The residuals demonstrated a normal distribution for two responses where the point followed a straight line (
Figure 2A and
2B). Regression model equations (Equations 1 written as the coded values of variables including concentration (A) and immunomodulator (B) are as follows:
The results of ANOVA for the effects of immunomodulator polysaccharides and their concentrations on the expression of IFN-γ and IL-2 are shown in
Table 2 and
Table 3, respectively. The results of Fisher (F) test for the two responses were F = 129.67 and F = 83.4 and the ANOVA test (P < 0.0001) showed that the model was statistically significant. The regression model fitted the data and there was a good correlation between the experimental and predicted data based on the non-significant lack of fit (F = 3.33 and F = 2.8; P = 0.056 and P = 0.066 for the IFN-γ and IL-2 expression, respectively), the determination coefficient (R
2 = 0.98 and R
2 = 0.96 for the IFN-γ and IL-2 expression, respectively), and adjusted determination coefficient (Adj. R
2= 0.97 and Adj. R
2 = 0.94 for the IFN-γ and IL-2 expression, respectively). The predicted determination coefficients (Pred. R
2 = 0.96 and Pred. R
2 = 0.92 for IFN-γ and IL-2, respectively) were in reasonable agreement with the adjusted R
2 values and confirmed that the models had good predictive ability. The adequate precision values, which indicated the signal to noise ratios, were above 4 (37.51 and 24.45 for IFN-γ and IL-2, respectively) and proved the established model could navigate the design space. The coefficient of variation (CV) was relatively low (5.34% and 19.84% for IFN-γ and IL-2 expression, respectively), which showed the reliability of the results. The ANOVA test also indicated that the effects of immunomodulators and their concentrations were statistically meaningful on both cytokines (P < 0.0001). In addition, the interaction effect was significant for IFN-γ expression (P = 0.03) (
Figure 3). As shown in
Figure 3, the mRNA expression of IFN-γ was enhanced with increasing the concentration of immunomodulators from 200 to 1000 μg/mL except for F
2 in which, a decrease in response was observed approximately above the 700 μg/mL concentration. This result revealed that higher concentrations of F
2 could negatively affect the expression of IFN-γ in chicken PBMCs. However, no interaction effect was observed for IL-2 expression. Indeed, the IL-2 expression in chicken PBMCs was enhanced by increasing the concentration of immunomodulatory polysaccharides from 200 μg/mL to 800 μg/mL regardless of immunomodulator type (
Figure 4). Furthermore, the optimization results by RSM revealed that F
1 at 786.68 μg/mL with the desirability of 0.87 could be selected to maximize the gene expression of IFN-γ and IL-2 by 23.74 and 21.08 folds, respectively, by chicken PBMCs (
Figure 5).