Abstract
The three-dimensional shape of various functions, for example, of electron density contours describing the body of molecules, is an essential tool for the characterization of molecules in drug design. A detailed description of such shapes is possible by the symmetry-independent shape group method, developed recently. The shape group analysis of molecules is based on the initial generation of a molecular surface, such as a surface of a quantum chemical isodensity contour, a contour of the electrostatic potential, a van der Waals, or solvent accessibility, or a so-called union surface obtained for an enzyme cavity by the superposition of contour surfaces of several active drug molecules. The curvature properties and mutual interpenetrations of such contour surfaces define a family of topological objects, which are characterized by their homology groups of algebraic topology. These homology groups are the shape groups of the original contour surface, applicable for a precise shape characterization of arbitrary, asymmetric molecules. The shape group method (SGM) is combined with a novel representation of molecular chirality properties, using a simple algebraic test for chirality, based on a recent finding in a branch of topology, called knot theory.
A generalization of point symmetry groups, called symmorphy groups, is proposed for a precise algebraic characterization of the shapes of arbitrary objects, based on various shape function classes. The application of this approach to the molecular shape problem provides an alternative to the SGM.
The shape group and shape function techniques are suitable for a precise, computer-based, non-visual analysis of molecular similarity, that is an important concern in modern pharmaceutical, pesticide and herbicide research.
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© 1989 Kluwer Academic Publishers
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Mezey, P.G. (1989). Topology of Molecular Shape and Chirality. In: Beltrán, J., Csizmadia, I.G. (eds) New Theoretical Concepts for Understanding Organic Reactions. NATO ASI Series, vol 267. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2313-3_4
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DOI: https://doi.org/10.1007/978-94-009-2313-3_4
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