Molecular descriptors topological torsions

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. 

Topological Indices are molecular descriptors based on connectivity data of atoms within a molecnle. These descriptors contain information abont the constitntion, size, shape, branching, and bond type of a chemical strnctnre, whereas bond length, bond angles, and torsion angles are neglected. 

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.

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

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