## 3 Results and Discussion
### RSM Analysis  
Table 2 shows the average percentage of two replicates of the pDNA(t) and pDNA(sc) released in the bead mill used as response variables in the RSM analysis.  
Estimates from the pDNA(t) and pDNA(sc) percentages were obtained with Equation (2) using the data in Table 1. The ANOVA analysis was conducted with a significance value of \(\alpha\) = 0.1, considering the sample sizes [18]. Using the Matlab function _ffl23_, it was concluded that the significant treatments for the pDNA(t) release were mill frequency, bead size, and the combination of cell concentration and bead size. In the release of pDNA(sc), the significant treatments were mill frequency, bead size, and the combination of the three variables used. With these results, the not-significant coefficients were removed from Equation (3) to obtain  
\[y_{pDNA(t)}=63.39+5.62x_{1}-16.24x_{3}-8.16x_{2}x_{3} \tag{6}\]  
\[y_{pDNA(sc)}=61.34-5.51x_{1}-19.10x_{3}-6.10x_{1}x_{2}x_{3}. \tag{7}\]  
Figure 3 shows the correlation between the model obtained by Equations (6) and (7) and the experimental data. The correlation between the predicted response and the experimental data for pDNA(t) and pDNA(sc) in the bead mill showed a good fit with an R\({}^{2}\) of 0.95 for both responses, indicating the accuracy of the model for predicting system behavior. When a significance value of \(\alpha\) = 0.05 was used, a good model fit was obtained only for pDNA(t).  
The RSM predicted responses for pDNA(t) and pDNA(sc), Equations (6) and (7), were plotted on three-dimensional graphs called \"response surface plots\" and are shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment** & **pDNA(t) \%** & **pDNA(sc) \%** \\ \hline
1 & 66.06 & 100.00 \\
2 & 71.87 & 67.30 \\
3 & 80.56 & 79.52 \\
4 & 100.00 & 74.93 \\
5 & 44.26 & 38.94 \\
6 & 61.37 & 45.90 \\
7 & 40.20 & 48.94 \\
8 & 42.80 & 35.20 \\ \hline Avg & 63.39 & 61.34 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average percentage of the pDNA(t) and pDNA(sc) released in the bead mill.  
Figure 3: Correlation between experimental data and predicted response. Data represent the means of two experiments. (**A**) pDNA(t) and (**B**) pDNA(sc).  
Figure 4A shows that, in the experimental range studied, the pDNA(t) release is more sensible to bead mill parameters at the higher cell concentration of 20 g/L (Surface A\({}_{2}\)). It can also be observed that, by using a high mill frequency (30 Hz) and the smallest bead size (0.10-0.25 mm), a maximum release of pDNA(t) of 77.10% for a cell concentration of 10 g wcw/L (Surface A\({}_{1}\)) and 93.41% of maximum release for a cell concentration of 20 g wcw/L (Surface A\({}_{2}\)) are obtained. [PERSON] et al. (2016) also found that bead milling is the best processing method for intact plasmid recovery, in which over 90% of the plasmid is solubilized without substantial degradation. However, the target molecule is the pDNA(sc) and the corresponding behavior is subsequent discussed.  
In general, Figure 4B indicates that, at low cell concentration, the milling process to obtain pDNA(sc) improves as bead size and mill frequency decrease. For high cell concentration, the milling process to obtain pDNA(sc) improves as bead size decreases and mill frequency increases. It can also be observed that, by using a low mill frequency (15 Hz) and the smallest bead size (0.10-0.25 mm), a maximum release of pDNA(sc) of 92.05% is obtained for a cell concentration of 10 g wcw/L (Surface B\({}_{1}\)); for a cell concentration of 20 g wcw/L (Surface B\({}_{2}\)), using high mill frequency (30 Hz) and small bead size (0.10-0.25 mm), a maximum release of pDNA(sc) of 81.03% is obtained. Further discussion of this results is presented in combination with the kinetic studies.