Topological torsions

Mixtures containing up to several thousand distinct chemical entities are often synthesized and tested in mix-and-split combinatorial chemistry. The descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules, e.g., using atom-pair and topological torsion descriptors. 

The atom pair, ap, and topological torsion, tt, descriptors are selected for illustrative purposes in the similarity searching context. 

Atom pairs, topological torsions 2D structure See Section 12.9.3... 

B and W J Howe 1991. Computer Design of Bioactive Molecules - A Method for Receptor-Based Novo Ligand Design. Proteins Structure, Function and Genetics 11 314-328. i H L 1965. The Generation of a Unique Machine Description for Chemical Structures - A hnique Developed at Chemical Abstracts Service. Journal of Chemical Documentation 5 107-113. J 1995. Computer-aided Estimation of Symthetic Accessibility. PhD thesis. University of Leeds, itan R, N Bauman, J S Dixon and R Venkataraghavan 1987. Topological Torsion A New )lecular Descriptor for SAR Applications. Comparison with Other Descriptors. Journal of emical Information and Computer Science 27 82-85. 

A wide variety of features have been used in bit vectors, including molecular fragments, 3-D potential pharmacophores, atom pairs, 2-D pharmacophores, topological torsions, and variety of topological indices. 

Figure 3.10 Histogram of Tanimoto coefficients based on topological torsions of the most similar CMC molecule for each of the drug-like molecules from the ACD. (Reprinted from [37] with permission, copyright 1998, American Chemical Society).

A tremendous number of various fragments are used in structure-property studies atoms, bonds, topological torsions , chains, cycles, atom- and bond-centered fragments, maximum common substructures, line notation (WLN and SMILES) fragments, atom pairs and topological multiplets, substituents and molecular frameworks, basic subgraphs, etc. Their detailed description is given below. 

The topological torsion is defined as a linear sequence of four consecutively bonded non-hydrogen atoms k-i-j-l, each described by its atom type (TYPE), the number of n electrons (NPI) and the number of non-hydrogen atoms (NBR) bonded to it [Nila-kantan et al., 1987]. Usually NBR does not include k-i-j-l atoms that go to make the torsion itself therefore it is minus 1 for k and / atoms, and minus 2 for the two central atoms i and j. The torsion around the i-j bond and defined by the four indices k-i-j-l is represented by the following TT descriptor ... 

An extension of topological torsions is given by binding property torsions that were proposed in an analogous way, but the atoms were assigned to seven different types cations, anions, hydrogen-bond donors and acceptors, polar atoms, hydrophobic atoms and others [Kearsley et al, 1996],... 

Nilakantan, R., Bauman, N., Dixon, J.S. and Venkataraghavan, R. (1987). Topological Torsion A New Molecular Descriptor for SAR Applications. Comparison with Other Descriptors. J.Chem.Inf.Comput.Sci., 27, 82-85. 

The TT descriptor is a topological analogue of the 3D torsion angle, defined by four consecutively bonded atoms. The topological torsion is a short-range descriptor, that is, it is sensitive only to local changes in the molecule and is independent of the total number of atoms in the molecule. 

Unlike topological torsions, atom pairs are sensitive to long-range correlations between the atoms in molecules and therefore to small changes in one part of even large molecules. Atom pair descriptors usually are Boolean variables encoding the presence or absence of a particular atom pair in each molecule. 

Figure 4 Example atom pair and topological torsion fragments. The information included in the circled atom environments is given below the fragment-type label.

Nilakantan R, Bauman N, Dixon JS, Venkataraghavan R. Topological torsion a new molecular descriptor for SAR applications. Comparison with other descriptors. J Chem Inf Comput Sci 1987 27 82-85. 

Fig. 13.1-4 Atom-pairs and topological torsions, (a) Illustration of atom-types used in atom-pair descriptor calculation including atomic identities, pi-bonding, and molecular topology, (b) Distinct atom-types, some of which occur multiple times, make up the basic unit of atom-pair calculation.

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