*4.5. Response 3 (Y3): Effect of Investigated Independent Factors on ZP*

The surface charge of the APG-loaded PEGylated CNPs formulations ranged from +19.41 to +26.56 mV (Table 2). The positive charge on the NP's surface indicates the existence of freely ionized amino groups that is necessary for electrostatic repulsion between particles to produce stable nano-dispersions. The measured response, Y3, has a mathematical concept of a polynomial equation, which is enumerated below.

Y3 (ZP) = +23.88 + 2.56 A + 1.02 B + 0.0762 C <sup>−</sup> 0.0375 AB + 0.0450 AC + 0.1475 BC <sup>−</sup> 1.42 A2 + 0.6650 B<sup>2</sup> <sup>−</sup>0.2275 C<sup>2</sup> (4)

**Figure 2.** Three-dimensional-response surface plot showing effect of independent variables (**A**) X1 and X2; (**B**) X1 and X3; and (**C**) X2 and X3 on DEE.

The obtained mathematical equation can be used to determine the relative effects of these factors by equating the factor's coefficients. The concentration of CS:TPP and PEG had more significant effects on ZP. The model's F-value of 116.01 suggests that it is really significant. Model terms with *p*-values below 0.05 are significant. This case show that that A, B, A2, and B2 are considered as significant model terms. If the value is higher than 0.10, the model's terms really are not significant. The F-value for the lack of fit is 1.48, which indicates that the lack of fit is insignificant in comparison to the pure error. An insignificant lack of fit is acceptable, and we desired to fit the model. The adjusted R2 of 0.9848 is probably close to the predicted R2 of 0.9390; the difference is below 0.2. Adequate precision was discovered at 35.779, indicating that the obtained model is used to processed the design space. 3D surface plots that analyze the impact of independent variables on ZP are reported in Figure 3A–C.

**Figure 3.** Three-dimensional-response surface plot showing effect of independent variables (**A**) X1 and X2; (**B**) X1 and X3; and (**C**) X2 and X3 on ZP.

#### *4.6. Formulation Optimization for the APG-PEGylated CNPs*

The impact of independent variables on responses, as well as the levels of such factors, was decided using the RSM statistical optimization process. Response optimization was used to accomplish an improved formulation with adequate PS, ZP, and high DEE. The selected optimized formulation produce values of independent variables, viz., at X1 (CS: TPP concentration) of 0.5% *w/v*, X2 (PEG 400 concentration) of 0.75% *w/v*, and X3 (sonication time) of 20 min, which granted predicted values for selected responses. Three formulation batches of optimal content were prepared, and their responses for each formulation were examined to confirm the model's appropriateness for prediction. The optimized formulation components, as well as the experimental and predicted values including all dependent responses, are shown in Table 5. The experimental values were

found to be very close to the predicted values, denoting the achievement of the BBD coupled with a preferable function for formulation evaluations and optimizations. For predicted versus observed values, the R2 values (>0.9) showed a linear correlation across all dependent variables, denoting the superior model's reliability (Figure 4).

**Table 5.** Results of optimization of APG-loaded PEGylated-CNPs prepared under optimum condition.


**Figure 4.** Predicted vs. actual plot representing the effects of X1 and X2 on the measured responses at the mid-level of X3 on (**A**) PS (Y1), (**B**) DEE (Y2), and (**C**) ZP (Y3).

#### *4.7. Characterization of Optimized APG-PEGylated CNPs*

The particle size distribution of NPs play a characteristic features in biodistribution, and as a drug carrier, its required a small particle size (i.e., a low PDI value) [4]. The PS distribution spectrum for the optimized APG-PEGylated CNPs is presented in Figure 5A, expressing the average PS of 139.63 ± 5.67 nm and PDI of 0.296 ± 0.014. The EE% and LC% of the formulation were found at 79.55 ± 3.12% and 37.78 ± 2.46%, respectively. The surface morphology of the optimized nanoparticle was examined by TEM (Figure 5B). The NPs were found to be nearly spheroidal vesicles in shape, with a size <200 nm, which matches the results of Zeta Sizer's PS analysis. The image also revealed that the NPs maintained their shape and that the vesicle's integrity is preserved. The layer seen around the nanoparticle's core could be the PEG molecules tied to the CS polymer.
