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Penicillin G acylase was immobilized onto superparamagnetite iron oxide nanoparticles employing response surface methodology through central composite design. Polynomial quadratic model was selected as a model. The value of the determination coefficient (R^{2}) calculated from the quadratic regression model was 0.845, while the value of the adjusted (R^{2}) was 0.74. The regression analysis of the data showed that the quadratic model selected were appropriate thereby enzyme concentration (A), reaction temperature (D), enzyme concentration^{*} reaction temperature (AD), quadratics enzyme concentration (A^{2}) and reaction temperature (D^{2}) were found to be significant factors in immobilization process of penicillin G acylase.

Penicillin G acylase is a biocatalyst produced by bacteria as well as fungi in order to acylate/deacylate penicillin G to its constituent 6-aminopenicilanic acid and phenyl acetic acid or vice versa which is termed as hydrolysis (H) and synthesis (S) respectively, (

Penicillin acylase in its soluble form is unstable, cannot be separated from the reaction mixture easily which will add to the production cost of the final product thus such a commercially, industrially important biocatalyst has been immobilized by different techniques employing various supports by many investigators [1-7]. Each technique or method has its own limitation and disadvantages where immobilization method can alter kinetic properties of immobilized enzyme as compared to its soluble counterpart. The changes can be brought about by the supports or the reagents employed. Investigators are trying to employ technique and reagents which will improve the kinetic properties of the enzyme under immobilization process as compared to its soluble counterpart [7-11]. In this article, we have attempted to optimize the immobilization process of penicillin G acylase onto super para magnetite iron oxide nanoparticles by considering factors such as, enzyme concentration, weight of nanoparticle, concentration of polyethyleneimine, temperature and time of reaction using surface response methodology. Response surface methodology (RSM) is a collection of statistical and mathematical techniques useful for developing, improving, and optimizing processes. The applications of RSM are in industry, biological & chemical sciences, pharmaceutical, physical and engineering sciences. Further the most extensive applications of RSM are in the particular situations where several input variables potentially influence some performance measure or quality characteristic of the process. In RSM, the main effects and interactions between various factors, each at different levels can be simultaneously studied [

Penicillin G acylase, 6-aminopenicilanic acid (6-APA), polyethyleneimine, p-dimethylaminobenzaldehyde (pDMBA), were obtained from Sigma, USA. Benzyl penicillin was procured from local market; other reagents used were of analytical grade.

Penicillin acylase activity was determined as reported by Norouzian et al. [

Penicillin G acylase was immobilized onto synthesized superparamagnetite iron oxide nanoparticles. The factors could influence the immobilization process were considered to be; enzyme concentration (A: U/ml/min) weight of iron oxide nanoparticles (B: µg), concentration of polyethyleneimine (C: %), reaction temperature (D: ˚C) and reaction time (E: h). The immobilization process was optimized by surface response methodology (SRM) through central composite design (CCD) employing Ease State program, version 6. Furthermore, central composite design contains an imbedded factorial or fractional factorial design with center point that is augmented with a group of start points that allow estimation of the curvature. The mathematical representation of RSM in this study is poly nominal quadratic second order model. Totally 50 experiments were designed by providing the actual low and high values by considering five factors which could influence the optimization process. The above mentioned factors were used to construct the experiment’s matrix (Tables 1 and 2).

Data obtained through the experimental matrix are computed for the determinations of regression coefficient of

the second order multiple regression model. The analysis of regression and variance was performed by Design Expert (Ease State Version 6.0).

where Y is the predicted response variable, b_{0}, b_{i}, b_{ii} and b_{ij} are regression coefficient of the model, x_{i}, x_{j} represent the independent variables in the form of actual value.

Since response surface methodology is a statistical technique employed to optimize the processes where several factors are involved. This methodology can be employed to optimize bioprocesses and the obtained model can be validated in order to follow up the accuracy of the model [13-16]. The statistical significance of regression equation was checked by F-test, and the analysis of variance (ANOVA) for response surface quadratic polynomial model done by software (Design-Expert) is shown in ^{2}) calculated from the quadratic regression model was 0.845, while the value of the adjusted (R^{2}) was 0.74 that almost indicates fairly high degree of correlation between the observed and predicted values. All these results suggested that the model, as evidenced by the calculated F value (7.95) and low probability value (P < 0.0001), was adequate for the prediction of the immobilization of penicillin G acylase within the variable range employed. The lack-of-fit test measures failure of the model to represent the data in the experimental domain at points which are not included in the regression. As shown in

As it can be observed from the ^{2} and D^{2} are < 0.0001, 0.001, 0.0049 and 0.0016 respectively showing the significance of the factors involved in immobilization process of penicillin G acylase.

The quadratic model was validated by performing the immobilization process under optimal conditions and the yield of penicillin acylase was comparable to that of calculated by the model thereby the selected model was appropirate.In this way penicillin G acylase (industrially and commercially important biocatalyst) could be immobilized through optimization by surface response methodology

The corresponding author thereby acknowledges the grant given by Iran National Science Foundation: INSF to carry out this research project.