Mixed 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] ... 

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. 

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]. 

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