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.     

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.      

The Effect of Diffusion Limitations on the Response of Amperometric Biosensors with Substrate Cyclic Conversion

A mathematical model of amperometric biosensors in which chemical amplification by cyclic substrate conversion takes place in a single enzyme membrane has been developed. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region where the analyte concentration is maintained constant. Using computer simulation the influence of the thicknesses of the enzyme layer and the diffusion region on the biosensor response was investigated. This paper deals with conditions when the mass transport in the exterior region may be neglected to simulate the biosensor response in a well-stirred solution. The digital simulation was carried out using the finite difference technique.     

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 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.     

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.     

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.     

Wavelet method for steady state immobilized enzyme kinetic model: an operational matrix approach

Journal of Mathematical Chemistry - This paper discusses a mathematical model of the diffusion and reaction in amperometric biosensor response with immobilized enzyme electrodes within a uniform...     

Analytical expression of non-steady-state concentrations and current pertaining to compounds present in the enzyme membrane of biosensor

A mathematical model of trienzyme biosensor at an internal diffusion limitation for a non-steady-state condition has been developed. The model is based on diffusion equations containing a linear term related to Michaelis-Menten kinetics of the enzymatic reaction. Analytical expressions of concentrations and current of compounds in trienzyme membrane are derived. An excellent agreement with simulation data is noted. When time tends to infinity, the analytical expression of non-steady-state concentration and current approaches the steady-state value, thereby confirming the validity of the mathematical analysis. Furthermore, in this work we employ the complex inversion formula to solve the boundary value problem.     

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.     

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.     

流动注入式乳酸生物传感器

研制了一种测定L－乳酸的生物传感器,将乳酸氧化酶（LOD）通过共价键固定在尼龙钢上制备乳酸氧化酶膜,将制得的酶膜固定在氧电极上构成乳酸生物传感器;将透析膜放在氧化酶膜上产生对L－乳酸扩散高度限制来改变该生物传感器的响应;酶膜机械强度高,在氧电极上反复装卸而不损坏,所构成的乳酸生物传感器的校正曲线的乳酸定量上限达5mmol/L,响应时间小于30s;初步血样测试的结果显示该乳酸生物传感器用于临床血乳酸的测定具有可行性。     

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.     

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 carbon nanotube based biosensor

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.     

Degradation of substrate and/or product: mathematical modeling of biosensor action

Mathematical model for evaluation of the multilayer heterogeneous biocatalytic system has been elaborated. The model consists of nonlinear system of partial differential equations with initial values and boundary conditions. An algorithm for computing the numerical solution of the mathematical model has been applied. Two cases: when product diffuses out of the biosensor and when the outer membrane is impermeable for product (product is trapped inside the biosensor) have been dealt with by adjusting boundary conditions in the mathematical model. Profiles of the impact of the substrate and product degradation rates on the biosensor response have been constructed in both cases. Value of the degradation impact has been analyzed as a function of the outer membrane thickness. The initial substrate concentration also affects influence of the degradation rates on the biosensor response. Analytical formulae, defining approximate values of relationships between the degradation rates and the outer membrane thickness or the initial substrate concentration, have been obtained. These formulae can be employed for monitoring of the biosensor response.     

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.     

Amperometric Determination of Hydrogen Peroxide and its Mathematical Simulation for Horseradish Peroxidase Immobilized on a Sonogel Carbon Electrode

A mathematical model of a horseradish peroxidase biosensor was applied to simulate the amperometric response for the detection of hydrogen peroxide. The development of the mathematical model was based on the Michaelis–Menten equation and Fick’s Second Law. The theoretical study is based on the determination of physico-chemical and geometric parameters of a horseradish peroxidase biosensor as well as the kinetic parameters of reaction mechanism such as diffusion coefficients of hydrogen peroxide, the thickness of enzymatic layer, and the Michaelis–Menten kinetic constant. The theoretical analysis provides an accurate estimate of parameters affecting the biosensor performance such as the diffusion coefficient of hydrogen peroxide in the biomembrane that was estimated to be 56?×?10^?12 m²/s. The thickness of diffusion layer was estimated to be 80–100?µm and the biomembrane 7.5?µm. The experimental and numerical values of kinetic parameters were 0.92 and 0.98?µM for the Michaelis–Menten constants and 0.010 and 0.012?µM/s for the catalytic activity rates. The model was validated for hydrogen peroxide detection and exhibited a good agreement with the experimental measurements.     

Superoxide dismutase biosensors working in non-aqueous solvent

Enzymatic electrodes based on superoxide dismutase enzyme were developed. Using the superoxide dismutase enzyme sensor assembled according to the classical model, poor results were obtained. Results were improved by adopting a new way of assembling the biosensor using a cellulose triacetate layer in which the SOD enzyme is entrapped and sandwiched between two gas-permeable membranes, or using a kappa-carrageenan gel layer entrapping the enzyme, sandwiched between an external gas permeable membrane and an internal cellulose acetate membrane, coupled in each case to the oxygen amperometric transducer. Results obtained by applying the newly developed biosensor to assaying hydrophobic compounds showing radical scavenging properties, operating in dimethylsulfoxide, were also satisfactory.     

Nanoscale patterning of solid-supported membranes by integrated diffusion barriers

Ultraflat nanostructured substrates have been used as a template to create patterned solid-supported bilayer membranes with polymerizable tethered lipids acting as diffusion barriers. Patterns in the size range of 100 nm were successfully produced and characterized. The diffusion barriers were embedded directly into the phospholipid bilayer and could be used to control the fluidity of the membrane as well as to construct isolated membrane corrals. By using nanosphere lithography to structure the templates it was possible to systematically adjust the lipid diffusion coefficients in a range comparable to those observed in cellular membranes. Single colloids applied as mask in the patterning process yielded substrates for creation of isolated fluid membrane patches corralled by diffusion barriers. Numerous potential applications for this new model system can be envisioned, ranging from the study of cellular interactions or of molecular diffusion in confined geometries to biosensor arrays.