Studies on the differential equations of enzyme kinetics. I. bimolecular scheme: simplified model

The main properties of the solution of the differential system of the model are obtained by qualitative integration. The integral curve is compared with the solutions given by the two classical approximations to the problem: it is shown that the steady-state approximation is to be preferred to the rapid equilibrium theory as a general method and the conditions under which they will furnish accurate results are discussed.

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The Legitimacy of the Quasi-Steady State Approximation in Enzyme Kinetics: A Singular Perturbation Approach

Nonlinear Phenomena in Chemical Dynamics - Springer Series in Synergetics ◽

10.1007/978-3-642-81778-6_47 ◽

1981 ◽

pp. 260-260

Author(s):

G. Fritzsch ◽

M. S. Seshadri

Keyword(s):

Steady State ◽

Singular Perturbation ◽

Enzyme Kinetics ◽

Perturbation Approach ◽

Quasi Steady State ◽

State Approximation ◽

Steady State Approximation

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STEADY-STATE DEPARTURE IN ENZYME REACTIONS

Canadian Journal of Chemistry ◽

10.1139/v61-330 ◽

1961 ◽

Vol 39 (12) ◽

pp. 2502-2507

Author(s):

Hyung Kyu Shin ◽

J. Calvin Giddings

Keyword(s):

Steady State ◽

Enzyme Reaction ◽

Steady State Concentration ◽

Simple Criterion ◽

Enzyme Reactions ◽

State Approximation ◽

Steady State Approximation ◽

State Concentration ◽

General Method

A method is described for calculating the departure from steady-state conditions in enzyme reactions. This provides an immediate and simple criterion for the validity of the steady-state approximation. Several variations of the general method, differing in the degree of simplicity and in the treatment of initial transients, are formulated and discussed. These methods are applied to the general case of an enzyme reaction following the Michaelis–Menten mechanism. Specific applications are made using the data of Chance and Gutfreund. While in these specific cases the steady-state concentration of intermediate is reasonably accurate, the extent of reaction may easily vary from that calculated by means of the steady state.

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Studies on the differential equations of enzyme kinetics. II. bimolecular reaction: the fitting of experimental data to the simplified model

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171288000687 ◽

1988 ◽

Vol 11 (3) ◽

pp. 575-583

Author(s):

Claude Marmasse ◽

Joseph Wiener

Keyword(s):

Experimental Data ◽

Differential Equations ◽

Enzyme Kinetics ◽

Least Squares ◽

Differential System ◽

Taylor Expansion ◽

Weighted Least Squares ◽

Bimolecular Reaction ◽

Simplified Model ◽

Unbiased Estimates

Efficient and unbiased estimates of the parameters of the differential system, as well as simultaneous fiducial limits, are obtained through an (eventually weighted) least-squares fitting to a Taylor expansion of the concentration of the products of the reaction.

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