An "Aufbau" Approach To Understanding How the King–Altman Method of Deriving Rate Equations for Enzyme-Catalyzed Reactions Works

2009 ◽  
Vol 86 (3) ◽  
pp. 385 ◽  
Author(s):  
Paul A. Sims
Keyword(s):  
Rate Equations ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions

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.

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.

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.

Parameter Evaluation in Second-Degree Rate Equations for Enzyme-Catalyzed Reactions

1972 ◽  
Vol 50 (12) ◽  
pp. 1369-1375 ◽  
Author(s):  
John W. Bunting ◽  
Joe Murphy
Keyword(s):  
Experimental Data ◽  
Iteration Process ◽  
Rate Equations ◽  
Parameter Estimates ◽  
Parameter Evaluation ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Two Parameters ◽  
Iteration Technique ◽  
Second Degree

An iteration technique has been developed for fitting curves to experimental data for velocity dependence on substrate concentration in enzyme-catalyzed reactions which give rise to second-degree rate equations. Initial estimates are required for only two parameters; these estimates may differ from acceptable values for these parameters by several orders of magnitude without influencing the convergence of the iteration process. Applications of the technique to specific sets of experimental data are given, and the independence of the values for each of the final parameters on the values of the initial parameter estimates is demonstrated.

A kinetic analysis of coupled sequential enzyme reactions

2018 ◽  
Author(s):  
Justin Eilertsen ◽  
Santiago Schnell
Keyword(s):  
Enzyme Assay ◽  
Sequential Reaction ◽  
Enzyme Reactions ◽  
Indicator Reaction ◽  
Single Substrate ◽  
Complex Sequences ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Single Enzyme

<div>As a case study, we consider a coupled enzyme assay of sequential enzyme reactions obeying the Michaelis--Menten reaction mechanism. The sequential reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction becomes the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the sequential reaction is described by a pair of interacting Michaelis--Menten equations. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis--Menten equations are derived. The theory can be extended to deal with more complex sequences of enzyme catalyzed reactions.</div>

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