RESUMO
We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
RESUMO
In 1974, Eisenthal and Cornish-Bowden published the direct linear plot method, which used the median to estimate the Vmax and Km from a set of initial rates as a function of substrate concentrations. The robustness of this non-parametric method was clearly demonstrated by comparing it with the least-squares method. The authors commented that the method cannot readily be generalized to equations of more than two parameters. Unfortunately, this comment has been misread by other authors. Comments such as "this method cannot be extended directly to equations with more than two parameters" were found in some publications. In addition, recently, the most drastic comment was published: "this method cannot be applied for the analysis of substrate inhibition." Given all of these presumptions, we have been motivated to publish a demonstration of the contrary: the median method can be applied to more than two-parameter equations, using as an example, the substrate uncompetitive inhibition equation. A computer algorithm was written to evaluate the effect of simulated experimental error of the initial rates on the estimation of Vmax, Km and KS. The error was assigned to different points of the experimental design. Four different KS/Km ratios were analyzed with the values 10, 100, 1000 and 10,000. The results indicated that the least-squares method was slightly better than the median method in terms of accuracy and variance. However, the presence of outliers affected the estimation of kinetic constants using the least-squares method more severely than the median method. The estimation of KS using the median method to estimate 1/KS was much better than the direct estimation of KS, causing a negative effect of non-linearity of KS in the kinetic equation. Considering that the median method is free from the assumptions of the least-squares method and the arbitrary assumptions implicit in the linearization methods to estimate the kinetic constants Vmax, Km and KS from the substrate uncompetitive inhibition equation, the median method is highly superior to all published methods, including the non-linear regression by least squares. We concluded that the median method can be applied to the substrate uncompetitive inhibition equation and other equations with more than two parameters. In addition, as we can project, the median method is the most reliable and robust method for the estimation of kinetic parameters from enzyme kinetic models.
