Hansch-type parameters

The procedure takes as input parameters the measured (or calculated) pKa and the measured (or calculated) octanol-water partition coefficient, log P. The latter parameter is used to estimate the intrinsic solubility So, using the Hansch-type expression [38], log So = 1.17 — 1.38 log P, or an improved version for ionizable molecules of moderate lipophilicity (Fig. 6.6) ... 

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) ... 

The classical QSAR methodology started 1964 with the publications of Hansch and Fujita (1964) and Free and Wilson (1964) and the statement of Hansch (1969) resulted from a proposal by Fujita. They proposed to combine several physiochemical parameters (tt, a), also called descriptors, in a quantitative model. This Hansch-type analysis is very flexible and describes many different kinds of biological activities, e.g. in vitro data such as enzyme inhibition (Kubinyi 2002) ... 

The mixed approach allows the description of data sets, when the structural variation is sufficient to derive a Hansch-type relationship for one or several sites of substitution (parameters with index] in eqs. 78 and 79), while for others indicator variables are appropriate because the structural variation is too narrow (group contributions with index i), e.g. eq. 60 (chapter 3.8) or eq. 81 for the inhibition of dihydrofolate reductase by dihydrotriazines (14) [28, 431, 432]. 

Sometimes, the derivation of a simple Hansch equation is the result of a complex series of analyses and hypotheses on the mechanisms underlying the biological activity/property under study. The final equation thus summarizes such preliminary work. The correct application of Hansch-type QSARs provides a powerful tool for estimating parameters in environmental sciences and its prevailing efficiency is illustrated throughout Part 2. 

Indicator variables which encode certain structural features that cannot otherwise be described are very important parameters. From a theoretical point of view, they are Free-Wilson-type parameters. Their additional consideration in Hansch equations broadens the scope and applicability of this approach (cf. equation 5, Section 2.2). " ... 

Ob-6 AvatyCO 1) In the QSAR-context, it is necessary and sufficient that p verifies conditions C2), i.e., to be a dissimilarity index. In this sense MSD was used as a steric parameter (instead of the Taft Eg constant, for example) in Hansch type structure-biological activity correlations. 2) These results obtained for MSD are valid... 

Here we will not discuss these problems and the intriguing observation that am and strong correlation which is, however, difficult to explain (reviews Charton, 1981 Cook et al., 1989 Hansch et al., 1991). These questions were intensively studied in the 1970s and 1980s, leading gradually to the development of field and resonance parameters denoted by F and R respectively (after an original proposal of Swain and Lupton, 1968), which can be considered as independent of each other. The secondary parameters R + and R reflect the potential for an additional mesomeric donor-acceptor interaction (as in 7.7, and the opposite type with a donor instead of NQ2 and the reaction site as acceptor). 

Although the Hammett equation was, and still is, very successful in quantifying electronic interactions between different molecular moieties and has led to a certainly large compendium of Hammett constants generated so far (Hansch et al., 1991), this approach is principally limited to certain reaction types, and among these to those compounds where substituent constants are available. More precisely, the application of the Hammett equation requires that the molecular system of interest can be broken down into some parent compound and substituents, such that for both the relevant reaction (referring to some specific reaction site) and the substituents parameters must be available. 

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 ... 

Methylthio TFMS Derivatives. Data for the meta- and para-substituted methylthio TFMS derivatives (3-SCH3, 4-SCH3) were not included in Hansch structure—activity correlations for the several weed types. This omission was a result of our noting that when herbicidal data for the methylthio derivatives were included in fits, much poorer Hansch correlations were obtained. This was true whether or not the TFMS compounds were separated into meta- and para-derivatives for fitting purposes. It was also true for all weed types examined, in the presence and absence of surfactant. A typical example of the improvement in statistical parameters effected by omitting methylthio points from the data pool is illustrated by the following Hansch correlation of TFMS activity on Foxtail grass in the presence of surfactant. 

Many different approaches to QSAR have been developed since Hansch s seminal work. As briefly discussed above, the major differences between these methods can be analyzed from two viewpoints (1) the types of structural parameters that are used to characterize molecular identities, starting from different representation of molecules, from simple chemical formulas to three-dimensional conformations and (2) the mathematical procedure that is employed to obtain the quantitative relationship between these structural parameters and biological activity. 

On the basis of the origin of molecular descriptors used in calculations, QSAR methods can be divided into three groups. One group is based on a relatively small number (usually many times smaller than the number of compounds in a data set) of physicochemical properties and parameters describing,for example, hydrophobic, steric, and electrostatic effects. Usually, these descriptors are used as independent variables in multiple regression approaches (18) Jn the literature, these methods are typically referred to as Hansch analysis (8).These types of descriptors and corresponding linear optimization methods used in traditional QSAR analyses are discussed extensively in the chapter by Celassie (7) and therefore is not reviewed here. 

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