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.

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.

scholarly journals Application of topological methods in enzyme kinetics

1977 ◽  
Vol 163 (3) ◽  
pp. 633-634
Author(s):  
K J Indge
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Algebraic Method ◽  
Rate Equations ◽  
Topological Methods ◽  
Steady State Rate ◽  
State Rate

A criticism [Cornish-Bowden (1976) Biochem. J. 159, 167] of an algebraic method for deriving steady-state rate equations [Indge & Childs (1976) Biochem. J. 155, 567-570] is theoretically founded.

scholarly journals The computerized derivation of steady-state rate equations for enzyme kinetics

1984 ◽  
Vol 223 (2) ◽  
pp. 551-553 ◽  
Author(s):  
D G Herries
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Rate Constants ◽  
Rate Equations ◽  
British Library ◽  
Steady State Rate ◽  
State Rate ◽  
Basic Version ◽  
Fortran 77

A FORTRAN 77 program is described for the derivation of steady-state rate equations for enzyme kinetics. Input is very simple and consists of the two enzyme forms and the two rate constants for each step in the mechanism. The program may be run interactively or off-line. The results are produced after collecting together the algebraic coefficients of like concentration terms, taking account of sign. A fully interactive BASIC version running on a BBC Microcomputer is also available. Details of the programs have been deposited as Supplementary Publication SUP 50126 (45 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained as indicated in Biochem. J. (1984) 217, 5.

scholarly journals An easy method for deriving steady-state rate equations

1992 ◽  
Vol 286 (2) ◽  
pp. 357-359 ◽  
Author(s):  
S G Waley
Keyword(s):  
Steady State ◽  
Relative Concentration ◽  
Turnover Time ◽  
Rate Equations ◽  
Flux Method ◽  
Easy Method ◽  
Satisfactory Method ◽  
Steady State Rate ◽  
Kinetic Mechanisms ◽  
State Rate

The scope and limitations of a simple and satisfactory method of deducing steady-state rate equations is described. This method (called the Flux Method) consists in writing down the flux in successive steps of the reaction, and calculating the relative concentration of enzyme forms and thence the turnover time. Kinetic mechanisms for linear and branched pathways are used as examples of this method.

The Effects of Substrate Concentration on the Mg-Adenosine Triphosphatase Activity of Myosin

1975 ◽  
Vol 53 (12) ◽  
pp. 1282-1287 ◽  
Author(s):  
T. Nihei ◽  
C. A. Filipenko
Keyword(s):  
Steady State ◽  
Substrate Concentration ◽  
Active Sites ◽  
Adenosine Triphosphatase ◽  
Kinetic Studies ◽  
Heavy Meromyosin ◽  
Adenosine Triphosphatase Activity ◽  
Steady State Rate ◽  
State Rate ◽  
Substrate Concentrations

Using myosin, heavy meromyosin, and subfragment-1 the steady state rate of Mg-modified adenosine triphosphatase (Mg-ATPase) was determined over a range of substrate concentrations between 10−8 M and 5 × 10−3 M, at 0.5 M and 0.05 M KCl (pH 7.4 at 20 °C). At the substrate concentrations below 10−5 M, myosin Mg-ATPase was observed to show that two active sites interact, as suggested by the analysis of transient kinetic studies (Walz, F. G., Jr.: J. Theor. Biol. 41, 357–373 (1973)). The increase in the activity at Mg-ATP concentrations higher than 10−4 M corresponds to the binding of Mg-ATP to myosin sites not responsible for the catalytic action. With heavy meromyosin and subfragment-1, the activity was best expressed by the Michaelis equation. With heavy meromyosin, the activation at high ATP concentrations is detectable, though not as pronounced as with myosin, but not with subfragment-1.

scholarly journals Calculation of steady-state rate equations and the fluxes between substrates and products in enzyme reactions

1977 ◽  
Vol 161 (3) ◽  
pp. 517-526 ◽  
Author(s):  
H G Britton
Keyword(s):  
Steady State ◽  
Enzyme Reaction ◽  
Rate Equations ◽  
Enzyme Mechanisms ◽  
Algebraic Form ◽  
Ping Pong ◽  
Steady State Rate ◽  
Enzyme Intermediates ◽  
State Rate ◽  
Velocity Equation

1. Two methods are described for deriving the steady-state velocity of an enzyme reaction from a consideration of fluxes between enzyme intermediates. The equivalent-reaction technique, in which enzyme intermediates are systematically eliminated and replaced by equivalent reactions, appears the most generally useful. The methods are applicable to all enzyme mechanisms, including three-substrate and random Bi Bi Ping Pong mechanisms. Solutions are obtained in algebraic form and these are presented for the common random Bi Bi mechanisms. The steady-state quantities of the enzyme intermediates may also be calculated. Additional steps may be introduced into enzyme mechanisms for which the steady-state velocity equation is already known. 2. The calculation of fluxes between substrates and products in three-substrate and random Bi Bi Ping Pong mechanisms is described. 3. It is concluded that the new methods may offer advantages in ease of calculation and in the analysis of the effects of individual steps on the overall reaction. The methods are used to show that an ordered addition of two substrates to an enzyme which is activated by another ligand will not necessarily give hyperbolic steady-state-velocity kinetics or the flux ratios characteristic of an ordered addition, if the dissociation of the ligand from the enzyme is random.

scholarly journals A new method for deriving steady-state rate equations suitable for manual or computer use

1976 ◽  
Vol 155 (3) ◽  
pp. 567-570 ◽  
Author(s):  
K J Indge ◽  
R E Childs
Keyword(s):  
Steady State ◽  
Computer Use ◽  
Computer Programs ◽  
New Method ◽  
Substantial Decrease ◽  
Rate Equations ◽  
British Library ◽  
Steady State Rate ◽  
State Rate

A schematic method for the derivation of steady-state enzyme rate equations by using the Wang algebra is described. The method is simple, easy to learn and offers a substantial decrease in analytical effort over previously published algorithms. Being essentially an algebraic procedure the method can be readily computerized. Computer programs in BASIC and ALGOL languages have been deposited as Supplementary Publication SUP 50065 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, W. Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1976). 153, 5.

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