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This paper deals with an analysis of the electrochemical biosensors and their response to multi-component mixtures. The main task is to build a mathematical model for estimation the concentration of each mixture component from the biosensor response data. Two different types of biosensors: amperometric and potenciometric are analysed. Due to high dimensionality of biosensor output data the principal component analysis is applied. Additional multivariate analysis of variance is used to analyze the response sensitivity of each biosensor type. Finally a concentration estimation model based on ensemble of neural networks is presented.

This paper presents a Bayesian approach rooted algorithm oriented to the properties of multi-objective optimization problems. The performance of the developed algorithm is compared with several other multi-objective optimization algorithms. The approach is applied to the multiobjective optimization of a batch stirred tank reactor based on spherical catalyst microreactors. The microbioreactors are computationally modeled by a two-compartment model based on reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten enzyme kinetics. A two-stage visualization procedure based on the multi-dimensional scaling is proposed and applied for the visualization of trade-off solutions and for the selection of favorable configurations of the bioreactor.

A model for the numerical simulation of the action of microbioreactor acting in the continuous flow mode was developed. The microbioreactor system was mathematically modelled by a two-compartment model based on transient reaction-diffusion equations containing a non-linear term related to the Michaelis–Menten kinetics of the enzymatic reaction. The effectiveness of microbioreactor and the process duration were numerically and partially analytically analysed at transition and steady-state conditions in a wide range of model parameters. The computational simulation was carried out using the finite difference technique. The performed calculations showed nonlinear effects of the internal and external diffusion limitations on the effectiveness and process duration.

The essential part of amperometric biosensor is an enzyme. It should be selective, i.e., react only with certain substrate. The selectivity of enzyme reduces the set of possible to use enzymes. This paper demonstrates that non selective enzymes (reacting with two substrates) can be used to determine concentrations of two substrates. For this purpose the steady-state current of two double biosensors was measured. The currents were used as input for an artificial neural network to determine concentrations of the substrates. The proposed approach was approved as the relative error of determined concentrations was relatively small. Paper analyses the influence of biosensor parameters to error values. The recommendations to error values minimisation were obtained.DOI: 10.15181/csat.v3i2.1109

Bioluminescence imaging experiments were carried out to characterize spatio-temporal patterns of bacterial self-organization in active suspensions (cultures) of bioluminescent Escherichia coli and its mutants. An analysis of the effects of mutations shows that spatio-temporal patterns formed in standard microtitre plates are not related to the chemotaxis system of bacteria. In fact, these patterns are strongly dependent on the properties of mutants that characterize them as self-phoretic (non-flagellar) swimmers. In particular, the observed patterns are essentially dependent on the efficiency of proton translocation across membranes and the smoothness of the cell surface. These characteristics can be associated, respectively, with the surface activity and the phoretic mobility of a colloidal swimmer. An analysis of the experimental data together with mathematical modelling of pattern formation suggests the following: (1) pattern-forming processes can be described by Keller–Segel-type models of chemotaxis with logistic cell kinetics; (2) active cells can be seen as biochemical oscillators that exhibit phoretic drift and alignment; and (3) the spatio-temporal patterns in a suspension of growing E. coli form due to phoretic interactions between oscillating cells of high metabolic activity.

The optimization-based quantitative determination of multianalyte concentrations from biased biosensor responses is investigated under internal and external diffusion-limited conditions. A computational model of a biocatalytic amperometric biosensor utilizing a mono-enzyme-catalyzed (nonspecific) competitive conversion of two substrates was used to generate pseudo-experimental responses to mixtures of compounds. The influence of possible perturbations of the biosensor signal, due to a white noise- and temperature-induced trend, on the precision of the concentration determination has been investigated for different configurations of the biosensor operation. The optimization method was found to be suitable and accurate enough for the quantitative determination of the concentrations of the compounds from a given biosensor transient response. The computational experiments showed a complex dependence of the precision of the concentration estimation on the relative thickness of the outer diffusion layer, as well as on whether the biosensor operates under diffusion- or kinetics-limited conditions. When the biosensor response is affected by the induced exponential trend, the duration of the biosensor action can be optimized for increasing the accuracy of the quantitative analysis.

In this paper, an amperometric glucose biosensor is modeled numerically. The model is based on non-stationary reaction-diffusion type equations. The model consists of four layers. An enzyme layer lies directly on a working electrode surface. The enzyme layer is attached to an electrode by a polyvinyl alcohol (PVA) coated terylene membrane. This membrane is modeled as a PVA layer and a terylene layer, which have different diffusivities. The fourth layer of the model is the diffusion layer, which is modeled using the Nernst approach. The system of partial differential equations is solved numerically using the finite difference technique. The operation of the biosensor was analyzed computationally with special emphasis on the biosensor response sensitivity to oxygen when the experiment was carried out in aerobic conditions. Particularly, numerical experiments show that the overall biosensor response sensitivity to oxygen is insignificant. The simulation results qualitatively explain and confirm the experimentally observed biosensor behavior.

This paper deals with the computational modeling of the pattern formation of luminous bacteria. Two bacterial self-organization models are investigated – Keller-Segel diffusion-advection-reaction type equations and the model with additional oxygen equation. These models were applied for the modeling of fluid cultures of lux-gene engineered Escherichia coli in the cylindrical container as seen from the side in 2 dimensions and in quasi-1 dimension along the top three phase contact line. The spatiotemporal patterns were simulated by using the finite difference technique. By applying these models the influence of the cylindrical container depth on the pattern formation was investigated.

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.

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.

A bacterial self-organization in a rounded container as detected by bioluminescence imaging is mathematically modeled by applying the the Keller–Segel approach with logistic growth. The pattern formation in a colony of luminous Escherichia coli is numerically simulated by the nonlinear reaction-advection-diffusion equations. In this work, the pattern formation is studied in 3D and the results are compared with previous and new 2D and 1D simulations. The numerical simulation at transition conditions was carried out using the finite difference technique. The simulation results showed that the developed 3D model captures fairly well the sophisticated patterns observed in the experiments. Since the numerical simulation based on the 3D model is very time-consuming, the reduction of spatial dimension of the model for simulating 1D spatiotemporal patterns is discussed. Due to the accumulation of luminous cells near the top three-phase contact line the experimental patterns of the bioluminescence can be qualitatively described by 1D and 2D models by adjusting values of the diffusion coefficient and/or chemotactic sensitivity.

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.

The response of a peroxidase-based optical biosensor was modelled digitally.A mathematical model of the optical biosensor is based on a system of non-linear reaction-diffusion equations. The modelling biosensor comprises two compartments, an enzyme layerand an outer diffusion layer. The digital simulation was carried out using finite differencetechnique. The influence of the substrate concentration as well as of the thickness of both theenzyme and diffusion layers on the biosensor response was investigated. Calculations showedcomplex kinetics of the biosensor response, especially at low concentrations of the peroxidaseand of the hydrogen peroxide.

The response of an amperometric biosensor at mixed enzyme kinetics anddiffusion limitations was modelled digitally in the case of substrate inhibition. Digitalsimulations were carried out using a finite difference technique. Calculations showedcomplex kinetics of biosensor response. At low enzyme activity and substrate concentration(S0), the response of the sensor looks like it is limited by a simple substrate diffusion. Atsubstrate concentration comparable to the Michaelis-Menten constant (KM), the responsechange shows a maximal value. A sharp response change was indicated at high enzymeactivity and high (4.9 > S0/KM > 4.5) substrate concentration. This was explained by multiconcentrationof substrate generation inside the enzyme layer. This conclusion wasconfirmed by the analytical solution of the simplified biosensor model with externaldiffusion limitation at steady-state conditions. The complex kinetics of response changeproduces different calibration graphs for biosensor response at transition and steady state.

A plate−gap model of a porous enzyme doped electrode covered by a porousinert membrane has been proposed and analyzed. The two−dimensional−in−spacemathematical model of the plate−gap biosensors is based on the reaction−diffusionequations containing a nonlinear term related to the Michaelis−Menten kinetics. Usingnumerical simulation of the biosensor action, the influence of the geometry of the outermembrane on the biosensor response was investigated at wide range of analyteconcentrations as well as of the reaction rates. The numerical simulation was carried outusing finite−difference technique. The behavior of the plate−gap biosensors was comparedwith that of a flat electrode deposited with a layer of enzyme and covered with the sameouter membrane.

This paper presents a two-dimensional-in-space mathematical model ofbiosensors based on an array of enzyme microreactors immobilised on a single electrode.The modeling system acts under amperometric conditions. The microreactors were modeledby particles and by strips. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The modelinvolves three regions: an array of enzyme microreactors where enzyme reaction as well asmass transport by diffusion takes place, a diffusion limiting region where only the diffusiontakes place, and a convective region, where the analyte concentration is maintained constant.Using computer simulation, the influence of the geometry of the microreactors and of thediffusion region on the biosensor response was investigated. The digital simulation wascarried out using the finite difference technique.

Biosensor response, in case of multi-substrate mixture, has nonlinear dependence on substrate concentrations. This work investigates the possibility to approximate this dependency with artificial neural network. Also the influence of external diffusion layer to results of multi-substrate determination was investigated. The numerically modelled biosensor response was used as experimental data. The principal components analysis was used to reduce the dimension of biosensor response. Prefered method gives acceptable acuratnes on multi-substrate determination and it can be improved by relatively large external diffusion layer.

Abstract: A mathematical model of biosensors acting in a trigger mode has been developed. One type of the biosensors utilized a trigger enzymatic reaction followed by the cyclic enzymatic and electrochemical conversion of the product (CCE scheme). Other biosensors used the enzymatic trigger reaction followed by the electrochemical and enzymatic product cyclic conversion (CEC scheme). The models were based on diffusion equations containing a non-linear term related to Michaelis-Menten kinetics of the enzymatic reactions. 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 demonstrated a significant gain (up to dozens of times) in biosensor sensitivity when the biosensor response was under diffusion control. In the case of significant signal amplification, the response time with triggering was up to several times longer than that of the biosensor without triggering.

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 kinetics of the enzymatic reaction. Using digital simulation, the influence of the thickness of enzyme membrane on the biosensor response was investigated. The digital simulation of the biosensor operation showed the non-monotonous change of the maximal biosensor current versus the membrane thickness at the various maximal enzymatic rates. Digital simulation was carried out using the finite difference technique. Results of the numerical simulation was compared with known analytical solutions. This paper presents a framework for selection of the membrane thickness, ensuring the sufficiently stable sensitivity of a biosensor in a required range of the maximal enzymatic rate.

This paper presents a one-dimensional-in-space mathematical model of a bacterial selforganization in a circular container along the contact line as detected by quasi-one-dimensional bioluminescence imaging. The pattern formation in a luminous Escherichia coli colony was modeled by the nonlinear reaction-diffusion-chemotaxis equations in which the reaction term for the cells is a logistic (autocatalytic) growth function. By varying the input parameters the output results were analyzed with a special emphasis on the influence of the model parameters on the pattern formation. The numerical simulation at transition conditions was carried out using the finite difference technique. The mathematical model and the numerical solution were validated by experimental data.

Biojutikliai yra analitiniai įrenginiai, skirti medžiagų koncentracijoms matuoti. Kuriant naujus biojutiklius reikia atlikti daug eksperimentų. Siekiant sumažinti atliekamų fizinių eksperimentų skaičių taikomas kompiuterinis biojutiklių veiksmo odeliavimas, kai įprastai kiekvienam struktūriškai naujam biojutikliui yra sudaromas matematinis modelis, tuomet jis keičiamas skirtuminiu, o jo lygčių sistemos sprendimas įgyvendinamas sudarant kompiuterinį modelį. Kiekvienas žingsnis reikalauja atidos ir turėtų būti automatizuotas. Straipsnyje yra pateikiamas biojutiklio metamodelis, leidžiantis formuluoti biojutiklių modelius dalykinės srities sąvokomis. Pasiūlytasis metamodelis aprašo biojutiklių modelius, formuluojamus dvimatėje erdvėje, apimančius biojutiklio struktūros, jo geometrinių savybių, biojutikliuose vykstančių reakcijų ir difuzijos procesų aprašus. Sudarius metamodelį, buvo sukurta programinė įranga, automatiškai sukonstruojanti kompiuterinį biojutiklio modelį pagal metamodelio sąvokomis išreikšto biojutiklio aprašą. Metamodelis ir programinė įranga buvo taikoma realiam biojutiklio modeliui sudaryti ir jo veiksmui modeliuoti kompiuteriniu būdu.", t. y. ištrinti žodžius "biojutiklių veiksmo. Computer-Aided Modeling of Biosensors with a Complex Geometrical Structure Romas Baronas, Karolis Petrauskas Summary Biosensors are analytical devices used to measure the concentration of substances. When developing new biosensors, a lot of experiments are needed to be performed. Mathematical modeling of biosensors is used to decrease the number of physical experiments. Models of biosensors are usually created for each structurally unique biosensor by defining its mathematical model and the corresponding numerical approximation. Equations of the numerical model are then solved using computer programs, usually created for a particular model of the biosensor. Each of these steps requires a great attention and should be automated. The article presents a metamodel for a biosensor, enabling one to define models of biosensors in domain-specific terms. The proposed metamodel describes biosensor models, defined in the two-dimensional space and including definitions of the structure of a biosensor, its geometrical properties, reactions and diffusion processes taking place in it. Upon defining the metamodel, we compiled the computer software able to create computer models for biosensors from the models formulated according to the proposed metamodel. The metamodel was practically used to define a model for a real biosensor, and the biosensor modeling software was used to simulate its operation.

Šiame straipsnyje yra tiriamas amperometrinis biojutiklis, kuriame biojutiklio atsakas yra stiprinamas chemiškai – sinerginiais substratais. Tokiuose biojutikliuose, be substrato, kurio koncentracija matuojama, naudojamas ir pagalbinis substratas, reikalingas substratų sinergetikai. Biojutiklis yra modeliuojamas naudojant nestacionarias netiesines reakcijos-difuzijos lygtis. Modeliuojami keturi biojutiklio sluoksniai: fermento sluoksnis, kuriame vyksta visos biocheminės reakcijos ir difuzija, dializės membrana ir difuzijos sluoksnis, kuriuose vyksta tik difuzija ir reakcijos, kuriose nedalyvauja fermentas, o ketvirtasis sluoksnis yra tirpalo dalis, kurioje palaikoma vienoda medžiagų koncentracija. Lygčių sistema sprendžiama skaitiškai, naudojant baigtinių skirtumų metodą. Tiriama biojutiklio atsako bei jautrio priklausomybė nuo substratų koncentracijų ir nuo difuzijos sluoksnio storio. Modelling Amperometric Biosensors with Synergistic Substrate Amplification Dainius Šimelevičius, Romas Baronas Summary Computational modelling of a biosensor in which chemical amplification by synergistic substrates takes place was investigated in this study. In the biosensors of this type, in addition to the substrate (analyte), another auxiliary substrate is used. It is necessary to achieve the substrates synergy. The operation of the biosensor is modelled using non-stationary reactiondiffusion equations. The model involves four regions: the enzyme layer where the enzymatic reactions as well as the mass transport by diffusion take place, the dialysis membrane and the diffusion limiting region where the mass transport by diffusion and non-enzymatic reactions take place, and the convective region in which the analyte concentration is maintained constant. The equation system is solved numerically using the finite difference technique. The biosensor response dependency on substrate concentrations and the diffusion layer thickness, as well as the biosensor sensitivity dependence on the same parameters have been studied. "line-height: 18px;">

Šiame darbe, siekiant nustatyti pagrindinius kinetinius peroksidazinio optinio biojutiklio matematinio modelio parametrus, buvo sudarytas bedimensis modelis. Biojutikliui taikomos reakcijos-difuzijos lygtys su netiesiniu nariu, aprašančiu fermentinę reakciją. Biojutiklio veikimas modeliuojamas fermento ir difuzijos sluoksniuose. Ištirta biojutiklio atsako ir jautrio priklausomybė nuo bedimensio biojutiklio modulio. Suformuluotas uždavinys sprendžiamas baigtinių skirtumų metodu. Gauti rezultatai pagrindžia šio modelio pritaikomumą. Atliekami peroksidazinio optinio biojutiklio eksperimentiniai tyrimai leis nustatyti modelio taikymo ribas. A Computational Investigation of the Optical Biosensor by a Dimensionless Model Evelina Gaidamauskaitė, Romas Baronas Summary In order to determine the main governing parameters, a dimensionless mathematical model of a peroxidase-based optical biosensor is derived. The mathematical model of the biosensor is based on a system of non-linear reaction-diffusion equations. The modelled biosensor comprises two compartments, an enzyme layer and an outer diffusion layer. The influence of the dimensionless diffusion modulus on the biosensor response and the sensitivity is investigated. The digital simulation was carried out using a finite difference method.

Biojutikliai yra plačiai naudojami tirti medžiagų koncentracijai tirpaluose. Viena pagrindinių biojutiklio sudedamųjų dalių yra fermentas. Fermentai yra gana brangios medžiagos, dėl to ir vykdyti eksperimentus yra brangu. Kuriant naujus biojutiklius tenka atlikti daug eksperimentų. Kad būtų sumažintas reikiamų eksperimentų skaičius, taikomas kompiuterinis biojutiklių veiksmo modeliavimas. Dažniausiai konkrečios geometrijos biojutikliui kuriamas konkretus jo kompiuterinis modelis. Šiame straipsnyje pristatoma sistema, kuri gali prisitaikyti prie konkrečios geometrijos biojutiklio. Sistema gali būti taikoma biojutikliams, kurių veiksmas aprašomas matematiniais modeliais, formuluojamais dvimatėje stačiakampėje srityje. Konkretaus biojutiklio matematinio modelio sprendinys komponuojamas parenkant konkrečius algoritmus. Computer aided model composition for biosensors modelled in two-dimensional space Karolis Petrauskas, Romas Baronas Summary Biosensors are analytical devices that use biological components, usually enzymes, which catalyse the interaction with a target analyte. Biosensors are widely used in clinical, environment and industrial applications for the determination of species concentrations. In some applications of biosensors, enzymes are very expensive and only available in very limited quantity. In design of novel highly sensitive biosensors a lot of experiments are required. Computer simulation of the biosensor action is an effective way to decrease a number of physical experiments. This paper presents a system adaptive to a concrete geometry of the biosensor. The system may be applied for biosensors, the action of which can be described by a mathematical model formulated in a two dimensional space. A simulator for a concrete biosensor is generated from the detailed description of the biosensor action. eight: 18px;">

This paper presents a two-dimensional-in-space mathematical model of amperometric biosensors with perforated membrane. The model is based on the diffusion equations containing a non-linear term related to the Michaelis–Menten kinetics of the enzymatic reaction. The digital simulation was carried out using the finite difference technique. Using computer simulation of the biosensors action, the influence of the geometry of the perforated membrane on the biosensor response was investigated.

In this paper total principal component regression is used for biosensors response to mixtures of compounds classification. The results are compared with the results obtained using artificial neural networks.

This paper presents a two-dimensional-in-space mathematical model of a sensor system based on an array of enzyme microreactors immobilised on a single electrode. The model is based on the diffussion equations containing a non-linear term related to the Michaelis–Menten kinetics of the enzymatic reaction. Using computer simulation the influence of the geometry of the enzyme microreactors on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique.

This paper presents a system which is used for the classification of biosensor signals. The proposed system is applied to the the synthesized and experimental data. The developed system showed good prediction perfomance.

A mathematical model of amperometric biosensors is presented. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzyme reaction. The model takes into concideration surface roughness of the enzyme layer. Using digital simulation, the influence of the geometry of the roughness on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique.