A central composite design (CCD) was used in the optimization of GA-Me production. The ranges and the levels of the variables investigated in this study are given in Table 1.

The results of CCD experiments for GA-Me production are presented in Table 2. Table 3 shows the analysis of variance for the experiment. The Fisher’s F-test with a very low probability value [(P_model > F) = 0.0002] for the total model indicated the model was highly significant. The goodness of fit of the model was examined by the coefficient of determination (R² = 0.9257), which implied that more than 92% of the sample variation was attributable to the variables and only 7.43% of the total variance could not be explained by the model. The adjusted determination coefficient (Adj. R² = 0.8570) was also satisfactory to confirm the significance of the model.

Table 4 reveals the analysis of variance (ANOVA) for three key factors on the production of GA-Me. The smaller the P-value, the more significant is the corresponding factor. X₃ (culture time) had extremely significant effect on GA-Me production (P < 0.01), followed by x₂ (peptone concentration), suggesting culture time and peptone concentration are very important for GA-Me production in submerged fermentation of G. lucidum.

The significance of each coefficient was determined by Student’s t-test and P-value, which is listed in Table 5 The larger the magnitude of t-test and smaller the P-value, the more significant is the corresponding coefficient. The polynomial model for GA-Me yield Y_GA-Me was regressed by all the terms and was expressed by Equation (1). The regression equation showed that the GA-Me yield was an empirical function of test variables in coded unit. (1) where Y_GA-Me is the predicted GA-Me yield, x₁ glucose, x₂ peptone, and x₃ is culture time.

Equation (1) also reveals that culture time (x₃) had a strong positive linear effect on the response (P < 0.01) of Y_GA-Me as it had the largest coefficient, followed by peptone (x₂), which showed a significant negative linear effect (P < 0.01). However, glucose (x₁) had no significant effect on GA-Me production at the tested concentrations (P > 0.05), and the above three variables also indicated negative quadric effects on GA-Me yield (P < 0.05). No significant interactions were noted between any two of the three variables (P > 0.05).

The 3D response surface is generally the graphical representation of the regression equation. Figure 1, Figure 2, Figure 3 represent the 3D response surfaces for the optimization of culture condtion of GA-Me production. Each figure presented the effect of two variables on the production of GA-Me, while another variable was held at zero level (coded value).

From the response surface plots, it is easy to understand the interactions between two nutrients and also to locate their optimum levels. It can be seen from Figure 1 and Figure 2 that the yield of GA-Me was high when the concentrations of peptone were in the range of 3.6–4.8 g·L⁻¹ and glucose in the range of 45–51 g·L⁻¹ synchronously. Figure 2 and Figure 3 showed that GA-Me yield increased upon increasing the culture time from 270 to 420 h. The model predicted a maximum GA-Me yield of 11.9 mg·L⁻¹ for glucose, peptone, culture time values of 44.4 g·L⁻¹, 5.0 g·L⁻¹, 437.1 h, respectively.

Triplicate experiments were carried out to verify the availability and accuracy of the model (Equation (1)) for GA-Me production in flask shake culture. The results are shown in Table 6. Under the calculated optimum culture conditions, a cell density of 11.3 g·L⁻¹ (by dry weight, DW) was obtained, and the content of GA-Me in mycelial cell was 42.7 μg·100 mg⁻¹ DW (also for 4.8 mg·L⁻¹ based on 11.3 g·L⁻¹ of mycelia), and that in fermented supernatant (removal of mycelia by centrifugation) it was 7.6 mg·L⁻¹, that is, a 12.4 mg·L⁻¹ of GA-Me production yield was obtained in G. lucidum cultures, which represented a 129.6% increase in titre compared to the the non-optimized culture conditions (5.4 mg·L⁻¹), and was also in agreement with the predicted value (11.9 mg·L⁻¹). The good agreement between the predicted and experimental results verifies the validity of the model and the existence of an optimum point. The feasibility of the regression model was further tested in a 30-L scaled fermenter under the optimized culture condition. A maximum yield (11.4 mg·L⁻¹) of GA-Me was obtained (Table 6), suggesting the culture condition optimized in the present study was also suitable for GA-Me production in a large scale.

Until now, GAs were mainly extracted from the solid cultivated fruiting bodies of G. lucidum [21]. It usually takes several months to cultivate the fruiting body, and the yield of GAs is very low [11]. Consequently, cell culture of G. lucidum is recognized as a promising alternative for efficient production of GAs [17,18,19]. Although it has been reported that GA accumulation was influenced by the culture medium and process conditions of G. lucidum, many studies were about total GAs production [16,17,18,19], and there are few reports available for individual GAs. Xu et al. studied the production of individual ganoderic acids (GA-Me, GA-T, GA-S and GA-Mk) by G. lucidum cell culture [22]. It was found that GA-Me yield in liquid static culture was higher than that obtained in liquid shaking culture. The GA-Me content in static culture was in the range of 9.6–11.5 mg·L⁻¹ (cell density: 10–12.5 g·L⁻¹; GA-Me content: 96 μg·100 mg⁻¹ DW), and the GA-Me content was higher than that obtained in the present study. However, the GA-Me yield was very low in shaking flask culture with a lactose-based culture medium, and the content of GA-Me in the mycelium was about 10.1 μg·100 mg⁻¹ DW, which is lower than that in the present work. Nevertheless the content of GA-Me in fermented supernatant (extracellular GA-Me) was not determined by Xu et al. In the present study, we obtained 7.6 mg·L⁻¹ of GA-Me from fermented supernatant, and 4.8 mg·L⁻¹ of GA-Me from mycelia, suggesting some quantity of GA-Me was excreted into the fermented broth during the culture process, a phenomenon also observed in several previous studies [17,21,22,23,24,25]. In addition, the optimized culture condition was successfully applied in GA-Me production in an agitated 30-L fermenter. Generally, in submerged mushroom cultures, it is necessary to agitate the culture broth in order to obtain good mixing and thereby promote heat and mass transfer [26]. However, agitation also creates shear force. The shear stress exerted by the impeller blades in an agitated fermenter usually reduces and modifies the mycelium pellet growth in terms of diameter, circularity and compactness, and the accumulation of metabolites. In this work, the mycelium showed no significant damage caused by the shear forces with a speed of 150 rpm·min⁻¹, and 9.1 g·L⁻¹ of mycelium pellets and a 11.4 mg·L⁻¹ titre of GA-Me was obtained, suggesting GA-Me could be also produced under the optimized culture conditions in a large-scale agitated bioreactor.