KINETIC EQUATIONS FOR ENZYME REACTIONS IN THE PRESENCE OF POWERFUL INHIBITORS

1959 ◽  
Vol 37 (8) ◽  
pp. 1268-1271 ◽  
Author(s):  
Richard M. Krupka ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Kinetic Equations ◽  
Competitive Inhibitor ◽  
Graphical Analysis ◽  
Rate Data ◽  
State Equations ◽  
Enzyme Reactions ◽  
Simple Addition

Steady-state equations are worked out for the case of a competitive inhibitor that is present in concentrations comparable with that of the enzyme; allowance is made for the inhibitor attached to the enzyme. Two cases are considered: in case 1 the enzyme and inhibitor form a simple addition complex, while in case 2 a molecule is split off. Methods of graphical analysis of rate data are described.

The influence of pH and inhibitors on the kinetics of enzyme reactions involving two intermediates

1967 ◽  
Vol 45 (5) ◽  
pp. 539-546 ◽  
Author(s):  
Harvey Kaplan ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ph Dependence ◽  
Free Enzyme ◽  
State Equations ◽  
Enzyme Reactions ◽  
Substrate Complex ◽  
Rate Determining Step ◽  
Enzyme Substrate ◽  
Special Cases ◽  
Influence Of Ph

General steady-state equations are worked out for enzyme reactions which occur according to the scheme [Formula: see text]Equations showing the pH dependence of the kinetic parameters are developed in a form which distinguishes between essential and nonessential ionizing groups. The pK dependence of [Formula: see text], the second-order constant extrapolated to zero substrate constant, gives pK values for groups which ionize on the free enzyme, but reveals such a pK only if the corresponding group is also involved in the breakdown of the Michaelis complex. General steady-state equations are also developed for the case in which an inhibitor can combine with the free enzyme, the enzyme–substrate complex, and also a second intermediate (e.g. an acyl enzyme). The equations are given in a form that is convenient for analyzing the experimental results, and a number of special cases are considered. It is shown how the type of inhibition depends not only on the nature of the inhibitor but also on that of the substrate, an important factor being the rate-determining step of the reaction. Examples of the various kinds of behavior are given.

scholarly journals Computer program for the kinetic equations of enzyme reactions. The case in which more than one enzyme species is present at the onset of the reaction

1991 ◽  
Vol 278 (1) ◽  
pp. 91-97 ◽  
Author(s):  
R Varón ◽  
B H Havsteen ◽  
M García ◽  
F García-Canóvas ◽  
J Tudela
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Enzyme System ◽  
Kinetic Equations ◽  
British Library ◽  
Transient Phase ◽  
Enzyme Reactions ◽  
Steady State Kinetic ◽  
State Kinetic ◽  
Enzyme Species

This paper presents an extension of the program developed by Varón, Havsteen, García, García-Cánovas & Tudela [(1990) Biochem. J. 270, 825-828] for the expression of the transient-phase and steady-state kinetic equations of a general enzyme system in which the only enzyme species present at the onset of the reaction is the free enzyme. The program has been extended to situations in which more than one enzyme species may be present at the onset of the reaction. The program is given in Supplementary Publication SUP50165 (5 pages), which has been deposited at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1991) 273, 5.

scholarly journals Interaction of difluoro-oxaloacetate with aspartate transaminase

1977 ◽  
Vol 161 (2) ◽  
pp. 383-387 ◽  
Author(s):  
P A Briley ◽  
R Eisenthal ◽  
R Harrison ◽  
G D Smith
Keyword(s):  
Steady State ◽  
Competitive Inhibitor ◽  
Aspartate Transaminase ◽  
Steady State Kinetic ◽  
High Concentrations ◽  
State Kinetic ◽  
Uncompetitive Inhibitor

Diffluoro-oxaloacetate behaves as a competitive inhibitor of 2-oxoglutarate and as an uncompetitive inhibitor with respect to aspartate in steady-state kinetic experiments with cytoplasmic aspartate transaminase. In the presence of high concentrations of aspartate transaminase, difluoro-oxaloacetate is slowly transaminated to difluoro-aspartate, suggesting its use as a kinetic probe to study the reactions of the aminic form of the enzyme.

α-Retaining glucosyl transfer catalysed by trehalose phosphorylase from Schizophyllum commune: mechanistic evidence obtained from steady-state kinetic studies with substrate analogues and inhibitors

2001 ◽  
Vol 360 (3) ◽  
pp. 727-736 ◽  
Author(s):  
Bernd NIDETZKY ◽  
Christian EIS
Keyword(s):  
Steady State ◽  
Transition State ◽  
Schizophyllum Commune ◽  
Catalytic Efficiency ◽  
Kinetic Studies ◽  
Competitive Inhibitor ◽  
Chemical Mechanism ◽  
Steady State Kinetic ◽  
State Kinetic ◽  
Trehalose Phosphorylase

Fungal trehalose phosphorylase is classified as a family 4 glucosyltransferase that catalyses the reversible phosphorolysis of α,α-trehalose with net retention of anomeric configuration. Glucosyl transfer to and from phosphate takes place by the partly rate-limiting interconversion of ternary enzyme–substrate complexes formed from binary enzyme–phosphate and enzyme–α-d-glucopyranosyl phosphate adducts respectively. To advance a model of the chemical mechanism of trehalose phosphorylase, we performed a steady-state kinetic study with the purified enzyme from the basidiomycete fungus Schizophyllum commune by using alternative substrates, inhibitors and combinations thereof in pairs as specific probes of substrate-binding recognition and transition-state structure. Orthovanadate is a competitive inhibitor against phosphate and α-d-glucopyranosyl phosphate, and binds 3×104-fold tighter (Ki≈ 1μM) than phosphate. Structural alterations of d-glucose at C-2 and O-5 are tolerated by the enzyme at subsite +1. They lead to parallel effects of approximately the same magnitude (slope = 1.14; r2 = 0.98) on the reciprocal catalytic efficiency for reverse glucosyl transfer [log (Km/kcat)] and the apparent affinity of orthovanadate determined in the presence of the respective glucosyl acceptor (log Ki). An adduct of orthovanadate and the nucleophile/leaving group bound at subsite +1 is therefore the true inhibitor and displays partial transition state analogy. Isofagomine binds to subsite −1 in the enzyme–phosphate complex with a dissociation constant of 56μM and inhibits trehalose phosphorylase at least 20-fold better than 1-deoxynojirimycin. The specificity of the reversible azasugars inhibitors would be explained if a positive charge developed on C-1 rather than O-5 in the proposed glucosyl cation-like transition state of the reaction. The results are discussed in the context of α-retaining glucosyltransferase mechanisms that occur with and without a β-glucosyl enzyme intermediate.

Validation of a new method for determination of free fatty acid turnover

1987 ◽  
Vol 252 (3) ◽  
pp. E431-E438 ◽  
Author(s):  
J. M. Miles ◽  
M. G. Ellman ◽  
K. L. McClean ◽  
M. D. Jensen
Keyword(s):  
Steady State ◽  
Fatty Acid ◽  
Free Fatty Acid ◽  
Clearance Rate ◽  
Experimental Period ◽  
Metabolic Clearance ◽  
Metabolic Clearance Rate ◽  
State Equations ◽  
Tracer Methods

The accuracy of tracer methods for estimating free fatty acid (FFA) rate of appearance (Ra), either under steady-state conditions or under non-steady-state conditions, has not been previously investigated. In the present study, endogenous lipolysis (traced with 14C palmitate) was suppressed in six mongrel dogs with a high-carbohydrate meal 10 h before the experiment, together with infusions of glucose, propranolol, and nicotinic acid during the experimental period. Both steady-state and non-steady-state equations were used to determine oleate Ra ([3H]oleate) before, during, and after a stepwise infusion of an oleic acid emulsion. Palmitate Ra did not change during the experiment. Steady-state equations gave the best estimates of oleate inflow approximately 93% of the known oleate infusion rate overall, while errors in tracer estimates of inflow were obtained when non-steady-state equations were used. The metabolic clearance rate of oleate was inversely related to plasma concentration (P less than 0.01). In conclusion, accurate estimates of FFA inflow were obtained when steady-state equations were used, even under conditions of abrupt and recent changes in Ra. Non-steady-state equations, in contrast, may provide erroneous estimates of inflow. The decrease in metabolic clearance rate during exogenous infusion of oleate suggests that FFA transport may follow second-order kinetics.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

The basic equations for a supplemented GSMP and its applications to queues

1988 ◽  
Vol 25 (03) ◽  
pp. 565-578 ◽  
Author(s):  
Masakiyo Miyazawa ◽  
Genji Yamazaki
Keyword(s):  
Stochastic Process ◽  
Steady State ◽  
Queueing Networks ◽  
General Setting ◽  
Main Concern ◽  
Stationary Condition ◽  
State Equations ◽  
Semi Markov Process ◽  
Basic Equations ◽  
Stieltjes Transforms

A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.

Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

1987 ◽  
Vol 109 (4) ◽  
pp. 894-898 ◽  
Author(s):  
K. H. Winters
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Gravity Waves ◽  
Traveling Waves ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Oscillatory Convection ◽  
Extended System ◽  
State Equations

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.

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