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The influence of the partitioning and diffusion limitations on the response of amperometric biosensors is investigated analytically and computationally using a three-compartment model: an enzyme layer, a diffusion limiting membrane and an outer diffusion layer. The biosensors are modelled by a system of reaction–diffusion equations involving a nonlinear term related to Michaelis–Menten kinetics. Exact steady state analytical solutions for the substrate and reaction product concentrations and the output current are presented for specific cases of first and zero-order reaction rates. The performance of the biosensor is numerically investigated at the transition conditions. Application of different specific types of the interface conditions, perfect contact and partition conditions, at which the steady state biosensor response is the same for both types of the interface conditions is analysed. The effective diffusion coefficients merging two diffusion layers are defined for reducing the three-compartment to the corresponding two-compartment model. The nonlinear and non-monotonic behaviour of the biosensor response is discussed. [Display omitted] • Three compartment mathematical model for amperometric enzyme-based biosensor. • Effective Biot number nonlinearly influences the biosensor response. • Influence of the type of interface conditions to the biosensor response. • Conditions for reducing the number of diffusion layers. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model of a batch stirred tank reactor based on an array of identical spherical porous microbioreactors loaded with non specific glucose dehydrogenase and oxygen reducing enzyme, i.e. laccase. The model was validated by experimental data. The microreactors (MR) are mathematically modeled by a two-compartment model, based on reaction–diffusion equations containing nonlinear terms related to the Michaelis–Menten kinetics of two enzymatic reactions with addition of the mass transport. The dynamics of oxygen concentration change is analysed numerically using the finite difference technique. The transient effectiveness factor and the process duration are investigated at different initial concentration of carbohydate (lactose) as well as at internal and external diffusion resistances. The simulation results show a non-monotonic effect of the initial concentration of lactose and nonlinear effects of the internal and external diffusion limitations on the transient effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: The peculiarities of an amperometric biosensor based on parallel substrates conversion are investigated digitally. The mathematical model of the biosensor is based on a system of non-linear reaction–diffusion equations. The model involving the enzyme and diffusion layers is defined in a one-dimensional domain. By changing input parameters the biosensor action is analysed numerically with a special emphasis to the influence of the catalytic activity and the geometry of the biosensor on its response and sensitivity. The digital simulation at the transition and steady-state conditions was carried out by using the finite difference technique. Calculations showed that the half maximal effective concentration of the substrate varies by several orders of magnitude by changing the concentrations of enzymes, the hydrogen peroxide concentration as well as the enzyme layer thickness. The behaviour of the biosensor sensitivity and the half maximal effective concentration is especially complex at large concentrations of the catalase as well as low concentrations of the peroxidase. [Copyright &y& Elsevier]

This paper presents a mathematical model of carbon nanotubes-based mediatorless biosensor. The developed model is based on nonlinear non-stationary reaction-diffusion equations. The model involves four layers (compartments): a layer of enzyme solution entrapped on a terylene membrane, a layer of the single walled carbon nanotubes deposited on a perforated membrane, and an outer diffusion layer. The biosensor response and sensitivity are investigated by changing the model parameters with a special emphasis on the mediatorless transfer of the electrons in the layer of the enzyme-loaded carbon nanotubes. The numerical simulation at transient and steady state conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data. The obtained agreement between the simulation results and the experimental data was admissible at different concentrations of the substrate. [ABSTRACT FROM AUTHOR]

In this paper the operation of an amperometric biosensor producing a chemically amplified signal is modelled numerically. The chemical amplification is achieved by using synergistic substrates. The model is based on non-stationary reaction-diffusion equations. The model involves three layers (compartments): a layer of enzyme solution entrapped on the electrode surface, a dialysis membrane covering the enzyme layer and an outer diffusion layer which is modelled by the Nernst approach. The equation system is solved numerically by using the finite difference technique. The biosensor response and sensitivity are investigated by altering the model parameters influencing the enzyme kinetics as well as the mass transport by diffusion. The biosensor action was analyzed with a special emphasis to the effect of the chemical amplification. The simulation results qualitatively explain and confirm the experimentally observed effect of the synergistic substrates conversion on the biosensor response. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional-in-space mathematical model of an amperometric biosensor based on an enzyme-loaded carbon nanotubes layer deposited on a perforated membrane. The developed model is based on non-linear non-stationary reaction-diffusion equations. By changing input parameters the output results are numerically analysed with a special emphasis to the influence of the geometry and the catalytic activity of the biosensor to its response. The numerical simulation at transition and steady state conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data. The obtained agreement between the simulation results and experimental data was admissible at different concentrations of the substrate and the mediator. [ABSTRACT FROM AUTHOR]

In this paper the response of an amperometric biosensor at mixed enzyme kinetics and diffusion limitations is modelled in the case of the substrate and the product inhibition. The model is based on non-stationary reaction–diffusion equations containing a non-linear term related to non-Michaelis–Menten kinetics of an enzymatic reaction. A numerical simulation was carried out using a finite difference technique. The complex enzyme kinetics produced different calibration curves for the response at the transition and the steady-state. The biosensor operation is analysed with a special emphasis to the conditions at which the biosensor response change shows a maximal value. The dependence of the biosensor sensitivity on the biosensor configuration is also investigated. Results of the simulation are compared with known analytical results and with previously conducted researches on the biosensors. [ABSTRACT FROM AUTHOR]

Abstract: A plate-gap model of a porous enzyme doped electrode covered by a porous membrane has been proposed and analyzed. The two-dimensional-in-space mathematical model of the plate-gap biosensor is based on the reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. The model involves four regions: the enzyme-filled gaps where the enzymatic reaction as well as the mass transport by diffusion take place, the porous membrane, a diffusion limiting region where only the mass transport by diffusion takes place, and a convective region where the analyte concentration is maintained constant. Using numerical simulation, the effect of the biosensor geometry on the biosensor response was investigated. The simulation was carried out using the finite difference technique. The mathematical model as well as numerical solution were validated using analytical solutions existing for specific cases of the model parameters. [Copyright &y& Elsevier]