1. Published data for absorption kinetics have been fitted by non-linear regression to (i) a single Michaelis-Menten function, (ii) a Michaelis-Menten function plus a linear term and (iii) a sum of two Michaelis-Menten functions. A series of criteria have been drawn up to establish the goodness of fit in each case. 2. In 17 out of 35 cases the Michaelis-Menten function was the "best fit". In nine cases the "best-fit" model also included a linear term, but never was the sum of two Michaelis-Menten functions accepted to be the "best-fit" model. 3. Linearity of a Lineweaver-Burk plot was of unreliable diagnostic value in assessing goodness of fit. 4. Since the fit of a Michaelis-Menten function was often poor, simulated data sets with error were used to study the influence of experimental design etc. on Michaelis-Menten parameter estimation. 5. Precision of estimation of Km is increased by increasing the number of data points, reducing their variance, increasing the data range and by straddling Km in the observations. For a given constant number of observations there is no advantage in using replicate observations at few concentrations or single values at relatively many concentrations, or in using single values rather than means. 6. The caution necessary in interpretation of kinetic models is emphasized.

Animals↗

PubMed1977

An evaluation of ways of using equilibrium dialysis to quantify the binding of ligand to macromolecule.

1. The effect of systematic error (loss of ligand, complex or macromolecule) on three of the experimental designs by which equilibrium dialysis may be used to quantify the interaction of ligand and macromolecule is examined theoretically, and the design that is least sensitive to systematic error is identified. 2. Thirteen methods for fitting the binding isotherm to experimental data are compared by using them to analyse simulated data containing random error, and the most reliable method is identified.

Dialysis↗

PubMed1977

Routines for calculating the first derivative of a function by numerical methods.

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Computers↗

PubMed1976

Methods for fitting equations with two or more non-linear parameters.

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

Enzymes↗

PubMed1976

Tests for the goodness of fit of models.

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Enzymes↗

PubMed1975

A comparison of seven methods for fitting the Michaelis-Menten equation.

The Michaelis-Menten equation was fitted to simulated data containing different sorts of error by using the three linear transformations, and the methods of S. R. Cohen [Anal. Biochem. (1968) 22, 549-552], R. Eisenthal & A. Cornish-Bowden [Biochem. J. (1974) 139, 715-120], F. de M. Merino [Biochem. J. 143, 93-95] and G. N. Wilkinson [Biochem. J. (1961) 808 324-332). The best methods were those of Eisenthal & Cornish-Bowden (1974) and Wilkinson (1961).

Kinetics↗