## 2 Materials and Methods
### Optimization of Sample Preparation Using Response Surface Methodology (RSM)  
The ultrasound-assisted solubilization of hydroxycinnamic acids was optimized with the employment of RSM using an artificial honey solution. An amount of 0.3 g honey solution was mixed thoroughly with different volumes (3, 6, 9 mL) of hydroethanolic mixtures (60, 75, and 90% ethanol in deionized water). The procedures were carried out in an ultrasonic bath (UCI-50, 35 KHz, Raypa-R. Espinar, S.L., Terrassa, Spain) at different temperatures (30, 45, and 60 \({}^{\circ}\)C) for varying periods (10, 25, and 40 min). After ultrasonic treatment, the mixture was filtered through a 0.45 \(\upmu\)m syringe filter and stored at \(-20\)\({}^{\circ}\)C for further analysis. All sample extracts were prepared in triplicate.  
The solubilization parameters were optimized using RSM based on Box-Behnken design (BBD). A three-level and four-factor BBD was applied to investigate the effect of ethanol concentration (A), temperature (B), solvent-to-sample ratio (C), and sonication time (D) on solubilization efficiency. The contents of caffeic acid (Y1), chlorogenic acid (Y2), and ferulic acid (Y3) were used as experimental responses for the optimization. Independent variables were selected based on preliminary studies with their coded and actual levels given in Table 1. The complete BBD consisting of 29 combinations including five replications at the central point is given in Table 2, where all measurements were performed in triplicate and in random order to minimize the effects of uncontrolled variables. The mean values of all measured responses were analyzed by multiple regressions and fitted to the quadratic polynomial model described in Equation (1). Analysis of variance (ANOVA) was conducted to assess the significance of linear, quadratic, and interaction regression coefficients (statistically significant at \(p<0.05\)) and to determine the validity of the quadratic models. Three-dimensional surface plots were generated based on the developed polynomial models to interpret the relationship between dependent variables and independent responses:  
\[Y=\beta_{0}+\sum_{i=1}^{n}\beta_{i}x_{i}+\sum_{\begin{subarray}{c}i=1\\ j>1\end{subarray}}^{n-1}\sum_{j=2}^{n}\beta_{ij}x_{i}x_{j}+\sum_{i=1}^{n} \beta_{ii}{x_{i}}^{2} \tag{1}\]  
where \(\beta_{0}\) is the constant coefficient, \(\beta_{i}\), \(\beta_{ii}\), and \(\beta_{ij}\) are the regression coefficients for linear, quadratic, and interaction terms, respectively, and \(x_{i}\) and \(x_{j}\) represent the independent variables.  
\begin{table}
\begin{tabular}{l l c c c} \hline \multicolumn{1}{c}{**Independent Variables**} & \multicolumn{1}{c}{**Symbol**} & \multicolumn{2}{c}{**Factor Level**} & \\  & & **Low (\(-\)1)** & **Medium (0)** & **High (\(+\)1)** \\ \hline Ethanol concentration (\%, \(v/v\)) & A & 60 & 75 & 90 \\ Temperature (\({}^{\circ}\)C) & B & 30 & 45 & 60 \\ Solvent-to-sample ratio (mL g\({}^{-1}\)) & C & 10 & 20 & 30 \\ Sonication time (min) & D & 10 & 25 & 40 \\ \hline \end{tabular}
\end{table}
Table 1: Natural and coded levels of independent variables used in three-level, four-factor Box-Behnken design (BBD).