scholarly journals Application of the principle of microscopic reversibility to the steady-state rate equation for a general mechanism for an enzyme reaction with substrate and modifier

1993 ◽  
Vol 295 (3) ◽  
pp. 897-898 ◽  
Author(s):  
M J Selwyn
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Enzyme Reaction ◽  
General Mechanism ◽  
Microscopic Reversibility ◽  
Steady State Rate ◽  
State Rate

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 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 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.

A computer program for writing the steady-state rate equation for a multisubstrate enzymic reaction

1969 ◽  
Vol 47 (10) ◽  
pp. 941-944 ◽  
Author(s):  
R. O. Hurst
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Rate Equation ◽  
Digital Computer ◽  
Memory Capacity ◽  
Enzymic Reaction ◽  
Steady State Rate ◽  
State Rate ◽  
Enzyme Species

The determinant procedure for deriving the rate equation for an enzymic mechanism has been converted into Fortran IV language for use with a digital computer. The distribution equations for three to nine enzyme species, which may interact along all possible pathways, can be determined readily, limited only by the size of the memory capacity of the computer employed. The method permits several mechanisms to be analyzed in a matter of a few minutes.

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