## 3 Results and Discussion
### Heterotrophic Medium Optimization Using Box-Behnken Design  
Based on the previous results, a response surface methodology (Box-Behnken) was performed to determine the optimal values of (NH\({}_{2}\))\({}_{2}\)CO, NaH\({}_{2}\)PO\({}_{4}\cdot\)H\({}_{2}\)O + K\({}_{2}\)HPO\({}_{4}\), and CuSO\({}_{4}\cdot\)5H\({}_{2}\)O, as well as their interactions to maximize _C. amblystomatis_ heterotrophic specific growth rates. The Box-Behnken layout, as well as the experimental and predicted results of specific growth rates, are shown in Table 2.  
The 12 th experiment (60 mM of (NH\({}_{2}\))\({}_{2}\)CO, 10m M of NaH\({}_{2}\)PO\({}_{4}\cdot\)H\({}_{2}\)O + K\({}_{2}\)HPO\({}_{4}\) and 0.015 mM of CuSO\({}_{4}\cdot\)5H\({}_{2}\)O) registered the highest specific growth rate (0.048 h\({}^{-1}\)), while the 7 th experiment (20 mM of (NH\({}_{2}\))\({}_{2}\)CO, 80 mM of NaH\({}_{2}\)PO\({}_{4}\cdot\)H\({}_{2}\)O + K\({}_{2}\)HPO\({}_{4}\) and 0.015 mM of CuSO\({}_{4}\cdot\)5H\({}_{2}\)O) resulted in the lowest value (0.028 h\({}^{-1}\)). The predicted results were obtained from the linear polynomial Equation (4), given by the model, as follows:  
\[Specific\;growth\;rate \tag{4}\] \[=0.027707+0.000596[A]-0.000124[B]+0.291714[C]\] \[-0.00000244306[A]\times[B]-0.020235[A]\times[C]\]  
The statistical analysis, described in Table 3, demonstrated the (NH\({}_{2}\))\({}_{2}\)CO, NaH\({}_{2}\)PO\({}_{4}\cdot\)H\({}_{2}\)O + K\({}_{2}\)HPO\({}_{4}\) and CuSO\({}_{4}\cdot\)5H\({}_{2}\)O concentrations, as well as their interactions, which significantly affected (\(p<0.05\)) _C. amblystomatis_-specific growth rate. The model registered a correlation coefficient \(R^{2}\) of 0.980, suggesting the suitability of this model for predicting the responses in this experiment. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{\begin{tabular}{c} **Run** \\ **Order** \\ \end{tabular} } & \multirow{2}{*}{**(NH\({}_{2}\))\({}_{2}\)CO**} & \multirow{2}{*}{\begin{tabular}{c} **NaH\({}_{2}\)PO\({}_{4}\cdot\)H\({}_{2}\)O** \\ **+ K\({}_{2}\)HPO\({}_{4}\)** \\ **mM** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **CuSO\({}_{4}\cdot\)5H\({}_{2}\)O** \\ **mM** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **\(\mu\)** \\ **Experimental** \\ **h\({}^{-1}\)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **\(\mu\) Predicted** \\ **h\({}^{-1}\)** \\ \end{tabular} } \\ \hline
1 & 60 & 80 & 0.015 & 0.032 & 0.033 \\ \hline
2 & 60 & 45 & 0.005 & 0.046 & 0.048 \\ \hline
3 & 20 & 10 & 0.015 & 0.036 & 0.037 \\ \hline
4 & 40 & 45 & 0.015 & 0.037 & 0.036 \\ \hline
5 & 40 & 10 & 0.025 & 0.037 & 0.037 \\ \hline
6 & 60 & 45 & 0.025 & 0.032 & 0.033 \\ \hline
7 & 20 & 80 & 0.015 & 0.028 & 0.029 \\ \hline
8 & 40 & 45 & 0.015 & 0.039 & 0.036 \\ \hline
9 & 40 & 80 & 0.025 & 0.029 & 0.029 \\ \hline
10 & 20 & 45 & 0.005 & 0.032 & 0.032 \\ \hline
11 & 40 & 45 & 0.015 & 0.037 & 0.036 \\ \hline
12 & 60 & 10 & 0.015 & 0.048 & 0.048 \\ \hline
13 & 20 & 45 & 0.025 & 0.034 & 0.033 \\ \hline
14 & 40 & 10 & 0.005 & 0.047 & 0.047 \\ \hline
15 & 40 & 80 & 0.005 & 0.034 & 0.033 \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental layout of Box–Behnken design; the experimental and predicted results of the specific growth rates (\(\mu\)) of heterotrophic cultures. Moreover, the interactions between (NH\({}_{2}\))\({}_{2}\)CO, NaH\({}_{2}\)PO\({}_{4}\)\(\cdot\)H\({}_{2}\)O + K\({}_{2}\)HPO\({}_{4}\), and CuSO\({}_{4}\)\(\cdot\)5H\({}_{2}\)O and specific growth rates (h\({}^{-1}\)) were revealed by response surface plots (Figure 1). Varying the concentration of these factors causes a significant effect on the specific growth rates.