Estimation of kinetic parameters using mathematical modeling of beta-galactosidase production under rapid growth of Bacillus licheniformis

Background & objectives: β-galactosidase is well known as an enzyme used in the food industry and health domains. Today special attention is paid to its production, therefore determining the appropriate kinetic model can be essential for optimizing its production process.
Material & Methods: The batch fermentation was performed in four different concentrations of lactose (20, 30, 40, and 50 g L^-1) as an inducer substrate to model and determine the kinetic parameters of β-galactosidase production by Bacillus licheniformis. The kinetic parameters were evaluated by the simultaneous solution of one of the Moser or logistic models with the set of differential equations in MATLAB software.
Results: Lactose (as substrate) has an inhibitory effect on enzyme production in the concentration of 50 g L^-1. More than 83% of the final biomass was produced in just the first 8 hours of incubation. Due to the inhibitory effect of substrate on growth, Moser and Logistic models were used to express specific growth rates. Malthus, Luedeking–Piret, and substrate consumption differential equations were used to express the bacterial growth rate, enzyme production, and substrate utilization rate, respectively. The high accuracy of the results (R²> 0.94) showed that the models have a reliable estimate of the experimental results to describe the kinetic of the β-galactosidase production process.
Conclusion: Scientific analysis of kinetic parameters showed the predictable behavior of B.licheniformis in enzyme production from rapid growth to long decelerating phase.