Topological descriptors are derived from hydrogen-suppressed molecular graphs, in which the atoms are represented by vertices and the bonds by edges. The connections between the atoms can be described by various types of topological matrices (e.g., distance or adjacency matrices), which can be mathematically manipulated so as to derive a single number, usually known as graph invariant, graph-theoretical index or topological index.[3][4] As a result, the topological index can be defined as two-dimensional descriptors that can be easily calculated from the molecular graphs, and do not depend on the way the graph is depicted or labeled and no need of energy minimization of the chemical structure.
The simplest topological indices do not recognize double bonds and atom types (C, N, O etc.) and ignore hydrogen atoms ("hydrogen suppressed") and defined for connected undirectedmolecular graphs only.[5] More sophisticated topological indices also take into account thehybridization state of each of the atoms contained in the molecule. TheHosoya index is the first topological index recognized in chemical graph theory, and it is often referred to as "the" topological index.[6] Other examples include theWiener index,Randić's molecular connectivity index,Balaban's J index,[7] and the TAU descriptors.[8][9] The extended topochemical atom (ETA)[10] indices have been developed based on refinement of TAU descriptors.
Hosoya index andWiener index areglobal (integral) indices to describe entire molecule, Bonchev and Polansky introducedlocal (differential) index for every atom in a molecule.[5] Another examples of local indices are modifications of Hosoya index.[11]
A topological index may have the same value for a subset of different molecular graphs, i.e. the index is unable to discriminate the graphs from this subset. Thediscrimination capability is very important characteristic of topological index. To increase the discrimination capability a few topological indices may be combined tosuperindex.[12]
Computational complexity is another important characteristic of topological index. The Wiener index, Randic's molecular connectivity index, Balaban's J index may be calculated by fast algorithms, in contrast to Hosoya index and its modifications for which non-exponential algorithms are unknown.[11]
QSARs represent predictivemodels derived from application of statistical tools correlatingbiological activity (including desirable therapeutic effect and undesirable side effects) of chemicals (drugs/toxicants/environmental pollutants) with descriptors representative ofmolecular structure and/orproperties. QSARs are being applied in many disciplines for examplerisk assessment, toxicity prediction, and regulatory decisions[13] in addition todrug discovery andlead optimization.[14]
For example, ETA indices have been applied in the development of predictive QSAR/QSPR/QSTR models.[15]
^González-Díaz H, González-Díaz Y, Santana L, Ubeira FM, Uriarte E (February 2008). "Proteomics, networks and connectivity indices".Proteomics.8 (4):750–78.doi:10.1002/pmic.200700638.PMID18297652.S2CID20599466.
^abKing, R. Bruce (1983).Chemical applications of topology and graph theory: a collection of papers from a symposium held at the University of Georgia, Athens, Georgia, U. S. A., 18–22 April 1983. Amsterdam: Elsevier.ISBN0-444-42244-7.
^Katritzky AR, Karelson M, Petrukhin R (2002)."Topological Descriptors". University of Florida. Retrieved2009-05-06.
^Pal DK, Sengupta C, De AU (1988). "A new topochemical descriptor (TAU) in molecular connectivity concept: Part I--Aliphatic compounds".Indian J. Chem.27B:734–739.
^Pal DK, Sengupta C, De AU (1989). "Introduction of A Novel Topochemical Index and Exploitation of Group Connectivity Concept to Achieve Predictability in QSAR and RDD".Indian J. Chem.28B:261–267.
^abTrofimov MI (1991). "An optimization of the procedure for the calculation of Hosoya's index".Journal of Mathematical Chemistry.8 (1):327–332.doi:10.1007/BF01166946.S2CID121743373.
^Bonchev D, Mekenyan O, Trinajstić N (1981). "Isomer discrimination by topological information approach".Journal of Computational Chemistry.2 (2):127–148.doi:10.1002/jcc.540020202.S2CID120705298.
^Roy K, Ghosh G (2004). "QSTR with extended topochemical atom indices. 2. Fish toxicity of substituted benzenes".Journal of Chemical Information and Computer Sciences.44 (2):559–67.doi:10.1021/ci0342066.PMID15032536.;Roy K, Ghosh G (February 2005). "QSTR with extended topochemical atom indices. Part 5: Modeling of the acute toxicity of phenylsulfonyl carboxylates to Vibrio fischeri using genetic function approximation".Bioorganic & Medicinal Chemistry.13 (4):1185–94.doi:10.1016/j.bmc.2004.11.014.PMID15670927.;Roy K, Ghosh G (February 2006). "QSTR with extended topochemical atom (ETA) indices. VI. Acute toxicity of benzene derivatives to tadpoles (Rana japonica)".Journal of Molecular Modeling.12 (3):306–16.doi:10.1007/s00894-005-0033-7.PMID16249936.S2CID30293729.;Roy K, Sanyal I, Roy PP (December 2006). "QSPR of the bioconcentration factors of non-ionic organic compounds in fish using extended topochemical atom (ETA) indices".SAR and QSAR in Environmental Research.17 (6):563–82.Bibcode:2006SQER...17..563R.doi:10.1080/10629360601033499.PMID17162387.S2CID10707472.;Roy K, Ghosh G (November 2007). "QSTR with extended topochemical atom (ETA) indices. 9. Comparative QSAR for the toxicity of diverse functional organic compounds to Chlorella vulgaris using chemometric tools".Chemosphere.70 (1):1–12.Bibcode:2007Chmsp..70....1R.doi:10.1016/j.chemosphere.2007.07.037.PMID17765287.
