title: Application of the median method to estimate the kinetic constants of the substrate uncompetitive inhibition equation.
abstract: In 1974, Eisenthal and Cornish-Bowden published the direct linear plot method, which used the median to estimate the Vmaxand Kmfrom 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, Kmand KS. The error was assigned to different points of the experimental design. Four different KS/Kmratios 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 KSusing the median method to estimate 1/KSwas much better than the direct estimation of KS, causing a negative effect of non-linearity of KSin 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, Kmand KSfrom 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.
authors.affiliation: Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María, PO Box 110-V, Valparaíso, Chile. Electronic address: pedro.valencia@usm.cl.
authors.forename: Pedro L
authors.initials: PL
authors.lastname: Valencia
authors.affiliation: Escuela de Alimentos, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
authors.forename: Carolina
authors.initials: C
authors.lastname: Astudillo-Castro
authors.affiliation: Department of Mathematics, Universidad Técnica Federico Santa María, Valparaíso, Chile.
authors.forename: Diego
authors.initials: D
authors.lastname: Gajardo
authors.affiliation: Department of Mathematics, Universidad Técnica Federico Santa María, Valparaíso, Chile.
authors.forename: Sebastián
authors.initials: S
authors.lastname: Flores
mesh_terms: D007700:Kinetics; D008956:Models, Chemical
keywords: Direct linear plot; Kinetic constants estimation; Median method; Substrate inhibition