## 2 Results and Discussion
### The Optimization of the Agrobacteriumium sp. IFO 13140 Immobilization on Loofa Sponge  
Figure 1 shows the optimization of curdlan production by immobilized and free _Agrobacteriumium_ sp. IFO 13140 cells under the interaction of different factors: shaking rate, initial biomass and incubation time. The immobilized cells of _Agrobacteriumium_ sp. IFO 13140 showed greater curdlan production (19.45 g/L) compared to free cells (14.50 g/L), when 50 mg of cells at 200 rpm were used, and the curdlan yield from the total sugars (glucose) was 38.90% and 29%, respectively. For each amount of cell used for immobilization and for each incubation time evaluated, the curdlan production was higher with the increase in the shaking rate. This could be a sign of mass transfer, but the shaking rate could also have been responsible for the increase in the curdlan production. Other factors could be added, such as increased oxygenation. Changes in the microenvironment caused by the matrix, as well as the easy access to and use of the substrate may have offered protection to the microorganism and provided beneficial and convenient immobilization. Previous report showed the same conclusions when loofa sponge was used as an immobilization matrix for gibberellic acid production. The authors added that the immobilization allowed for faster removal of the end products of fermentation [27]. In the ethanol production by _Saccharomyces cerevisiae_ M30, the cell regeneration and protection offered by the immobilization of cells were the main factors that acted synergistically to preserve cellular activity and provide greater stability of the immobilized cell culture compared to free cell culture [29]. The regression model used to analyze the results of the optimization of the _Agrobacteriumium_ sp. IFO 13140 immobilization in loofa sponge was adjusted properly to the experimental data, with a statistically-significant R\({}^{2}\)\({}_{\text{A}\text{D}\text{J}}\) of 0.82. According to the equation obtained for the coded variables (Equation (1)), synergistic interactions were observed among the factors evaluated, demonstrating that the isolated analysis of each variable alone is not appropriate. Figure 1: Curdlan production by _Agrobacteriumium_ sp. IFO 13140. Free cells after 48 h (open bars) and 72 h of incubation (closed bars black); immobilized cells after 48 h (closed bars gray) and 72 h of incubation (closed bars striped). Assay conditions: 10 days of incubation in production medium at 30 \({}^{\circ}\)C and 150 rpm. The error bars represent standard deviations of triplicates. \[ \begin{array}{l}\text{Curdlan (g / L) = 15.46+0.77\times incubation time + 0.16\times initial biomass + 0.36}\\ \times initial biomass^{2}+0.35\times shaking rate+1.68\times cells+0.36\times incubation time\\ \times shaking rate-0.32\times incubation time\times cells+0.81\times initial biomass\times cells\\ +0.66\times shaking rate\times cells\end{array}  \tag{1}\]  
The effects of greater magnitude in curdlan production, in decreasing order, were as follows: free or immobilized cells, interaction between cells and initial biomass (Figure 2A), incubation time and interaction between cells and shaking rate (Figure 2B). Considering the regression model (Equation (1)) and the respective contour surfaces (Figure 2), it is suggested that the best immobilization conditions were 72 h of incubation, 50 mg of cells and a shaking rate of 200 rpm. Based on the regression model used, it was found that the process of _Agrobacterium_ sp. IFO 13140 immobilization significantly increased the production in 17.27% of curdlan. The \(\varepsilon\)-poly-L-lysine production by _Kitasatospora_ spp. MY 5-36 immobilized on loofa sponge was 1.35-times greater than the production by free cells [32]. The immobilization of _Agrobacterium_ sp. IFO 13140 for 72 h showed better results compared to those for 48 h and resulted in an increase of 7.92% in curdlan production.