Abstract
A Mathemataical model for a modified micro- cylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion Equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction. Here a new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential Equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Here we report an analytical expressions pretaining to the concentration of catechol and o-quinone and corresponding current in terms of dimensionless reaction-diffusion parameters in closed form. An excellent agreement with available limiting case is noticed.
Highlights
Microelectrodes are increasingly being used in biosensors [1,2,3]
A Mathemataical model for a modified microcylinder electrode in which polyphenol oxidase ( PPO) occurs for all values of the concentration of catechol and o-quinone is analysed. This model is based on system of reaction-diffusion equations containing a non-linear term related to Michaelis Menten kinetics of the enzymatic reaction
A new analytical technique Homotopy Perturbation Method is used to solve the system of non-linear differential equations. that describe the diffusion coupled with a MichaelisMenten kinetics law
Summary
Microelectrodes are increasingly being used in biosensors [1,2,3]. This is due to factors such as fast response times, high signal: noise ratios and the ability to operate in low conductivity media, sub-micro volume and in vivo [4]. Layer-by-layer (LbL) self assembly process is a simple technique which may be applied to a wide range of enzymes and that it is one of the few immobilization procedures which allows control over the amount and spatial distribution of the enzyme [7]. This property is important both for constructing and modeling studies of biosensors.
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