Further Topological Descriptors

Some further topological descriptors are the Kier-Hall connectivity indices [13] and the electrotopological state index (or -state index) [14]. A comprehensive overview of topological molecular desaiptors is given by Todeschini and Consonni [15]. 

Physical, chemical, and biological properties are related to the 3D structure of a molecule. In essence, the experimental sources of 3D structure information are X-ray crystallography, electron diffraction, or NMR spectroscopy. For compounds without experimental data on their 3D structure, automatic methods for the conversion of the connectivity information into a 3D model are required (see Section 2.9 of this Textbook and Part 2, Chapter 7.1 of the Handbook) [16]. 

Two of the widely used programs for the generation of 3D structures are CONCORD and CORINA. CONCORD was developed by Pearlman and co-workers (17, 18] and is distributed by TRIPOS (19). The 3D-structure generator CORINA originates from Gasteiger s research group [20-23] and is available from Molecular Networks [24], 

These programs generate one low-energy conformation for each molecule. 

In the calculation of a 3D autocorrelation vector the spatial distance is used as given by Eq. (20). 

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Further topological descriptors come from the distance matrix, containing the distances between nodes, introduced in Definition 2.5,... 

A further shortcoming of the most commonly used topological indices is the inability to take into account stereo-specific properties of molecules, such as atomic chiralities, enantiomers (R-and S-isomers), and - and I J-diastereomers (Z- and E-isomers). Topological descriptors proposed to fill the gap to account for chirality and ZE-isomerism can be found in Schultz et al. (1995), de Julian-Ortiz et al. (1998), and Golbraikh et al. (2001) as well as in Lekishvili (1997 2001), and Golbraikh et al., (2002), respectively. It is probably a question of availability and time until the power of these descriptors is demonstrated and they begin to be used routinely in QSPR analysis. 

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. 

Example (Basic topological Indices) The following list contains functions that lead to very basic topological descriptors. Further topological indices will be mentioned below as they require additional notions. 

In another approach, with an aim to offer a realistic motive towards handling millions of databases and hundreds of descriptors for a fruitful structure-activity relationship (SAR), Putz and coworkers have proposed a unique QSAR model called spectral-SAR (S-SAR) [220], which considers the spectral norm in quantifying toxicity and reactivity with molecular structure. A handful of applications of the S-SAR algorithm in dealing with ecotoxicity, enzyme activity, and anticancer bioactivity are well established [221-227]. The S-SAR model coupled with Element Specific Influence Parameter (ESIP) formulations [228] are also utilized for predicting ecotoxicity measures. QSAR studies on the anti-HIV-1 activity of HEPT (l-[(2-hydroxyethoxy)methyl]-6-(phenylthio)thymine) [229] and further studies involving the minimum topological difference (MTD) method [230, 231] are also reported [232]. 

The R-group descriptor from Holliday et al. [20] is a further example of a topological pharmacophore fingerprint. However, this approach characterizes a distribution of pharmacophoric properties at topological distances from an attachment point. 

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