*2.8. Optimum Temperature and Thermal Stability of Mal-mPEG5000-SPA and SPA*

According to Figure 9a, the maximum specific activity of SPA was found to be (1.733 ± 0.050) × <sup>10</sup><sup>4</sup> U/mg at 55 ◦C, while the maximum of Mal-mPEG5000-SPA was (2.121 ± 0.058) × <sup>10</sup><sup>4</sup> U/mg at 45 ◦C, an increase by 22.38% compared to the untreated one. Moreover, the activities of Mal-mPEG5000-SPA at 50 ◦C, 55 ◦C and 60 ◦C were determined as (2.074 ± 0.060) × <sup>10</sup><sup>4</sup> U/mg, (2.057 ± 0.062) × <sup>10</sup><sup>4</sup> U/mg, and (2.031 ± 0.064) × 104 U/mg respectively, all significantly higher than that of untreated SPA (*p* < 0.05). These results indicated that the enzymatic specific activity of modification enzyme was significantly improved after Mal-mPEG5000 modification.

Figure 9b showed the thermal stability of Mal-mPEG5000-SPA and SPA. No significant difference in SPA specific activity at 20 ◦C and 25 ◦C for 1 h was noted. However, when the temperature rose to 30 ◦C, the specific activity of SPA was significantly reduced (*p* < 0.05), which indicated high sensitiveness of SPA to temperature. No significant difference in the specific activity of Mal-mPEG5000-SPA from 20 ◦C to 45 ◦C for 1 h was found. But when the temperature rose to 50 ◦C, the specific activity of Mal-mPEG5000-SPA started to decline (*p* < 0.05), which suggested significant improvement of the thermal resistance of Mal-mPEG5000-SPA. These results showed that hydrolyzed starch by Mal-mPEG5000-SPA has a wider range of application in the food industry, which can significantly enhance enzymatic efficiency to reduce production costs.

**Figure 9.** Temperature profiles of Mal-mPEG5000- SPA and SPA. (**a**) Optimum enzymolysis temperature; (**b**) Thermal stability. Significant difference in each column are expressed as different superscript letters (*p* < 0.05).

#### *2.9. Optimum pH and pH Stability of Mal-mPEG5000-SPA and SPA*

Figure 10a showed that Mal-mPEG5000-SPA and SPA both showed relatively high specific activity from pH 5.0 to 7.0. At pH 6.0, the specific activity of Mal-mPEG5000-SPA and SPA reached respective maximum values at (2.061 ± 0.051) × 104 U/mg and (1.733 ± 0.050) × 104 U/mg, and the specific activity was improved by 18.92% after modification.

Figure 10b showed the pH stability of Mal-mPEG5000-SPA and SPA. A significant difference in SPA's specific activity at pH 6.0 and 6.5 was found (*p* < 0.05), while the difference for Mal-mPEG5000-SPA was not significant (*p* = 0.05), which indicated higher adaptability of Mal-mPEG5000-SPA to a pH environment. In addition, the specific activity of Mal-mPEG5000-SPA was constantly higher than that of SPA under pH value from 4.0 to 7.5, which indicated lower susceptibility of Mal-mPEG5000-SPA to pH environment. This means Mal-mPEG5000-SPA could applied more broadly and is more suitable for industrial application.

**Figure 10.** pH profiles of Mal-mPEG5000- SPA and SPA. (**a**) Optimum enzymolysis pH; (**b**) pH stability. Significant difference in each column are expressed as different superscript letters (*p* < 0.05).

#### *2.10. Kinetic Parameters of Mal-mPEG5000-SPA*

The results of kinetic parameters of Mal-mPEG5000-SPA were shown in Table 3, the Km value for sweet potato starch, potato starch, corn starch, soluble starch, amylase and amylopectin by Mal-mPEG5000-SPA hydrolysis was respectively (1.63 ± 0.033) mg/mL, (2.06 ± 0.028) mg/mL, (2.36 ± 0.063) mg/mL, (1.84 ± 0.025) mg/mL, (2.18 ± 0.029) mg/mL and (2.11 ± 0.052) mg/mL. The Vmax value was respectively (32.06 ± 0.61) mmol/min/mL, (16.23 ± 0.32) mmol/min/mL, (10.66 ± 0.37) mmol/min/mL, (20.88 ± 0.78) mmol/min/mL, (13.35 ± 0.38) mmol/min/mL, (13.89 ± 0.41) mmol/min/mL. The *Ea* value was respectively (11.07 ± 0.43) kJ/mol, (18.24 ± 1.12) kJ/mol, (26.52 ± 1.21) kJ/mol, (14.71 ± 1.15) kJ/mol, (21.16 ± 1.12) kJ/mol and (21.66 ± 0.8) kJ/mol. These results indicated that Mal-mPEG5000-SPA had the lowest Michaelis constant for sweet potato starch. Therefore, Mal-mPEG5000-SPA was determined to have the strongest binding affinity for sweet potato starch. Next only to sweet potato starch, soluble starch was followed by potato starch, amylase and amylopectin. Compared with the SPA kinetic parameters reported in earlier studies [20], for sweet potato starch hydrolyzed by Mal-mPEG5000-SPA, Km declined by 12.95%, Vmax increased by 26.87%, and *Ea* dropped by 12.63%, which suggested Mal-mPEG5000-SPA showed stronger affinity for sweet potato starch than SPA.

**Table 3.** Kinetic and activation energy parameters of Mal-mPEG5000-SPA.



**Table 3.** *Cont.*

Significant difference in each column are expressed as different superscript letters (*p* < 0.05).
