Applications Hansch analysis

A difficulty with Hansch analysis is to decide which parameters and functions of parameters to include in the regression equation. This problem of selection of predictor variables has been discussed in Section 10.3.3. Another problem is due to the high correlations between groups of physicochemical parameters. This is the multicollinearity problem which leads to large variances in the coefficients of the regression equations and, hence, to unreliable predictions (see Section 10.5). It can be remedied by means of multivariate techniques such as principal components regression and partial least squares regression, applications of which are discussed below. 

Introduced by Corwin Hansch in the early 1960s, Hansch analysis considers both the physicochemical aspects of drug distribution from the point of application to the point of effect and the drug-receptor interaction. In a given group of drugs that have analogous structures and act by the same mechanism, three parameters seem to play a major role ... 

The most common error in application of this method lies in a lack of appreciation of the minimum statistical requirements involved. Thus, one needs to have about five well-chosen compounds for every variable term in a Hansch analysis in order to feel confident about the results. For example, an equation such as Equation 2 above should be derived from 10 or more compounds, and one such as Equation 3, from 15 or more examples. A smaller number of examples per term may lead to useful results, but one cannot often support these results by statistics. A frequent abuse is seen when a large number of variable terms are used in a complex equation (four or more terms) which was derived from only 10 or 12 examples. The statistician would prefer to have 15 to 20 more compounds than the degrees of freedom in the resulting equation not often is this luxury met. 

Hemmateenejad B, Akhond M, Miri R, Shamsipur M. Quantitative structure-activity relationship study of recently synthesized 1,4-dihydropyridine calcium channel antagonists. In Application of the Hansch analysis method. Weinheim Arch Pharm, 2002. p. 472-80. 

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

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... 

Only one illustrative example is given here to describe and explain the proper application of Hansch analysis (for further examples see chapter 7). Graham and Karrar [397] determined the antiadrenergic activities of a series of a-bromo-phenethylamines (8). Hansch and Lien [398] derived eq. 63, which was at this time considered to give the best quantitative description of the data (Table 12 only some... 

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. 

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). 

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]. 

No attempt has been made to present a comprehensive overview, of the use of Hansch analysis in medicinal chemistry. Only a subjective selection of typical applications is given in this chapter to demonstrate its proper use and its value for rational drug design. For more examples the reader is referred to refs. [39 — 44] and to the abstracts services listed in chapter 1.1 [85 — 88]. 

According to the aim of this new series Hugo Kubinyi gives a practice-oriented introduction into Hansch analysis and related approaches which familiarizes the reader with the proper application of these methodologies. The comprehensive list of references gives an excellent access to current literature and comfortably introduces the reader to fields of his special interest. 

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). 

Indirectly, the additivity concept of biological activity values follows from many thousands of successful applications of Hansch analysis. It has also has been proven by several dedicated investigations. For inhibitor complexes with known 3D structures, the biological activities of the ligands could be correlated with the ionic, polar, and nonpolar interactions with their binding sites. ... 

There is a long history of efforts to find simple and interpretable /i and fi functions for various activities and properties (29, 30). The quest for predictive QSAR models started with Hammett s pioneer work to correlate molecular structures with chemical reactivities (30-32). However, the widespread applications of modern predictive QSAR and QSPR actually started with the seminal work of Hansch and coworkers on pesticides (29, 33, 34) and the developments of various powerful analysis tools, such as PLS (partial least squares) and neural networks, for multivariate analysis have fueled these widespread applications. Nowadays, numerous publications on guidelines, workflows, and... 

Thanks largely to the work of Hansch and his collaborators, the general relationship used in the application of correlation analysis to bioactivities is of the form... 

The QSAR analysis of the monoamine oxidase (MAO) inhibitors by Kutter and Hansch is one of the earliest successes in the application of Es constante). They... 

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