## 3 Results and Discussion  
### \(\beta\)-Galactosidase Recovery and Concentration Using Ultrafiltration  
The use of enzymatic extracts at various pH values and membranes with different molecular weight cut-offs (MWCO) showed no significant changes (\(p<0.05\)) in the parameters evaluated during the \(\beta\)-galactosidase ultrafiltration process (Table 1). All runs, except for the 30 and 50 kDa membranes at pH 6.5, presented purification factors >1. These low purification factors might be due to the similar sizes of the contaminating proteins and the target enzyme. Another hypothesis for the low purification factor found in the present work is the retention caused by the dynamic membrane formed by the proteins retained on the membrane surface layer (gel layer) [41], which contributes to an increase in filtration resistance, rapid flow reduction, and the shortening of the operational cycles, affecting the process viability [42]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**pH** & **MWCO (kDa)** & **\%R**\({}^{\rm A}\) & **PF**\({}^{\rm B}\) & **R\({}_{\rm\textbf{P}}\)(\%) C** & **Fc (V)**\({}^{\rm D}\) & **Fc (A)**\({}^{\rm E}\) & **Fc(P)**\({}^{\rm F}\) \\ \hline \multirow{4}{*}{6.5} & 30 & 93.0 \(\pm\) 0.01 b  & 0.93 \(\pm\) 0.03 cd  & 98.5 \(\pm\) 1.16 ab  & 6.7 \(\pm\) 0.0 ab  & 5.79 \(\pm\) 0.68 ab  & 6.31 \(\pm\) 0.84 a  \\  & 50 & 79.5 \(\pm\) 4.8 b  & 0.89 \(\pm\) 0.06 d  & 99.4 \(\pm\) 0.66 ab  & 6.4 \(\pm\) 0.26 b  & 5.0 \(\pm\) 0.3 b  & 5.67 \(\pm\) 0.05 ab  \\  & 60 & 89.3 \(\pm\) 2.9 ab  & 0.95 \(\pm\) 0.09 cd  & 99.0 \(\pm\) 0.96 ab  & 6.4 \(\pm\) 0.5 b  & 5.7 \(\pm\) 0.30 ab  & 5.93 \(\pm\) 0.58 ab  \\  & 100 & 96.2 \(\pm\) 2.2 ab  & 1.08 \(\pm\) 0.08  & 99.2 \(\pm\) 0.96 ab  & 7.2 \(\pm\) 0.5 ab  & 6.9 \(\pm\) 0.66 a  & 6.16 \(\pm\) 0.53 ab  \\ \hline \multirow{4}{*}{7.0} & 30 & 98.1 \(\pm\) 1.4 ab  & 1.09 \(\pm\) 0.02  & 99.9 \(\pm\) 0.16 a  & 7.6 \(\pm\) 0.64 ab  & 7.03 \(\pm\) 0.64 a  & 6.44 \(\pm\) 0.59 a  \\  & 50 & 96.4 \(\pm\) 2.7 ab  & 1.2 \(\pm\) 0.08 ab  & 99.7 \(\pm\) 0.12 ab  & 6.8 \(\pm\) 0.67 ab [FONOTE:a]Footnote a: footnotemark: [ENDFOOTNOTE] & 5.54 \(\pm\) 0.73 a  & 5.42 \(\pm\) 0.54 ab  \\  & 60 & 96.3 \(\pm\) 2.7 ab  & 1.03 \(\pm\) 0.11 & \(\pm\) 0.13 ab  & 6.3 \(\pm\) 0.36 b  & 5.83 \(\pm\) 0.7 ab  \\  & 100 & 99.5 \(\pm\) 0.3 ab  & 1.19 \(\pm\) 0.06 ab  & 99.0 \(\pm\) 0.42 ab  & 6.4 \(\pm\) 0.36 b  & 6.42 \(\pm\) 0.46 ab [FONOTE:b]Footnote b: footnotemark: [ENDFOOTNOTE] & 5.38 \(\pm\) 0.24 ab  \\ \hline \multirow{4}{*}{7.5} & 30 & 86.0 \(\pm\) 6.2 ab  & 1.14 \(\pm\) 0.03  & 1.08 \(\pm\) 0.12  & 6.97 \(\pm\) 0.36 a  & 6.12 \(\pm\) 0.46 ab  \\  & 50 & 108.9 \(\pm\) 4.2 a  & 1.22 \(\pm\) 0.06 ab  & 96.9 \(\pm\) 2.7 ab  & 6.6 \(\pm\) 0.18 ab  & 7.15 \(\pm\) 0.41 a  & 5.88 \(\pm\) 0.06 ab  \\  & 60 & 96.4 \(\pm\) 2.3 ab  & 1.28 \(\pm\) 0.14 ab  & 98.9 \(\pm\) 0.3 ab  & 6.8 \(\pm\) 0.78 ab  & 6.17 \(\pm\) 0.39 ab  & 4.82 \(\pm\) 0.38 b  \\  & 100 & 97. The runs using the 50 kDa membrane at pH 7.5 exhibited the highest enzyme recovery rate (108.9%). This behavior can be explained by the presence of metabolites during the purification process, which can inhibit the enzyme activity. When the contaminants are removed from the medium, the enzyme may be activated [43; 44; 45]. All membranes tested, regardless of the pH, were able to fully retain the enzyme, while the enzymatic activity was not verified in the permeate flux. The high recovery rates of enzymatic activity (in relation to the total activity at the beginning of the process) ranged from 79.5 to 108.9%. The volume, activity, and protein concentration factor values were up to 8.1, 7.1, and 6.4-fold greater, respectively. These results demonstrated the effectiveness of the ultrafiltration steps for the recovery and concentration of \(\beta\)-galactosidase. Furthermore, the ultrafiltration reduced the working volume, which is a crucial factor in the purification processes [1].