Topological descriptors with QSAR

In our contribution we have focused the discussion on descriptors. The understanding of descriptors is essential for transparency of models and can also lead to mechanistic interpretation of models. Several questions are associated with descriptors. First of all, nowadays thousand of descriptors are defined and can be easily calculated with available software and the first question is how to the select the most relevant descriptors. The topological descriptors are sometimes promising, but there is no clear physicochemical interpretation for them. 3D molecular structure is a problematic quantity as it depends on the media where the molecule is, or on the method of determination. Quantum chemical descriptors, which have a clear physicochemical interpretation, are difficult to calculated. In the cases studies we have addressed some of those questions. We have discussed the sensitivity of the models, and particularly predictions, to descriptors used. According to the critical review of Snyder and Smith [87] on QSAR models for mutagenicity prediction a lot of work still remains to be done. 

Practical problems in the estimation of the lipophilicity of araliphatic and aliphatic compoimds led to the / hydrophobicity scales of Rekker and Leo/Hansch. However, all such descriptor scales depend on experimental determinations. New molecular descriptors were developed from scratch, starting with the work of Randic, Kier and Hall, i.e. the various molecular connectivity parameters %. Later the electrotopological state parameters and the Todeschini WHIM parameters were added. Whereas topological descriptors are mathematical constructs that have no unique chemical meaning, they are clearly related to some physicochemical properties and are suited to the description of compound similarities in a quantitative manner. Thus, despite several critical comments in the past, they are now relatively widely used in QSAR studies. Only a meaningless and excessive application in quantitative models, as far as the number of tested and included variables is concerned, still deserves criticism. 

Gao et al. [36] used binary QSAR based on topological descriptors and indicator variables (including one for the phenolic hydroxyl group) to derive a classification model that separates active from inactive compounds. The model was trained on 410 diverse molecules, and it demonstrated its predictive power on a test set of 53 randomly selected molecules from which 94% were correctly classified. The biological data were selected from four different laboratories, so there might be some inconsistency with respect to the classification of the model. 

Several series of novel chirality descriptors of chemical organic molecules were introduced by Golbraikh et al. [5, 6]. These descriptors have been implemented in a QSAR study with a high content of chiral and enantiomeric compounds. It was shown fhat for all data sets 2D-QSAR models that use a combination of chirahty descriptors wifh conventional topological descriptors afford better or similar predictive abihty when compared to models generated wifh 3D-QSAR approaches. 2D-QSAR mefhods enhanced by chirahty descriptors present a powerful alternative to popular 3D-QSAR approaches. 

CH2-CH2-N-CH2-CH2 (179), and linear discriminant analysis with topological descriptors (180). In 1997 the first 3D-QSAR (quantitative structure-activity relationships) analysis of phenothiazines and related drugs known to be P-gp inhibitors was described... 

The kappa shape indexes are relatively new descriptors, and few studies have been reported to date. It is expected that the kappa indexes will generally be used along with other topological indexes in QSAR equations rather than by themselves as in most of the examples above. Shape is not the sole determinant... 

Finally, three further studies on QSAR of artemisininoids applying a variety of quantum-chemical and conventional molecular descriptors [105], molecular quantum-similarity measures (MQSM, [111]) and topological descriptors based on molecular connectivity [112] have led to models of quite satisfactory statistical performance. However, apart from showing the applicability of the respective QSAR approaches to this type of compounds both studies offer comparatively little new information with respect to structure-activity relationships. 

Structure-property-activity studies. The other is the pair of shape indices of Randic [28], proposed in 2001, which is one of very few indices that have shown very good regressions with several physicochemical properties of octane isomers. There are not two but at least two dozen that would be worth mentioning here, but this is a book about solved and unsolved problems in structural chemistry and not a book about topological indices. As one can see, both above-mentioned indices came after a good 25 years of intensive search for simple novel mathematical descriptors for QSAR, which resulted in several hundred reports on new indices of various complexities. In contrast, the Estrada index and the proposed shape indices of Randic are conceptual and computationally unusually simple and elegant. 

By considering QSAR orthogonal descriptors with associate min-max prescription in chemical reactivity (as exposed for the consecrated chemical reactivity descriptors, to which other may be added, as related to solubility, topology, etc.) ... 

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