Romas Baronas

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.

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.

Modelling Amperometric Biosensors Based on Chemically Modified Electrodes

The response of an amperometric biosensor based on a chemically modified electrode was modelled numerically. A mathematical model of the biosensor is based on a system of non-linear reaction-diffusion equations. The modelling biosensor comprises two compartments: an enzyme layer and an outer diffusion layer. In order to define the main governing parameters the corresponding dimensionless mathematical model was derived. The digital simulation was carried out using the finite difference technique. The adequacy of the model was evaluated using analytical solutions known for very specific cases of the model parameters. By changing model parameters the output results were numerically analyzed at transition and steady state conditions. The influence of the substrate and mediator concentrations as well as of the thicknesses of the enzyme and diffusion layers on the biosensor response was investigated. Calculations showed complex kinetics of the biosensor response, especially when the biosensor acts under a mixed limitation of the diffusion and the enzyme interaction with the substrate.

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.

Modelling a biosensor based on the heterogeneous microreactor

Modelling of the amperometric biosensors based on carbon paste electrodes encrusted with a single heterogeneous microreactor is analyzed. The microreactor was constructed from CPC‐silica carrier and was loaded with glucose oxidase. The model is based on non‐stationary diffusion–reaction equations containing a non‐linear term related to the enzymatic reaction. A homogenization process having an effective algorithm for the digital modelling of the operation of the microreactor is proposed. The influence of the size, geometrical form, and the position of a microreactor on the operation of biosensors are investigated.

A multi-cellular network of metabolically active E. coli as a weak gel of living Janus particles

Bioluminescence images of nutrient rich liquid cultures of lux-gene reporter Escherichia coli were recorded for several hours after being placed into small diameter cylindrical containers (glass tubes and microtiter plate wells). It was found that luminous cells distribute near the three-phase contact line forming an irregular array of clumps, channels and plumes at the solid–liquid interface. The experimentally observed quasi-2-dimensional spatiotemporal patterns (‘venation patterns’) were simulated fairly well by the mean field Keller–Segel equations of chemotactic aggregation. The equations use a logistic cell growth term whose carrying capacity depends on oxygen concentration. The experimental and numerical results are interpreted as follows: (1) the patterns of bioluminescence form due to arrested phase separation in the culture; (2) the luminous phase formed along the upper part of the solid–liquid interface is a weak gel-like network of metabolically active bacteria which exhibit ligand–receptor type cell–cell adhesion and high rates of oxidative phosphorylation; (3) active bacteria in this gel can be viewed as self-generated Janus particles, i.e., polarized particles whose surface is divided into two chemically varying regions, the adhering region and the non-adhering region; (4) the life-time of the metabolically active bacterium (living Janus particle) in the weak gel phase is estimated to be ∼25 s; (5) the observed network of luminous bacteria can be viewed as a biofilm, in which bacteria move due to self-phoresis by generating pH gradients via metabolic reactions; and (6) the reversible clustering of cells near interfaces is attributed to the bacterial energy-taxis phenomenon.

Numerical simulation of a plate-gap biosensor with an outer porous membrane

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.

The influence of wood specimen surface coating on moisture movement during drying

Summary A model of wood drying under isothermal conditions taking into consideration coating of the surface of a specimen is presented in this paper in a two-dimensional formulation. The influence of the surface coating degree as well as geometrical shape of a wood specimen on the dynamics of drying is investigated. Exponentials, describing the dependence of the halfdrying time on the degree of coating of the edges, as well as on the ratio of the width to the thickness of the transverse section of specimens from the northern red oak (Quercus rubra), are presented for drying from above the fiber saturation point. This paper describes the conditions of usage of the two-dimensional moisture transfer model in contrast to the one-dimensional model for accurate prediction of the drying process taking into consideration the coating of edges of specimens having a rectangular transverse section. A measure of reliability of the one-dimensional model to predict the wood drying process of sawn boards is introduced in this paper.

Modelling carbon nanotubes-based mediatorless biosensor.

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.

Modelling of Amperometric Biosensor Used for Synergistic Substrates Determination

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.