scholarly journals Analytical Expressions Pertaining to the Concentration of Substrates and Product in Phenol-Polyphenol Oxidase System Immobilized in Laponite Hydrogels: A Reciprocal Competitive Inhibition Process

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
K. Indira ◽  
L. Rajendran
Keyword(s):  
Homotopy Perturbation Method ◽  
Competitive Inhibition ◽  
Coupled System ◽  
Current Response ◽  
Product Concentration ◽  
Matlab Program ◽  
Nonlinear Coupled System ◽  
Diffusion And Kinetics ◽  
Analytical Expressions ◽  
Kinetics Of

Theoretical analysis corresponding to the diffusion and kinetics of substrate and product in an amperometric biosensor is developed and reported in this paper. The nonlinear coupled system of diffusion equations was analytically solved by Homotopy perturbation method. Herein, we report the approximate analytical expressions pertaining to substrate concentration, product concentration, and current response for all possible values of diffusion and kinetic parameters. The numerical solution of this problem is also reported using Scilab/Matlab program. Also, we found excellent agreement between the analytical results and numerical results upon comparison.

scholarly journals Analysis of Mathematical Modelling on Potentiometric Biosensors

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
N. Mehala ◽  
L. Rajendran
Keyword(s):  
Homotopy Perturbation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Full Description ◽  
Response Curves ◽  
First Order ◽  
First Order Kinetics ◽  
Matlab Program ◽  
Flux Response ◽  
Analytical Expressions

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Kinetic Aspects of the Interaction of Blood Clotting Enzymes

1968 ◽  
Vol 19 (03/04) ◽  
pp. 364-367 ◽  
Author(s):  
H. C Hemker ◽  
P. W Hemker
Keyword(s):  
Enzyme Kinetics ◽  
Blood Clotting ◽  
Competitive Inhibition ◽  
Competitive Inhibitor ◽  
Kinetics Of

SummaryThe enzyme kinetics of competitive inhibition under conditions prevailing in clotting tests are developed and a method is given to measure relative amounts of a competitive inhibitor by means of the t — D plot.

The Kinetics of Inhibition of the Action of Thrombin by the Fibrinopeptides Formed during the Clotting of Fibrinogen

1966 ◽  
Vol 16 (01/02) ◽  
pp. 277-295 ◽  
Author(s):  
A Silver ◽  
M Murray
Keyword(s):  
Amino Acids ◽  
Competitive Inhibition ◽  
Amorphous Material ◽  
Peptide Bond ◽  
Initial Reaction ◽  
Reaction Products ◽  
Coagulation Mechanism ◽  
Kinetics Of ◽  
Kinetics Of Inhibition ◽  
Burk Plot

SummaryVarious investigators have separated the coagulation products formed when fibrinogen is clotted with thrombin and identified fibrinopeptides A and B. Two other peaks are observed in the chromatogram of the products of coagulation, but these have mostly been dismissed by other workers. They have been identified by us as amino acids, smaller peptides and amorphous material (37). We have re-chromatographed these peaks and identified several amino acids. In a closed system of fibrinogen and thrombin, the only reaction products should be fibrin and peptide A and peptide B. This reasoning has come about because thrombin has been reported to be specific for the glycyl-arginyl peptide bond. It is suggested that thrombin also breaks other peptide linkages and the Peptide A and Peptide B are attacked by thrombin to yield proteolytic products. Thrombin is therefore probably not specific for the glycyl-arginyl bond but will react on other linkages as well.If the aforementioned is correct then the fibrinopeptides A and B would cause an inhibition with the coagulation mechanism itself. We have shown that an inhibition does occur. We suggest that there is an autoinhibition to the clotting mechanism that might be a control mechanism in the human body.The experiment was designed for coagulation to occur under controlled conditions of temperature and time. Purified reactants were used. We assembled an apparatus to record visually the speed of the initial reaction, the rate of the reaction, and the density of the final clot formed after a specific time.The figures we derived made available to us data whereby we could calculate and plot the information to show the mechanism and suggest that such an inhibition does exist and also further suggest that it might be competitive.In order to prove true competitive inhibition it is necessary to fulfill the criteria of the Lineweaver-Burk plot. This has been done. We have also satisfied other criteria of Dixon (29) and Bergman (31) that suggest true competitive inhibition.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

Features of determining the deformed state of a particle material during hot stamping of porous moldings

2021 ◽  
pp. 21-30
Author(s):  
B. G. Gasanov ◽  
A. A. Aganov ◽  
P. V. Sirotin
Keyword(s):  
Displacement Vector ◽  
Hot Stamping ◽  
Strain Tensor ◽  
Particle Material ◽  
Software Algorithms ◽  
Deformed State ◽  
Metal Strain ◽  
Scalar Products ◽  
Analytical Expressions ◽  
Kinetics Of

The paper describes main methods for assessing the deformed state of porous body metal frames developed by different authors based on the analysis of yield conditions and governing equations, using the principle of equivalent strains and stresses, and studying the kinetics of metal strain during pressing. Formulas were derived to determine the components of the powder particle material strain tensor through dyads, as scalar products of the basis vectors of the convected coordinate system at each moment of porous molding strain. The expediency of using the analytical expressions developed to determine the deformed state of the particle material was experimentally substantiated subject to the known displacement vector parameters of representative elements (macrostrains) of porous billets. The applications of well-known analytical expressions were established, and the proposed formulas proved applicable for the deformed state assessment of particle metal during the pressure processing of powder products of different configurations and designing billets with a defined porosity and geometric parameters as a basis for compiling software algorithms for the computer simulation of porous molding hot stamping.

Extrusion of stiffening ribs on body parts with local heating

2021 ◽  
pp. 72-74
Author(s):  
Keyword(s):  
Velocity Field ◽  
Stress Relaxation ◽  
Local Heating ◽  
Hot Extrusion ◽  
Body Parts ◽  
Calculation Results ◽  
Energy Equilibrium ◽  
Stiffening Ribs ◽  
Analytical Expressions ◽  
Kinetics Of

A scheme is proposed and analytical expressions are obtained for calculating the kinematics, pressure and damageability of the material during hot extrusion of ribs on body parts. The equations of states during creep, energy equilibrium, kinetics of material discontinuity are used. The calculation results are presented. Keywords: extrusion, local heating, stiffening rib, viscosity, plasticity, stress relaxation, pressure, velocity field [email protected], [email protected]

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