## 3 Results and Discussion
### Correlation Between Cells Growth and Its Production of CMCase  
The correlation between the dry cells weights during the cell growth of _E. coli_ KACC 91335P and its production of CMCase was analyzed using SigmaPlot (Systat Software Inc., San Jose, CA, USA) for Windows Version 10.0. A quadratic regression analysis of data obtained from experiments without shifts in optimal conditions of the aeration rate and/or agitation speed gave the second-order polynomial Equation (4), which represented the correlation between the cell growth (X) and its production of CMCase (Y) as shown in Figure 4a.  
\[\mathrm{Y}=1132.9-77.8\mathrm{X}-1.2\mathrm{X}^{2} \tag{4}\]  
The multiple correlation coefficient (\(R^{2}\)) of above regression equation was 0.9751, which can explain the 97.51% variation in the response. Its value of the adjusted coefficient of determination (Adj. \(R^{2}\) = 0.9442) was relatively high to advocate for this model's significance [26]. This model with the multiple correlation and adjusted coefficients indicated that the above equation was adequate for predicting the production of CMCase by _E. coli_ KACC 91335P without shifts in optimal conditions of the agitation speed and/or aeration rate. Based on the regression equation of these experimental data, the optimal conditions of the aeration rate and agitation speed for the cell growth of _E. coli_ KACC 91335P were proven to be different from those for its production of CMCase. A higher cell growth of _E. coli_ KACC 91335P resulted in a lower production of CMCase.  
However, the quadratic regression analyses of the correlation between the cell growth and its production of CMCase with shifts in optimal conditions of the aeration rate and/or agitation speed were different from those without shifts in optimal conditions of the aeration rate and/or agitation speed. The higher cell growth with shifts in the aeration rate and/or agitation speed resulted in the enhanced production of CMCase by _E. coli_ KACC 91335P, as shown in Figure 4b-d. The multiple correlation coefficients (\(R^{2}\)) obtained from the experimental data with shifts in optimal conditions of the aeration rate and/or agitation speed at 24, 36 and 48 h were 0.7753, 0.9376 and 0.8820, respectively. The second-order polynomial Equation (5) from the correlation between the cell growth (X) and its production of CMCase (Y) with shifts in optimal conditions of the aeration rate and/or agitation speed at 36 h was as follows:  
\[\mathrm{Y}=-2780.4+1305.9\mathrm{X}-113.4\mathrm{X}^{2} \tag{5}\]  
The CMCase produced by a wild type, _B. velezensis_ A-68, was a growth-associated product, whereas that by its recombinant, _E. coli_ KACC 91335P, was a mixed-growth-associated product [7; 16]. The production of CMCase by _E. coli_ KACC 91335P was partially correlated with its cell growth. Owing to the mixed-growth-associated production of CMCase by _E. coli_ KACC 91335P, shifts in the optimal conditions of the aeration rate and/or agitation speed from the cell growth to its production of CMCase at the mid-log phase of cell growth resulted in relatively higher cell growth, which in turn enhanced the production of CMCase.