Integrated steady-state rate equations for enzyme-catalyzed reactions

1964 ◽  
Vol 85 (1) ◽  
pp. 1-10 ◽  
Author(s):  
I.G. Darvey ◽  
J.F. Williams
Keyword(s):  
Steady State ◽  
Rate Equations ◽  
Steady State Rate ◽  
State Rate ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions

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 Theory on the rate equation of Michaelis-Menten type single-substrate enzyme catalyzed reactions

2017 ◽  
Author(s):  
Rajamanickam Murugan
Keyword(s):  
Steady State ◽  
Critical Parameters ◽  
Rate Equations ◽  
Differential Rate ◽  
Single Substrate ◽  
Progress Curve ◽  
Catalyzed Reactions ◽  
Space Dynamics ◽  
Time Required ◽  
Enzyme Catalyzed Reactions

AbstractAnalytical solution to the Michaelis-Menten (MM) rate equations for single-substrate enzyme catalysed reaction is not known. Here we introduce an effective scaling scheme and identify the critical parameters which can completely characterize the entire dynamics of single substrate MM enzymes. Using this scaling framework, we reformulate the differential rate equations of MM enzymes over velocity-substrate, velocity-product, substrate-product and velocity-substrate-product spaces and obtain various approximations for both pre- and post-steady state dynamical regimes. Using this framework, under certain limiting conditions we successfully compute the timescales corresponding to steady state, pre- and post-steady states and also compute the approximate steady state values of velocity, substrate and product. We further define the dynamical efficiency of MM enzymes as the ratio between the reaction path length in the velocity-substrate-product space and the average reaction time required to convert the entire substrate into product. Here dynamical efficiency characterizes the phase-space dynamics and it would tell us how fast an enzyme can clear a harmful substrate from the environment. We finally perform a detailed error level analysis over various pre- and post-steady state approximations along with the already existing quasi steady state approximations and progress curve models and discuss the positive and negative points corresponding to various steady state and progress curve models.

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.

Computer-based derivation of rate equations for enzyme-catalyzed reactions. I. Effects of modifiers on kinetics of multireactant systems

1969 ◽  
Vol 47 (9) ◽  
pp. 889-894 ◽  
Author(s):  
Arthur R. Schulz ◽  
Donald D. Fisher
Keyword(s):  
Steady State ◽  
Reaction Mechanism ◽  
Rate Equations ◽  
Connection Matrix ◽  
Computer Based ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Kinetics Of

A computer-based method for the derivation of rate equations of enzyme-catalyzed reactions under steady-state assumptions is presented. This method is based on the description of the reaction mechanism in terms of a connection matrix. The utility of the method is demonstrated by applying it to complete the derivation of rate equations of multireactant enzymic mechanisms with modifiers as discussed by Henderson.

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.

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