2D QSAR

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

Indeed, considering the latter 3D QSAR model, the features that make a molecule suitable to bind to the hERG channel start delineating in a chemically interpretable manner, but, it is rather dear how these kinds of models emphasize mostly the 3D steric aspects of molecules, depending mainly on factors such as the conformation (or the conformational analysis protocol) or the alignment of the molecules. To obtain a description of the characteristics of hERG-blocking molecules in terms of measurable (computable) properties in a way that the physicochemical determinants of the activity can be identified, the classical 2D QSAR approach is well suited. 

In an independent study, Yoshida and Niwa [20] analyzed a larger and more diverse set of molecules (104 compounds) and developed a 2D QSAR model, which gave results similar to that of Cronin [19] but added some more details with regard to the physicochemical properties involved in the hERG blockade by drugs. Equation 5.2 represents the best model ... 

The relevance of size-related properties of hERG-blocking molecules was also detected in a 2D QSAR model developed by Coi et al. [22] after the analysis of 82 compounds through the CODESSA method. These authors developed two multiparameter models with strong predictive properties, from which, besides the involvement of hydrophobic features, the importance of linearity as opposed to globularity of the hERG blockers emerged. 

In Table 5.1, we present a list of the main physicochemical and structural properties associated with the descriptors included in the 2D QSAR models discussed above. Of course, we did some generalizations in an attempt to refer different parameters and descriptors to the same property, but the effort was devoted at identifying the smallest number of significant features positively or negatively correlated to the hERG blockade by small molecules. Examining the properties... 

Table 5.1 Molecular properties identified as relevant in 2D QSAR models of hERG blockade by small molecules.

Different from 2D QSAR, classification models reported in the papers cited above do not always allow the identification of descriptors related to the hERG activity however, in some cases, descriptors or molecular features crucial for the assignment to either of the classes were explicitly indicated. This allowed us to tentatively collect them in Table 5.2, which when compared with Table 5.1 provides (as expected) a very similar picture of the molecular properties involved in the blockade of hERG by drugs. Even though the properties listed in Table 5.2 are not associated with a positive or a negative sign (they can only be indicated as relevant for the classification), they... 

Hoffman, B.T., Kopajtic, T., Katz, J.L., and Newman, A.H. 2D QSAR Modeling and preliminary database searching for dopamine transporter inhibitors using genetic algorithm variable selection of Molconn Z descriptors./. Med. Chem. 

Key Words 2D-QSAR traditional QSAR 3D-QSAR nD-QSAR 4D-QSAR receptor-independent QSAR receptor-dependent QSAR high throughput screening alignment conformation chemometrics principal components analysis partial least squares artificial neural networks support vector machines Binary-QSAR selecting QSAR descriptors. 

Traditional 2D-QSAR descriptors are generally considered to be the characteristics of a molecule, as a chemist would perceive the molecules. The molecules are described by their physical properties, subdivided surface area (86), atom counts and bonds, Kier and Hall connectivity and kappa shape indices... 

QSAR methods can be divided into several categories dependent on the nature of descriptors chosen. In classical one-dimensional (ID) and two-dimensional (2D) QSAR analyses, scalar, indicator, or topological variables are examples of descriptors used to explain differences in the dependent variables. 3D-QSAR involves the usage of descriptors dependent on the configuration, conformation, and shape of the molecules under consideration. These descriptors can range from volume or surface descriptors to HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) energy values obtained from quantum mechanics (QM) calculations. 

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. 

In 2D-QSAR, model building is based on 2D representation of molecules and 2D descriptors. However, it has become very common to generate 3D-QSAR models. 

D-QSAR Two-dimensional quantitative structure-activity relationships 3D-QSAR Three-dimensional quantitative structure-activity relationships... 

A fundamental difference between 3D- and a 2D-QSAR equation is the non-existence of conformational dependent secondary sites in the latter. Hence, a direct transposition of 3D- and 2D-models is not always possible but the global properties of the chemical structures, if relevant to the activity, may show their presence in both of them. Moreover, in a broader perspective, all 2D-QSAR parameters—physicochemical as well as structural—can be considered as one or the other form of global descriptors. In light of this, to bridge the 2D- and 3D-features the following 2D-QSAR equations have been derived for the antifungal activity of 2,3,4-substituted thiazolidines (Table 21). 

Many different approaches to QSAR have been developed since Hansch s seminal work. These include both 2D (two-dimensional) and 3D (three-dimensional) QSAR methods. Most of the 2D QSAR methods employ graph theoretic indices to characterize molecular structures, which have been extensively studied by Radio, Kier and Hall. Similarly, ADAPT system employs topo-... 

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