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The dependencies of the internal and external diffusion limitations on the response and sensitivity of amperometric biosensors are investigated computationally using a two-compartment model, and a framework for evaluating and selecting the biosensor configuration is proposed. Enzyme-based biosensors are mathematically modelled by a system of reaction-diffusion equations containing a nonlinear term related to Michaelis-Menten kinetics. The biosensor response, sensitivity and stability are numerically analysed at the transition and steady state conditions in a wide range of model parameters, and attractive biosensor configurations are derived. The performed calculations show nonlinear effects of internal and external diffusion limitations on the biosensor current, response time and sensitivity as well as on the linear range of the calibration curve. The phenomenon of the non-monotonicity of the biosensor response is also investigated.

This paper presents a method combining mathematical modeling, multi-objective optimization and multi-dimensional visualization intended for the design and optimization of amperometric biosensors. An approach for optimizing the biosensor parameters is based on the availability of mathematical model of a catalytic biosensor (bioelectrode). A multi-objective visualization of trade-off solutions and Pareto optimal decisions is applied for the selection of the most favorable decision by a human expert when designing the biosensor. The proposed method is applied to the industrially relevant optimization of a glucose dehydrogenase-based amperometric biosensor utilizing the synergistic substrates conversion. The following three objectives were optimized: the apparent Michaelis constant, the output current and the enzyme amount.

Bacteria are a widespread group of organisms. On the microscale, bacteria colonies are of discrete nature. Looking from the mechanical point of view the suspension containing the bacteria may be considered as a system of living active ultrafine particles (size: 0.1–10 μm). In order to understand the mechanical behaviour of the bacteria system it is important to understand the behaviour of a single bacterium. The present paper proposes an adhesive interaction model for the simulation of bacteria cells, which can be also applied for the interaction for other biological cells. The main attention is given to describe and numericaly simulate the interaction of a bacterium with a flat surface within a liquid medium. In the simulations an adhesive force is taken into account. Adhesion plays a significant role, because it can keep a bacterium on the surface. It is described by the attractive van der Waals force. In order to achieve the stick of adhesive particles, additionally developed adhesive–dissipative models are presented. The bacterium interaction is described by an elastic–plastic model; these results are thereafter compared with results from an elastic model. Different known models such as Derjaguin, Muller and Toporov (DMT) and Derjaguin, Landau, Verwey, Overbeek (DLVO) models are considered. Obtained results show the approach and deformation process of an adhesive–dissipative bacterium by presenting force displacement diagrams. The bacterium–surface interaction model is developed in the framework of the discrete element method (DEM). The numerical experiments confirm that force–displacement plots exhibit a hysteresis similar to those observed in Atomic Force Microscopy (AFM) experiments. The proposed model can be applied for the numerical simulation of the interaction process of bacteria with a surface, as well as simulations of the sticking process.

A set of oxidized graphite samples have been newly synthesized using different protocols. Atomic force microscopy, Raman spectroscopy, thermal gravimetric analysis and Brunauer–Emmett–Teller analysis revealed the changes in structure and functionalities of obtained graphite oxidation products (GOPs) compared to pristine graphite. The substances have been tested as electrode materials applicable for bioelectrocatalytic systems using pyrroloquinoline quinone-dependent glucose dehydrogenase (PQQ-GDH). The application of GOPs allowed achieving the direct electron transfer (DET) from active site of PQQ-GDH to the electrode surface. Needless of additional electron transfer (ET) mediating compounds highly improved features of the biosensors. The efficiency of the biosensors has been evaluated for all types of biosensors varied from 32 μA/cm 2 to 64 μA/cm 2 using as electrode materials GOP1 and thermally reduced graphite oxide (TRGO), respectively. TRGO containing function groups (according TGA, ∼6% of the weight loss) and smallest particles (average diameter was ∼11 nm and the average height was ∼0.5 nm) exhibited the higher efficiency for ET acceleration in the biosensor acting on principle of DET.

In order to understand the behaviour system of the bacteria it is important understand the behaviour of a single bacteria. The suspension forming bacteria may be considered as system of living active ultrafine particles (size 1 μm). Present investigation addresses to the simulation of the S. aureus bacterium-surface interactions in a framework of the Discrete Element Method (DEM). Bacterium is of the spherical shape, while the glass surface is flat and considered as elastic. In this work the theoretical model for bacteria is similar to that used for the ultrafine size stiff particles. We investigate the behaviour of the active particle by applying two known Derjaguin, Muller, Toporov (DMT) [1] and Derjaguin, Landau, Verwey, Overbeek (DLVO) [2,3] models, which are used for simulation of ultrafine size objects. These models are enhanced by applying suggested dissipation mechanism related to the adhesion. It was assumed that energy can be dissipated and the force-displacement hysteresis can occur through the adhesion effect, where an amount of dissipated energy is fixed and independent on initial kinetic energy. This force-displacement hysteresis was observed at the physical experiments with bacteria provided by the means of the atomic force microscopy (AFM), Ubbink and Schar-Zammaretti (2007) [4]. It was illustrated that the presented adhesive-dissipative model, which applies DEM, offers the opportunity to capture dissipation effect during the contact. The numerical experiments confirm that force-displacement plots exhibit hysteresis typical to those which are observed in AFM experiments. This model can be useful for numerical simulation of interaction of bacterium to the substrate.

A scheme of a glucose dehydrogenase-based bioelectrocatalytical system where ferricyanide is converted to ferrocyanide in the presence of highly reactive organic electron transfer compounds is investigated digitally. Glucose dehydrogenase (GDH) is highly reactive towards organic electron acceptors compared to the low reactivity of GDH with inorganic electron acceptors. In this bioelectrocatalytical scheme, the enzyme efficiently catalyzes biocatalytical conversion of an organic mediator, which is followed by the fast chemical cross reaction of the product in the presence of ferricyanide excess. By changing input parameters a special emphasis was directed towards the influence of the kinetic constants and reagents concentration on the sensitivity of the bioelectrode. The digital simulation of the system confirmed that the high sensitivity of the bioelectrode achieved in the presence of organic mediators is due to the synergistic substrates conversion demonstrated experimentally. in (Electroanalysis, 2012 (24) 273-277).

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.

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.

A mathematical model of amperometric enzyme electrodes in which chemical amplification by cyclic substrate conversion takes place in a single enzyme membrane 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. The digital simulation was carried out using the finite difference technique. The influence of the substrate concentration, the maximal enzymatic rate as well as the membrane thickness on the biosensor response was investigated. The numerical experiments demonstrate significant (up to dozens of times) gain in biosensor sensitivity at low concentrations of substrate when the biosensor response is under diffusion control.

A model of the moisture movement in solid wood under isothermal conditions taking into consideration coating (insulation) of the surface of the material, is presented in a 2-D-in-space formulation. The validity of using a corresponding 1-D model on a 2-D problem is investigated. A measure of reliability of the 1-D model is introduced. This paper presents a new technique, which adjusts the width of a material as well as the degree of coating of the edges, to ensure the relative error of the problem solution is less than the required, resulting from reducing the model from 2-D to 1-D-in-space. This technique is based on the computer simulation of 2-D diffusion to estimate the reliability of the corresponding 1-D diffusion model.