Assisted NMR Deconvolution

The MS intensities of the assigned chromatographic peaks were converted into concentrations using the slope of the linear correlations. These values were then averaged with those measured by NMR, employed to update the profiles obtained after the first round, and finally applied these profiles as starting points for the second round. Finally, the second round of deconvolution was performed.

Figure 2a,b follows the evolution of the calculated profile for two samples after the first (upper panel) and second-round (lower panel) of deconvolution. Main variations are evident for low concentrated metabolites, such as 4-pyridoxate (blue) and 2-oxoglutarate (purple).

**Figure 2.** Example of the deconvolution process for two different samples (**a**,**b**) in the zone between 2.47 and 2.37 ppm. The first and second deconvolution steps are shown in the upper and lower panels for each spectrum, respectively. Black and green lines represent the experimental and calculated spectra, respectively. Signals from glutamine (orange), 2-oxoglutarate (light purple), carnitine (red), 3-hydroxy-3-methylglutarate (black), 4-pyridoxate (blue), trans-4-hydroxyproline (light green), pyroglutamate (gray), glutaric acid monomethyl ester (dark green), succinate (pink), levulinate (dark purple), and 3-hydroxybutyrate (electric blue) are shown. (**c**) Percent coefficients of variation (%CV).

One thing worth noting is that there was no significant improvement in the agreement between the calculated (green) and experimental (black) profiles after the second round compared to the first one, although the metabolite concentrations on which they were based were very different. Because there were multiple ways to replicate the profile by combining the levels and positions of the metabolite signals, a precise reproduction of the measured spectrum did not warrant obtaining accurate concentrations. A deconvolution process assisted by the HRMS values would likely yield the most reliable results.

The ratios between first- and second-round concentrations were first calculated for each of the 46 samples. Next, the percent coefficients of variation (%CV) for each metabolite were calculated to assess the degree of change in concentration of this set of metabolites after mass-assisted deconvolution (Figure 2c). Metabolites showing low changes are the only ones that NMR can reliably quantify. On the other hand, the high percentage of variation for many metabolites shows the extent to which it is necessary to cross-reference the data between NMR and MS to obtain accurate results relying on two orthogonal measurements.
