Computer-based derivation of rate equations for enzyme-catalyzed reactions. II. Rate equations for isotopic exchange

1970 ◽  
Vol 48 (8) ◽  
pp. 922-934 ◽  
Author(s):  
Arthur R. Schulz ◽  
Donald D. Fisher
Keyword(s):  
Initial Rate ◽  
Maximum Velocity ◽  
Rate Equations ◽  
Exchange Constant ◽  
Exchange Constants ◽  
Computer Based ◽  
Inhibition Constants ◽  
Catalyzed Reactions ◽  
Definition Of ◽  
Enzyme Catalyzed Reactions

A computer-based method is employed for the reformulation of rate equations for enzyme-catalyzed reactions from the coefficient form to the kinetic form. This method is applied to equations for the initial rate of enzyme-catalyzed isotope exchange. In the reformulated equations, the coefficients of each rate equation term are expressed as maximum velocity of the initial rate of the net reaction, Michaelis constants, inhibition constants, and exchange constants. The definition of the exchange constant for a given reactant may be identical to one of the inhibition constants for that reactant.

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 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.

Kinetic method having a linear range for substrate concentrations that exceed Michaelis-Menten constants.

1982 ◽  
Vol 28 (12) ◽  
pp. 2359-2365 ◽  
Author(s):  
S D Hamilton ◽  
H L Pardue
Keyword(s):  
Uric Acid ◽  
Kinetic Method ◽  
Maximum Velocity ◽  
Linear Calibration ◽  
Michaelis Constant ◽  
Relative Standard ◽  
Rate Form ◽  
Catalyzed Reactions ◽  
Total Absorbance ◽  
Enzyme Catalyzed Reactions

Abstract We describe a new data-processing method for the kinetic quantification of substrates of enzyme-catalyzed reactions. Nonlinear regression is used to fit data for absorbance (A) and rate (dA/dt) vs time to the rate form of the Michaelis-Menten equation. Fitting parameters are the maximum velocity (Vmax), the Michaelis constant (Km), and the total absorbance change (delta A infinity) that would be observed if the reaction were monitored to completion. The method is evaluated with use of the uricase-catalyzed oxidation of uric acid, monitored at 293 nm, as a model reaction. Results for aqueous solutions demonstrate linear calibration plots for concentrations from well below to 3.5-fold the Michaelis constant, a zero temperature coefficient (36-38 degrees C), and near zero dependence on inhibitor (xanthine) concentrations that reduce the initial rate of 28% of its uninhibited value. Relative standard deviations (RSDs) vary from about 2 to 15%, depending on the data range (95-65% completion) used to process the data. For an 80% reaction data range, the pooled RSD was 6%. The sensitivity for uric acid is 1.15 x 10(4) L mol-1 cm-1 and the detection limit (95% confidence level) is 1.2 x 10(-6) mol/L.

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