PBD

Hadamard matrix designs are a particular form of two-level fractionate factorial designs (resolution III) developed by Plackett and Burman, which explores the effects of various parameters on a particular production process and prevents unwanted repetitions utilizing just a limited number of experiments³⁵. The purpose of PBD was to identify the critical nutrimental parameters among a large number of variables with a significant effect either positively or negatively on ALP production through shake-flask submerged cultivation of Lysinibacillus sp. strain APSO concerning their main effect. Unless such a predictive model approach has been used, no interaction between various influences in the range of variables under consideration is assumed. By this, nine independent variables [molasses, NaNO₃, (NH₄)₃SO₄, eggshell, NaCl, MgCl₂·6H₂O, CuSO₄·5H₂O, CoCl₂·6H₂O, and ZnSO₄·H₂O] were screened with three center points in 23 combination trials with the corresponding response (ALP activity) to generate regression coefficient values. For each, the independent variable was evaluated at three levels. All experiments were duplicated to estimate the standard deviation, and the means of ALP productivity were taken as a response. Table ​Table11 displays the list of variables under study and their coded and actual levels as well as the layout of the design matrix, illustrating that each variable is equal at high and low levels 10 times in each column. The following first-order polynomial approach was used for mathematical modeling for the screening process:

where Y is the predicted response (ALP activity; U L⁻¹ min⁻¹), β_o is the model intercept, β_i is the linear regression coefficient, and X_i is the coded independent variable estimate. The design allows the estimation of the main influence of the variables analyzed and manages data in a rank order depending on the magnitude and sign of the effects.

The experimental design and statistical analysis of the data were done using the essential experimental design free software to estimate t-values, ρ-values, and confidence levels as a percent expression of the ρ-value via ANOVA. The Student’s t-test was used to evaluate the significance level (p-value) of each concentration effect:

The standard error (SE) is the square root of the variance of the factor effect. Factors with the highest t-values and confidence levels above 95% (p < 0.05) were considered extremely significant on ALP productivity. To check the significance and the fitness of the obtained regression model, the R and R² coefficients were calculated. The Pareto diagram was utilized for ranking the independent variables according to their significant effects on productivity. From the Pareto chart, factors that exhibited the highest positive effects (X₁, molasses; X₂, NaNO₃; and X₆, MgCl₂·6H₂O) were picked for further optimization using CCD-uniform precision³⁶. A validation test was carried out in which the predicted optimal levels of the independent variables were examined and compared to the basal condition setting, and the average enzyme production was calculated.