## 2 Materials and Methods
### Almond Proteins  
In order to understand UAE effect on almond proteins, the remaining almonds from the previous extractions were recovered and their proteins were extracted. Protein extraction: pure protein extracts from almonds were extracted according to [PERSON] et al. 2017 [PERSON] et al. (2017) with some modifications from the defatted almond flour (obtained after Soxlet extraction, dried at room temperature). Thus, 10 g of each sample was mixed with 100 mL of phosphate buffer (pH 7.4) and stirred with a magnetic stirrer for one hour. The mixture was centrifuged at 9000 rpm for 20 min and filtrated using a Buchner filter. The filtrate was put in dialysis membranes for 48 h then for 3 h to remove molecules (including proteins) with an atomic mass unit below 10 kDa. The samples were afterwards put in the freeze-dryer to get purified proteins for electrophoresis analysis. Electrophoresis: To determine the molecular weight distribution of soluble proteins, Sodium Dodecyl Sulfate-Polyacrylamide Gel Electrophoresis (SDS-PAGE) was used. Molecular weight distribution of almond proteins of NA, UA and BA was evaluated under reducing (with 2-mercaptoethanol) and non-reducing conditions (without 2-mercaptoethanol). This was executed to evaluate the impact of initial treatment or processing on the almond protein profile. Under reducing conditions, the soluble protein 2 mg/mL in milli-Q water was denatured by addition of equal volume of Laemmli sample buffer (65.8 mM Tris-HCl at pH 6.8, 26.3% (_w/v_) glycerol, 2.1% SDS, 0.01% bromophenol blue, 5% 2-mercaptoethanolhanol) at 90 \({}^{\circ}\)C for 5 min. The electrophoresis was run in a Bio-Rad mini-PROTEAN system using TGX pre227 cast gels (4-15%). The same protocol was adopted without 2-mercaptoethanolanol for non-reducing conditions. Protein Dispersibility Index: PDI determines the dispersible protein in soybean products under the conditions of the test. It is a means of comparing the solubility of a protein in water. Total protein: nitrogen content in almond samples (%total protein) was analyzed by [PERSON] (Buchi speed digester K-425 system) and the protein content in liquid fractions (%water dispersible protein) was calculated by Lowry method with BSA as standard. The defatted almond flour protein quality was evaluated according to the quality analyses manual for soybean products in the feed industry [22] where the Protein Dispersibility Index (_PDI_) was calculated:  
\[PDI=\frac{\text{\text{\text@underline{\text@underline{\text@underline{\text@underline{ \text@underline{\text@underline{\text@underline{\text@underline{\text@underline{ \text@underline{\text@underline{\text@underline{\text@underline \texttext@underline{\texttext@  
* Phenolics were distributed homogeneously within almond skins before extraction;
* Phenolic diffusivity kept constant during extraction, and phenolic content in almond skin varied with position and time;
* External mass transfer resistance was neglected due to sonication or periodic stirring at each sampling time.  
Accordingly, the governing equation and initial and boundary conditions for the diffusional model specifying slab geometry are written as:  
\[\frac{\partial C_{s}}{\partial t}=D_{e}\frac{\partial C_{s}^{2}}{\partial x^{2}} \tag{7}\]  
\[C_{s}=C_{s}\quad C_{L}=0\quad t=0 \tag{8}\]  
\[\left.\frac{\partial C_{s}}{\partial x}\right|_{x=0}=0 \tag{9}\]  
\[-D_{e}A\frac{\partial C_{s}(x,t)}{\partial x}\right|_{x=Ll}=V\frac{dC_{L}(t)} {dt} \tag{10}\]  
where \(Cs\) is the total phenolic content in almond skin (mg/g), \(Cs_{,o}\) is the initial phenolic content in almond skin, being 40 mg/g almond skins, \(t\) is time (min), \(D_{e}\) is effective diffusivity of phenolics (m\({}^{2}\)/s), \(x\) is the mass transfer distance (m), \(C_{L}\) is the total phenolic content in the solution (mg/L), \(A\) is the surface area of almond samples used for each extraction (m\({}^{2}\)), \(L\) is the thickness value of almond skin, \(V\) is the volume of solvent used for each extraction (mL).