## 2 Materials and Methods
### Extraction of Non-Extractable Polypphenols (NEPs)  
To obtain NEPs, an ultrasound-assisted extraction technique (UAE) was employed along with the different NaDES grouped in Table 1. Briefly, 50 mg of the extraction residue, recovered after the conventional extraction of EPPs of mangosteeen peel, was mixed with 1 mL of NaDES:water (70:30, \(v/v\)). The mixture was sonicated with an ultrasound probe (model VCX130, Sonics Vibra-Cell, Hartford, CT, USA) for 1 min at 30% amplitude ([PERSON] et al., 2019). The extracts obtained were subsequently centrifuged for 15 min at 10 \({}^{\circ}\)C and 12,000\(\times\)\(g\). The supernatant obtained was saved and used for the following analysis. All the extractions were performed in triplicate. After the selection of NaDES and the molar ratio between NaDES components (1:1, 1:2, and 1:3), a second-order Box-Behnken design based on three levels and three central points was employed to optimize conditions using Statgraphics Centurion XVII software (Statpoint Technologies, Inc., Warrenton, VA, USA). The effects of the percentage of water (10, 20, and 30%, \(v/v\)), ultrasound amplitude (30, 45, and 60%), and extraction time (1, 8, and 15 min) were investigated. In total, 15 experiments were achieved in a random run order (Table S1). The total proanthocyanidin content (DMAC and butanol/HCl assays) and total antioxidant capacities (capacity to inhibit the formation of hydroxyl radical, capacity to scavenge free radicals, and ferric-reducing antioxidant power (FRAP)) were the response variables (\(Y_{i}\)). Experimental data were fitted with the second-order polynomial equation:  
\[\begin{split} Y_{i}=\beta_{0}+\beta_{1}W+\beta_{2}A+\beta_{3}T+ \beta_{1,2}W\times A+\beta_{1,3}W\times T+\beta_{2,3}A\times T\\ +\beta_{1,2,3}W\times A\times T+error\end{split} \tag{1}\]  
where \(W\) was the water percentage in the solvent; \(A\) was the ultrasound amplitude; \(T\) was the extraction time; \(\beta_{0}\) was the linear regression coefficient; \(\beta_{1}\), \(\beta_{2}\), and \(\beta_{3}\) were the linear effects; \(\beta_{1,2}\), \(\beta_{1,3}\), and \(\beta_{2,3}\) were the two-factor interaction effects; \(\beta_{1,2,3}\) was the three-factor interaction effect; and error was the error variable. To evaluate the adequacy of the fitted model settled between water percentage, ultrasound amplitude, and extraction time, and the different responses, analysis of variance (ANOVA) was employed. A combination of experimental factors looking to maximize the desirability function was used to calculate a  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Component 1 (HBA)** & **Component 2 (HBD)** & **Abbreviation** & **Molar Ratio** & **Reference** \\ \hline Choline chloride & Glycerol & ChCl-gly & 1:2 & [(29)] \\ Choline chloride & Ethylene glycol & ChCl-EG & 1:2 & [(30)] \\ Choline chloride & Urea & ChCl-urea & 1:2 & [(31)] \\ Choline chloride & Sorbitol & ChCl-sorb & 1:1 & [(32)] \\ Choline chloride & Lactic acid & ChCl-LA & 1:2 & [(33)] \\ Choline chloride & Citric acid & ChCl-CA & 2:1 & [(34)] \\ Choline chloride & Formic acid & ChCl-FA & 1:2 & [(33)] \\ \hline \end{tabular}
\end{table}
Table 1: Hydrogen bond acceptors (HBAs) and hydrogen bond donors (HBDs) employed in the synthesis of natural deep eutectic solvents (NaDES).  
multiple response optimization. The experimental extractions under the theoretical optimal extraction conditions using UAE with NaDEs were performed in triplicate to verify the experimental design.