# Approximate analytical expressions for the steady-state concentration of substrate and cosubstrate over amperometric biosensors for different enzyme kinetics

M. Rasi, K. Indira, L. Rajendran

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first-order and nonlinear term related to the Michaelis-Menten and ping-pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed-form analytical solutions for the nonlinear equations under steady-state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.

Original language English 322-336 15 International Journal of Chemical Kinetics 45 5 https://doi.org/10.1002/kin.20768 Published - 01-05-2013

### Fingerprint

Enzyme kinetics
Biosensing Techniques
bioinstrumentation
Biosensors
enzymes
kinetics
Substrates
Enzymes
Nonlinear equations
MATLAB
nonlinear equations
mathematical models
Theoretical Models
Mathematical models
Computer simulation
simulation

### All Science Journal Classification (ASJC) codes

• Biochemistry
• Physical and Theoretical Chemistry
• Organic Chemistry
• Inorganic Chemistry

### Cite this

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abstract = "Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first-order and nonlinear term related to the Michaelis-Menten and ping-pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed-form analytical solutions for the nonlinear equations under steady-state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.",
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In: International Journal of Chemical Kinetics, Vol. 45, No. 5, 01.05.2013, p. 322-336.

Research output: Contribution to journalArticle

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T1 - Approximate analytical expressions for the steady-state concentration of substrate and cosubstrate over amperometric biosensors for different enzyme kinetics

AU - Rasi, M.

AU - Indira, K.

AU - Rajendran, L.

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N2 - Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first-order and nonlinear term related to the Michaelis-Menten and ping-pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed-form analytical solutions for the nonlinear equations under steady-state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.

AB - Mathematical models of amperometric biosensors at three basic types of enzyme kinetics in nonstationary diffusion conditions are discussed. The models are based on nonstationary diffusion equations containing a linear term related to the first-order and nonlinear term related to the Michaelis-Menten and ping-pong of the enzymatic reaction mechanism. In this paper, we obtain approximate closed-form analytical solutions for the nonlinear equations under steady-state condition by using the homotopy analysis method. Analytical expressions for concentrations of substrate and cosubstrate and corresponding current response have been derived for all possible values of parameters. Furthermore, in this work, the numerical simulation of the problem is also reported using Scilab/MATLAB program. An agreement between analytical and numerical results is noted.

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