Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes. (English) Zbl 1207.92016

Rahamathunissa, G.; Manisankar, P.; Rajendran, L.; Venugopal, K.

J. Math. Chem. 49, No. 2, 457-474 (2011).

Summary: A mathematical model of steady state mono-layer potentiometric biosensors is developed. The model is based on non stationary diffusion equations containing a nonlinear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a complex numerical method [J. H. He’s variational iteration method, Methods Appl. Mech. Eng. 167, 57ff (1998)] to solve the nonlinear differential equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Approximate analytical expressions for substrate concentration and corresponding current response have been derived for all values of the saturation parameter \(\alpha \) and the reaction diffusion parameter \(K\) using the variational iteration method. These results are compared with available limiting case results and are found to be in good agreement. The obtained results are valid for the whole solution domain.

MSC:

92C45	Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
65N99	Numerical methods for partial differential equations, boundary value problems

Keywords:

Michaelis-Menten kinetics

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