A procedure based on statistical criteria for discrimination between steady state kinetic models

Bartfai, Tamás; Mannervik, Bengt

doi:10.1016/0014-5793(72)80585-4

Cited by 56 publications

(17 citation statements)

References 26 publications

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“…The residual sum of squares, which should be smallest for the 'best' fit of the data (cf. [6,7]), could not be improved by inclusion of a third-degree term (model VIII). The superiority of model VII as compared with models 1-111 is clear on the basis of a significantly lower residual sum of squares (as tested by the F statistic and the 'extra sum of squares' principle [17]).…”

Section: Error In the Dependent Variablementioning

confidence: 99%

“…When initial velocity was treated as the 'independent variable', the mean of the replicates in an experimental point was used. The selection of good mathematical models was based on the results of the regression analysis and the procedure previously described [6,7]. The distribution of residuals was analyzed by two statistical programs (SPSSH and BMDPSD) in the IBM library.…”

Section: Analysis O J Kinetic Datamentioning

confidence: 99%

“…An analysis of experiments with variable enzyme concentrations is presented in Table 1. The results can be analyzed by statistical tests [6,7] and are directly convertible to variance as a function of velocity, because the latter quantity is directly proportional to enzyme concentration (cf. Fig.2).…”

Section: Error In the Dependent Variablementioning

confidence: 99%

“…Both discrimination between rival kinetic models and parameter estimation in a particular model are fundamentally dependent on the distribution of error in the data set under consideration. Even the experi-ment designs for discrimination [6,7] and parameter estimation [8] should be optimized with due attention to the error structure.…”

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Error Structure of Enzyme Kinetic Experiments

Askelöf

Korsfeldt

Mannervik

1976

European Journal of Biochemistry

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Knowledge of the error structure of a given set of experimental data is a necessary prerequisite for incisive analysis and for discrimination between alternative mathematical models of the data set. A reaction system consisting of glutathione S-transferase A (glutathione S-aryltransferase), glutathione, and 3,4-dichloro-l-nitrobenzene was investigated under steady-state conditions. It was found that the experimental error increased with initial velocity, u, and that the variance (estimated by replicates) could be described by a polynomial in vor by a power function These equations were good approximations irrespective of whether different v values were generated by changing substrate or enzyme concentrations. The selection of these models was based mainly on experiments involving varying enzyme concentration, which, unlike v, is not considered a stochastic variable. Different models of the variance, expressed as functions of enzyme concentration, were examined by regression analysis, and the models could then be transformed to functions in which velocity is substituted for enzyme concentration owing to the proportionality between these variables.Thus, neither the absolute nor the relative error was independent of velocity, a result previously obtained for glutathione reductase in this laboratory [BioSysterns 7, 101 -119 (1975)l. If the experimental errors or velocities were standardized by division with their corresponding mean velocity value they showed a normal (Gaussian) distribution provided that the coefficient of variation was approximately constant for the data considered. Furthermore, it was established that the errors in the independent variables (enzyme and substrate concentrations) were small in comparison with the error in the velocity determinations.For weighting in regression analysis the inverted value of the local variance in each experimental point should be used. It was found that the assumption of proportionality between variance and v a (where a is an empirically determined exponent) was a good approximation for the weighting. The value of a was 1.6 in the present case. The weight function was tested in the fitting of a rate equation to a kinetic-data set involving variable substrate concentrations.Recommendations are given regarding the establishment of the error structure in a general case and its application in regression analysis.

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Section: Error In the Dependent Variablementioning

confidence: 99%

Section: Analysis O J Kinetic Datamentioning

confidence: 99%

Section: Error In the Dependent Variablementioning

confidence: 99%

mentioning

confidence: 99%

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Error Structure of Enzyme Kinetic Experiments

Askelöf

Korsfeldt

Mannervik

1976

European Journal of Biochemistry

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“…Several workers (Anscombe & Tukey, 1963;Haarhoff, 1969;Bartfai & Mannervik, 1972;Reich et al, 1972Reich et al, , 1974Storer et al, 1975;Atkins, 1976) have examined the properties of the normalized residual (r) defined by eqn. (1): virtually any curvilinear model would have eliminated the correlation between the residual and the independent variable.…”

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confidence: 99%

What happens when data are fitted to the wrong equation?

Ellis¹,

Duggleby²

1978

Biochemical Journal

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In many problems of data analysis it is necessary to fit the data to a mathematical equation. Random errors of measurement will be responsible for deviations between the data and the equation, but superimposed on this there may be deviations that result from the equation being an inadequate description ofthe system from which the data were obtained. Plots of the residual (i.e. the difference between the experimental and calculated values of the dependent variable) against each of the experimental variables have been previously used to detect a misfit between the data and the equation. In the present paper, we show that the shape of the residual plots may be used as a guide in choosing a more appropriate equation. In addition, residual plots give useful information on the error structure of the data, and hence the weighting factors that should be used in the analysis. The purpose of the present paper is to show that, when data are fitted to the wrong equation, the shape of the residual plot contains valuable information that can be utilized to determine the way in which the equation should be modified to achieve a better description of the data.

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Experimental Designs for the Distribution-Free Analysis of Enzyme Kinetic Data

Duggleby

1981

Kinetic Data Analysis

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A procedure based on statistical criteria for discrimination between steady state kinetic models

Cited by 56 publications

References 26 publications

Error Structure of Enzyme Kinetic Experiments

Error Structure of Enzyme Kinetic Experiments

What happens when data are fitted to the wrong equation?

Experimental Designs for the Distribution-Free Analysis of Enzyme Kinetic Data

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