A new graphical method for determining parameters in Michaelis-Menten-type kinetics for enzymatic lactose hydrolysis

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Abstract
A new graphical method was developed to determine the kinetic parameters in the Michaelis–Menten‐type equation. This method was then applied to studying the kinetics of lactose hydrolysis by Aspergillus niger β‐galactosidase. In this study, the reaction temperature ranged between 8 and 60°C, and the initial lactose concentration ranged between 2.5 and 20%. A kinetic model similar to the conventional Michaelis–Menten equation with competitive product inhibition by galactose was tested using this graphical method as well as a nonlinear computer regression method. The experimental data and the model fit together fairly well at 50°C. However, a relative large disparity was found for reactions at 30°C. A three‐parameter integrated model derived from the reversible reaction mechanism simulates the experimental data very well at all temperatures studied. However, this reversible reaction model does not follow the Arrhenius temperature dependence. Nevertheless, reaction rate constants for the proposed model involving the enzyme‐galactose complex (in addition to the Michaelis complex) as an intermediate in lactose hydrolysis follow the Arrhenius temperature dependence fairly well, suggesting that this model can be best used for describing the enzymatic lactose hydrolysis. The lack of fit between the model predictions and data may be largely attributed to the effects of galactose mutarotation and oligosaccharide formation during lactose hydrolysis.