Comparison of box-behnken design and gaussian process for optimising pectinase-assisted extraction of flavonoids from Malva sylvestris L.

The aim. The aim of this study was to compare the predictive performance of classical Box-Behnken response surface methodology and Gaussian Process regression for the optimisation of pectinase-assisted extraction of total flavonoids from Malva sylvestris L. and to identify the more reliable approach. Methods. Shade-dried leaves and flowers of Malva sylvestris L. were used. Enzyme-assisted extraction was performed using enzyme pectinase with 7 process variables screened by Plackett-Burman design. Three most significant factors were optimized by a Box-Behnken design and Gaussian Process and compared by the total yield of flavonoids in optimised extract of Malva sylvestris L. Results. Plackett-Burman screening identified solid-to-liquid ratio, extraction time and enzyme concentration as the dominant variables. The Box-Behnken quadratic model predicted optimal condition of 0.43 g/10 ml, 123.9 min, 7.31 mg enzyme/10 ml with experimental yield of 2.01±0.07 mg QE/g DW. The Gaussian Process model confirmed the same ranking of the factor significance with lower values of optimal condition (0.40 g/10 ml, 120 min, 6.88 mg enzyme/10 ml) with experimental yield of 2.08±0.03 mg QE/g DW. Discussion. Both modelling approaches converged on a narrow optimal operating window. The Gaussian Process provided additional quantitative sensitivity analysis and uncertainty estimates, while the quadratic model offered clearer statistical interpretability of linear and quadratic effect. Conclusion. Sequential application of Plackett-Burman screening followed by Box-Behnken and Gaussian Process allowed reliable identification of optimal condition for maximising flavonoid recovery from Malva sylvestris L. Both models proved suitable; the Gaussian Process demonstrated slightly better flexibility for capturing non-linear relationships