Rotatable central composite design versus artificial neural network for modeling biosorption of Cr6+ by the immobilized Pseudomonas alcaliphila NEWG-2

Heavy metals, including chromium, are associated with developed industrialization and technological processes, causing imbalanced ecosystems and severe health concerns. The current study is of supreme priority because there is no previous work that dealt with the modeling of the optimization of the biosorption process by the immobilized cells. The significant parameters (immobilized bacterial cells, contact time, and initial Cr6+ concentrations), affecting Cr6+ biosorption by immobilized Pseudomonas alcaliphila, was verified, using the Plackett–Burman matrix. For modeling the maximization of Cr6+ biosorption, a comparative approach was created between rotatable central composite design (RCCD) and artificial neural network (ANN) to choose the most fitted model that accurately predicts Cr6+ removal percent by immobilized cells. Experimental data of RCCD was employed to train a feed-forward multilayered perceptron ANN algorithm. The predictive competence of the ANN model was more precise than RCCD when forecasting the best appropriate wastewater treatment. After the biosorption, a new shiny large particle on the bead surface was noticed by the scanning electron microscopy, and an additional peak of Cr6+ was appeared by the energy dispersive X-ray analysis, confirming the role of the immobilized bacteria in the biosorption of Cr6+ ions.


Materials and methods
P. alcaliphila strain. In a previous study, P. alcaliphila NEWG-2 was found to be efficient in biosorption of Cr 6+ and molecularly identified with an accession number of MN025267 16 . This strain was used during the current investigation. The bacterial strain was grown on slants contains a fermentation medium solidified with 15 g/L agar and incubated for 48 h at 25 ± 1 °C. P. alcaliphila NEWG-2 was regularly sub-cultured and preserved at 4 °C.
Bacterial immobilization. Immobilization of P. alcaliphila NEWG-2 was performed in the sodium alginate gel according to the method of EL-Naggar et al. 23 . To make sphere beads, the cells of P. alcaliphila NEWG-2 has been mixed with sodium alginate gel, to count 10 5 CFU per one ml of sodium alginate gel, with continual mixing at room temperature for 5 min. Using a 3-mL syringe, beads of inoculated sodium alginate (1.5 ± 0.2 mm in diameter) were created by dropping in a cold sterile CaCl 2 (2.5%) with gentle mixing at room temperature. The beads were washed with distilled sterilized water several times to remove calcium chloride traces. For stabilization and rigidity, the beads were then held overnight in distilled sterilized water at 4 °C. Another set of beads were created using only sodium alginate without bacterial biomass.
The biosorption process was carried out in sterilized separating funnels, which were packed with the alginate beads without bacterial cells or alginate-bacterial beads. Solutions of Cr 6+ with different concentrations were added and mixed with the beads and left at 30 °C, with initial pH 7. Samples from the various trials were collected from the separating funnel effluent and analyzed for the residual ions of Cr 6+ .
Potassium dichromate (K 2 Cr 2 O 7 ). K 2 Cr 2 O 7 (Sigma-Aldrich) was used to prepare various concentrations based on the content of Cr 6+ ions. Samples of each sterilized concentration were allowed to contact alginate beads, inoculated or not, inside the separating funnel (Simax) for a specific time then fractions of the effluent samples were collected to determine the residual Cr 6+ .
Screening Cr 6+ removal factors using Plackett-Burman. Because the complete knowledge about the Cr 6+ removal system is unavailable, the fractional-factorial Plackett-Burman matrix was performed to check the effect, contribution, and significance of the most important process parameters (bacterial cell immobilization in alginate beads, the contact time of alginate beads with Cr 6+ , and initial concentration of Cr 6+ ) on Cr 6+ removal by P. alcaliphila. The Plackett-Burman design is a screening matrix that aims to find out the importance of factor(s) The experimental matrix was constructed from a mixture of categorical and numerical factors to validate the relative importance of the tested factors. The three independent variables were screened at low and high levels ( Table 1). The design matrix and statistical calculations were operated using Minitab software (version 19, Minitab Inc., USA) (https ://www.minit ab.com/en-us/).

Modeling using RSM.
The modeling technique of RSM was employed. For multiple regression analysis, a properly designed experiment was performed to simultaneously resolve multivariate equations. Two variables at five levels have been tested using a rotatable central composite design (RCCD). The tested independent variables selected for the modeling of the Cr 6+ biosorption process using the immobilized P. alcaliphila NEWG-2 were; contact time between bacterial-alginate complex with Cr 6+ and the initial Cr 6+ concentration ( Table 2).
The efficiency of the biosorption process was evaluated by measuring the response variable (Cr 6+ removal, %), which depends on the two input factors. The design matrix of RCCD, in terms of coded units, contained four factorials (± 1), four axial (± 1.414), and five center (0) points; the latter is to estimate the pure error. The relationship between actual values and the coded values of the tested parameters is calculated by the following equation: where x i is the coded value of an independent factor, ∆X i is the step-change in the actual value of the variable i, X 0 is the actual value of an independent factor at the center point and Xi is the actual value of an independent factor. The Cr 6+ removal percent was determined as the response variable. The experimental data were statistically assessed by using multiple regression analysis, then F-test, values of correlation coefficient (R 2 ), prediction error sum of squares (PRESS), predicted R 2 and adjusted R 2 were checked to compare and evaluate the significance of the regression model. The selected polynomial quadratic model was fitted to the next second-order equation: where Y is the Cr 6+ removal percent; β ij , is the interaction coefficients; β ii is the quadratic coefficients; β 0 model constant; β i , is linear coefficients; X i and X j are the independent factors.
The predicted response value was calculated based on the preceding equation model was subjected to laboratory validation to confirm the fitness and accuracy of the theoretically estimated value of each factor. Determination of residual Cr 6+ . Collected sample fractions were examined for the residual Cr 6+ . The residual Cr 6+ concentrations were assessed using Atomic Absorption Spectrophotometer "Buck Scientific Accusys 211 series, USA by an air/acetylene flame system" 24 , then the Cr 6+ -removal percent was calculated.
Modeling using ANN. A fully connected neural networks platform was constructed with one hidden layer, all nodes within the layer have the same activation function (Tan H sigmoid function, exp(− x 2 )). Response data of the RCCD matrix was used to train the machine and develop the predictive model. The data were portioned into three sets, i.e., training, testing, and cross-validation, in which 17 runs were used randomly for training, while the other 9 data sets were used for testing and validation.
The neural network had three layers. The ANN topology was designated as 2-h-1. The input layer composed of two neurons (contact time and initial Cr 6+ concentration, ppm) and the output layer has one neuron (Cr 6+   www.nature.com/scientificreports/ removal %), which is fixed by the number of the tested independent and response factor, respectively. The inbetween layer was tested using h neurons that varied from 3 to 10 in a single hidden layer (Fig. 1).
The trial-and-error search method was applied to train the ANN until a minimum of the root mean square error (RMSE) and the sum of squared errors (SSE) was reached, accompanied by the highest value of the (R 2 ) in the validation process. The trained network performance test was calculated based on the precision of the neural network to predict outputs that are either similar or very close to the response target value.
Testing the fitness of RCCD and ANN models. To assess the fitness of Cr 6+ biosorption models of RCCD and ANN models, R 2 , RMSE, mean absolute deviation (MAD), and SSE were used to compare models. Besides, the values predicted by both models were plotted against the corresponding trial values to explore the fitness of models.
Trial design and statistical examination. Both the statistical regression analysis of the RCCD matrix with the experimental results and also the analysis of variance (ANOVA) were accomplished using the statistical software package Design-Expert (version 12, Stat-Ease, Minneapolis, USA) (https ://www.state ase.com/softw are/ desig n-exper t/). The ANN topology was set up using JMP 11 software (JMP, Version 11 SAS Institute Inc., Cary, NC, 1989-2019), which enables training, validating, and testing using experimental data with several hidden neurons. Training of ANN was performed using 17 randomly selected runs by the software, whereas the other 9 runs were used to check the validity of the trained ANN model. To enhance the prediction accuracy of both models, experiments of RCCD were repeated twice, each with three replicates. The mean of each experimental run was calculated.
Surface morphology analysis. The immobilized P. alcaliphila NEWG-2 samples were coated with gold before and after the biosorption process of Cr 6+ and examined by Scanning Electron Microscopy (SEM).

Energy-dispersive X-ray analysis (EDX). The dehydrated immobilized P. alcaliphila NEWG-2 samples
were examined before and after the biosorption process of Cr 6+ using TEM/EDX to determine the elemental sample composition.

Results and discussion
Screening of Cr 6+ removal using Plackett-Burman. It is already known that Plackett-Burman is used to achieve two main important approaches; the first is to determine the significance of the examined factors and the second is to detect the level (high or low) that significant factor(s) should be tested around. The main goal, herein, was to determine the starting point of each of the involved variables in the biosorption of Cr 6+ .
A combination of one categorical element (bacterial inoculation) and two numerical elements (contact time of alginate beads with Cr 6+ and initial concentration of Cr 6+ ) were investigated, based on the matrix of Plackett-Burman design, to estimate their significance and relative importance on Cr 6+ removal ( Table 1). The results show obvious variation among the various runs, yet, the values of the residuals recorded remarkably lower values. Residuals are the differences between the experimental (observed) value of the dependent variable (Cr 6+ removal) and its corresponding predicted value at each data point. The lower the value of the residuals, the fitness of the model data that, consequently, signifies the accuracy of the parameter selection.
The statistical analysis of the Plackett-Burman results was performed. Pareto chart (Supplementary Fig. 1) of the standardized effects figures the relative magnitude and the statistical significance of the three variables in the descending order. Parameters that pass the reference line (2.31) are significant at 0.05, therefore, the three tested parameters were significant on Cr 6+ removal by the investigated bacterium.
According to Table 3, the impact of the three tested variables was explored at the probability (P) level of 0.05, in which model terms with P < 0.05 are significant. The three tested variables show significance (P < 0.05). Initial chromium concentration followed by contact time recorded the highest contribution percent with a negative effect, whereas the bacterial inoculation was positive in its effect. If the effect is negative, a lower concentration is to be required during further optimization studies, the vice versa. Also, the positive effect of bacterial inoculation reflects the importance of the tested bacteria in the bioremoval process under immobilization conditions.
To evaluate the aptness of the data and select the model with the best fit, R 2 , and adjusted R 2 are estimated. R 2 defines the variation quantity in the experiential response values that are described by the factor(s). Adding items to the model lead to get bigger R 2 , but adjusted R 2 is not, because it depends on the significance of the factors, not their number, of the model. However, the higher the adjusted R 2 the additional accuracy of the relationship between the factors and the response (Cr 6+ removal), consequently, the model fits well the data. Predicted R 2 illustrates how well the model predicts for the responses in the new experiments, without over-fitting. Increased R 2 predicted values suggest high prediction efficiency of the model. Current values show that all the kinds of R 2 display high validity with the selected variables, being 96.85 (R 2 ), 95.67 (adjusted R 2 ), and 92.92% (predicted R 2 ).
Free microbial cells have a key role in the biosorption of heavy metals. Various mechanisms were suggested, such as ion exchange, complexation, precipitation, chelation 25 . Likewise, the biosorption arises through interaction among charges of metal ions, exopolysaccharides, and cell surface. In this respect, several functional groups, i.e., amine, sulfhydryl, phosphate, phosphodiester, hydroxyl in polysaccharides, carboxyl groups in proteins provides the polymer an overall negative charge 26 . The biosorption by Pseudomonas genus could effectively occur through exopolysaccharides, which have a high content of uronic acid that enhanced their capability with binding to metal ions 27 .
Immobilization techniques have been reported to boost the biological reaction kinetics, especially reaction rate, in which the immobilization process stimulates the production of the exopolysaccharides without altering www.nature.com/scientificreports/ specific growth rates 28 . For example, the immobilized Chryseomonas luteola showed efficiency in the sorption of copper, nickel, cobalt, and cadmium compared to alginate beads alone 27 .
On the other side, the role of sodium alginate beads alone was stated and was found to absorb some of the heavy metals, e.g., Cr 6+ 16 and Cu 2+ 11 ions. The sodium alginate is a natural polymer produced by marine algae, with a chemical structure of mannuronate and guluronate arranged with 1, 4-linkage. The ionic strength, permeability, viscosity, and stability could be different due to molecular weight and the ratio of mannuronate to guluronate 29 . Briefly, all these characters may play a vital task in the sorption process of metals by sodium alginate beads.
Modeling of Cr 6+ removal by RCCD. Built on the previous screening of Plackett-Burman the three investigated factors, were subjected to further study, regarding their interaction and modeling process. Contact time and initial chromium concentration were tested around the low levels, because of their negative effect, while all experiments were performed using inoculated beads (alginate-immobilized P. alcaliphila), which showed a positive effect. The empirical design of RCCD of RSM was applied, and the modeling technique was accomplished based on the quantitative data acquired from the experimental design. The RCCD has two factors at five levels for optimizing the two process variables for maximum removal of Cr 6+ .
The results of Table 2 represent the experimental response values of Cr 6+ removal obtained by the various RCCD combinations in 26 runs; also the predicted values of RCCD and their residuals were introduced. Residual is the difference between the experimental variable (Cr 6+ removal) and its corresponding predicted value at each data point. Lower values of the residuals reflecting a close correlation between the experimental values and the RCCD-predicted values, subsequently, the appropriateness of the generated model.

Multiple regression analysis.
To select the most appropriate kind of regression, the linear, interactive, and quadratic models were compared using multiple regression analyses based on the experimental data ( Table 4). Analysis of the sequential model sum of squares shows that the P value of the quadratic model is the only significant model (P < 0.0001), the lack-of-fit value displays insignificant behavior, which a pre-request for the model to be fitted. The other summary of the fit statistics confirms that the quadratic model is the most fitting one, having the largest values of predicted R 2 (0.9779), adjusted R 2 (0.9827), and R 2 (0.9862) with a small standard deviation (3.005). Models with supreme adjusted R 2 and the predicted R 2 are desired 17 .
Accordingly, the quadratic second-order polynomial equation was selected and modeled using the results of RCCD. The resultant prediction equation was applied for the given levels of contact time and initial Cr 6+ concentration, and so, the equation structure, in terms of coded factors, is assumed to be:

ANOVA examination.
To check if the equation adequately reflected a genuine association between the independent variables (contact time and initial Cr 6+ conc.) and the response (Cr 6+ removal), ANOVA was performed ( Table 5).
The high model F-value of 285.30 together with the low lack-of-fit F-value (2.97) means that the model is significant. Model fitting is required to be significant; on the other hand, the lack-of-fit is wanted to be insignificant because its significance is a source of trouble to the model. Both model and lack-of-fit are opposite to each other.   www.nature.com/scientificreports/ The calculation of the relative dispersion of the experimental data from the predictions of the polynomial model of the second-order indicates the coefficient of variance is sufficiently low (3.996%) to designate that the deviation between the experimental and prediction values at each data point is low 18 .
The value of R 2 was calculated to be 0.9862, which denotes that 98.62% of investigational data were wellmatched. The adjusted R 2 value (0.9827) is also high to support the model significance. The predicted R 2 of 0.9779 is in reasonable agreement with the adjusted R 2 indicating the wellness of the model to predict new observations. Increased R 2 values indicate that the model is stronger and it has higher predictive efficiency for the response 30 .
The sum of squares of prediction error (PRESS) value was reasonably low (288.748), reflecting the lower opportunity of an error through the experimental work, consequently, and the predicted values. Estimating the signal to noise ratio, using adequate precision, shows a ratio of 44.55, the present ratio is high enough to indicate an adequate signal, a ratio greater than 4 is desired which indicate that the tested model can precisely be used to navigate the space of design 18 .
The two independent variables were further statistically examined for interaction and quadratic effect on Cr 6+ removal. All P values were found to be < 0.0001, values less than 0.05 denote that model terms are significant. Table 4. Fitness and adequacy of the models based on the experimental data of the design matrix of the RCCD. df the degree of freedom, 2FI two factors interaction, SD standard deviation, R 2 determination coefficient, PRESS the sum of squares of prediction error.

Residuals normality and 3D-surface.
To test the normality of the residuals, the normal probability plot of the residuals is displayed in Fig. 2A. Expect some scatter, there are no definite patterns, like curves, could be observed. On the other hand, the residual points were tightly clustered along the standard line indicating that the residuals must follow the normal distribution 32 . The 3D response surface plot in relation to the two factors ( Fig. 2B) was used to understand both the linear and the interaction effects of the two tested variables, also to calculate the optimal level of each factor for maximum removal of Cr 6+ ions. The elliptical curve of the response surface plot displays a clear interaction between the tested parameters 20 . However, the 3D plot displays that Cr 6+ removal reached its peak (99.995%) with the increment of initial Cr 6+ conc. around nearly the center points of the design, reflecting the precision of the selected range of both tested factors.

Experimental validation.
To resolve the optimal combination of the tested variables, which maximize the response. The optimal predicted levels of both tested factors were estimated using the modeling regression equation and were found to be 224.6 min of contact time between chromium and immobilized bacteria and 315.98 ppm of initial Cr 6+ concentration, at these conditions, Cr 6+ removal reached 99.995%. These theoretical estimations from the equation were experimentally validated and the response was found to be 99.81%. This value is closely related to the theoretical value, substantiating the suitability of the developed model.

Modeling of Cr 6+ removal by ANN.
The most common and popular multilayer feed-forward ANN architecture with the sigmoidal function was developed for modeling the bio-removal process of Cr 6+ by the immobilized P. alcaliphila. The RCCD matrix and their respective experimental response were used for training the ANN. The network has two input nodes (contact time and initial Cr 6+ concentration) and one output node (Cr 6+ removal).
To determine the architectural structure and the best number of neurons in the hidden layer, numerous hidden neurons, and various combinations of ANN-specific parameters such as learning rate, as well as, the initial weight and bias value of each layer were tested. Hence, the optimal number of neurons in the hidden layer of the ANN was found to be 7 (Fig. 1). Consequently, the resulted architecture of ANN that has the maximum performance was found to be 2-7(h)-1. Previous work found that the optimal number of neurons in ANN architecture for modeling biosorption of chromium was 4-10-1 22 .
The generality of the ANN model was certified by minimizing the errors in training and validation. The network was trained until the R 2 reached its maximum and RMSE, MAD and SSE recorded the lowest values (Table 6). Hence, the predicted values, for each experimental run based on the developed ANN model, were estimated and given along with the predicted RCCD and experimental values in Table 2. Because any linear regression model is not always appropriate for the data, residuals are generally used to assess the aptness of the model by defining residual values and determining its trend. The residuals presented as the variance between the experimental value of Cr 6+ removal and its corresponding predicted data point at each dataset was found to be very low at all tested points. This implies that the ANN can fit the actual experimental data exactly. Recently, the ANN modeling has found its way in biosorption of toxic metals such as lead 21 , copper 28 , and zinc 33 , but none of them used immobilized cells during modeling process neither by RCCD nor ANN. RCCD versus ANN models. Both RCCD and the well-learned ANN models were compared regarding their predictive capability to remove Cr 6+ by the immobilized P. alcaliphila NEWG-2 strain. The statistical parameters that measure and compare the accuracy of both models were estimated ( Table 6). The modeling ability of a given model is reliant on the high value of R 2 and lower values of the RMSE, MAD, and SSE. R 2 measures the correlation between the response values and the predicted values, so, higher value (up to 1) reflects a strong correlation between both datasets. Commonly, RMSE is used in regression analysis to authenticate experimental results, since the lower value means that the data are concentrated around the line of best fit (prediction errors). MAD, is another statistic that determines the average dispersion of the data around the mean, a lower value indicates a lower spread of the data around the mean. Finally, SSE, another assessment of the goodness-of-fit, determines the total deviation of the response values from their fitted values, lower value implies more fitness of the model.
Given the preceding statistics, both models exhibited high predictive ability. However, comparing the two models reveals that RCCD is lower in R 2 and higher in the other goodness-of-fit statistic than the ANN model. Therefore, the ANN model has a higher predictive ability than the RCCD model for Cr 6+ removal by the immobilized P. alcaliphila NEWG-2. The current conclusion is conceding with that obtained by Shafi et al. 19 , who found that the ANN models were superior to RSM, recording lower RMSE, MAD, and chi-square and higher for R 2 .
Likewise, another overall comparison was performed, in which the linear regression analysis between the actual values and those of predicted were drawn for both RCCD and ANN (Fig. 3). Again, the chart plot of ANN displays better fitting with a higher R 2 value, which also infers that ANN gives improved optimization results compared to RCCD. The graph also shows that the ANN model prediction points lie much closer to the line of perfect prediction than the RCCD model. Thus, the ANN model has a significantly higher generalization capacity than the RCCD model.
However, there are some merits when modeling using RCCD i.e., the structured nature of the RCCD can demonstrate the contributions of each factor in the regression models, thus recognizing the insignificant factors, wither single, interaction, or quadratic, in the model and thereby can be eliminated from the model. Moreover, www.nature.com/scientificreports/ compared to RCCD, ANN modeling consumed extended computational time through many iterative calculations. However, the generated model by ANN had high predictive accuracy than RCCD. This can be attributed to its universal ability to approximate the nonlinearity of the system, compared with the restricted nature of RCCD www.nature.com/scientificreports/ to the second-order polynomial, which requires only a sole step calculation for a response surface model 18,20 . However, ANN has consistently performed better than the RCCD in all aspects. The ANN models were adopted in various wastewater treatment, since these techniques are useful in forecasting effluent quality and estimation of metals in a given source, as well as, updating the prediction points upon selection of any input or output variables 33,34 . Contrarily, the other mathematical methods have difficulty in the prediction of desired output in wasted effluents, due to different types of metals, variety of salts, the variation of pH and temperatures 33 , wherein, the ANN models have been a promising technique in biosorption process of heavy metals in the industrial effluent.
Surface morphology analysis. The surface morphology of the immobilized P. alcaliphila NEWG-2 was examined by Scanning Electron Microscopy (SEM) before and after the Cr 6+ biosorption. Figure 4A revealed a regular surface of the immobilized cells of P. alcaliphila NEWG-2 before the biosorption process. Figure 4B clearly shows the presence of glossy particles on the surface of the alginate beads after Cr 6+ biosorption which are absent before Cr 6+ biosorption.
Energy-dispersive X-ray analysis (EDX). EDX was performed to determine the elemental composition and to verify the presence of Cr 6+ attached to the immobilized P. alcaliphila NEWG-2 surface. Comparing the EDX spectrum before (Fig. 5A) and after (Fig. 5B) the Cr 6+ biosorption process shows the presence of an additional Cr 6+ peak after the Cr 6+ biosorption compared to the EDX spectrum before the Cr 6+ biosorption. That, Regarding the overall biosorption process, there are two main topics. The first belongs to sodium alginate beads that were reported to absorb Cr 6+ ions 16 , and the second belongs to the microbial cell.
Different mechanisms of bacterial biosorption. Among microbial groups, bacteria have been identified to be one of the most important bio-sorbents. The biosorption capacity depends not only on the type of metal ions but also the type of bacteria, especially the cell wall that contains a variety of surface organic functional-groups, with a high affinity to binding metals 35 . The kinetic biosorption process by individual bacterium biomass may have several mechanisms that work complementary or individually. The different mechanisms of biosorption are shown in Fig. 6. Generally, the microbial activity towards metal removal including two phases; physical adsorption or ion exchange at the cell surface, followed by a slower phase involving active metabolism-dependent transport of metal into bacterial www.nature.com/scientificreports/ cells 36,37 . It is, therefore, possible that the metal ion is transferred into the cell and reacts to form a precipitate and remaining within the cells, or forming an affine colloidal entrapped by extracellular polymers 38 . www.nature.com/scientificreports/ In details, bacteria share several mechanisms for heavy metal biosorption, including ion exchange, physical adsorption on specific binding sites (negatively-charged functional groups) of the cell wall, complexation, diffusion, intracellular accumulation, or physicochemical interactions between the metal ions and the bacterial cell wall 39 .
Concerning Pseudomonas spp., the kinetic process of chromium biosorption suggests an efficient intracellular mechanism of chromate uptake by P. aeruginosa and the adsorption process has an endothermic nature 40 . The rhamnolipids (a low-molecular-weight biosurfactant) content of Pseudomonas spp. plays another important role in the bioremoval of chromium and its efficiency may be back to the anionic nature and complexation ability, therefore the bio-removal process is positively correlated with rhamnolipids quantity 36,37 . additionally, rhamnolipid production increased when Pseudomonas sp. was exposed to chromium 37 .
P. aeruginosa ASU 6a is an example of a bacterium that contains negatively-charged functional groups (carboxylate, phosphate, sulfhydryl, and amino groups) that were reported to play a vital role in the biosorption process 41 . However, ionic exchange by some of the functional groups (e.g., -NH, -OH, -CH, and -CONH) and electrostatic interaction were reported as the dominant mechanisms presented in biosorption of heavy metals by P. plecoglossicida 42 . Another work reported that the cell wall of P. aeruginosa S22 contains potential complexation sites such as carboxylate, phosphate, sulfahydryle, and amino (aspartic acid, glutamic acid, histidine, and cysteine) groups, the latter group, in especial, has a strong affinity for metal ions 43 .

Conclusion
The Plackett-Burman design studies the significance of immobilized cell, contact time, and initial Cr 6+ concentration on biosorption process by P. alcaliphila NEWG-2. Both RCCD and ANN models have a high accuracy in the modeling of the Cr 6+ removal process. However, the ANN model showed to be more robust and accurate in assessing the prediction of dependent variables, with skill in prediction and generalization, within the training region, than the RCCD model. Finally, the ANN model could be recommended to be a fit technique in forecasting and accurate for heavy metals removal throughout industrial effluent treatment.