## 3 Results and Discussion
### Effect of Parameters and Optimization of Cell Lysis
The response surface plots of the combined effects of the factors on spent brewer's yeast cell disruption efficiency are presented in Figure 2. Yeast cell suspension concentration determined the decrease of disruption efficiency. On the other hand, the increase of the yeast/glass bead ratio and the number of vortexing cycles led to an increase in cell wall disruption efficiency. These observations were supported by previous results obtained by [PERSON] and [PERSON] (1990), who reported that an increase in cell concentration decreases the efficiency of cell rupture [24]. This could have been caused by an insufficient collision between the glass beads and the yeast cells in the effective disruption region as a result of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Yeast Suspension Concentration (\%)** & **Yeast/Glass Bead Ratio (\(v\)/\(tv\))** & **Vortexing Cycles** & **Disruption Efficiency (\%)** \\ \hline
15 & 1:2 & 3 & 49.0 \({}^{\text{d}}\) \\
15 & 1:3 & 2 & 21.5 \({}^{\text{j}}\) \\ \hline \hline \end{tabular} a-1–different letters in the same column show significant differences among samples (\(p<0.05\)).  
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Sum of Squares** & **Mean Square** & **F-Value** & \(p\)**-Value** \\ \hline Quadratic & 9768.51 & 1085.39 & 393.43 & \textless{}0.0001 \\ A-Yeast suspension concentration & 3157.34 & 3157.34 & 1144.46 & \textless{}0.0001 \\ B-Yeast/glass bead ratio & 1594.71 & 1594.71 & 578.05 & \textless{}0.0001 \\ C-Number of cycles & 3665.39 & 3665.39 & 1328.62 & \textless{}0.0001 \\ AB & 342.81 & 342.81 & 124.26 & \textless{}0.0001 \\ AC & 102.82 & 102.82 & 37.27 & 0.0005 \\ BC & 361.38 & 361.38 & 130.99 & \textless{}0.0001 \\ A\({}^{2}\) & 0.0002 & 0.0002 & 0.0001 & ns \\ B\({}^{2}\) & 73.44 & 73.44 & 26.62 & 0.0013 \\ C\({}^{2}\) & 488.50 & 488.50 & 177.07 & \textless{}0.0001 \\ Residual & 19.31 & 2.76 & & \\ Lack of fit & 19.31 & 6.44 & & \\ Fit statistics & & & & \\ Mean & 44.76 & & & \\ Standard deviation & 1.66 & & & \\ C.V. (\%) & 3.71 & & & \\ \(R^{2}\) & 0.9980 & & & \\ _Adj.-R\({}^{2}\)_ & 0.9955 & & & \\ Predicted \(R^{2}\) & 0.9684 & & & \\ Adeq. Precision & 67.5219 & & & \\ \hline \hline \end{tabular} ns-not significant.  
\end{table} 
Table 3: ANOVA results for the effects of factors on cell disruption efficiency. y a weak concentration and cell wall fragments in suspension. Furthermore, [PERSON] et al. (2007) investigated whether a decrease in cell wall disruption rate is caused by a lack of action of the breaking surface formed by the glass beads and high yeast concentration ([PERSON] et al. (2007). [PERSON] et al. (2017) underlined the significant effects (\(p<0.05\)) of spent brewer's yeast cell lysis temperature and time on the amount of bioactive compounds released ([PERSON] et al. (2018). Another study conducted by [PERSON] and [PERSON] (2018) revealed that the highest disruption efficiency (99.5%) was obtained after freezing-defreezing, combined with glass-bead treatment of a 15% spent brewer's yeast suspension, the results being in line with our data ([PERSON] et al. (2018). Figure 2: 3-D plots of combined effects of factors: (**a**) yeast suspension concentration (A) and yeast/glass beads ratio (B), (**b**) yeast/glass bead ratio (B) and number of cycles (C), (**c**) yeast suspension concentration (A) and number of cycles (C) on cell disruption efficiency. The optimization of spent brewer's yeast cell lysis is essential and advantageous for subsequent \(\beta\)-glucan extraction. Thus, after investigating the effects of the factors on cell disruption efficiency, an optimization process was performed by using a desirability function that implies the transformation of the predicted response occurs in a dimensionless partial desirability function (d\({}_{i}\)), which comprises the researcher's particular requirements. The partial desirability functions obtained are put together into an overall desirability function, D, which is the geometric mean of the d\({}_{i}\) values [27].