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.      

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.     

Immobilised tyrosinase-based biosensor for the detection of tea polyphenols

An amperometric principle-based biosensor containing immobilized enzyme tyrosinase has been used for detection of polyphenols in tea. The immobilized tyrosinase-based biosensor could detect tea polyphenols in the concentration range 10–80 mmol L⁻¹. Immobilization of the enzyme by the crosslinking method gave good stable response to tea polyphenols. The biosensor response reached the steady state within 5 min. The voltage response was found to have a direct linear relationship with the concentration of polyphenols in black tea samples. Enzyme membrane fouling was observed with number of analyses with a single immobilised enzyme membrane. The tyrosinase-based biosensor gave maximum response to tea polyphenols at 30°C. The optimum pH was 7.0. This biosensor system can be applied for analysis of tea polyphenols. Variation in the biosensor response to black tea infusions gave an indication of the different amounts of theaflavins in the samples, which is an important parameter in evaluating tea quality. A comparative study of the quality attributes of a variety of commercially available brands of tea were performed using the biosensor and conventional analytical techniques such as spectrophotometry.     

Electrochemical detection of phenolic compounds using composite film of multiwall carbon nanotube/surfactant/tyrosinase on a carbon paste electrode

A new tyrosinase-based biosensor was developed for detection of phenolic compounds using composite film of multiwall carbon nanotube (MWCNT)/dimethylditetradecylammonium bromide (DTDAB)/tyrosinase (Tyr) on a Nafion-incorporated carbon paste electrode. The biosensor showed a sensitive electrochemical response to the reduction of the oxidation products of different phenolic compounds (phenol, catechol, p-cresol, and p-chlorophenol) by dissolved O₂ in the presence of the immobilized enzyme. The effects of pH, operating potential, MWCNT concentration, and the DTDAB/Tyr ratio on electrochemical response were explored for optimum analytical performance. The biosensor exhibited a linear response range of 1.5–25.0, 2.0–15.0, 2.0–15.0, and 2.5–25.0 μM and sensitivity of 2,900, 3,100, 3,100, and 1,500 μA/mM for phenol, catechol, p-cresol, p-chlorophenol, respectively. In addition, the response of the enzyme electrode showed Michaelis–Menten behavior at concentrations of the phenolic compounds higher than 5.0 μM. The stability and the application of the biosensor were also evaluated.     

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.     

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 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.     

Development of a new biosensor for superoxide radicals

A superoxide dismutase (SOD) biosensor for determination of superoxide radicals has been developed by immobilization of superoxide dismutase within gelatin (G) on a Pt electrode surface. The properties of the biosensor have been investigated and optimum conditions–enzyme concentration, glutaraldehyde concentration, and pH–were determined. The response of the G-SOD biosensor was proportional to concentration and the detection limit was 0.01 mmol L⁻¹ at a signal-to-noise ratio of 3. The biosensor retained 89% and 60% of its sensitivity after use for three and four weeks, respectively. Immobilization of SOD on gelatin provides a biocompatible microenvironment around the enzyme and stabilizes the activity of the enzyme very efficiently. The superoxide dismutase biosensor was used to determine the antioxidant properties of acetylsalicylic acid-based drugs and the anti-radical activity of healthy and cancerous human brain tissues.     

On the origin of Turing instability

A reaction–diffusion system consisting of one, two or three chemical species and taking place in an arbitrary number of spatial dimensions cannot exhibit Turing instability if none of the reaction steps express cross‐inhibition. A corollary of this result – obtained by elementary calculations – underlines the importance of nonlinearity in the formation of stationary structures, a kind of self‐organization on a chemical basis. Relations to global stability of reaction–diffusion systems, and results on multispecies systems are also mentioned. The statements are not restricted to mass action type models. As a by‐product, the solution of a basic inverse problem of formal kinetics is also presented which extends a previous result by Hárs and Tóth (1981) to models with arbitrary – including rational – functions as reaction rates so often occurring, e.g., in enzyme kinetics. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling of nonlinear boundary value problems in enzyme-catalyzed reaction diffusion processes

A mathematical model of steady state mono-layer potentiometric biosensor is developed. The model is based on non stationary diffusion equations containing a non linear term related to Michaelis-Menten kinetics of the enzymatic reaction. This paper presents a complex numerical method (He’s variational iteration method) to solve the non-linear differential equations that describe the diffusion coupled with a Michaelis-Menten kinetics law. Approximate analytical expressions for substrate concentration and corresponding current response have been derived for all values of saturation parameter α and reaction diffusion parameter K using variational iteration method. These results are compared with available limiting case results and are found to be in good agreement. The obtained results are valid for the whole solution domain.     

Amperometric biosensor based on tyrosinase immobilized in hydrotalcite-like compounds film for the determination of polyphenols

A tyrosinase (Tyr) biosensor has been constructed by immobilizing tyrosinase on the surface of Mg–Al–CO₃ hydrotalcite-like compound film (HTLc) modified glassy carbon electrode (GCE) for the determination of polyphenols. The negatively charged tyrosinase was adsorbed firmly on the surface of a positively charged HTLc/GCE by electrostatic interactions and retained its activity to a great degree. The modified electrode was characterized by cyclic voltammetry and AC impedance spectra. Polyphenols were determined by a direct reduction of biocatalytically generated quinone species. The different parameters, including pH, temperature, and enzyme loading were investigated and optimized. Under the optimum conditions, Tyr/HTLc electrode gave a linear response range of 3–300, 0.888–444, and 0.066–396 μM with a detection limit (S/N = 3) of 0.1, 0.05, and 0.003 μM for catechol, caffeic acid, and quercetin, respectively. In addition, the repeatability and stability of the enzyme electrode were estimated. Total polyphenol contents of real samples were also determined to study the potential applicability of the Tyr/HTLc/GCE biosensor.     

Glucose Biosensor Using Glucose Oxidase Immobilized in Polyaniline

A biosensor for glucose utilizing kinetics of glucose oxidase (EC 1.1.3.4.) was developed. The enzyme was immobilized on polyaniline by covalent bonding, using glutaraldehyde as a bifunctional agent. The system showed a linear response up to 2.2 mM of glucose with a response time of 2.5–4.0 min. In addition, the immobilized enzyme had a higher activity between pH 6.5 and 7.5. The system retained 50% of its activity after 30 d of daily use. The optical absorption spectra of the polyaniline/glucose oxidase electrode after glucose had been added to the buffer solution showed that the absorption band around 800 nm had changed considerably when glucose was allowed to react with the electrode. This optical variation makes polyaniline a very promising polymer for use as a support in optical sensor for clinical application.     

Apparent Michaelis constant of the enzyme modified porous electrode

Plate-gap model of enzyme doped porous electrode was utilized in order to calculate apparent Michaelis constants () and apparent maximal currents () of modeled amperometric biosensor for the wide range of given reaction/diffusion parameters. It was found that of plate-gap biosensor linearly depends on when rates of enzymatic reaction are lower than critical. Theoretically predicted linear correlation between apparent parameters was observed experimentally for the case of carbon paste electrodes, which were modified by PQQ-dependent alcohol dehydrogenases. At overcritical rates (or apparent maximal currents), is practically independent on Michaelis constant of soluble enzyme. Therefore, apparent Michaelis constant can be regarded as biosensor’s topology representing parameter which, in fact, is not related to the specificity of enzyme kinetics. High and rate-independent values of indicate that reaction proceeds at substrate-exposed top layer of the gap. In this case, reaction–diffusion system formally is stratified into separate reaction (top) and diffusion (bottom) zones. Topology of such reaction–diffusion system reminds “inverted” planar electrode, which contains diffusion layer below reaction layer. The net effect of plate-gap topology of working electrode on apparent Michaelis constant is similar to the effect of diffusion layer covering enzymatic planar electrode.     

Bioelectrochemical response of a choline biosensor fabricated by using polyaniline

On the basis of the isoelectric point of an enzyme and the doping principle of conducting polymers, choline oxidase was doped in a polyaniline film to form a biosensor. The amperometric detection of choline is based on the oxidation of the H₂O₂ enzymatically produced on the choline biosensor. The response current of the biosensor as a function of temperature was determined from 3 to 40°C. An apparent activation energy of 22.8 kJ·mol⁻¹ was obtained. The biosensor had a wide linear response range from 5 × 10⁻⁷ to 1 × 10⁻⁴ M choline with a correlation coefficient of 0.9999 and a detection limit of 0.2 μM, and had a high sensitivity of 61.9 mA·M⁻¹·cm⁻² at 0.50 V and at pH 8.0. The apparent Michaelis constant and the optimum pH for the immobilized enzyme are 1.4 mM choline and 8.4, respectively, which are very close to those of choline oxidase in solution. The effect of selected organic compounds on the response of the choline biosensor was studied.     

The Construction of Glucose Biosensor Based on Platinum Nanoclusters—Multiwalled Carbon Nanotubes Nanocomposites

One-step synthesis method was proposed to obtain the nanocomposites of platinum nanoclusters and multiwalled carbon nanotubes (PtNCs–MWNTs), which were used as a novel immobilization matrix for the enzyme to fabricate glucose biosensor. The fabrication process of the biosensor was characterized by cyclic voltammetry, electrochemical impedance spectroscopy, atomic force microscopy and scanning electron microscope. Due to the favorable characteristic of PtNCs–MWNTs nanocomposites, the biosensor exhibited good characteristics, such as wide linear range (3.0 μM–12.1 mM), low detection limit (1.0 μM), high sensitivity (12.8 μA mM⁻¹), rapid response time (within 6 s). The apparent Michaelis–Menten constant ( K_m^\textapp K_m^{\text{app}} ) is 2.1 mM. The performance of the resulting biosensor is more prominent than that of most of the reported glucose biosensors. Furthermore, it was demonstrated that this biosensor can be used for the assay of glucose in human serum samples.     

A solid-state pH transducer fabricated from a self-plasticized methacrylic-acrylic membrane for potentiometric acetylcholine chloride biosensor

A solid-state pH sensor based on a self-plasticizing film of methacrylic-acrylic copolymer was developed. The sensor was able to detect changes in pH after tridodecylamine ionophore was immobilized together with a lipophilic anionic salt. The pH sensor exhibited almost a Nemstian response (57.6 mV pH⁻¹) with a linear pH response range of 6–10. It demonstrated a fast response (<2 min) to changes in pH and good selectivity against other common cations such as sodium, potassium, magnesium, lithium, and calcium. The sensor has a shelf life of at least 30 days without an obvious deterioration in response. By depositing a layer of poly(hydroxylethymethacrylate) immobilized with enzyme acetylcholinesterase on top of the pH selective methacrylic-acrylic film, the pH sensor was able to detect acetylcholine chloride (AChCl). The linear response range of the potentiometric biosensor to AChCl was dependent on the buffer concentrations used, and for a buffer concentration less than 1 mM, the linear response range obtained was 3.98–31.62 μM. The text was submitted by the authors in English     

Development of a novel enzyme reactor and application as a chemiluminescence flow-through biosensor

A novel enzyme reactor was prepared using calcium alginate fiber (CAF) and amine-modified nanosized mesoporous silica (AMNMS) as a support. Combination of the adsorption of the enzyme on AMNMS with the cage effect of the polymer greatly increases the catalytic activity and the stability of the immobilized enzyme. It was shown that the lifetime, stability, and catalytic activity of the enzyme reactor were greatly improved by incorporating AMNMS into CAF to efficiently encapsulate the enzyme. Glucose oxidase was chosen as a model enzyme to explore the possibility of using CAF–AMNMS as a matrix for enzyme immobilization in the design of a chemiluminescence (CL) flow-through biosensor. The sensitivity of the flow-through biosensor combined with a novel luminol-diperiodatonickelate CL system was higher than for other reported CL biosensors. The proposed biosensor exhibits short response time, easy operation, long lifetime, high catalytic activity, high sensitivity, and simple assembly.     

Analysis of a theoretical model for anisotropic enzyme membranes application to enzyme electrodes

A theoretical model of diffusion and reaction in an anisotropic enzyme membrane is presented with particular emphasis on the application of such membranes in enzyme electrodes. The dynamic response of systems in which the kinetics are linear, which comprises the practical operating regime for enzyme electrodes in analysis, is investigated via an analytic solution of the governing differential equations. The response is presented as a function of a single dimensionless group, Μ, that is the membrane modulus.     

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.