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.

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.

scholarly journals Thermodynamics and Kinetics of Glycolytic Reactions. Part I: Kinetic Modeling Based on Irreversible Thermodynamics and Validation by Calorimetry

2020 ◽  
Vol 21 (21) ◽  
pp. 8341
Author(s):  
Kristina Vogel ◽  
Thorsten Greinert ◽  
Monique Reichard ◽  
Christoph Held ◽  
Hauke Harms ◽  
...  
Keyword(s):  
Equilibrium State ◽  
Kinetic Models ◽  
Metabolic Pathways ◽  
Irreversible Thermodynamics ◽  
Titration Calorimetry ◽  
Metabolic Network Analysis ◽  
Arrhenius Relation ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Kinetics Of

In systems biology, material balances, kinetic models, and thermodynamic boundary conditions are increasingly used for metabolic network analysis. It is remarkable that the reversibility of enzyme-catalyzed reactions and the influence of cytosolic conditions are often neglected in kinetic models. In fact, enzyme-catalyzed reactions in numerous metabolic pathways such as in glycolysis are often reversible, i.e., they only proceed until an equilibrium state is reached and not until the substrate is completely consumed. Here, we propose the use of irreversible thermodynamics to describe the kinetic approximation to the equilibrium state in a consistent way with very few adjustable parameters. Using a flux-force approach allowed describing the influence of cytosolic conditions on the kinetics by only one single parameter. The approach was applied to reaction steps 2 and 9 of glycolysis (i.e., the phosphoglucose isomerase reaction from glucose 6-phosphate to fructose 6-phosphate and the enolase-catalyzed reaction from 2-phosphoglycerate to phosphoenolpyruvate and water). The temperature dependence of the kinetic parameter fulfills the Arrhenius relation and the derived activation energies are plausible. All the data obtained in this work were measured efficiently and accurately by means of isothermal titration calorimetry (ITC). The combination of calorimetric monitoring with simple flux-force relations has the potential for adequate consideration of cytosolic conditions in a simple manner.

Steady-State Kinetics of Enzyme Reactions in the Presence of Added Nucleophiles

1972 ◽  
Vol 50 (12) ◽  
pp. 1334-1359 ◽  
Author(s):  
Irwin Hinberg ◽  
Keith J. Laidler
Keyword(s):  
Specific Binding ◽  
Specific Binding Sites ◽  
Steady State Kinetics ◽  
Special Cases ◽  
Kinetics Of Formation ◽  
Catalyzed Reactions ◽  
Enzyme Catalyzed Reactions ◽  
Concentration Graphs ◽  
Kinetics Of ◽  
Hydrolysis Of

Many enzyme-catalyzed reactions, such as hydrolyses, give rise to two products P1 and P2 which are formed in different reaction steps. The second product P2 is frequently formed by hydrolysis of an intermediate such as an acyl-enzyme or a phosphoryl-enzyme. An alternative nucleophile N introduced into the system forms an additional product P3. The present paper is concerned with the kinetics of formation of P1, P2, and P3 in the presence of added nucleophiles. A number of alternative mechanisms are considered, and equations are derived for the rates of formation of the three products, and the Michaelis constant, as functions of nucleophile concentration. Graphs are presented showing the variations of these parameters with the concentration of N, for a variety of special cases. Special attention is given to the possibility of specific binding sites for the water and the nucleophile molecules.The data for a number of enzyme systems are discussed with reference to the treatment. For reactions catalyzed by alkaline phosphatase it is concluded that only one mechanism (mechanism VI) is consistent with the results.

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