Mathematical modeling and Kinetic analysis of β-galactosidase production by Bacillus licheniformis in batch cultivation

β-galactosidase, is one of the most important and widely used enzymes in three areas of health, Food Industry and environment, so kinetic modeling of this enzyme could be playing an important role in the optimization of its industrial production process. First, in this study kinetic of β-galactosidase production by Bacillus licheniformis bacteria in batch fermentation was evaluated during 22 hours, in the range of 20-50 g/l of initial lactose concentration as a limiting substrate, at 30 ° C. Then, with the observation of inhibition at the highest concentration of this range, logistic and Haldane kinetic models were selected to model and determine the kinetic parameters of fermentation. These models were obtained a good approximation of the experimental results of substrate utilization in all phases and microbial growth data in the exponential growth phase and the stationary phase, but minor deviations of the experimental data were observed in the decelerating growth phase. In addition, β-galactosidase activity results were in good agreement with experimental data, and the maximum deviation in this data was observed in initial concentrations 30 and 40 g/l of substrate simultaneously with the end of the exponential phase and beginning of decelerating phase of microbial growth (The fourth hours of starting inoculum). The linear regressions between experimental data and results obtained from the models, in all initial concentration of lactose and for each variable biomass concentration, substrate concentration and enzyme activity, was more than 0.95.