Mechanisms controlling the sensitivity of amperometric biosensors in flow injection analysis systems

This paper numerically investigates the sensitivity of an amperometric biosensor acting in the flow injection mode when the biosensor contacts an analyte for a short time. The analytical system is modelled by non-stationary reaction-diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of an enzymatic reaction. The mathematical model involves three regions: the enzyme layer where enzymatic reaction as well as the mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region. The biosensor operation is analysed with a special emphasis to the conditions at which the biosensor sensitivity can be increased and the calibration curve can be prolonged by changing the injection duration, the permeability of the external diffusion layer, the thickness of the enzyme layer and the catalytic activity of the enzyme. The apparent Michaelis constant is used as a main characteristic of the sensitivity and the calibration curve of the biosensor. The numerical simulation was carried out using the finite difference technique.     

A simple model for an amperometric channel biosensor

A simple model is presented for the channel biosensor where an oxidase enzyme layer is located upstream of a detector electrode. In this model the enzyme kinetics are restricted to the linear region. The model enables the elucidation of the parameters important in tuning the response of the biosensor. Two extreme regimes of operation are identified; the kinetically limited and mass transport limited regimes both provide features which overcome reproducibility problems associated with the classical enzyme electrode geometry.     

Modelling synergistic action of laccase-based biosensor utilizing simultaneous substrates conversion

The response of a laccase-based amperometric biosensor that acts in a synergistic manner was modelled digitally. A mathematical model of the biosensor is based on a system of non-linear reaction diffusion equations. The modelling biosensor comprises three compartments, an enzyme layer, a dialysis membrane and an outer diffusion layer. By changing input parameters the biosensor action was analysed with a special emphasis to the influence of the species concentrations on the synergy of the simultaneous substrates conversion. The digital simulation was carried out using the finite difference technique.     

Which Parameters Affect the Response of the Channel Biosensor?

The important parameters in defining the response of the portable channel biosensor described previously are explored by connecting the portable flow cell to a gravity feed flow system and using a highly defined enzyme immobilization protocol which ensures the enzyme reaction is a surface reaction. The enzyme glucose oxidase (GOD) was immobilized by covalent attachment to a self‐assembled monolayer modified gold surface. As a glucose solution flowed down the rectangular duct defined by the flow cell, it passed over the enzyme layer where the enzyme reaction produced hydrogen peroxide. The hydrogen peroxide was swept further downstream to the detector electrode. The response of such an enzyme electrode was shown to be limited by mass transport of the cosubstrate oxygen to the enzyme layer. Increasing the amount of oxygen in the sample meant the response of the biosensor became limited by the enzyme kinetics. The influence of parameters such as flow rate, height of the channel, enzyme layer length and the gap between the enzyme layer and the detector electrode were explored.     

Modelling of Amperometric Biosensors with Rough Surface of the Enzyme Membrane

A two-dimensional-in-space mathematical model of amperometric biosensors has been developed. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction. The model takes into consideration two types of roughness of the upper surface (bulk solution/membrane interface) of the enzyme membrane, immobilised onto an electrode. Using digital simulation, the influence of the geometry of the roughness on the biosensor response was investigated. Digital simulation was carried out using the finite-difference technique.     

Computational modelling of amperometric biosensors in the case of substrate and product inhibition

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.     

Mathematical modeling of the action of biosensor possessing variable parameters

Electrochemical biosensor containing flat semi-permeable membrane covering enzyme-containing layer has been investigated. Mathematical modeling of the action modes of electrochemical biosensors with outer diffusion membrane was performed. Operation of the biosensor under the conditions when the permeability of the membrane and the activity of the biocatalytic layer depend on the parameters of the probe has been examined. The pH and temperature were selected as the main parameters which often affect the action of biosensors. A set of parameters was selected when the biosensor operates in kinetic and diffusion modes of action. The response time of the biosensor was shown to be sensitive to the mode of the biosensor action especially in the boundary region of the biosensor action. The linearity of the biosensor (the linear dependence of the biosensor response on the substrate concentration) in the deep diffusion mode can be increased by several magnitudes, whereas the response time increases only several times.     

Computational Modelling of the Behaviour of Potentiometric Membrane Biosensors

This paper presents a mathematical model of a potentiometric biosensor based on a potentiometric electrode covered with an enzyme membrane. The model is based on the reaction–diffusion equations containing a non-linear term related to theMichaelis–Menten kinetics of the enzymatic reaction. Using computer simulation the influence of the thickness of the enzyme membrane on the biosensor response was investigated. The digital simulation was performed using the finite difference technique. Results of the numerical simulation were compared with known analytical solutions.      

Mathematical Model and Numerical Simulation of Conductometric Biosensor of Urea

In this article, a mathematical model was developed to describe and optimize the configuration of the urea biosensor. The biosensor is based on interdigitated gold microelectrodes modified with a urease enzyme membrane. The model presented here focuses on the enzymatic reaction and/or diffusion phenomena that occur in the enzyme membrane and in the diffusion layer. Numerical resolution of differential equations was performed using the finite difference technique. The mathematical model was validated using experimental biosensor data. The responses of the biosensor to various conditions were simulated to guide experiments, improve analytical performance, and reduce development costs.     

Mathematical Modelling of a Non‐enzymatic Amperometric Electrochemical Biosensor for Cholesterol

Thickness of the electro‐polymerized layer grown on a substrate and used as the recognition element for the analyte is critical to measuring the response of a biosensor, with high sensitivity and accuracy. However, it is difficult to control the thickness during synthesis. A mathematical model is developed in this study that considers thickness of the electro‐polymerized layer in simulating the electrochemical response of a non‐enzymatic biosensor for cholesterol in blood. The model includes transient kinetics and one‐dimensional diffusion of the analyte in the poly‐methyl orange (PMO) recognition layer electrochemically grown on the electrode. The governing partial differential equations resulting from the species conservation balances in the PMO layer are numerically solved. Time and spatial concentration profiles of the analyte in the PMO layer are determined. Model predictions are calibrated with the experimental data for different PMO thicknesses. Interestingly, model predictions show a linear response over the calibrated concentration range of cholesterol for all PMO layer thicknesses. Based on the chronoamperometry measurements, the model predictions for the cholesterol concentrations measured in the laboratory samples were also found to be remarkably accurate. This is the first mathematical model developed to understand the transport and kinetics of an analyte in the electro‐polymerized layer used as the recognition element of a non‐enzymatic biosensor.     

Numerical simulation of the ordered catalyst layer in cathode of proton exchange membrane fuel cells

A steady-state, one-dimensional numerical model based on cylindrical electrode structure is presented to analyze the performance of the ordered cathode catalyst layer in Proton Exchange Membrane Fuel Cells. The model equations account for the Tafel kinetics of oxygen reduction reaction, proton migration, oxygen diffusion in the cylindrical electrolyte and the gas pores, oxygen distribution at the gas/electrolyte interface. The simulation results reveal that ordered catalyst layers have better performance than conventional catalyst layers due to the improvements of mass transport and the uniformity of the electrochemical reaction rate across the whole width of the catalyst layer. The influences of oxygen diffusivity in gas phase and electrolyte, and the proton conductivity have been shown. The limitation by oxygen diffusion in gas phase drives the active region of the catalyst layer to the catalyst layer/gas diffuser interface. The limitation by proton migration confines the active region of the catalyst layer to the membrane/catalyst layer interface. The limitation due to oxygen diffusion in electrolyte film maintains the uniform distribution of the active region throughout the ordered catalyst layer.     

The effect of membrane permeability on the response of a catechol biosensor

A mathematical model is developed for the simulation of the amperometric response of a biosensor for catechol using polyphenoloxidase. The model is based on transient diffusion equations containing nonlinear terms of Michaelis-Menten for two space regions: the diffusion layer and the biomembrane containing the immobilized enzyme. The set of partial derivatives of nonlinear equations and the corresponding boundary and initial conditions was solved using the implicit finite difference technique. This numerical solution was then exploited to study the effects of permeability and thickness of the biomembrane on the maximum response of the reduction current and the amplification factor corresponding to the maximum of catalytic activity of the enzyme. This amplification factor increases with the thickness of the biomembrane while permeability is weak. In the case of the low initial concentrations (10^?6 to 5.10^?4 mM), its value is maximal and remains independent of substrate concentration. Also, the amplification factor is more significant when the diffusion resistance is more important, i.e. for high thicknesses or weak permeabilities of the biomembranes.     

Modelling Dynamics of Amperometric Biosensors in Batch and Flow Injection Analysis

A mathematical model of amperometric biosensors has been developed. The model is based on non-stationary diffusion equations containing a non-linear term related to Michaelis–Menten kinetic of the enzymatic reaction. Using digital simulation, the influence of the substrate concentration as well as maximal enzymatic rate on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique. The model describes the biosensor action in batch and flow injection regimes.     

Performance of a polymer electrolyte fuel cell with long oxygen channel

Along-the-channel analytical model of a polymer electrolyte fuel cell is developed. The model takes into account oxygen diffusion in backing layer, diffusion and electroosmotic transport of water in membrane and oxygen depletion in a feed channel. Voltage current curve of a cell, which takes into account all these processes is obtained and expression for limiting current density is derived. The latter shows, that cell performance is described by design parameters, which are combinations of geometrical and working parameters. The region of optimal cell performance on the plane of the design parameters is determined.     

Mathematical modeling of biosensor action in the region between diffusion and kinetic modes

We describe the action of electrochemical enzyme-based biosensor by applying mathematical modeling. We consider two types of biosensors: a biosensor containing a single heterogeneous enzyme layer and biosensor containing an additional protecting polymer-based layer. The initial parameters of the biosensor were selected on the basis of typical immobilized glucose oxidase-based electrochemical biosensor. A phenomenon of the accumulation of the electrochemically active product inside the biocatalytic layer was evaluated. It was shown that accumulation of the product can increase sensitivity of the biosensor no more than 2.6 times. Due to the asymmetric distribution of the electrochemically active product inside the enzyme-containing membrane and asymmetric diffusion of the substrate, it was shown that the thickness of the membrane possesses an optimal value. For the selected set of initial parameters, the optimal thickness of the enzyme-containing layer was 2.9–4.5  $\upmu $ m. Real profiles of the impact of the thickness of the membranes were evaluated. A method for the evaluation of acceptable fluctuations of the membrane diffusion parameters on biosensor response was created, and the profiles of the dependence were calculated. These dependencies can be used for development of the software for biosensor monitoring.     

Role of Hydrodynamic Conditions in the Distribution of Anodic Dissolution Rates in Cavity Etching Regions during Electrochemical Micromachining of Partially Insulated Surfaces

Experimental study of the distribution of local rates of electrochemical micromachining in the presence of photoresist masks in various hydrodynamic conditions (macroscopically nonuniform rotating disk electrode, sprayer flow, an electrode placed into a cell with chaotic bulk electrolyte mixing) shows that the maximum etching localization is achieved at the control of the dissolution rate by the mass transport rate (at achieving the anodic limiting current). The localization enhancement as compared to the primary current distribution takes place in the case of a turbulent flow at hydrodynamic conditions where the removal of dissolution products from the undercutting region is hindered. These conditions (electrochemical reaction limited by the ion mass transport rate, high resistance to the mass transport in the undercutting region) are necessary for the localization enhancement using a pulsed anodic–cathodic treatment.     

电化学酶传感器在环境污染监测中的应用

电化学酶传感器是一种应用广泛的生物传感器,它将酶及其底物相互作用的特异性与电化学的强大分析功能相结合,已经被广泛应用于药理学、临床、食品、农业以及环境监测中。制备电化学酶传感器的关键步骤是酶的固定化,选择用于制备电化学酶传感器的合适的酶固定化方法,在传感器电子转移动力学、稳定性和重现性等方面起着主要作用。本文在阐述电化学酶传感器工作原理的基础上,简要介绍了用于电化学酶传感器制备过程中的酶固定化方法,重点讨论了电化学酶传感器在监测环境中广泛存在的有机污染物、无机污染物和重金属等方面的应用,并对电化学酶传感器的发展方向进行了展望。     

An Analysis of Mixtures Using Amperometric Biosensors and Artificial Neural Networks

This paper presents a sensor system based on a combination of an amperometric biosensor acting in batch as well as flow injection analysis with the chemometric data analysis of biosensor outputs. The multivariate calibration of the biosensor signal was performed using artificial neural networks. Large amounts of biosensor calibration as well as test data were synthesized using computer simulation. Mathematical and corresponding numerical models of amperometric biosensors have been built to simulate the biosensor response to mixtures of compounds. The mathematical model is based on diffusion equations containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. The principal component analysis was applied for an optimization of calibration data. Artificial neural networks were used to discriminate compounds of mixtures and to estimate the concentration of each compound. The proposed approach showed prediction of each component with recoveries greater that 99% in flow injection as well as in batch analysis when the biosensor response is under diffusion control.     

Computational Modelling of Biosensors with Perforated and Selective Membranes

This paper presents a two-dimensional-in-space mathematical model of amperometric biosensors with perforated and selective membranes. The model is based on the diffusion equations containing a non-linear term of the Michaelis–Menten enzymatic reaction. Using numerical simulation of the biosensors action, the influence of the geometry of the perforated membrane on the biosensor response was investigated. The numerical simulation was carried out using finite-difference technique. The calculations demonstrated non-linear and non-monotonous change of the biosensor steady-state current at various degree of the surface of the perforated membrane covering. The non-monotonous behaviour of the biosensor response was also observed when changing the thickness of the perforated membrane.     

Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions

The paper presents nonlinear model which stands for effective digital simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep and cyclic voltammetry conditions. The model is based on a system of diffusion equations, also involving the Nernst diffusion layer. The mass transport is assumed to be regular in the entire diffusion space. The influence of the thickness of the resist layer on the behavior of the partially blocked electrodes is investigated. The agreement between the theoretical results and experimental ones is obtained to be admirable for several model electrodes with different blocking degree.