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An approach to obtaining an optimal design in the non‐linear least squares determination of binding parameters in a complex biochemical system
Author(s) -
Crisponi Guido,
Nurchi Valeria,
Ganadu M. Luisa
Publication year - 1990
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1180040204
Subject(s) - diagonal , mathematics , matrix (chemical analysis) , least squares function approximation , diagonal matrix , explained sum of squares , design matrix , expression (computer science) , linear least squares , mathematical optimization , linear model , statistics , computer science , chemistry , chromatography , estimator , programming language , geometry
Abstract The design of an experiment for the determination of binding parameters in the association between a ligand and a macromolecule with two groups of non‐interacting binding sites is proposed. In the Gauss–Newton non‐linear least squares treatment the standard deviation of each parameter is given as the product of two terms: one depending on the experimental error and the other, the diagonal element of the dispersion matrix, depending only on the independent variables of the system. In order to reach an optimal experimental design, these diagonal elements of the information matrix have to be minimized. In our approach this is achieved by searching those values of the independent variable which maximize the determinant of the information matrix. Furthermore, the limits of validity of the model are deduced from an analysis of the diagonal elements of the information matrix obtained under optimal conditions.