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.

Effects of modifiers on the kinetics of two-substrate enzyme reactions

1968 ◽  
Vol 46 (11) ◽  
pp. 1381-1396 ◽  
Author(s):  
J. Frank Henderson
Keyword(s):  
Steady State ◽  
Binding Sites ◽  
Rate Equations ◽  
Enzyme Reactions ◽  
Ping Pong ◽  
Steady State Rate ◽  
State Rate ◽  
Kinetics Of

Steady state rate equations have been derived for ordered bi bi and ping pong bi bi reactions in which there are (a) one or two nonsubstrate modifiers, (b) two different binding sites for a single nonsubstrate modifier, (c) one or two substrates acting as modifiers, and (d) both nonsubstrate modifiers and substrates acting as modifiers. The deviation of these equations from the Michaelis–Menten equation is shown and methods are suggested by which many of these mechanisms can be distinguished experimentally.

A COMPARISON BETWEEN THE INITIAL RATE EXPRESSIONS OBTAINED UNDER STRICT CONDITIONS AND THE RAPID EQUILIBRIUM ASSUMPTION USING, AS EXAMPLE, A FOUR SUBSTRATE ENZYME REACTION

2011 ◽  
Vol 10 (05) ◽  
pp. 659-678
Author(s):  
J. M. YAGO ◽  
C. GARRIDO-DEL SOLO ◽  
M. GARCIA-MORENO ◽  
R. VARON ◽  
F. GARCIA-SEVILLA ◽  
...  
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Initial Rate ◽  
Enzyme Reaction ◽  
Rate Equations ◽  
Steady State Rate ◽  
State Rate ◽  
Rapid Equilibrium ◽  
Kinetics Of ◽  
Substrate Concentrations

The software WinStes, developed by our group, is used to derive the strict steady-state initial rate equation of the reaction mechanism of CTP:sn-glycerol-3-phosphate cytidylyltransferase [EC 2.7.7.39] from Bacillus subtilis. This enzyme catalyzes a reaction with two substrates and operates by a random ordered binding mechanism with two molecules of each substrate. The accuracy of the steady-state rate equation derived is checked by comparing the rate values it provides with those obtained from the simulated progress curves. To analyze the kinetics of this enzyme using the strict steady-state initial rate equation, several curves for different substrate concentrations and different rate constants are generated. A comparison of these curves with the curves obtained from the rapid equilibrium initial rate equation, with different substrate concentration values, serves to analyze how the strict steady-state rate equation values are closer to those of rapid equilibrium rate equations when rapid equilibrium conditions are fulfilled.

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.

scholarly journals Methods of determining rate constants in single-substrate–single-product enzyme reactions. Use of induced transport: limitations of product inhibition

1973 ◽  
Vol 133 (2) ◽  
pp. 255-261 ◽  
Author(s):  
H. G. Britton
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Enzyme Reaction ◽  
Product Inhibition ◽  
Single Product ◽  
Single Substrate ◽  
Product Term ◽  
Steady State Kinetics ◽  
Steady State Rate ◽  
State Rate

1. The calculation of the rate constants from steady-state kinetics of a single-substrate–single-product enzyme reaction in which there is an isomerization of the enzyme is described. 2. It is shown that even with the use of isotopically labelled substrates a set of solutions for the constants is obtained rather than a unique solution. However, limits are derived within which they must lie. 3. The most appropriate observations to determine the rate constants are measurements of Vmax. and Km for both substrate and product, and measurement of the degree of countertransport in an induced-transport test. 4. Experimental procedures for induced-transport tests and the quantitative interpretation of the results obtained are discussed. 5. Product inhibition is shown to be an ambiguous and imprecise means of determining the rate constants. Further, the absence of a [substrate]×[product] term in the denominator of the steady-state rate equation does not necessarily mean that the isomerization of the enzyme is rapid, since the term also disappears when the isomerization is very slow. 6. Similar considerations apply to carrier mechanisms.

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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