## 3 Results and Discussions
### RSM Optimization of Hempesed Protein Extraction
#### 3.5.2 The Potential Impact of Optimising Extraction Conditions on HPI Functionality  
The 3D RSM plots were obtained from the two responses according to regression Equations (7) and (8). Figure 10 plots the response of any two independent factors, with \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Coefficient**} & \multicolumn{2}{c}{**SE**} & \multirow{2}{*}{**F-Value**} & \multirow{2}{*}{_p-Value_} \\  & & **Coefficient** & & \\ \hline \multicolumn{5}{c}{Hempesed protein concentration} \\ pH & 0.6425 & 0.0434 & 219.54 & \textless{}0.0001 \\ Time & 0.5600 & 0.0434 & 166.78 & \textless{}0.0001 \\ Temperature & 0.4150 & 0.0434 & 91.59 & \textless{}0.0001 \\ pH \(\times\) Time & 0.2175 & 0.0613 & 12.58 & 0.0094 \\ pH \(\times\) Temp & 0.0175 & 0.0613 & 0.0814 & 0.7836 \\ Time \(\times\) Temp & 0.0625 & 0.0613 & 1.04 & 0.3420 \\ pH \(\times\) pH & \(-\)0.2038 & 0.0598 & 11.62 & 0.0113 \\ Time \(\times\) Time & \(-\)0.4438 & 0.0598 & 55.12 & 0.0001 \\ Temp \(\times\) Temp & \(-\)0.2837 & 0.0598 & 22.54 & 0.0021 \\ \multicolumn{5}{c}{Free sulfhydryl (-SH) content} \\ pH & \(-\)7.60 & 0.5736 & 175.56 & \textless{}0.0001 \\ Time & \(-\)14.25 & 0.5736 & 617.10 & \textless{}0.0001 \\ Temperature & \(-\)9.19 & 0.5736 & 256.49 & \textless{}0.0001 \\ pH \(\times\) Time & \(-\)2.72 & 0.8112 & 11.24 & 0.0122 \\ pH \(\times\) Temp & \(-\)2.09 & 0.8112 & 6.61 & 0.0370 \\ Time \(\times\) Temp & \(-\)1.35 & 0.8112 & 2.76 & 0.1406 \\ pH \(\times\) pH & 6.71 & 0.7906 & 72.00 & \textless{}0.0001 \\ Time \(\times\) Time & 12.89 & 0.7906 & 265.64 & \textless{}0.0001 \\ Temp \(\times\) Temp & 6.21 & 0.7906 & 61.62 & 0.0001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimated regression coefficients for hempseed protein concentration and free -SH content. the third factor kept fixed, which can be used to analyse the interaction impacts between independent factors. Regarding the protein yield, only the interaction between pH and time (X\({}_{1}\)X\({}_{2}\)) was significant (\(p\) = 0.0094), while the interactions between pH-Temp (X\({}_{1}\)X\({}_{3}\)) and Temp-time (X\({}_{2}\)X\({}_{3}\)) were not significant (\(p\) > 0.05) (Table 4). This suggests that the pH exerts a substantial impact during the extraction, which fits our empirical findings. Optimised extraction parameters were determined to maximise the functionality of HPI on the basis of maximising both the free -SH content (and a minimum criterion of \(\geq\) 65 \(\upmu\)mol/g, as reasoned in Section 3.3) and protein yield. The reliability of the optimum conditions was determined by the desirability values of the responses, which range from 0 to 1, analysed by Design Expert 13 software. The value of desirability closer to 1 indicated better extraction conditions. The optimised independent variables were at pH 11.0 for 5 min under 31.8 \({}^{\circ}\)C, with a desirability of 0.862. Under such extraction conditions, the projected protein yield was 1.343 mg/mL with 65.0 \(\upmu\)mol/g of free -SH content. Subsequently, verification experiments under these optimised conditions were conducted to confirm the validity of the model results. The practical values of protein yield and free -SH content were 1.2 mg/mL and 64.1 \(\upmu\)mol/g, respectively. The results have demonstrated a good agreement between the practical and the projected values. Furthermore, the functionality of the optimised HPI was compared with the hempseed protein extracted by the original protocol (Table 5). Expectedly, compared with HPI extracted under conventional extraction conditions, the emulsifying properties were significantly improved. Notably, even though the protein solubility was enhanced, the improvement did not meet the required threshold. At a pH value most relevant to food processing (pH 4.0), the solubility only slightly improved from 11.1 \(\pm\) 0.5% to 18.5 \(\pm\) 3.8% after optimization. In addition, according to our findings, the maximum protein yield was 3.6 \(\pm\) 0.2 mg/mL without considering the functionality.