## 3 Materials and Methods
### Gas Chromatography-Mass Spectrometry (GC-MS)  
A Focus GC (Thermo Scientific) coupled to DSQ II (Thermo Scientific) with a single quadrupole and split-splitless injector was used. The carrier gas was used in the constant flow mode (He, purity 99.995%) at 20 mL/min. The injector was kept at 280 \({}^{\circ}\)C. Separation of analytes was performed by means of a fused-silica capillary column (RXI-5, Restek) with a 0.25 \(\upmu\)m (30 m \(\times\) 0.25 mm \(\times\) 0.25 \(\upmu\)m) methyl-silicone (5% phenyl) film. MS conditions were as follows: interface temperature at 280 \({}^{\circ}\)C; ion source temperature at 230 \({}^{\circ}\)C. The mass spectrometer was operated in the EI positive mode (70 eV). The mass spectra were collected with a 41-500 m/z fragmentation rate.  
The analysis was carried out using a sample quantity of less than 1 mg (Table S1). The considered internal standards were: tetracosane (50 \(\upmu\)L of a 0.1 mg/mL solution \(w/v\)) for the fatty acids analysis; norleucine (50 \(\upmu\)L of a 0.1 mg/mL solution \(w/v\)) for the amino acids analysis.  
For the fatty acid extraction, the sample was treated with 4N-HCl in methanol (1 mL) and n-hexane (1 mL) for 2 h at 50 \({}^{\circ}\)C. The n-hexane phase containing fatty acid methyl-esters was used for GC-MS analysis (1 \(\upmu\)L). Separation of the methyl ester of fatty acids was achieved using the following temperature program: isothermal conditions at 60 \({}^{\circ}\)C for 2 min, with 20 \({}^{\circ}\)C/min heating up to 220 \({}^{\circ}\)C and isothermal conditions at 220 \({}^{\circ}\)C for 8 min, lasting up to 280 \({}^{\circ}\)C with an increment of 20 \({}^{\circ}\)C/min and 4 min at 280 \({}^{\circ}\)C. The mass spectra were collected with a 40-400 m/z fragmentation rate. After the previous phase, the extraction of amino acids was carried out: after dry evaporation of the residual methanol phase, the residues were dissolved using 6N hydrochloric acid (2 mL) and hydrolyzed in a screw-capped container for six hours at 90 \({}^{\circ}\)C in an oil bath, under a nitrogen atmosphere.  
For the amino acids' extraction, after evaporation, the methanol phase to dryness, the residues were dissolved in 6N hydrochloric acid (2 mL) and hydrolyzed in a screw-capped container for six hours at 90 \({}^{\circ}\)C in an oil bath under a nitrogen atmosphere. After evaporation to dryness, the hydrolyzed residues were esterified using 0.4 mL of 2N HCl in propane-2-ol at 90 \({}^{\circ}\)C for one hour. After cooling, the solvent was evaporated under vacuum and the residue was dissolved in 0.3 mL of dichloromethane and derivatized with 0.2 mL of trifluoroacetic anhydride at 60 \({}^{\circ}\)C for 30 min. After evaporation to dryness, the residue of the paint sample was dissolved in 0.3 mL of dichloromethane, and then the solution was used for GC-MS analysis (1 \(\upmu\)L). The separation of N-trifluoroacetyl-O-2-propyl esters amino acids derivatives was achieved using the following temperature program: isothermal conditions at 60 \({}^{\circ}\)C for 3 min, with 20 \({}^{\circ}\)C/min heating up to 280 \({}^{\circ}\)C and isothermal conditions at 280 \({}^{\circ}\)C for 12 min.  
The basic methodology relied on the identification of fatty acids and amino acids in the same samples. Two chromatograms were collected for each sample: the first for fatty acid derivatives and the second for amino acid derivatives [24].  
To identify the proteinaceous binders, the percentage content of amino acids in each sample was related to those from a dataset of 43 reference samples of egg (whole, egg white, egg yolk), skimmed milk, animal glue, and the mixtures of them [25; 26]. Principal component analysis (PCA) was carried out on the relative percentage of eight amino acids (aspartic acid, glutamic acid, proline, hydroxyproline, phenylalanine, alanine, glycine and leucine) using the correlation matrix of the values [27].