Applications Free Wilson analysis

Kubinyi, H. (1988b). Free Wilson Analysis. Theory, Applications and its Relationship to Hansch Analsyis. Quant.Struct.-Act.Relat., 7,121-133. [R]... 

Kubinyi, H. (1988b) Free-Wilson analysis. Theory, applications and its relationship to Hansch analysis. Quant. Struct. -Act. Relat., 7, 121—133. 

By its definition the Free Wilson analysis is limited to linear additive structure-activity relationships (its application to nonlinear relationships and the combination with Hansch analysis to a mixed approach are described in chapter 4.3). A detailed discussion of the scope and limitations of the Free Wilson model is given in refs. [390, 391] some applications are discussed in chapter 8. 

Due to the relationships between Hansch analysis and the Free Wilson model, indicator variables (chapter 3.8) have relatively early been included in Hansch analyses (e.g. [21, 427, 428]). Both models can be combined to a mixed approach, in a linear (eq. 78) and a nonlinear form (eq. 79), which offers the advantages of both, Hansch analysis and Free Wilson analysis, and widens their applicability in quantitative structure-activity relationships [22]. 

Applications of Free Wilson Analysis and Related Models... 

QSARs include statistical methods to relate biological activities (most often expressed by logarithms of equipotent molar activities) with structural elements (Free Wilson analysis), physicochemical properties (Hansch analysis), or fields (3D QSAR). The parameters used in a QSAR model are also called (molecular) descriptors. Classical QSAR analyses (Hansch and Free Wilson analyses) consider only 2D structures. Their main field of application is in substituent variation of a common scaffold. 3D-QSAR analysis (CoMFA) has a much broader scope. It starts from 3D structures and correlates biological activities with 3D-property fields (McKinney et al. 2000). 

A further improvement came from the combination of Hansch and Free-Wilson analysis in a mixed approach, which widens the applicability of both QSAR methods. In equation (5), physicochemical parameters describe parts of the molecules with broad structural variation, whereas indicator variables encode structural variations which cannot be included otherwise (the lipophilicity parameter tx may be used instead of log P) ... 

The application of Hansch and Free-Wilson analysis can best be explained with the help of a practical example. The antiadrenergic activities of meta-, para-, and disubsti-tuted iV,iV-dimethyl-o(-bromophenethylamines 3 are listed in... 

Application of Free-Wilson Selectivity Analysis for Combinatorial Library Design... 

These special cases of multiple linear regression analysis have been developed for the determination of the impact of individual molecular substructures (independent variables) on one dependent variable. Both techniques are similar yet, the Free-Wilson method considers the retention of the unsubstituted analyte as base, while Fujita-Ban analysis uses the less substituted molecule as reference. These procedures have not been frequently employed in chromatography only their application in QSRR studies in RP TLC and HPLC have been reported. 

The proper application of Hansch and Free-Wilson analyses and the associated problems can best be illustrated with a well-investigated example. The antiadrenergic activities of meta-, para-, and met<2,/><2ra-disubstituted A/A-dimethyl-a-bromophene-thylamines have been investigated by Hansch and Lien [27], Unger and Hansch [28], Cammarata [29], and Kubinyi and Kehrhahn [30]. Table 1 presents the substituents, experimentally observed activity values, the parameter values for n,a+ and Efeta, as well as biological activity values calculated from Eqs. (14) and (16), respectively. To perform a Hansch analysis, the biological data are taken as Y values and an... 

Hansch analysis and the Free Wilson method differ in their application, but they are nevertheless closely related [390, 391, 394]. From the general formulation of a linear Hansch equation (eq. 71 is any physicochemical property) group contributions a can be derived for each substituent under consideration (eq. 72 4>ij is the physicochemical property j of the substituent Xj). 

Like the continuous physico-chemical descriptor Z variables, indicators of the presence or absence of certain substructures have also been treated by multiple regression analysis. As modified by Fujita and Ban (Seydel and Schaper, 1979), this group contribution method can be a useful alternative to the LFER approach, if only limited knowledge is available about the relevant molecular properties or no uniform physico-chemical descriptors for the various compounds in the data set are accessible. For activities and properties of compounds that may be attributed to the occurrence of certain substructures in the molecules (e.g. biodegradation section 4.8), Free-Wilson-type substructure models have their major application in environmental sciences. 

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