*2.2. Effect of the Molar Ratio on Modification*

The results from Figure 2 indicated that as the molar ratio rose from 1:1 to 1:4, increasingly high SPA specific activity was found along with the increase of Mal-mPEG5000 concentration. The enzymatic specific activity reached the maximum (2.143 ± 0.050) × 104 U/mg when the molar ratio was 1:4, an increase by 23.66% compared with that of the untreated SPA. As the concentration of Mal-mPEG5000 increased further, and the molar ratio increased to 1:6, the enzymatic specific activity decreased to (2.016 ± 0.051) × <sup>10</sup><sup>4</sup> U/mg, and there was a significant difference between the molar ratio of 1:4 and 1:6 (*p* < 0.05). Therefore, the optimal response molar ratio of SPA to Mal-mPEG5000 was concluded to be 1:4.

**Figure 2.** Effect of the molar ratio of SPA to Mal-mPEG5000 on SPA activity.

#### *2.3. Effect of Temperature on Modification*

The results from Figure 3 indicated that the Mal-mPEG5000-SPA specific activity gradually increased as the temperature rose from 25 ◦C to 55 ◦C. The specific activity reached the maximum (2.131 ± 0.059) × 104 U/mg at 55 ◦C. As the temperature increased to 65 ◦C, the specific activity dropped to (1.801 ± 0.055) × <sup>10</sup><sup>4</sup> U/mg, and decreased by 15.49%, and there was a significant difference between 55 ◦C and 65 ◦C (*p* < 0.05). Therefore, the optimal modification temperature was concluded to be 55 ◦C.

**Figure 3.** Effect of modification temperature on modification.

#### *2.4. Effect of pH on Modification*

The results from Figure 4 indicated that the Mal-mPEG5000-SPA specific activity gradually increased as the pH moved from 3 to 6. The specific activity reached the maximum (2.155 ± 0.046) × <sup>10</sup><sup>4</sup> U/mg at pH 6.0. As pH increased to 7.0, the specific activity was (1.925 ± 0.045) × 104 U/mg and decreased by 10.69%, and there was a significant difference between pH 6.0 and 7.0 (*p* < 0.05). Therefore, the optimal modification pH was concluded to be 6.0.

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**Figure 4.** Effect of modification pH values on modification.

#### *2.5. Effect of Time on Modification*

The results from Figure 5 indicated that the Mal-mPEG5000-SPA specific activity increased as the modification time rose from 5 min to 10 min. The specific activity reached the maximum (2.142 ± 0.059) × 104 U/mg at 10 min. As the modification time further increased, no significant change was noted in the enzymatic specific activity (*p* = 0.05). The ANVOA results showed no significant difference of enzymatic specific activity between 10 min and 30 min. Therefore, taking into account of practical application, the optimal modification time was concluded to be 10 min.

**Figure 5.** Effect of modification time on modification.

#### *2.6. Optimizing the Modification Procedure*

According to the effect of the molar ratio, modification temperature, pH and time, the time has little effect on modification, and modification pH (A), the molar ratio (B) and modification temperature (C) were selected as three factors to optimize the modification procedure by central composite design (CCD). With modification time set at 10 min, and Mal-mPEG5000-SPA specific activity (Y) as the response value, Box-Behnken design principles were followed to conduct a test of three factors and three levels. Results were shown in Table 1.


**Table 1.** Experimental design and results for the activity of Mal-mPEG5000-SPA.

8 1 −1 0 1.9097


**Table 1.** *Cont.*

Multiple regression analysis was adopted to the experimental data by using the software Design-Expert V8.0.6. The response, Y (Mal-mPEG5000-SPA specific activity), was selected as the test variables, and by the second order, a polynomial equation was developed (Equation (1)).

$$\text{Y} = 2.15 + 0.025\text{A} + 0.00528\text{B} + 0.016\text{C} - 0.033\text{AB} + 0.027\text{AC} + 0.0011\text{BC} - 0.17\text{A}^2 - 0.13\text{B}^2 - 0.13\text{C}^2 \tag{1}$$

The analysis of variance (ANOVA) for the response Y, the Mal-mPEG5000-SPA specific activity, was shown in Table 2. The regression model was highly significant (*p* < 0.01), while the lack of fit was not significant (*p* = 0.317 > 0.05) and the value of the determination coefficient (R2) was 0.996, which indicated the goodness of fit of the regression model [19]. Based on the analysis of experimental data in Tables 1 and 2, the regression model demonstrated a high correlation, and can be used as theoretical prediction for the enzymatic specific activity of Mal-mPEG5000 modified SPA. The significance test on the regression model suggested that the effect on enzymatic specific activity was as follows: Modification pH > modification temperature > Molar ratio of SPA to Mal-mPEG5000.


**Table 2.** Analysis of variance (ANOVA) for the experimental results.

\* indicate significant (*p* < 0.05); \*\* indicate highly significant (*p* < 0.01).

In order to further comprehend the interaction between the parameters, the response surfaces were obtained using Equation (2), which were plotted between two independent variables and the other independent variable was set at the zero-coded level. The analysis on the response was shown in Figure 6a–c.

**Figure 6.** Response surface plot showing the effects of the variables on the activity of Mal-mPEG5000-SPA. The three independent variables set were modification pH (**a**), the molar ratio of SPA to Mal-mPEG5000 (**b**) and modification temperature (**c**).

Figure 6a indicated that with the increase of the modification pH and the molar ratio, the Mal-mPEG5000-SPA specific activity first increased, and then declined, meanwhile, steep response surfaces and oval contour line were found, which indicated significant interaction of the pH value and the molar ratio.

Figure 6b suggested that with the increase of modification pH and temperature, the Mal-mPEG5000-SPA specific activity firstly increased, and then decreased, and the oval contour line was noticed, which demonstrated a significant interaction of modification pH value temperature.

Figure 6c revealed that with the increase of the molar ratio and modification temperature, the Mal-mPEG5000-SPA specific activity increased firstly before it declined, and the occurrence of circular contour line showed no significant interaction of the molar ratio and modification temperature.

Through the analysis by the software Design-Expert, the optimized combination for maximum Mal-mPEG5000-SPA specific activity was determined through canonical analysis of the response surfaces and contour plots as A = 6.08, B = 4.04 and C = 58.85 ◦C, i.e., the predicted value of Mal-mPEG5000-SPA specific activity of 2.247 × 104 U/mg. under modification pH 6.08, the molar ratio 1:4.04, and modification temperature 58.85 ◦C. Considering the practicality of the validation test, the optimum parameters were corrected into modification pH 6.0, the molar ratio 1:4, and modification temperature 58 ◦C. The specific activity of Mal-mPEG5000-SPA was determined under the corrected parameters to be (2.150 ± 0.055) × <sup>10</sup><sup>4</sup> U/mg, an increase by 24.06% than that of the untreated one. The validation test showed that the optimization results from the response surface method were reliable, and adopting response surface method to optimize the modification process of Mal-mPEG5000 on SPA was feasible.
