A matrix transformation method for writing the rate equations for complementary enzymic reactions

1969 ◽  
Vol 47 (6) ◽  
pp. 643-656 ◽  
Author(s):  
R. O. Hurst
Keyword(s):  
Transformation Method ◽  
Product Inhibition ◽  
Kinetic Constants ◽  
Matrix Transformation ◽  
Rate Equations ◽  
Enzymic Reaction ◽  
Enzyme Intermediates ◽  
Inhibition Pattern

A procedure is outlined for writing two rate equations that will yield the same product-inhibition pattern for an enzymic reaction. The definitions of the kinetic constants and the structure of the distribution equations for the enzyme intermediates as well as the order of interaction of the enzyme with the reactants will be different. A list of several mechanisms which can be qualified in this way is included.

Alternative mechanism for a bimolecular nonsequential enzymic reaction

1969 ◽  
Vol 47 (2) ◽  
pp. 111-115 ◽  
Author(s):  
R. O. Hurst
Keyword(s):  
Reaction Mechanism ◽  
Product Inhibition ◽  
Alternative Mechanism ◽  
Enzymic Reaction ◽  
Dead End ◽  
Ping Pong ◽  
Inhibition Studies ◽  
Different Order ◽  
Inhibition Pattern

An enzymic reaction mechanism characterized as 'di-Uni Iso Ping Pong' which has the same product inhibition pattern as the 'Ping Pong Bi Bi' mechanism but a different order for the release of products is discussed. A basis for differentiating the two mechanisms by dead-end inhibition studies is given.

Deriving the rate equations for product inhibition patterns in bisubstrate enzyme reactions

2006 ◽  
Vol 21 (6) ◽  
pp. 617-634 ◽  
Author(s):  
Vladimir Leskovac ◽  
Svetlana Trivić ◽  
Draginja Peričin ◽  
Julijan Kandrač
Keyword(s):  
Product Inhibition ◽  
Rate Equations ◽  
Enzyme Reactions

scholarly journals Estimating the Product Inhibition Constant from Enzyme Kinetic Equations Using the Direct Linear Plot Method in One-Stage Treatment

Catalysts ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 853
Author(s):  
Pedro L. Valencia ◽  
Bastián Sepúlveda ◽  
Diego Gajardo ◽  
Carolina Astudillo-Castro
Keyword(s):  
Least Squares Method ◽  
Competitive Inhibition ◽  
Kinetic Equations ◽  
Initial Reaction Rate ◽  
Product Inhibition ◽  
Kinetic Constants ◽  
Initial Reaction ◽  
Mathematical Treatment ◽  
One Stage ◽  
Linear Plot

A direct linear plot was applied to estimate kinetic constants using the product’s competitive inhibition equation. The challenge consisted of estimating three kinetic constants, Vmax, Km, and Kp, using two independent variables, substrates, and product concentrations, in just one stage of mathematical treatment. The method consisted of combining three initial reaction rate data and avoiding the use of the same three product concentrations (otherwise, this would result in a mathematical indetermination). The direct linear plot method was highly superior to the least-squares method in terms of accuracy and robustness, even under the addition of error. The direct linear plot method is a reliable and robust method that can be applied to estimate Kp in inhibition studies in pharmaceutical and biotechnological areas.

scholarly journals Reversible enzyme-catalysed reactions: the quasi steady state as a a quasi-equilibrium, and a correction to Haldane's kinetic constants and to secondary relationships involving kinetic constants.

2021 ◽  
Author(s):  
Eric A Barnsley
Keyword(s):  
Steady State ◽  
Rate Constants ◽  
Rate Of Change ◽  
Kinetic Constants ◽  
Rate Equations ◽  
Quasi Equilibrium ◽  
Quasi Steady State ◽  
Enzyme Substrate ◽  
State Approximation ◽  
Specificity Constant

For reversible enzyme-catalysed reactions obeying Henri-Michaelis-Menten kinetics, theoretical solution of the rate equations for the enzyme-substrate intermediate are generally incorrect when the quasi-steady state approximation, equating the rate of change of the concentration of the enzyme-substrate intermediate to zero, is used.  For the simplest kinetic model used by Haldane, such a procedure does not reveal that in one direction, that starting with the reactant having the lower binding constant, the quasi-steady state is one of quasi-equilibrium, and Haldane’s structure of the Km written in terms of rate constants is incorrect. This is probably also true of more complex mechanisms in which the structure of kcat may also be in error.  Modern methods of numerical integration for the solution of rate equations, if applied to reversible reactions to obtain rate constants from measured catalytic constants, will require the correct expressions for kcat and Km. Furthermore, the (now called) Haldane relationship, relating the kinetic constants kcat and Km for the forward and reverse reactions to the equilibrium constant of a reaction, is now seen to be generally incorrect, and in addition another exception for a the theoretical validation of kcat /Km as a specificity constant arises.

scholarly journals On the validity and errors of the pseudo-first-order kinetics in ligand–receptor binding

2016 ◽  
Author(s):  
Wylie Stroberg ◽  
Santiago Schnell
Keyword(s):  
Receptor Binding ◽  
Approximate Equation ◽  
Approximate Solutions ◽  
Kinetic Constants ◽  
Rate Equations ◽  
Phase Plane Analysis ◽  
Binding Interaction ◽  
First Order ◽  
First Order Kinetics ◽  
Pseudo First Order

AbstractThe simple bimolecular ligand–receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor concentration. The validity of the derived condition is analyzed from two viewpoints. In the first, time courses of the exact and approximate solutions to the ligand–receptor rate equations are compared when all rate constants are known. The second viewpoint assess the validity through the error induced when the approximate equation is used to estimate kinetic constants from data. Although these two interpretations of validity are often assumed to coincide, we show that they are distinct, and that large errors are possible in estimated kinetic constants, even when the linearized and exact rate equations provide nearly identical solutions.

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