THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS

1955 ◽  
Vol 33 (10) ◽  
pp. 1614-1624 ◽  
Author(s):  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Special Reference ◽  
Transient Phase ◽  
Kinetic Behavior ◽  
State Equations ◽  
Enzyme Systems ◽  
Great Excess ◽  
Special Case

The steady-state hypothesis is discussed for enzyme systems, and the conditions under which the steady-state equations will be valid over the main course of the reaction are obtained. It is shown that this is so if the substrate is in great excess, and also under several other circumstances. Equations are derived for the kinetic behavior during the transient phase of the reaction. Two-substrate systems, and the special case of catalase, are considered.

Transient-Phase and Steady-State Kinetics for Enzyme Systems Involving Two Substrates

1973 ◽  
Vol 51 (6) ◽  
pp. 832-840 ◽  
Author(s):  
Nasrat H. Hijazi ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Ternary Complex ◽  
Transient Phase ◽  
Complex Mechanism ◽  
State Equations ◽  
Enzyme Systems ◽  
Steady State Kinetics ◽  
Ping Pong ◽  
The Individual ◽  
Individual Rate

The transient-phase and steady-state equations are derived for four enzyme mechanisms involving two substrates, namely (1) Theorell–Chance mechanism, (2) ping pong bi bi mechanism, (3) ordered ternary-complex mechanism, and (4) random ternary-complex mechanism. In each case, a discussion is presented of the way in which the individual rate constants can be separated on the basis of experimental transient-phase investigations.

Transient-Phase and Steady-State Kinetics for Enzyme Activation

1973 ◽  
Vol 51 (6) ◽  
pp. 806-814 ◽  
Author(s):  
Nasrat H. Hijazi ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Kinetic Data ◽  
Enzyme Activation ◽  
Transient Phase ◽  
Time Curve ◽  
Substrate Complex ◽  
Enzyme Substrate ◽  
Substrate Activation ◽  
Steady State Kinetics ◽  
Special Case

A non-steady-state analysis has been worked out for two mechanisms in which an activator Q can become attached to an enzyme–substrate complex EA, the species EAQ breaking down more rapidly than EA. It is shown that if EAQ breaks down into EQ + product there can be no steady state. If, however, EAQ breaks down into E + Q + product, the transient phase is followed by a steady state in which the product versus time curve is linear. A special case of this mechanism is when Q is the substrate (substrate activation). Some published kinetic data on carboxypeptidase are analyzed with reference to the equations derived.

A Windows program for the derivation of steady-state equations in enzyme systems

2006 ◽  
Vol 181 (2) ◽  
pp. 837-852 ◽  
Author(s):  
J.M. Yago ◽  
F. García Sevilla ◽  
C. Garrido del Solo ◽  
R.G. Duggleby ◽  
R. Varón
Keyword(s):  
Steady State ◽  
State Equations ◽  
Enzyme Systems

THEORY OF THE TRANSIENT PHASE IN KINETICS, WITH SPECIAL REFERENCE TO ENZYME SYSTEMS: II. THE CASE OF TWO ENZYME–SUBSTRATE COMPLEXES

1956 ◽  
Vol 34 (2) ◽  
pp. 146-150 ◽  
Author(s):  
Ludovic Ouellet ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Substrate Concentration ◽  
Kinetic Scheme ◽  
Rate Equations ◽  
Theoretical Treatment ◽  
Transient Phase ◽  
Enzyme Substrate ◽  
Enzyme Systems ◽  
Steady State Rate ◽  
State Rate

A theoretical treatment is worked out for the kinetic scheme[Formula: see text]in which two enzyme–substrate complexes are formed consecutively. The steady-state rate equations are obtained, and equations are given for the transient phase subject to the condition that the substrate concentration is greatly in excess of that of the enzyme. Some kinetic consequences of the resulting equations are discussed.

Transient-Phase and Steady-State Kinetics for Inhibited Enzyme Systems. II. Double-Intermediate Mechanisms

1973 ◽  
Vol 51 (6) ◽  
pp. 822-831 ◽  
Author(s):  
Nasrat H. Hijazi ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Enzyme Concentration ◽  
Transient Phase ◽  
Enzyme Systems ◽  
Steady State Kinetics ◽  
Inhibited Enzyme

Equations for the pre-steady state and the steady state are derived for enzyme systems in which the enzyme E, the substrate A, and an inhibitor Q are present together, the enzyme concentration being much lower than the concentrations of A and Q. Various mechanisms are considered, ail of them involving two intermediates EA and EA′ (e.g. an acyl enzyme). When the inhibition is reversible the transient phase is followed by the establishment of a steady state. It is shown how experimental pre-steady-state and steady-state results can be analyzed to obtain rate constants, including those for the binding of inhibitor. If the binding of inhibitor is irreversible there is no steady state.

Transient-Phase and Steady-State Kinetics for Inhibited Enzyme Systems. I. Single-Intermediate Mechanisms

1973 ◽  
Vol 51 (6) ◽  
pp. 815-821 ◽  
Author(s):  
Nasrat H. Hijazi ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Enzyme Concentration ◽  
Experimental Results ◽  
Transient Phase ◽  
Steady State Analysis ◽  
Noncompetitive Inhibition ◽  
Enzyme Systems ◽  
Steady State Kinetics ◽  
Inhibited Enzyme ◽  
State Analysis

Equations for the pre-steady state and the steady state are derived for enzyme systems in which enzyme E, substrate A, and inhibitor Q are present, the enzyme concentration being lower than the substrate and inhibitor concentrations. It is assumed that the mechanism involves a single intermediate EA. Equations for competitive, anticompetitive, and pure noncompetitive inhibition are derived. When the inhibition is reversible the transient phase is followed by the establishment of a steady state. Analysis of experimental results is discussed for each type of inhibition. If the inhibition is irreversible, there is no steady state.

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.

THEORY OF THE TRANSIENT PHASE IN AN ENZYME SYSTEM INVOLVING TWO ENZYME-SUBSTRATE COMPLEXES: THE CASE OF THE FORMATION OF PRODUCTS FROM THE FIRST COMPLEX

1959 ◽  
Vol 37 (4) ◽  
pp. 737-743 ◽  
Author(s):  
Ludovic Ouellet ◽  
James A. Stewart
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Active Site ◽  
Substrate Concentration ◽  
Enzyme System ◽  
Kinetic Scheme ◽  
Enzyme Concentration ◽  
Theoretical Treatment ◽  
Transient Phase ◽  
Enzyme Substrate

A theoretical treatment is worked out for the kinetic scheme[Formula: see text]in which the concentration of P1 is followed. The steady-state and transient phase equations are obtained subject to the condition that the substrate concentration is greatly in excess of the enzyme concentration. The conditions under which evidence in favor of this mechanism can be obtained from experimental data are discussed. Under certain conditions, the weight of the enzyme corresponding to one active site can be determined. Methods for the evaluation of the different constants are described.

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