An efficient method for finding analytical expressions of substrate concentrations for different particles in an immobilized enzyme system

Analysis of the hysteresis of the enzyme-substrate due to enzyme flow calorimetry is presented based on the mathematical modeling of an immobilized enzyme using kinetic and diffusion parameters. The model is represented by ordinary differential equations containing a nonlinear term representing the substrate inhibition kinetics of the enzymatic reaction. In this paper, analytical expressions of substrate concentration for planar, cylindrical, and spherical particles at steady state condition are derived using a new analytical method. To confirm the validity and accuracy of the proposed method, the results will be compared with those obtained by the well-established homotopy perturbation method and the numerical results obtained by the highly-reputed fourth order Runge-Kutta method. Also, the results of the proposed method will be used to conduct a sensitivity analysis to understand the effect of parameters on concentration profiles.