Hansch-Free-Wilson model

Equations (9) and (10) constitute the fundament of all QSAR studies. Since 1964, they have remained essentially unchanged, with the exception of two minor modifications. Improvements resulted from the combination of Hansch equations with indicator variables [22], which may be considered as a mixed Hansch/Free-Wilson model (Eq. (11)) [23], and from the formulation of a theoretically derived nonlinear model for transport and distribution of drugs in a biological system, the bilinear model (Sec. 4 Eq. (30)) [24] ... 

Principal components analysis can also be used in the case when the compounds are characterized by multiple activities instead of a single one, as required by the Hansch or Free-Wilson models. This leads to the multivariate bioassay analysis which has been developed by Mager [9]. By way of illustration we consider the physicochemical and biological data reported by Schmutz [41] on six oxazepines... 

Hansch-Free-Wilson mixed models - Hansch analysis... 

Hansch-Free-Wilson mixed models were also proposed [Kubinyi, 1976a] by combining the two approaches in a single model. A quadratic term accounting for hydrophobic interactions (usually log P or n Hansch-Fujita constant) can be added to the Free-Wilson (or Fujita-Ban) model as... 

Hansch bilinear models —> Hansch analysis Hansch descriptors —> Hansch analysis Hansch-Free-Wilson mixed models Hansch analysis... 

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. 

This theoretical relationship between Hansch analysis and the Free Wilson model was first recognized by Singer and Purcell [392]. Although it was questioned by Cammarata [399,425], later investigations confirmed it theoretically and by practical examples [390, 391, 393, 394],... 

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]. 

The Free Wilson model never became as popular as the Hansch model, due to the limitations inherent in its applicability and predictive ability. Only a few hundred studies [390, 391] have been published since 1964. 

The interpretation of the result of a Free-Wilson analysis is somewhat different from that of a Hansch analysis. The coefficients in the Hansch model represent absolute contributions to the biological activity of a compound from the various... 

The statistical methods of QSAR modelling are based on the correlation of changes in biological/toxicological activity (AO) resulting from certain chemical modifications (AC), either directly by structural parameters, called Free Wilson-type relationships, or by the corresponding changes of molecular properties, called Hansch-type analyses (Kubinyi 2002) ... 

Tihe two methods of structure-activity correlation which have received the most application in the past decade are the Hansch multiple parameter method, or the so-called extrathermodynamic approach, and the Free-Wilson, or additive model. The basic differences and similarities of these methods are discussed in this presentation. 

The epoch of QSAR (Quantitative Structure-Activity Relationships) studies began in 1963-1964 with two seminal approaches the a-p-7i analysis of Hansch and Fujita " and the Free-Wilson method. The former approach involves three types of descriptors related to electronic, steric and hydrophobic characteristics of substituents, whereas the latter considers the substituents themselves as descriptors. Both approaches are confined to strictly congeneric series of compounds. The Free Wilson method additionally requires all types of substituents to be suflficiently present in the training set. A combination of these two approaches has led to QSAR models involving indicator variables, which indicate the presence of some structural fragments in molecules. 

Although the predictive power of a model is considered to be a criterion for the relevance of QSAR models, the main purpose of Hansch analysis and related approaches such as Free-Wilson analysis concerns not prediction, but a better understanding of the chemical problem. 

This equation shows the relationship between the Hansch and the Free-Wilson equations. It has been suggested (217, 220) that the Bocek-Kopecky interaction model holds for the parabolic dependence of biological activity on the partition coefficient. 

Statistical methods. Certainly one of the most important considerations in QSAR is the statistical analysis of the correlation of the observed biological activity with structural parameters - either the extrathermodynamic (Hansch) or the indicator variables (Free-Wilson). The coefficients of the structural parameters that establish the correlation with the biological activity can be obtained by a regression analysis. Since the models are constructed in terms of multiple additive contributions the method of solution is also called multiple linear regression analysis. This method is based on three requirements (223) i) the independent variables (structural parameters) are fixed variates and the dependent variable (biological activity) is randomly produced, ii) the dependent variable is normally and independently distributed for any set of independent variables, and iii) the variance of the dependent variable must be the same for any set of independent variables. 

D QSAR Models Hansch and Free-Wilson Analyses... 

On the other hand, Free-Wilson analysis can be used to ease the derivation of a Hansch model. An inspection of the coefficients of the different terms in Eq. (17) shows that activity increases with increasing lipophilicity of the halogens, that methyl leads to a higher activity than to be expected from its lipophilicity (corresponds to chlorine),... 

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