**2. Results**

#### *2.1. Optimizing the Relaxation Delay for Semi-Quantitative Metabolomics*

A fundamental principle of NMR spectroscopy is that increasing the number of experimental scans (N) increases the S/N ratio by a factor of √N [16]. For pulsed NMR experiments, the relaxation delay, commonly known as d1, is the time required between scans to allow spins to return to equilibrium. The optimal d1 time depends on the longitudinal relaxation (T1) rate—the time required for full restoration of the nuclear spin to equilibrium along the direction of the polarizing magnetic field [16]. Each nuclei in a molecule has a different T1 value, and for small molecules like metabolites T1 values can be several seconds long. For example, formate has a T1 > 9 s at 600 MHz [17]. For quantitative NMR, it is advised to set d1 to 5 × T1 of the slowest relaxing nuclei in a sample [17]. This would require a d1 of upwards of a minute in length, leading to impractically long acquisition times that are not feasible for high-throughput NMR metabolomics. In practice, d1 is commonly set to a pre-determined value that allows for a relative quantitative comparison between spectra collected under identical conditions. It is important to note that only a comparison between the same metabolite can be made in this manner across the spectral dataset. A comparison between two or more different metabolites would be meaningless because of the d1-dependent variation in peak integrals that distorts the relationship between peak integral and metabolite concentration.

A model mixture ("Reference 1") was composed of 29 commonly observed human metabolites, which included amino acids, organic acids, biogenic amines, sugars, etc., from the literature [18–21] as well as metabolites commonly observed in our own clinical studies. To find the optimal d1 for a model mixture of 29 metabolites (Reference 1), we recorded time equivalent experiments (4 min ± 8 s) with varying d1 values of 1.5 s, 1.2 s, 0.8 s and 0.6 s and observed the changes in both the 1D 1H NMR spectra and 2D 25% NUS 1H-13C HSQC spectra (Figure 1). At first, as the d1 decreased, the signal intensity for the majority of the metabolites increased, which is expected due to the increased number of scans (N = 64 to 92 for the 1D- and N = 36 to 84 for the 2D-experiments). For the 25% NUS 1H-13C HSQC spectra, we observed a steady increase in the mean intensity of metabolites from 2.9 × 107 to 4.9 × 107 as d1 decreased from 1.5 s to 0.8 s. Similarly, the mean S/N increased from 98.48 to 115.34. However, the mean S/N and intensity reached a maximum at a d1 of 0.8 s. As evident by the expanded regions of the 1D 1H NMR spectra (Figure 1a), peak intensities began to decrease at a d1 of 0.6 s despite the larger number of scans. This is consistent with the 25% NUS 1H-13C HSQC spectra at a d1 of 0.6 s, where the mean S/N and intensity decreased to 106.18 and 4.7 × 107, respectively. Furthermore, significant solvent artifacts were observed in the HSQC spectra relative to longer d1 values. Presumably, at a d1 of 0.6 s, factors related to T1 dominate spectral sensitivity, which could not be negated by the

allowed increase in the number of scans. This led us to select 0.8 s as the optimal d1 value for improved S/N.

**Figure 1.** An optimized combination of relaxation delay (d1) and number of scans (N) improved the S/N for (**a**) 1D 1H and (**b**–**e**) 2D 1H-13C HSQC spectra of a model mixture of metabolites in time equivalent experiments. Four 1D 1H NMR spectra are overlaid and color-coded according to the d1 value: 1.5 s (blue), 1.2 s (red), 0.8 s (green), 0.6 s (purple). The boxed regions in the 1D 1H NMR spectra are shown as expanded inserts above each corresponding arrow.
