Topological descriptors graphs

Because of the fundamental role of graph theory for the understanding of topological descriptors, some terms from graph theory are defined below. Then a selection of topological descriptors are discussed. 

Figure 6.14 Bar graph comparing the analysis All calculations were performed on a 2.5 GHz capacity, in number of ligands bite angles and desktop computer (analysis capacity will flexibility ranges calculated per hour, using improve with better computers and software, topological descriptors (2D), and 3D descriptors but the 2D/3D cost-effectiveness ratio will based on MM force fields, semi-empirical remain constant).

More recent methods are based on quantitative characteristics of molecular graphs (molecular topological descriptors). Because... 

Special cases are discussed in some detail in the literature [112,197,198], where the shape representation P is chosen as a space curve representing a protein backbone and the topological descriptors Fj(s) on the local tangent plane projections are either graphs or knots defined by the crossing pattern on the planar projection at each tangent plane T(s) of the sphere S. 

Very similar to the electronic-topological descriptors, electron charge density connectivity index is defined for an - H-depleted molecular graph in which net atomic charges, calculated by computational chemistry, are used as weights for vertices [Estrada and Montero, 1993 Estrada, 1995d] ... 

A vector of molecular topological descriptors can be calculated for the whole iterated line graph sequence. For example, a line graph Randic connectivity index was calculated as ... 

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 ... 

Again, there are a large number of topological descriptors available (Table 14.1) that can be calculated from the 2D structure (graph) of a compound. 

The following section gives an overview of feature trees and 2D autocorrelation vectors, the two most important graph-based topological descriptors used for virtual screening. 

Another series of successfully applied topological descriptors is derived from graph theory using atom connectivity information of a molecule. An example is the connectivity index developed by Randic [21], In the simple form,... 

Topological descriptors calculated by TOMOCOMD are divided into linear indices, bilinear indices, and quadratic indices. They are distinguished into atom-based indices and bond-based indices [Marrero-Ponce, 2004b Marrero-Ponce, Torrens et al, 2006] depending on whether they are derived from the kth power of the —> adjacency matrix ofa general graph Pt or from the fcth power of the —> edge adjacency matrix... 

Galvez, J., Garci a-Domenech, R. and de Gregorio Alapont, C. (2000) Indices of differences of path lengths novel topological descriptors derived from electronic interferences in graphs./. Comput. Aid. Mol. Des., 14, 679-687. 

Connective eccentricity index a novel topological descriptor for predicting biological activity. /. Mol. Graph. Model, 18, 18-25. 

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