## 3 Results and Discussion
### Cultivation of R. qingshengii IGTS8 Under Batch and Repeated Batch Modes
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & & & \(\mathbf{Y_{\mathrm{x/s}}}\) & **Biomass** & **CDA** \\  & **X** & **\(\mathbf{\mu}\)** & **Xmax** & **(g DCW/g glycerol)** & **Volumetric** & **(Units/mg DCW)** \\ \hline Batch & 2.62 \(\pm\) 0.04 & 0.054 \(\pm\) 0.001 ** & 3.44 \(\pm\) 0.08 & 0.46 \(\pm\) 0.03 & 0.03 \(\pm\) 0.001 & 12.0 \(\pm\) 0.1 \\ \hline Repeated Batch & & & & & \\
1 st cycle & 3.08 \(\pm\) 0.09 & 0.072 \(\pm\) 0.003  & 3.93 \(\pm\) 0.10 & 0.43 \(\pm\) 0.02 & 0.07 \(\pm\) 0.001 & 13.0 \(\pm\) 0.4 \\
2 nd cycle & 1.77 \(\pm\) 0.02 & 0.071 \(\pm\) 0.001  & 2.57 \(\pm\) 0.03 & 0.24 \(\pm\) 0.02 & 0.05 \(\pm\) 0.001 & 12.6 \(\pm\) 0.3 \\ \hline Fed-batch & 8.35 \(\pm\) 0.17 & 0.093 \(\pm\) 0.005  & 8.56 \(\pm\) 0.14 & 0.55 \(\pm\) 0.05  & 0.09 \(\pm\) 0.001 & 20.7 \(\pm\) 0.1 \\ \hline \hline \end{tabular}  
* \({}^{1}\): R\({}^{2}\) = 0.989, \(p\) \(<\) 0.0001, 2 R\({}^{2}\) = 0.992, \(p\) \(<\) 0.0001, 3 R\({}^{2}\) = 0.976, \(p\) \(<\) 0.0001, 4 R\({}^{2}\) = 0.981, \(p\) \(<\) 0.0001.
* up to 48 h total cultivation time. *
* at the end of the process.  
\end{table} 
Table 1: Overall performance of batch, repeated batch and fed-batch processes. Figure 2: Evolution of cell mass concentration during batch (\(\bullet\)) and repeated batch [(\(\Circinus\)) 1 st cycle and (\(\blacktriangle\)) 2 nd cycle] cultivation of _R. qingshengii_ IGTS8. Gray bars indicate the CDA at different time intervals in each culture. Solid lines represent model fitting (Equation (2)). This equation is categorized as an unstructured model to describe the sigmoid relationship between time and microbial growth [56]. Integrating Equation (1) with the initial condition \(t\) = 0, \(X\) = \(X_{0}\), which is known according to the inoculum procedure employed, yields  
\[X=\frac{X_{0}e^{\mu t}}{1-\left(\frac{X}{X_{max}}\right)\left(1-e^{\mu t}\right)} \tag{2}\]  
where \(\mu\) (h\({}^{-1}\)) is the specific growth rate, \(X_{max}\) (g DCW/L) is the maximum biomass concentration at the end of growth, \(X_{0}\) (g DCW/L) is the initial biomass concentration and \(t\) (h) is the cultivation time. The logistic growth model was used to fit all experiments carried out in this work, and the results are summarized in Table 1. In all cases the R\({}^{2}\) values were found to be greater than 0.97 and the \(p\) values \(\leq\) 0.001, indicating a very good fit. The specific growth rate (\(\mu\)), which is a measure of the dynamic behavior of microorganisms, was 0.054 \(\pm\) 0.001 h\({}^{-1}\) when \(R\). _qingshengii_ IGTS8 was cultivated under the batch process mode. [PERSON] et al. [52] reported that 1.8 g DCW/L of the same bacterium could be obtained under batch cultivation using 20 g/L of glucose and 1.3 mM DMSO with a higher specific growth rate (\(\mu\) = 0.202 h\({}^{-1}\)), but with a lower cell yield (Y\({}_{x/s}\) = 0.14 g DCW/g glucose). In general, the specific growth rate of a microorganism is influenced by the type or amount of carbon available in the growth medium, the environmental conditions of growth (pH, T, DO, etc. ), as well as the cultivation process. During the repeated batch cultivation, the specific growth rate was found to be similar in the two cycles and was increased by 25% compared with the batch process (Table 1). Cells' desulfurization activity (CDA) can be considered a measure of the overall performance of the Dsz enzymes involved in the 4S pathway. CDA varied with the growth phase of the culture and, as reported earlier, the cells exhibited a maximum CDA at the beginning of the exponential phase when the cell concentration is very low [32]. According to [PERSON] et al. [57] the activities of the different Dsz enzymes (Dsz A, Dsz B and Dsz C) involved in the 4S pathway reach their maximum at different stages of growth, causing variations in CDA with the age of the cells. A high cell concentration and high specific activity of desulfurization (CDA) are the most important factors for the industrial application of the Biodsulfurization technique to oil refining processes [11].