*3.5. Selection of Relevant Variables and Experimental Design*

SPA was modified by Mal-mPEG5000 at the molar ratio of SPA to Mal-mPEG5000 from 1:1 to 1:6, for modification temperature from 25 ◦C to 75 ◦C and for modification pH from 3.0 to 8.0. The enzyme specific activity of modified enzyme (expressed as Mal-mPEG5000- SPA) was used as the index for evaluating the effects of the different modification parameters to be optimized via response surface methodology (RSM). A central composite design (CCD) were used with three variables and three levels for optimizing the modification conditions. These three factors were modification pH (A), the molar

ratio of SPA to Mal-mPEG5000 (B) and modification temperature (C) (Table 5). A second-order polynomial equation (Equation (2)) for the variables was developed:

$$\mathbf{Y} = \mathbf{a}\_0 + \mathbf{a}\_1 \mathbf{A} + \mathbf{a}\_2 \mathbf{B} + \mathbf{a}\_3 \mathbf{C} + \mathbf{a}\_{11} \mathbf{A}^2 + \mathbf{a}\_{22} \mathbf{B}^2 + \mathbf{a}\_{33} \mathbf{C}^2 + \mathbf{a}\_{12} \mathbf{A} \mathbf{B} + \mathbf{a}\_{13} \mathbf{A} \mathbf{C} + \mathbf{a}\_{23} \mathbf{B} \mathbf{C} \tag{2}$$

Y is the predicted response, α<sup>0</sup> is the intercept; α1, α2, α3, linear coefficients; α11, α22, α33, squared coefficients; and α12, α13, α23, interaction coefficients. Analysis of variance was used to evaluate the model's adequacy and to determine the regression coefficients and their statistical significance. The response surface contour plots showed how the independent variables interacted and how those interactions influenced the overall response [20].


**Table 5.** Independent variables and levels for central composite design (CCD).

#### *3.6. Enzyme Characterization*

Influence of temperature on Mal-mPEG5000-SPA and SPA: The optimum temperature of Mal-mPEG5000-SPA was investigated at pH 5.8 over a temperature range of 20–75 ◦C. SPA and Mal-mPEG5000-SPA was incubated in 20 mM disodium-hydrogen phosphate-citric acid buffer (pH 5.8) during 60 min, respectively. The thermostability of the enzyme residual specific activity were determined under different temperature conditions (20–75 ◦C).

Influence of pH on Mal-mPEG5000-SPA and SPA: The optimum pH of Mal-mPEG5000-SPA was investigated at 50 ◦C over a pH range of 3.0–8.5. Mal-mPEG5000-SPA was preincubated for 60 min under 50 ◦C, the residual specific activity was determined at a pH range of 3.0–8.5 to evaluate the pH stability.
