# NMR in Metabolomics: From Conventional Statistics to Machine Learning and Neural Network Approaches
## Appendix A Technical Aspects  
Nuclear magnetic resonance (NMR) is one of the most employed experimental techniques for investigating the wide composition and structural complexity of biological samples. The NMR technique is characterized by high reproducibility and ease of sample preparation and measurement proceedings. NMR is a non-destructive technique able to perform different measurements on the same sample, providing increasingly accurate and detailed information. NMR also allows to reach a quantitative analysis and to carry out in vivo metabolomics studies. Unfortunately, it has a relatively low sensitivity (\(\upmu\)M), but, in combination with chromatography, it shows a great potentiality for targeted analysis. However, it is a relatively young experimental technique with continuous development from both the hardware and software point of view (see Ref. [3] for a more details). For instance, cryoprobes [132; 133; 134] and magic angle techniques [135; 136; 137] are today commonly used for improving the signal-to-noise ratio, while AI methods are used both for signal pre-processing, such as baseline optimization [138; 139; 137], and for data analysis, as discussed in the main text of this review. Briefly, the NMR working principle is based on the resonant excitation of the precession dynamics of the nuclear magnetic moment under the effect of a static magnetic field. Nuclei characterized by an odd number of protons and/or neutrons show a magnetic moment, associated to the nuclear spin characterized by the corresponding quantum number (I). Nuclei with I \(\
eq\) 0 possess an intrinsic nuclear magnetic moment (\(\mu\)) so producing a slight local magnetic field (B\({}_{0}\)). Once immersed in an external magnetic field (B), these nuclei, previously randomly orientated, align themselves either in the same or opposite direction of B. These nuclei, subject to B, move in a precessional motion at a frequency called Larmor frequency, which takes on values in the range of 50-900 MHz (see Figure 11). Indeed, it is characteristic for each nucleus and increases with the strength of the external magnetic field B. In this condition, if the system is irradiated with an electromagnetic radiation at the corresponding Larmor frequency (resonance condition), nuclei can absorb the radiation energy, and the nuclear spins can be promoted to a different Zeeman level. When spins relax toward the fundamental state, they emit a radio frequency (damped in time, called free induction decay (FID)) that well characterizes each nucleus of the system, depending on the corresponding chemical environment that essentially exerts a local magnetic field, causing a shift (chemical shift) from the pure Larmor frequency value. This is commonly indicated by \(\delta\) and measured in parts per million since the recorded frequency is divided by the spectrometer working frequency such that the spectra acquired with different instruments can be compared. Note that nuclei with I = 0, such as \({}^{12}\)C and \({}^{16}\)O, are NMR inactive [140,141]. Figure A1B reports the most common NMR active nuclei. Among them, \({}^{13}\)C and \({}^{15}\)N show a wide chemical shift range, together with a sharp line signal, but their poor natural abundance and the low sensitivity (compared to other nuclei as \({}^{1}\)H or \({}^{19}\)F) limit their employment in the metabolomic investigation. \({}^{31}\)P has a good sensitivity (6.6 \(\times\) 10\({}^{-2}\) relative to \({}^{1}\)H) and a wide spectral range, but only few metabolites, such as nucleoside or phospholipids, contain it, restricting its employment to a few compounds. The same comments can be done about \({}^{19}\)F.  
The high abundance in nature, high sensitivity and relevant gyromagnetic ratio of \({}^{1}\)H makes 1D \({}^{1}\)H NMR spectra especially useful in the metabolomic investigation. The 1D \({}^{1}\)H NMR spectra are fast to record (few minutes) and just the information contained in only one spectrum can provide useful data to identify and quantify from 50 to 100 metabolites [142,143].