### Applied and Computational Mathematics

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### Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism

In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.

Mathematical Modeling, Nonlinear Differential Equations, Modified Adomian Decomposition Method, Michaelis-Menten Kinetics, Immobilized Enzyme

Krishnan Lakshmi Narayanan, Velmurugan Meena, Lakshman Rajendran, Jianqiang Gao, Subbiah Parathasarathy Subbiah. (2017). Mathematical Analysis of Diffusion and Kinetics of Immobilized Enzyme Systems that Follow the Michaelis – Menten Mechanism. Applied and Computational Mathematics, 6(3), 143-160. https://doi.org/10.11648/j.acm.20170603.13