Structural descriptors, molecular graphs

Ivanciuc, O. (2001c) Design of topological indices. Part 19. Computation of vertex and molecular graph structural descriptors with operators. Rev. Roum. Chim., 46, 243-253. 

Ivanciuc, O., Ivanciuc, T. and Cabrol-Bass, D. (2002d) QSAR for dihydrofolate reductase inhibitors with molecular graph structural descriptors. /. Mol. Struct. (Theochem), 582, 39—51. 

Many of the descriptors which can be calculated from the 2D structure rely upon the molecular graph representation because of the need for rapid calculations. Kier and Hall have developed a large number of topological indices, each of which characterises the molecular structure as a single number [Hall and Kier 1991]. Every non-hydrogen atom ir the molecule is characterised by two delta values, the simple delta Si and the valence delta SJ ... 

Ivanduc, O., Ivanduc, T. Matrices and structural descriptors computed from molecular graph distances. In Topological Indices and Related Descriptors in QSAR and QSPR, Devillers, J. Balahan, A. T. (eds.), Gordon Breach, Amsterdam, 1999, pp. 221-277. 

D., Balahan, A. T. Comparison of weighting schemes for molecular graph descriptors application in quantitative structure-retention relationship models for alkylphenols in gas-liquid chromatography. J. Chem. Inf. Comput. Sci. 2000, 40, ITl-lM,. 

Classes of Estimation Methods Table 1.1.1 summarizes the property estimation methods considered in this book. Quantitative property-property relationships (QPPRs) are defined as mathematical relationships that relate the query property to one or several properties. QPPRs are derived theoretically using physicochemical principles or empirically using experimental data and statistical techniques. By contrast, quantitative structure-property relationships (QSPRs) relate the molecular structure to numerical values indicating physicochemical properties. Since the molecular structure is an inherently qualitative attribute, structural information has first to be expressed as a numerical values, termed molecular descriptors or indicators before correlations can be evaluated. Molecular descriptors are derived from the compound structure (i.e., the molecular graph), using structural information, fundamental or empirical physicochemical constants and relationships, and stereochemcial principles. The molecular mass is an example of a molecular descriptor. It is derived from the molecular structure and the atomic masses of the atoms contained in the molecule. An important chemical principle involved in property estimation is structural similarity. The fundamental notion is that the property of a compound depends on its structure and that similar chemical stuctures (similarity appropriately defined) behave similarly in similar environments. 

Indicator Variables Indicator variables are binary variables having a value of either 0 or 1, indicating if a particular structural or substructural characteristic is present or is missing in the molecular graph. Indicator variables are used by some authors in QSPR equations presenting correlations between a property and descriptors, including indicator variables. However, indicator variables are redundant. Instead of using an indicator, a QSPR model can be split into two separate models, one for all those compounds for which the indicator variable is zero, and one for all those compounds for which the indicator variable is 1. 

Autocorrelation of Topological Structure Moreau and Broto [24,25] have suggested the autocorrelation vector of a molecular graph as the source for molecular descriptors. This method assumes that each atom i in the graph is uniquely associated with a numeric quantity, qit such as the atomic number, atomic mass, (v)(, (ds), Sv, or electronegativity. The intrinsic atom values of the electrotopological state [26] and the atomic Rd and log Kow parameters [27,28] are other potential atomic descriptors suitable to construct autocorrelation vectors. Generally, the fcth element of the autocorrelation vector is defined as... 

Nowadays, more than 4000 types of descriptors are known.17 There exist different ways to classify them. With respect to the type of molecular representation used for their calculations—chemical formula, molecular graph, or spatial positions of atoms—one speaks about ID, 2D, and 3D descriptors, respectively. Descriptors can be global (describing the molecule as a whole) and local (only selected parts are considered). One could distinguish information-based descriptors, which tend to code the information stored in molecular structures, and knowledge-based (or semiempir-ical) descriptors issued from the consideration of the mechanism of action. Most of those descriptors can be obtained with the DRAGON, CODESSA PRO, and ISIDA programs. 

Figure 4.1 Ligand-based virtual screening methods. The figure shows different computational methods for screening compound databases that take either a local or a global view on molecular structure. Molecular similarity methods that operate on molecular descriptors, histogram representations, superposition or (reduced) molecular graphs evaluate molecular structure globally. By contrast, local structural features are explored by substructure and pharmacophore searching or QSAR modeling.

These are global molecular descriptors derived from an H-depleted molecular graph where each vertex is weighted by a local vertex invariant called Atom-in-Structure Invariant Index (ASII) defined as [Bangov, 1988] ... 

To take into account the absolute contribution that a single double-bond makes to the whole size and shape of alkene molecules, second-grade structural parameters were derived from a - molecular graph [Zhang et ai, 1997]. The topological descriptors representing the size w and the shape related to the presence of a double bond are, respectively ... 

Ivanciuc, O., Ivanciuc, T and Diudea, M.V. (1997a). Molecular Graph Matrices and Derived Structural Descriptors. SAR QSAR Environ.Res., 7,63-87. 

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