Topological path descriptor

Depending on the task, topological path descriptors are represented in either peak mode (i.e similar to a distance pattern) or in the conventional smoothed mode containing the probability distribution. With analysis methods that rely on interpolation, like neural networks, the smoothed representation is necessary to preserve interpolation features. 

Topological shape descriptors ""k defined in terms of the number of graph vertices A and the number of paths " P with length m (m = 1,2,3) in the H-depleted molecular graph, according to the following ... 

Some of the effects previously described are valuable for automatic RDF interpretation. In fact, this sensitivity is an elementary prerequisite in a rule base for descriptor interpretation. However, since many molecular properties are independent of the conformation, the sensitivity of RDF descriptors can be an undesired effect. Conformational changes occur through several effects, such as rotation, inversion, configuration interchange, or pseudo-rotation, and almost all of these effects occur more or less intensely in Cartesian RDF descriptors. If a descriptor needs to be insensitive to changes in the conformation of the molecule, bond-path descriptors or topological bond-path descriptors are more appropriate candidates. Figure 5.7 shows a comparison of the Cartesian and bond-path descriptors. 

In addition, three distance modes — Cartesian, bond-path, and topological-path distances — are compared. Cartesian RDF descriptors are usually quite sensitive to small constitntional changes in the molecule. The bond-path descriptors exhibit less sensitivity, whereas topological bond-path descriptors only indicate extreme changes in the entire molecnle or in the size of the molecule. 

RDF. The distance mode dehnes the mode for distance calculation available modes are Cartesian distances, bond-path distances, and topological distances. Descriptors may be calculated on particular atoms. Exclusive mode restricts the calculation to the atom type, and with ignore mode the selected atom type is ignored when calculating the descriptor. In partial-atom mode an atom number has to be given instead of the atom type. The second atom property is available if 2D RDF is selected as code method. 

The number of aromatic bonds minimum, average, and maximum value of the aromaticity of the aromatic bonds percentage of aromatic bonds number of aromatic molecular zones or aromaticity of the peripheral topological path can be calculated as descriptors. Some descriptors simultaneously reflect the aromaticity and size of the molecule. Other descriptors reflect the concentration of aromaticity in small areas of the molecule. 

Topological Representation and Topology), geometrical, electronic, and physicochemical. Topological de.scriptors are derived directly from the connection table repre.sentation of the structure and include atom and bond counts,. substructure counts, molecular connectivity indices (see Topological Indices), kappa indices, substructure environments, path descriptors, distance-sum connectivity, and molecular symmetry. Substructure-ba.sed descriptors are topological de.scriptors which allow the tailoring of the descriptor set to. specific user-defined substructures contained in the molecules of the data set. 

Figure 6.15 Examples of topological descriptors calculated on backbone and R groups of three bidentate ligands. The broken arrows on the left indicate the minimum Pn-P2 connectivity path (Dt) and the second Pn-P2 path (D2). The dotted arrows indicate freely rotating bonds. The R group descriptor SAMR<3 pertains to the sum of the mass units of atoms that are connected within three bonds of the ligating P atoms.

Carhart et al. [15] described a generalized structural descriptor called an atom pair which is defined in terms of the atomic environments of, and shortest path separation between, all pairs of atoms in the topological representation of a chemical structure. A similar descriptor has been suggested by Klopman [16]. More recently, Judson [20] described a more sophisticated approach to analyze structural feature of molecules for structure-activity studies. 

The idea of using atom pairs as molecular features in structure-activity studies vas first proposed by Carhart et al. (84). AP descriptors are defined by their atom types and topological distance bins. An AP is a substructure defined by two atom types and the shortest path separation (or graph distance) between the atoms. The graph distance is defined as the smallest number of atoms along the path connecting two atoms in a molecular structure. The general form of an atom-pair descriptor is as follows ... 

By generalization, Harary indices and hyper-Harary indices (or hyper-Harary numbers) are all molecular descriptors derived from the application of the Wiener operator to reciprocal topological matrices Harary indices are obtained from the 1 -order - sparse matrix, i.e. considering only the graph edges, while the hyper-Harary indices are from the whole matrices, i.e. considering the paths [Diudea, 1997c]. 

A terminator may be an atom, a lone pair or a bond the link is derived from a topological representation of the molecules as the length of the path between the considered terminators. For each pair of terminators, different REX descriptors are defined according to each different link between them, i.e. all paths and not only the shortest path are considered. 

---