Evaluating Hansch Analysis

Thus far, this chapter has extolled the virtues of Hansch analysis. The method is simple to understand, easy to execute, and can lead to QSAR equations that may provide insight into the activity of a lead compound. The Hansch method has many clear and appealing 

One challenge to Hansch analysis is also its strength simplicity. The binding of a drug to a target is a complex process with many relevant factors. To reduce biological ac- 

FIGURE 12.6 A portion of the Topliss tree for aromatic substitution 

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Hansch analysis and other classical QSAR approaches evaluate the QSAR model based on the correlation of rows of compounds with known activities (dependent variables) to columns of parameters (independent variables). For this reason, classical QSAR is sometimes called 2D QSAR. CoMFA is an example of 3D QSAR because lead analogues are modeled and analyzed in a virtual three-dimensional space. The value of both methods ultimately hinges on how well experimental and calculated activities correlate (Figure 12.2) and how well the model predicts the activity of compounds not included in the training set. 

Tlie main assumption of this approach is that the shape of the molecule is closely related to the shape of the - binding site cavity and, as a consequence, to the biological activity. Therefore, a shape reference compound is chosen which represents the binding site cavity, and the similarity (or commonality) measured between the reference shape and the shape of other compounds is used to determine the biological activity of these compounds. As well as the shape similarity measures, other molecular descriptors such as those in - Hansch analysis can be used to evaluate the biological response. The MSA model is thus defined as ... 

Substituent Parameters. A significant advance was made, in the structure-activity studies with the Hill reaction, when Hansch and Deutsch (12) evaluated some of the published Hill inhibition data with a multiple regression analysis, an extra-thermodynamic approach, or the so-called sigma, pi (a, T ) regression analysis. The principle of the approach rests on the assumption that changes in biological activity can be correlated with measurable molecular or substituent parameters. This analysis involved equations of the following type ... 

We have shown that the intrinsic electronic contribution to the Hammett substituent constant, cre(o>), may be obtained from a statistical analysis that follows from the comparison of the experimental <7p values and the electronic electrophilicity index co evaluated for isolated molecules.127 The analysis was performed for the electrophilicity of a series of substituted ethylenes, X-CH=CH2, and the crp values reported by Hansch et al.12S for a wide list of functional groups (FG), X-, commonly present in organic compounds. 

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