Kinetic mechanism for modelling of electrochemical mediatedenzyme reactions and determination of enzyme kinetics parameters.

The non-steady state current density for reversible electrochemical coupled with a homogeneous enzyme reaction and a constant potential is presented in this manuscript for the first time. The model is based on non-stationary diffusion equations with semi infinite boundary condition containing a nonlinear term related to the kinetics of an enzymatic reaction. The nonlinear differential equation for the mediator is solved for reversible homogeneous enzyme reaction. Approximate analytical expressions for the concentration of the mediator and corresponding current for non-steady state conditions are derived. Kinetic parameters are also determined such as Michaelis–Menten constants for substrate (KMS) and mediator (KMM) as well as catalytic rate constant (kcat). Upon comparison, we found that the analytical results of this work are in excellent agreement with the numerical (Matlab program) and existing limiting case results. The significance of the analytical results has been demonstrated by suggesting two new graphical procedures for estimating the kinetic parameters from the current densities

Theoretical analysis of concentration of lactose hydrolysis in a packed bed reactor using immobilized β-galactosidase

A theoretical analysis of concentration of lactose hydrolysis in a packed bed reactor using immobilized β-galactosidase was discussed. The model is based on system of reaction diffusion equations containing a non-linear term related to Michalies-Menten kinetics of enzymatic reaction. In this paper, we obtained approximate analytical expressions for the concentrations of lactose and galactose for an isothermal reaction occurring under diffusive conditions in a packed bed tubular reactor containing immobilized enzyme using a new approach of homotopy perturbation method. The obtained analytical results were found to be in good agreement with the simulation results. Keywords: Mathematical modeling, Lactose hydrolysis, Immobilized enzyme, Michaelis–Menten kinetic