## 3 Results and Discussion  
### Effect of Parameters and Optimization of Cell Lysis  
The cell lysis parameters are key factors that influence the breakage of the cell wall. The effects of yeast suspension concentrations, yeast/glass bead ratios, and the number of vortexing cycles on spent brewer's yeast cell disruption are presented in Table 2. The disruption efficiency varied from 14.5 to 99.8%, depending on the conditions applied, with significant differences (\(p\) < 0.05) among samples. [PERSON] et al. (2008) reported an autolysis ratio of 5 to 49% when spent brewer's yeast was lysed in a 3% sodium chloride solution at 55 \({}^{\circ}\)C and a pH of 5.5. The efficiency of cell lysis depends on the method selected, a fact also supported by the findings of [PERSON] et al. (2014), who stated that the highest efficiency was observed after cell disruption through homogenization in a bead mill and combined autolysis with bead milling. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Run**} & \multicolumn{3}{c}{**Actual Values**} & \multicolumn{3}{c}{**Coded Values**} \\ \cline{2-7}  & **Yeast Suspension** & **Yeast/Glass Bead** & **Vortexing** & **A** & **B** & **C** \\  & **Concentration (\%)** & **Ratio (\(v\)/\(iv\))** & **Cycles** & & & \\ \hline
1 & 5 & 1:1 & 2 & \(-1.00\) & \(-1.00\) & 0.00 \\
2 & 5 & 1:2 & 1 & \(-1.00\) & 0.00 & \(-1.00\) \\
3 & 5 & 1:2 & 3 & \(-1.00\) & 0.00 & 1.00 \\
4 & 5 & 1:3 & 2 & \(-1.00\) & 1.00 & 0.00 \\
5 & 10 & 1:1 & 1 & 0.00 & \(-1.00\) & \(-1.00\) \\
6 & 10 & 1:1 & 3 & 0.00 & \(-1.00\) & 1.00 \\
7 & 10 & 1:2 & 2 & 0.00 & 0.00 & 0.00 \\
8 & 10 & 1:2 & 2 & 0.00 & 0.00 & 0.00 \\
11 & 10 & 1:2 & 2 & 0.00 & 0.00 & 0.00 \\
12 & 10 & 1:3 & 1 & 0.00 & 1.00 & \(-1.00\) \\
13 & 10 & 1:3 & 3 & 0.00 & 1.00 & 1.00 \\
14 & 15 & 1:1 & 2 & 1.00 & \(-1.00\) & 0.00 \\
15 & 15 & 1:2 & 1 & 1.00 & 0.00 & \(-1.00\) \\
16 & 15 & 1:2 & 3 & 1.00 & 0.00 & 1.00 \\
17 & 15 & 1:3 & 2 & 1.00 & 1.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Actual vs. coded values of the factors. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Yeast Suspension Concentration (\%)** & **Yeast/Glass Bead Ratio (\(v\)/\(iv\))** & **Vortexing Cycles** & **Disruption Efficiency (\%)** \\ \hline
5 & 1:1 & 2 & 34.8 h \\
5 & 1:2 & 1 & 45.6 e \\
5 & 1:2 & 3 & 99.8 a \\
5 & 1:3 & 2 & 78.9 e \\
10 & 1:1 & 1 & 21.5 j \\
10 & 1:1 & 3 & 44.0 f \\
10 & 1:2 & 2 & 41.6 g \\
10 & 1:3 & 1 & 33.4 i \\
10 & 1:3 & 3 & 93.9 b \\
15 & 1:1 & 2 & 14.5 l \\
15 & 1:2 & 1 & 15.1 k \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Effects of method parameters on spent brewer’s yeast cell disruption efficiency. The data obtained were fitted to the quadratic model (Equation (3)), which showed significance at the \(p<0.05\) level (\(F\)-value = 393.43) and described 99.80% of data variation (Table 3). \[ \begin{array}{l}\text{Disruption efficiency }(\%)\\ =41.66-19.87\text{A}+14.12\text{B}+21.41\text{C}-9.26\text{AB}-5.07\text{AC} \\ +9.50\text{BC}-0.01\text{A}^{2}-4.18\text{B}^{2}+10.77\text{C}^{2}\end{array}  \tag{3}\]  
The predicted \(R^{2}\) of 0.9684 is in reasonable agreement with the _adj.R\({}^{2}\)_ of 0.9955, the difference being less than 0.2, which supports model adequacy. Furthermore, the lack of fit value was not significant (\(p>0.05\)) and the Adeq. precision was >4 for the considered response, indicating an adequate signal-to-noise ratio. According to the data presented in Table 3, the yeast suspension concentration (A), yeast/glass bead ratio (B), and number of vortexing cycles (C) factors and their interactions influenced disruption efficiency response in a significant way (\(p<0.05\)), except the quadratic term of yeast suspension concentration (A\({}^{2}\)). The highest negative influence was observed for the linear term of the yeast suspension concentration factor, while the vortexing cycles factor showed the greatest positive influence on the response.