## 3 Results and Discussion
### Optimization of the Production Conditions by RSM Design  
According to the results of PB and the steepest ascent path design, a three-factor (time point of L-Met addition, glucose concentration and yeast extract concentration) and three-level BBD were used to optimize the best fermentation conditions for 3-Met production by YHM-G. Various maximum and minimum levels of three factors were used for the 15 experimental runs in Table 4. The results showed considerable variation in 3-Met production with a maximum of 3.04 g/L in test number 10 and a minimum of 1.04 g/L in test number 4. A second order polynomial equation 2 was obtained to explain 3-Met production by applying multiple regression analysis on the experimental data:  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Test** &  
\(\mathrm{Y}=2.95-0.1845\) A + 0.2781 B + 0.2906 C + 0.0356 AB \(-\) 0.0135 AC \(-\) 0.1315 BC \(-\) 0.4765 A\({}^{2}\) \(-\) 0.4564 B\({}^{2}\) \(-\) 0.5955 C\({}^{2}\)  
where Y is the predicted response and A, B and C are the time point of L-Met addition, glucose concentration and yeast concentration, respectively. The ANOVA (\(F\)-test) shows that the model was statistically significant. The \(R^{2}\) was 0.9709, indicating that the sample variation of 97.09% for 3-Met production was attributed to the independent variables and only about 2.93% of the total variation was unexplained by the model (Table 7). Furthermore, the model terms of A (the time point of L-Met addition); B (glucose concentration); C (yeast extract concentration); and A\({}^{2}\), B\({}^{2}\) and C\({}^{2}\) were significant at the 5% level, and the lack of fit was not significant with a \(p\) value of 0.2658 (Table 7). Thus, the model was adequate for prediction with the range of factors used. The \(p\) values and coefficients suggested the independent B (glucose concentration), and C (yeast extract concentration) had a significant positive effect on 3-Met production (Table 7), indicating that they could cause an increase linearly in 3-Met production. Additionally, factor A (time point of L-Met addition) significantly negatively affected 3-Met production, indicating that factor A caused 3-Met production to decrease (Table 7). The quadric term of A, B and C also had a significant effect, whereas there was no evidence of interaction among them (Table 7). The three-dimensional (3D) response surface plots for 3-Met production described by the above model were drawn to illustrate the effects of the independent variables and to depict the interactions between two variables by keeping the third variables at their zero levels (Figure 3). As shown in Figure 3a, 3-Met production increased first then decreased gradually as the time point of L-Met addition or glucose concentration increased, and the higher yield of 3-Met was obtained when time point of L-Met addition was at 4.2-5.6 h and glucose concentration was in the range of 41.3-43.8 g/L. The similar trend of 3-Met production was observed in Figure 3b as time point of L-Met addition or yeast concentration increased, and the yield of 3-Met was higher 3.0 g/L when time point of L-Met addition was in the range of 4.4-5.2 h and yeast concentration was in the range of 0.88-0.92 g/L. In addition, 3-Met production increased then decreased as glucose concentration or yeast concentration increased, and more than 3.0 g/L of 3-Met was obtained by YHM-G when glucose concentration was in the range of 40.7-44.6 g/L and yeast concentration was in the range of 0.82-0.95 g/L (Figure 3c).