Error structure as a function of substrate and inhibitor concentration in enzyme kinetic experiments

Abstract

Optimal design of experiments as well as proper analysis of data are dependent on knowledge of the experimental error. A detailed analysis of the error structure of kinetic data obtained with acetylcholinesterase showed conclusively that the classical assumptions of constant absolute or constant relative error are inadequate for the dependent variable (velocity). The best mathematical models for the experimental error involved the substrate and inhibitor concentrations and reflected the rate law for the initial velocity. Data obtained with other enzymes displayed similar relationships between experimental error and the independent variables. The new empirical error functions were shown superior to previously used models when utilized in weighted non-linear-regression analysis of kinetic data. The results suggest that, in the spectrophotometric assays used in the present study, the observed experimental variance is primarily due to errors in determination of the concentrations of substrate and inhibitor and not to error in measuring the velocity.

Paradoxical inhibition of rat glutathione transferase 4-4 by indomethacin explained by substrate-inhibitor-enzyme complexes in a random-order sequential mechanism

“…Non-linear-regression analysis was performed essentially as described previously (Mannervik, 1982;Mannervik et al, 1986). The experimental error in the kinetic data was not constant, as judged from the replicate 4-Hydroxydec- Alin et al (1985b).…”

Optimization of the Cost and Sensitivity of Receptor- and Enzyme-Based Assays

“…Although P rel is often assumed to be a function of v, it can depend on other variables as well (24). Because Z rel is a monotonicly increasing function of I, the lowest I will be found at Z ϭ P and not at Z Ͼ P. Therefore, in order to find the lowest detectable I we need to equate Z rel to P rel and minimize I.…”

Fitting Straight Lines with Replicated Observations by Linear Regression. III. Weighting Data

“…From theoretical grounds, the bias in the absorbance A may be expressed as dA = UA + V + WA 2 [28] where U ,V , and W are the coefficients of proportional, constant and quadratic error (188). Though photometric errors in absorbance (191) have an exponential dependence on A, Equation 28 is a reasonable approximation when A is small.…”

“…1), but it is much better (27) to have replications. Knowledge of the variance of experimental data is fundamental (28) to optimal design and proper analysis in many areas of investigation. With replications we can check the assumption before even fitting a model (29), and can in fact use the information obtained in choosing a form of weighting for weighted least squares (21).…”