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Estimating Michaelis-Menten Parameters: Bias, Variance and Experimental Design

David J. Currie
Biometrics
Vol. 38, No. 4 (Dec., 1982), pp. 907-919
DOI: 10.2307/2529871
Stable URL: http://www.jstor.org/stable/2529871
Page Count: 13
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Estimating Michaelis-Menten Parameters: Bias, Variance and Experimental Design
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Abstract

The accuracy and precision with which the parameters of the Michaelis-Menten function can be estimated are known to depend upon the technique used to fit the function to experimental data. In this paper it is demonstrated that the design matrix (or choice of values for the independent variable) is equally important. The efficiency of parameter estimation by three fitting techniques is compared by Monte Carlo simulations, and the sensitivity of each technique to changes in the design matrix is examined. Minimum variance unbiased estimates of the parameters are obtained by taking half the observations at exactly K and the other half as high as possible, and then fitting the data by a maximum likelihood technique. Some designs which spread the observations across the range of substrate concentrations produce biased, high-variance parameter estimates. A geometric sequence of observations, fitted by either a maximum likelihood technique or Eisenthal and Cornish-Bowden's (1974, Biochemical Journal 139, 721-730) nonparametric technique, yields acceptable estimates.

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