scholarly journals Algebraic methods for deriving steady-state rate equations. Practical difficulties with mechanisms that contain repeated rate constants

1976 ◽  
Vol 159 (1) ◽  
pp. 167-167 ◽  
Author(s):  
A Cornish-Bowden
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Algebraic Methods ◽  
Rate Equations ◽  
Steady State Rate ◽  
State Rate

Methods of deriving rate equations that rely on repetition of terms for identification of redundant or invalid terms give incorrect results if used with mechanisms in which some rate constants appear more than once.

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.

Effect of the potential-energy surface on the diatom dissociation rate constant for F 2 in Ar at 3000 K

1987 ◽  
Vol 414 (1847) ◽  
pp. 297-314
Keyword(s):  
Steady State ◽  
Rate Constant ◽  
Rate Constants ◽  
Reaction Rate ◽  
Energy Surface ◽  
Rate Coefficient ◽  
Classical Mechanics ◽  
Rate Coefficients ◽  
Steady State Rate ◽  
State Rate

Gas-phase dissociation of fluorine ( 1 Ʃ + g ) molecules in an agron bath at 3000 K was studied by using the 3D Monte Carlo classical trajectory (3DMCCT) method. To assess the importance of the potential energy surface (PES) in such calculations, three surfaces, with a fixed, experimentally determined F 2 dissociation energy, were constructed. These surfaces span the existing experimental uncertainties in the shape of the F 2 potential. The first potential was the widest and softest; in the second potential the anharmonicity was minimized. The intermediate potential was constructed to ‘localize’ anharmonicity in the energy range in which the collisions are most reactive. The remaining parameters for each PES were estimated from the best available data on interatomic potentials. By using the single uniform ensemble (SUE) method (Kutz, H. D. & Burns, G. J. chem. Phys . 72, 3652-3657 (1980)), large ensembles of trajectories (LET) were generated for the PES. Two such ensembles consisted of 30000 trajectories each and the third of 26200. It was found that the computed one-way-flux equilibrium rate coefficients (Widom, B. Science 148, 1555-1560 (1965)) depend in a systematic way upon the anharmonicity of the potential, with the most anharmonic potential yielding the largest rate coefficient. Steady-state reaction-rate constants, which correspond to experimentally observable rate constants, were calculated by the SUE method. It was determined that this method yields (for a given trajectory ensemble, PES and translational temperature) a unique steady-state rate constant, independent of the initial, arbitrarily chosen, state (Tolman, R. C. The principles of statistical mechanics , p. 17. Oxford University Press (1938)) of the LET, and consequently independent of the corresponding initial value of the reaction rate coefficient. For each initial state of the LET, the development of the steady-state rate constant from the equilibrium rate coefficient was smooth, monotonic, and consistent with the detailed properties of the PES. It was found that, although the increased anharmonicity of the F 2 potential enhanced the equilibrium rate coefficients, it also enhanced the non-equilibrium effects. As a result, the steady-state rate constants were found to be insensitive to the variation of the PES. Thus, the differences among the steady-state rate constants for the three potentials were of the order of their standard errors, which was about 15% or less. On the other hand, the calculated rate constants exceeded the experimental rate constant by a factor of five to six. Because within the limitations of classical mechanics the calculations were ab initio , it was tentatively concluded that the discrepancy of five to six is due to the use of classical mechanics rather than details of the PES structure.

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 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.

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.

A New Method for Determining Individual Rate Constants for Specific Non-chromophoric Substrates of Proteolytic Enzymes

1975 ◽  
Vol 53 (4) ◽  
pp. 564-571
Author(s):  
Lewis J. Brubacher
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Proteolytic Enzymes ◽  
Enzyme Mechanism ◽  
Steady State Kinetics ◽  
Steady State Rate ◽  
State Rate ◽  
Individual Rate ◽  
Kinetics Of ◽  
Hydrolysis Of

Equations are developed for the pre-steady state kinetics of the proteolytic enzyme-catalyzed hydrolysis of a substrate A in the presence of a monitoring substrate (or covalent inhibitor) S of known properties. A two-intermediate acyl–enzyme mechanism is assumed in which the first intermediate is in instantaneous equilibrium with enzyme and substrate. The appearance of the first product of substrate S is characterized by two relaxation rate constants. From these constants it is possible to determine the dissociation constant and the acylation and deacylation rate constants of substrate A. Criteria are also developed for using the steady state rate parameters of A to establish conditions for which the slower relaxation process is equivalent to the deacylation rate constant of A. The technique of premixing enzyme with substrate A has certain advantages in this approach.

Sign in / Sign up

Export Citation Format

Share Document