## 2 Materials and Methods
### Sample Preparation and UHPLC-QTOF/MS Analysis  
Individual milk samples collected in the last week of treatment were submitted for lipidomics analysis. Frozen goat's milk samples were thawed at room temperature overnight, vortexed for 1 min, and extracted by a modified Folch extraction method [23]. Briefly, 100 \(\mu\)L of each milk sample was transferred to a microtube containing 10 \(\mu\)L of the internal mixture of standards (Splash, Lipidomics, Sigma Aldrich, Milan, Italy) and then were extracted using 250 \(\mu\)L of methanol and 125 \(\mu\)L of chloroform. Samples were vortexed every 15 min for four times with Wizard IR (VELP Scientific SrI, Usmate (MB), Italy), then 380 \(\mu\)L of chloroform and 90 \(\mu\)L of aqueous 0.2 M potassium chloride were added. The suspension was centrifuged at 14,000\(\times\)\(g\) for 10 min at 4 \({}^{\circ}\)C with a Hermle Z236 (LaborTechnik, GmbH, Wehingen, Germany), and then the lipophilic layer was transferred to a glass vial and dried by a gentle nitrogen stream. The same phase has been resuspended in 30 \(\mu\)L of a methanol/chloroform solution (1:1, \(v/v\)), and then 970 \(\mu\)L of an isopropanol/acetonitrile/water solution (2:1:1, \(v/v/v\)) were added. Each sample was then filtered through a 0.22-\(\mu\)m MS nylon syringe filter, and the lipophilic phase was analyzed with a 6560 Q-TOF/MS (Agilent Technologies, Palo Alto, CA, USA) coupled with an Agilent 1290 Infinity II LC system. An aliquot of 2 \(\mu\)L for positive ionization mode and 5 \(\mu\)L for a negative ionization mode, from each sample was injected in a Kinetex 5 \(\mu\)m EVO C18 100 A, 150 mm \(\times\) 2.1 \(\mu\)m column (Agilent Technologies, Palo Alto, CA, USA). The column was thermostated at 50 \({}^{\circ}\)C at a flow rate of 0.3 mL/min. For the negative ionization mode, the mobile phases consisted of (A) acetonitrile:water (2:3, \(v/v\)) with ammonium acetate (10 mM) and (B) acetonitrile:isopropanol (1:9, \(v/v\)) with ammonium acetate (10 mM). For the positive ionization mode, the mobile phases consisted of (A) acetonitrile:water (2:3, \(v/v\)) with ammonium formate (10 mM) and (B) acetonitrile:isopropanol (1:9, \(v/v\)) with ammonium formate (10 mM). The chromatographic separation was obtained with the following gradient: 0 min 70% B kept for 1 min; 1-3.5 min 86% B; 3.5-10 min 86% B; 10.1-17 min 100% B; 17.1-19 min 70% B. Mass spectrometry platform was equipped with an Agilent jet stream technology source, which was operated in both positive and negative ion modes with the following parameters: gas temperature, 200 \({}^{\circ}\)C; gas flow (nitrogen), 10 L/min; nebulizer gas (nitrogen), 50 psig; sheath gas temperature, 300 \({}^{\circ}\)C; sheath gas flow, 12 L/min; capillary voltage 3500 V for positive and 3000 V for negative; nozzle voltage 0 V; fragmentor 150 V; skimmer 65 V, octupole RF 7550 V; mass range, 40-1700 \(m/z\); capillary voltage, 3.5 kV; collision energy 20 eV in positive and 25 eV in negative mode. An Agilent MassHunter software was used for instrument control [22]. Representative extracted ion chromatograms obtained in the positive and negative ionization modes are reported in Figure S1.