Apparent Parameters of Enzymatic Plate-Gap Electrode

2005 ◽  
Vol 10 (3) ◽  
pp. 211-211 ◽  
Author(s):  
I. Kaunietis ◽  
R. Šimkus ◽  
V. Laurinavičius ◽  
F. Ivanauskas
Keyword(s):  
Enzymatic Reaction ◽  
Reaction Diffusion ◽  
Wide Range ◽  
Steady State Current ◽  
Substrate Diffusion ◽  
Michaelis Constants ◽  
Complete Set ◽  
Kinetics Of ◽  
Substrate Concentrations ◽  
Biosensor Response

It was suggested that reaction-diffusion conditions in pores of bulk enzymatic electrode resemble particular conditions in thin enzyme filled gap between parallel conducting plates. The plate-gap model of porous enzymatic electrode is based on the diffusion equations containing a nonlinear term related to the Michaelis-Menten kinetics of the enzymatic reaction inside the gap. Steady state current was calculated for the wide range of given values of substrate diffusion coefficient, depth of the gap and substrate concentrations. Simple approximate relationships between “apparent” parameters of amperometric biosensor (maximal currents and apparent Michaelis constants) and given values of diffusion characterising parameters were derived. Association of these dependences with previously reported relationships led to derive approximate formulae that bind apparent parameters with the complete set of given parameters of the plate-gap enzymatic electrode. The limit case of slow diffusion into deep gap was also characterised. In this specific case, the highest numerical values of the apparent parameters were obtained. However, this gain is achievable at the expense of biosensor response time.

scholarly journals Computational Modelling of Biosensors with an Outer Perforated Membrane

2009 ◽  
Vol 14 (1) ◽  
pp. 85-102 ◽  
Author(s):  
K. Petrauskas ◽  
R. Baronas
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
D Model ◽  
Kinetics Of ◽  
Biosensor Response

This paper presents one-dimensional (1-D) and two-dimensional (2-D) in-space mathematical models for amperometric biosensors with an outer perforated membrane. The biosensor action was modelled by reaction-diffusion equations with a nonlinear term representing the Michaelis-Menten kinetics of an enzymatic reaction. The conditions at which the 1-D model can be applied to simulate the biosensor response accurately were investigated numerically. The accuracy of the biosensor response simulated by using 1-D model was evaluated by the response simulated with the corresponding 2-D model. A procedure for a numerical evaluation of the effective diffusion coefficient to be used in 1-D model was proposed. The numerically calculated effective diffusion coefficient was compared with the corresponding coefficients derived analytically. The numerical simulation was carried out using the finite difference technique.

MODELING OF NONLINEAR REACTION–DIFFUSION PROCESSES OF AMPEROMETRIC POLYMER-MODIFIED ELECTRODES

2008 ◽  
Vol 07 (01) ◽  
pp. 113-138 ◽  
Author(s):  
G. RAHAMATHUNISSA ◽  
L. RAJENDRAN
Keyword(s):  
Steady State ◽  
Diffusion Processes ◽  
Padé Approximation ◽  
Enzymatic Reaction ◽  
Modified Electrodes ◽  
Reaction Diffusion ◽  
Electrode System ◽  
Pade Approximation ◽  
Steady State Current ◽  
Nonsteady State

A mathematical model of amperometric response for a polymer-modified electrode system has been developed. The model is based on nonstationary diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. In particular, the interplay between chemical reaction and substrate diffusion is specifically taken into account. The limiting situations of catalytic site unsaturation and site saturation are considered. The analytical solutions for substrate concentration and transient current for both steady and nonsteady-state are obtained using Danckwerts' relation and variable and separable method. An excellent agreement with the previous analytical results are noted. The combined analytical set of solution of steady-state current in all the nearest sites is also described in a case diagram. A general simple analytical approximate solution for steady-state current for all values of α is also given. A two-point Padé approximation is also derived for the nonsteady-state current for all values of saturation parameter α. Limiting case results (α ≪ 1 and α ≫ 1) are compared with Padé approximation results and are found to be in good agreement.

Computational Modelling of a Sensor Based on an Array of Enzyme Microreactors

2004 ◽  
Vol 9 (3) ◽  
pp. 203-218 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys ◽  
M. Sapagovas
Keyword(s):  
Digital Simulation ◽  
Enzymatic Reaction ◽  
Computational Modelling ◽  
Enzyme Reaction ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Analyte Concentration ◽  
Finite Difference Technique ◽  
Kinetics Of ◽  
Biosensor Response

This paper presents a two-dimensional-in-space mathematical model of a sensor system based an array of enzyme microreactors immobilised on a single electrode. The system acts under amperometric conditions. The model is based on the diffusion equations containing a non-linear term related to the Michaelis-Menten kinetics of the enzymatic reaction. The model involves three regions: an array of enzyme microreactors (cells) 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 geometry of the enzyme cells and the diffusion region on the biosensor response was investigated. The digital simulation was carried out using the finite difference technique.

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Computer Simulation ◽  
Enzymatic Reaction ◽  
Diffusion Equations ◽  
Response Data ◽  
Finite Difference Technique ◽  
Stationary Diffusion ◽  
Biosensor Array ◽  
Menten Kinetic ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.

Scintigraphic studies in rats. Kinetics of insulin analogues covering wide range of receptor affinities

Diabetes ◽  
1991 ◽  
Vol 40 (5) ◽  
pp. 628-632 ◽  
Author(s):  
I. Jensen ◽  
V. Kruse ◽  
U. D. Larsen
Keyword(s):  
Insulin Analogues ◽  
Wide Range ◽  
Kinetics Of

Kinetics of Methane-Oxidizing Biofilms for Degradation of Toxic Organics

1988 ◽  
Vol 20 (11-12) ◽  
pp. 167-173 ◽  
Author(s):  
S. E. Strand ◽  
R. M. Seamons ◽  
M. D. Bjelland ◽  
H. D. Stensel
Keyword(s):  
Chlorinated Hydrocarbons ◽  
Enzymatic Oxidation ◽  
Diffusion Kinetics ◽  
Toxic Compound ◽  
Biofilm Model ◽  
Uptake Rates ◽  
Substrate Diffusion ◽  
Toxic Organics ◽  
Competitive Substrate ◽  
Kinetics Of

The kinetics of methane-oxidizing bioreactors for the degradation of toxic organics are modeled. Calculations of the fluxes of methane and toxic chlorinated hydrocarbons were made using a biofilm model. The model simulated the effects of competition by toxics and mediane on their enzymatic oxidation by the methane monooxygenase. Dual-competitive-substrate/diffusion kinetics were used to model biofilm co-metabolism, integrating equations of the following form:where S1 and S2 are the local concentrations of methane and toxic compound, respectively, and r and K are the maximum uptake rates and Monod coefficients, and x is the distance into the biofilm.

Nonlinear solution of the reaction–diffusion equation using a two-step third–fourth-derivative block method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Oluwaseun Adeyeye ◽  
Ali Aldalbahi ◽  
Jawad Raza ◽  
Zurni Omar ◽  
Mostafizur Rahaman ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Block Method ◽  
Wide Range ◽  
Higher Derivatives ◽  
Fourth Derivative ◽  
Improved Accuracy

AbstractThe processes of diffusion and reaction play essential roles in numerous system dynamics. Consequently, the solutions of reaction–diffusion equations have gained much attention because of not only their occurrence in many fields of science but also the existence of important properties and information in the solutions. However, despite the wide range of numerical methods explored for approximating solutions, the adoption of block methods is yet to be investigated. Hence, this article introduces a new two-step third–fourth-derivative block method as a numerical approach to solve the reaction–diffusion equation. In order to ensure improved accuracy, the method introduces the concept of nonlinearity in the solution of the linear model through the presence of higher derivatives. The method obtained accurate solutions for the model at varying values of the dimensionless diffusion parameter and saturation parameter. Furthermore, the solutions are also in good agreement with previous solutions by existing authors.

scholarly journals Controlling the Kinetics of an Enzymatic Reaction through Enzyme or Substrate Confinement into Lipid Mesophases with Tunable Structural Parameters

2020 ◽  
Vol 21 (14) ◽  
pp. 5116
Author(s):  
Marco Mendozza ◽  
Arianna Balestri ◽  
Costanza Montis ◽  
Debora Berti
Keyword(s):  
Reaction Kinetics ◽  
Self Assembly ◽  
Liquid Crystalline ◽  
Structural Parameters ◽  
Enzymatic Reaction ◽  
X Ray Scattering ◽  
Nitrophenyl Phosphate ◽  
Vis Spectroscopy ◽  
Kinetics Of ◽  
Enzyme Alkaline Phosphatase

Lipid liquid crystalline mesophases, resulting from the self-assembly of polymorphic lipids in water, have been widely explored as biocompatible drug delivery systems. In this respect, non-lamellar structures are particularly attractive: they are characterized by complex 3D architectures, with the coexistence of hydrophobic and hydrophilic regions that can conveniently host drugs of different polarities. The fine tunability of the structural parameters is nontrivial, but of paramount relevance, in order to control the diffusive properties of encapsulated active principles and, ultimately, their pharmacokinetics and release. In this work, we investigate the reaction kinetics of p-nitrophenyl phosphate conversion into p-nitrophenol, catalysed by the enzyme Alkaline Phosphatase, upon alternative confinement of the substrate and of the enzyme into liquid crystalline mesophases of phytantriol/H2O containing variable amounts of an additive, sucrose stearate, able to swell the mesophase. A structural investigation through Small-Angle X-ray Scattering, revealed the possibility to finely control the structure/size of the mesophases with the amount of the included additive. A UV–vis spectroscopy study highlighted that the enzymatic reaction kinetics could be controlled by tuning the structural parameters of the mesophase, opening new perspectives for the exploitation of non-lamellar mesophases for confinement and controlled release of therapeutics.

scholarly journals Combining experimental and simulation data of molecular processes via augmented Markov models

2017 ◽  
Vol 114 (31) ◽  
pp. 8265-8270 ◽  
Author(s):  
Simon Olsson ◽  
Hao Wu ◽  
Fabian Paul ◽  
Cecilia Clementi ◽  
Frank Noé
Keyword(s):  
Force Field ◽  
Structural Changes ◽  
Markov Models ◽  
Force Fields ◽  
Divide And Conquer ◽  
Simulation Data ◽  
Wide Range ◽  
Simulation And Experiment ◽  
Kinetics Of

Accurate mechanistic description of structural changes in biomolecules is an increasingly important topic in structural and chemical biology. Markov models have emerged as a powerful way to approximate the molecular kinetics of large biomolecules while keeping full structural resolution in a divide-and-conquer fashion. However, the accuracy of these models is limited by that of the force fields used to generate the underlying molecular dynamics (MD) simulation data. Whereas the quality of classical MD force fields has improved significantly in recent years, remaining errors in the Boltzmann weights are still on the order of a few kT, which may lead to significant discrepancies when comparing to experimentally measured rates or state populations. Here we take the view that simulations using a sufficiently good force-field sample conformations that are valid but have inaccurate weights, yet these weights may be made accurate by incorporating experimental data a posteriori. To do so, we propose augmented Markov models (AMMs), an approach that combines concepts from probability theory and information theory to consistently treat systematic force-field error and statistical errors in simulation and experiment. Our results demonstrate that AMMs can reconcile conflicting results for protein mechanisms obtained by different force fields and correct for a wide range of stationary and dynamical observables even when only equilibrium measurements are incorporated into the estimation process. This approach constitutes a unique avenue to combine experiment and computation into integrative models of biomolecular structure and dynamics.

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