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Shape characterization of some molecular model surfaces
Author(s) -
Arteca Gustavo A.,
Mezey Paul G.
Publication year - 1988
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540090513
Subject(s) - surface (topology) , computation , intersection (aeronautics) , characterization (materials science) , algebraic number , topology (electrical circuits) , hierarchy , homology (biology) , algebraic surface , position (finance) , mathematics , algebraic topology , computer science , pure mathematics , geometry , combinatorics , algorithm , chemistry , materials science , mathematical analysis , nanotechnology , biochemistry , finance , homotopy , economics , engineering , market economy , gene , aerospace engineering
An algebraic method is proposed to represent and to characterize in a concise way the shape of an arbitrarily asymmetrical surface composed from spherical pieces. These surfaces include, among others, the well‐known van der Waals surfaces. The procedure is based on the computation of a hierarchy of homology groups (“shape groups”) of algebraic topology, for a family of objects defined by the original surface. The technique uses the same input information as that necessary to produce a graphical display of the molecular surface. However, the actual figure is not necessary for the computation of the shape groups. Only a classification of the points on the surface, according to their position with respect to the intersection of two or more spheres, is needed. The result is a purely algebraic characterization that can be obtained and stored by a computer, and that may prove to be useful when comparing shapes of different molecules. Illustrative examples are provided for different molecules, as well as for different conformations of the same molecule.