A New Model System for the Study of Complex Dynamical Enzyme Reactions. II. Oscillations in a Reaction-Diffusion-Convection System

1988 ◽  
Vol 43 (11) ◽  
pp. 995-1001
Author(s):  
Gerold Baier ◽  
Peter Urban ◽  
Klaus Wegmann
Keyword(s):  
Temperature Gradient ◽  
Complete System ◽  
Convective Motion ◽  
Enzyme Reaction ◽  
Reaction Diffusion ◽  
Model System ◽  
Chemical Gradient ◽  
Constant Temperature Gradient ◽  
Enzyme Reactions ◽  
Diffusion Convection

Abstract A nonlinear enzyme reaction in a chemical gradient with an artificial feed-back loop is modified by the application of a constant temperature gradient leading to laminar convective motion of the fluid at an electrode. The complete system is shown to undergo a bifurcation into a limit cycle as a function of the applied temperature gradient. The effect of other parameters on the oscillation is described. More complicated types of behavior are expected in parameter space.

A New Model System for the Study of Complex Dynamical Enzyme Reactions. I. A Nonlinear Enzyme Reaction in a Chemical Gradient

1988 ◽  
Vol 43 (11) ◽  
pp. 987-994 ◽  
Author(s):  
Gerold Baier ◽  
Peter Urban ◽  
Klaus Wegmann
Keyword(s):  
Feedback Loop ◽  
Reaction Rate ◽  
Reaction Dynamics ◽  
Enzyme Reaction ◽  
Experimental System ◽  
Model System ◽  
Chemical Gradient ◽  
Theoretical Concepts ◽  
Fixed Parameter ◽  
Parameter Values

Abstract An experimental system for the study of biochemical reaction dynamics is introduced and de­ scribed. A one-enzyme reaction is extended by an artificial feedback loop in an electrochemical device. Cyclic voltammetry is used to show that the reaction rate depends nonlinearly on the amount of cosubstrate offered. For some sets of fixed parameter values a damped oscillatory approach of the steady state was observed. The usefulness of the systems theoretical concepts is discussed.

scholarly journals Existence of reaction-diffusion-convection waves in unbounded strips

2005 ◽  
Vol 2005 (2) ◽  
pp. 169-193 ◽  
Author(s):  
M. Belk ◽  
B. Kazmierczak ◽  
V. Volpert
Keyword(s):  
Implicit Function Theorem ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Fredholm Property ◽  
Implicit Function ◽  
Solvability Conditions ◽  
All Speeds ◽  
Diffusion Convection ◽  
Rayleigh Numbers ◽  
Property Index

Existence of reaction-diffusion-convection waves in unbounded strips is proved in the case of small Rayleigh numbers. In the bistable case the wave is unique, in the monostable case they exist for all speeds greater than the minimal one. The proof uses the implicit function theorem. Its application is based on the Fredholm property, index, and solvability conditions for elliptic problems in unbounded domains.

Competition between transport phenomena in a reaction–diffusion–convection system

2011 ◽  
Vol 512 (4-6) ◽  
pp. 290-296 ◽  
Author(s):  
L. Ciotti ◽  
M.A. Budroni ◽  
M. Masia ◽  
N. Marchettini ◽  
M. Rustici
Keyword(s):  
Transport Phenomena ◽  
Reaction Diffusion ◽  
Diffusion Convection

scholarly journals Towards a multi-physics modelling framework for thrombolysis under the influence of blood flow

2015 ◽  
Vol 12 (113) ◽  
pp. 20150949 ◽  
Author(s):  
Andris Piebalgs ◽  
X. Yun Xu
Keyword(s):  
Blood Flow ◽  
Thrombolytic Therapy ◽  
Effective Means ◽  
Reaction Diffusion ◽  
Clot Lysis ◽  
Local Flow ◽  
Pressure Drops ◽  
Modelling Framework ◽  
Internal Bleeding ◽  
Diffusion Convection

Thrombolytic therapy is an effective means of treating thromboembolic diseases but can also give rise to life-threatening side effects. The infusion of a high drug concentration can provoke internal bleeding while an insufficient dose can lead to artery reocclusion. It is hoped that mathematical modelling of the process of clot lysis can lead to a better understanding and improvement of thrombolytic therapy. To this end, a multi-physics continuum model has been developed to simulate the dissolution of clot over time upon the addition of tissue plasminogen activator (tPA). The transport of tPA and other lytic proteins is modelled by a set of reaction–diffusion–convection equations, while blood flow is described by volume-averaged continuity and momentum equations. The clot is modelled as a fibrous porous medium with its properties being determined as a function of the fibrin fibre radius and voidage of the clot. A unique feature of the model is that it is capable of simulating the entire lytic process from the initial phase of lysis of an occlusive thrombus (diffusion-limited transport), the process of recanalization, to post-canalization thrombolysis under the influence of convective blood flow. The model has been used to examine the dissolution of a fully occluding clot in a simplified artery at different pressure drops. Our predicted lytic front velocities during the initial stage of lysis agree well with experimental and computational results reported by others. Following canalization, clot lysis patterns are strongly influenced by local flow patterns, which are symmetric at low pressure drops, but asymmetric at higher pressure drops, which give rise to larger recirculation regions and extended areas of intense drug accumulation.

Optimized Determination of γ-Glutamyltransferase by Reaction-Rate Analysis

1974 ◽  
Vol 20 (9) ◽  
pp. 1121-1124 ◽  
Author(s):  
Sidney B Rosalki ◽  
David Tarlow
Keyword(s):  
Dilute Hydrochloric Acid ◽  
Reaction Rate ◽  
Enzymatic Reaction ◽  
Enzyme Reaction ◽  
Enzyme Reactions ◽  
Rate Analysis ◽  
Acid Substrate ◽  
Incubation Buffer ◽  
Optimal Ph

Abstract We describe a method for measuring γ-glutamyltransferase (EC 2.3.2.2) activity in serum, which can be used with automated enzyme analyzers (such as the LKB 8600 Reaction Rate Analyzer) that require enzyme reactions to be initiated with substrate. The method also permits optimal determination conditions to be obtained at 37 °C. The enzymatic reaction is commenced by adding γ-glutamyl-p-nitroanilide dissolved in dilute hydrochloric acid to samples pre-incubated with tris(hydroxymethyl)aminomethane—glycylglycine buffer. The p-nitroaniline liberated is continously monitored at 37 °C at 405 nm. The pH of the pre-incubation buffer is such that the optimal pH for the enzyme reaction results from addition of the acid substrate solution.

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