Application of third-order polynomial approximate solution to enzymatic glucose isomerization and lactose hydrolysis reactions

In this study, an approximate method based on a third-order polynomial equation was developed to describe diffusion - reaction model for immobilized enzyme system following reversible Michaelis-Menten kinetics in porous spherical particles. This kinetic model is used to describe glucose isomerization to fructose by the enzyme glucose isomerase. The approximate method is utilized to calculate the substrate concentration profile across the particle and the effectiveness factor. Although the model was derived assuming reversible Michaelis-Menten kinetics, It is able to describe other kinetics such as Michaelis-Menten with competitive product inhibition which is used to describe lactose hydrolysis to glucose and galactose by the enzyme β-galactosidase. The necessary condition for using the approximate method was presented for the two kinetic models. The prediction of the approximate method was compared with the numerical method, the approximate method agrees with the numerical method at wide range of kinetic and operating conditions.