Hansch and Free-Wilson approaches

P.N. Craig, Comparison of the Hansch and Free-Wilson approaches to structure-activity correlation, In Biological Correlations — The Hansch Approach (R.F. Gould, Ed.). Advances in Chemistry Series, No. 114. American Chemical Society, Washington DC, 1972, pp. 115-129. P.N. Craig, Interdependence between physical parameters and selection of substituent groups for correlation studies. J. Med. Chem., 14 (1971) 680-684. 

Comparison of the Hansch and Free-Wilson Approaches to Structure-Activity Correlation... 

Kubinyi, H. (1976a). Quantitative Structure-Activity Relationships. 2. A Mixed Approach, Based on Hansch and Free-Wilson Analysis. J.Med.Chem., 19,587-600. 

Kubinyi H. Quantitative structure-activity relationships 1. The modified free-Wilson approach. 2. A mixed approach, based on Hansch and Free-Wilson analysis. J Med Chem 1976 19 587-600. 

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) ... 

A large combined data set of 48 propafenones was then analyzed by both Free-Wilson analysis and a combined Hansch/Free-Wilson approach using an artificial neural network (ANN). With this approach it was possible, in contrast to conventional MLR analysis, to correctly predict the MDR-reversing activity of 34 compounds of the data set after the ANN was trained by only 14 compounds. Best results were obtained using those descriptors showing the highest statistical significance in MLR analysis [150]. 

The similarity in approaches of Hansch analysis and Free-Wilson analysis allows them to be used within the same framework. This is based on their theoretical consistency and the numerical equivalencies of activity contributions. This development has been called the mixed approach and can be represented by the following equation ... 

The term classical QSAR is often used to denote the - Hansch analysis, -> Free-Wilson analysis, -> Linear Free Energy Relationships (LFER) and -> Linear Solvation Energy Relationships (LSER), i.e. those SRC approaches developed between 1960 and 1980 that can be considered the beginning of the modern QSAR/QSPR methods. 

The most well-known approaches based on substituent descriptors are the Hansch analysis and - Free-Wilson analysis in the latter technique, the substituents are defined by - indicator variables representing their presence/absence in the substitution sites of the parent molecule. 

Tmej, C., Chiba, P., Huber, M., Richter, E., Hitzler, M., Schaper, KJ., and Ecker, G. (1998) A combined Hansch/ Free-Wilson approach as predictive tool in QSAR studies on propafenone-type modulators of multidrug resistance. Archiv der Pharmazie, 331, 233-240. 

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]. 

Besides the Hansch apvproach, other methodologies were also developed to deal with structure- activity questions. The Free-Wilson approach (Free and Wilson, 1964) addresses structure-activity studies in a congeneric series in which the contribution of each structural feature was a parameter of interest. These parameters, also called indicator variables, codify the presence or absence of particular structural feature. They are assigned the binary values of 1 and 0, accordingly. 

The second extrathermodynamic method that we discuss here differs from Hansch analysis by the fact that it does not involve experimentally derived substitution constants (such as o, log P, MR, etc.). The method was originally developed by Free and Wilson [29] and has been simplified by Fujita and Ban [30]. The subject has been extensively reviewed by Martin [7] and by Kubinyi [8]. The method is also called the de novo approach, as it is derived from first principles rather than from empirical observations. The underlying idea of Free-Wilson analysis is that a particular substituent group at a specific substitution site on the molecule contributes a fixed amount to the biological activity (log 1/C). This can be formulated in the form of the linear relationship ... 

The Free-Wilson method of deriving quantitative structure-activity-relationships 101 uses implicit representations of physico-chemical properties and there are also numerous examples where indicator variables have been successfully included in the Hansch approach. 

Several SARs and QSARs have been derived from data on antineoplastic activity as well as for MDR-reversing activity. The Hansch approach, Free-Wilson, and neural network analysis have been applied. The importance of lipophilicity, molar refractiv-ity (MR), and charge for the description of activity is common to all derived relations. 

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. 

In organic chemistry, decomposition of molecules into substituents and molecular frameworks is a natural way to characterize molecular structures. In QSAR, both the Hansch-Fujita " and the Free-Wilson classical approaches are based on this decomposition, but only the second one explicitly accounts for the presence or the absence of substituent(s) attached to molecular framework at a certain position. While the multiple linear regression technique was associated with the Free-Wilson method, recent modifications of this approach involve more sophisticated statistical and machine-learning approaches, such as the principal component analysis and neural networks. ... 

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. 

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