A comparative study using response surface methodology and artificial neural network for modeling the bio-reduction of hexavalent chromium (Cr⁶⁺) by immobilized cells of Paenibacillus taichungensis strain MAHA in an alginate-gellan gum matrix

Chromium (Cr⁶⁺) waste poses a hazard as it leads to imbalanced ecosystems and severe health issues. Although, it is widely associated with many industries. Chromium (Cr⁶⁺) reduction by the immobilized cells of Paenibacillus taitungensis strain MAHA-MIE was optimized using response surface methodology (RSM) and artificial neural networks (ANN). The RSM-Box-Behnken Design (BBD) was selected to investigate the effects of chromium (Cr⁶⁺) concentration, alginate concentration, gellan gum concentration, bead size, and the number of beads on chromium (Cr⁶⁺) reduction rate. Experimental data from the BBD was used to train a feed-forward, multilayer artificial neural network (ANN). Results show that the ANN model outperformed the response surface methodology (RSM) based on actual and predicted data, with lower errors and a higher R2 value. The ANN model predicted the optimum points as follows: 155 ppm chromium (Cr⁶⁺), 0.32% alginate, 0.65% gellan gum, 0.5 cm beads, and 27 beads. The validation confirmed a high agreement of chromium (Cr⁶⁺) reduction rate between the validation value (99.00%) and the predicted value (99.99%), with the lowest deviation at 0.1%. Modeling abilities were compared using statistical criteria, including Root Mean Square Error (RMSE), Standard Error of Prediction (SEP), Relative Percent Deviation (RPD), and regression coefficients (R2). The ANN analysis showed the high predictive performance, with high R2 (0.9911), low SEP (0.45%), RPD (1.88), and RMSE (1.37%). The results of this study approved that alginate-gellan gum immobilized cells of Paenibacillus taitungensis strain MAHA-MIE could be effectively used for the handling of chromium (Cr⁶⁺).