*4.3. Metabolomic Analysis*

We prepared urine samples for NMR by thawing and centrifuging them for 15 min at 18,630× *g* at 4 ◦C. We added the supernatant (350 μL) to bi-distilled water (350 μL) and to a D2O solution (200 μL) of TSP (3-(trimethylsilyl)-propionic-2,2,3,3-d4 acid) 10 mM and of NaN3 2 mM. A 1M phosphate bu ffer had been used to set the D2O solution to pH of 7.00 ± 0.02. After a further centrifugation, we recorded 1H-NMR spectra at 298 K with an AVANCE III spectrometer (Bruker, Milan, Italy), at a frequency of 600.13 MHz, equipped with Topspin software (Ver. 3.5).

According to Zhu et al. [17], we suppressed the signals from broad resonances using a CPMG-(Carr-Purcell-Meiboom-Gill) filter composed of 400 echoes with a of 400 s and a 180◦ pulse of 24 s, for a total filter of 330 ms. We also applied pre-saturation, to reduce the signal from water. We employed Topspin software to apply a line broadening of 0.3 Hz and to adjust the phase of each spectrum. We set the recycle delay to 5 s, by considering the relaxation time of the protons under investigation. We employed R computational language [45] for any further processing of spectra, quantification of molecules, and data mining, with custom scripts.

We aligned the spectra by using the TSP signal as a reference (−0.017 ppm). We adjusted the baseline of each spectrum by distinguishing irregularities of the baseline from genuine signals, according to the "rolling ball" idea [46], implemented in the R package "baseline" [47]. We performed the assignment of the signals by comparing chemical shift and multiplicity with the libraries (Ver. 10) of Chenomx software (Chenomx Inc., Canada, v. 8.3).

According to Dieterle et al. [48], water intake behavior can change the dilution of urine as much as five times, obscuring any trend in metabolite concentrations. We removed this confounding factor by calculating, for each sample, the ratio between the area of TSP peak and the intensity of the spectrum. This allowed us to estimate the dilution of each sample and to select the one with the mostly representative dilution. We used this sample as a reference by quantifying the molecules from the added TSP. We then normalized the other samples towards the reference by probabilistic quotient normalization (PQN) [48].
