Design expert 13

Design Expert^® 13 software (Stat-Ease Inc., Minneapolis, MN, USA) and GraphPad Prism software (GraphPad Inc., version 5, San Diego, CA, USA) were used for graphical presentation and the statistical analysis of mean ± SD triplicate data using raw means/totals and one-way ANOVA, and a p-value < 0.05 was considered as statistically significant.

To optimize the β-galactosidase entrapping process, numerical optimization was carried out using Design-Expert 13 software (Stat-Ease, USA). The major goal was to maximize the enzyme activity and the minor goal was to obtain a gelation time in the range of 60–90 min. Goals were combined into the overall desirability function. The program aims to maximize this feature. The target search starts at a random starting point and goes up the steepest slope to the maximum. As a result, the software determines such composite synthesis parameters that the assumed goals are met.

To examine the induction of recombinant VHSV glycoprotein expression, various concentrations of NaCl were added in the early log phase (long-term induction) or late log phase (short-term induction) according to the Chlorella growth curve. Transformed C. vulgaris was inoculated into BGPK broth with 200 mM KClO₃ at an initial concentration of 1.5 × 10⁶ cells/mL. For long-term induction, cells were cultured for 2 days and then treated at the same concentrations of NaCl mentioned above. After incubation for an additional 5 days, protein was extracted and Western blotting analysis was performed. For short-term induction, cells were cultured for 7 days and NaCl was added at those same concentrations. After 30, 60, or 120 min, total protein was extracted and Western blotting was performed as described above. The expression level was compared via density analysis using iBright software (Thermo Fisher). The effects of two induction variables, i.e., NaCl concentration and treatment time, on the expression of VHSV glycoprotein in transformed Chlorella were evaluated using Design Expert 13 software (Stat-Ease Inc., Minneapolis, MN, USA).

Statistica 13 Software (Statsoft Inc., Tulsa, OK, USA) was utilized for statistical data evaluation using one-way Analysis of variance (ANOVA) and post-hoc Tukey-test. Differences among samples were considered significant if p < 0.05. BBD and multiple linear regression analysis were performed using Design Expert 13 software (Stat-Ease, Minneapolis, MN, USA). Fisher’s test was executed to evaluate model quality parameters (adequacy, correlation coefficients, and model statistical significance). The model adequacy was examined according to the obtained correlation coefficient (R²), adjusted correlation coefficient (Adj R²), coefficient of variance (CV), and p-values of applied models and lack of fit testing. Linear, interactive, and quadratic regression coefficients of targeted responses were statistically significant for 0.01 ≤ p < 0.05.

Statistical analysis was conducted utilizing Design Expert 13 software (Stat-Ease, Inc., Minneapolis, MN, USA). Analysis of variance (ANOVA) and coefficients of determination (R²), coupled with Tukey’s test p ≤ 0.05, were used to evaluate the regression model’s goodness of fit. Three-dimensional response surface methodology (RSM) analyses were carried out to determine the optimal extraction conditions.

MAE of polyphenols from OW was carried out in a microwave digester (Milestone Ethos One, Sorisole, Italy) at 500 W power using aqueous ethanol or aqueous acetone solutions as solvent. Approximately 1 g of dried OW (W₁) was mixed with 20 mL of solvent (i.e., 1/20 m/v sample-to-solvent ratio) and placed in teflon vessels which were closed before starting the experiments in the microwave digester. The heating time to reach the desired temperature was set to 7 min, while the time to cool down the samples was set to 10 min. The obtained extracts were filtered in cellulose filter paper, dried in an oven at 40 °C, weighed (W₂), and stored at 4 °C until they were analyzed using HPLC. A Box–Behnken experimental design was carried out using Design Expert 13 software (Stat-Ease, Inc., Minneapolis, MN, USA). The independent variables were process temperature (T), extraction time (t), and solvent-to-water ratio (S:W), as illustrated in Table 1, while the dependent variable was the extraction yield (η_MAE). Similarly to SE, the extraction yield of MAE was calculated as follows: $${\eta }_{MAE}(\%)=\frac{W_2}{W_1}\times 100$$
As a result of the design of experiments, fifteen MAE were run (Table 2), each of them in triplicate.

DesignExpert 13 software (Stat-Ease Inc., Minneapolis, MN, USA) was used for DoE. CPPs and optimum buffer conditions for AFC, AEX, RPC, and CEX chromatography were identified using 2-level factorial optimal (Custom) design. Data were analyzed using surface response methodology. Combinations of pH levels and NaCl concentrations for AFC (Supplementary Table S1) and AEX (Supplementary Table S2), pH and aquous:organic solvent for RPC (Supplementary Table S3), and pH and CV for CEX (Supplementary Table S4) were analyzed, respectively. The recommended chromatography conditions for each chromatography step were completed in static mode in 1 mL size in microcentrifuge tube. Recovery % of eluted samples of each step for all run conditions was analyzed by analytical size exclusion chromatography (SEC). Recovery data of target product satisfying QTPP for all chromatography steps were processed in DesignExpert 13 software. Optimum operating conditions and CPPs were identified from the surface response plot. All data points were validated using series of triplicate experiments.