Molecular shape analysis method description

Spherical harmonics provide a parameterization of three-dimensional shape which is especially useful for protein structure description (4). Overlap volume comparisons are the basis for the Molecular Shape Analysis (MSA) method of Hopfinger (5,6). TTiis technique has been extended to include a quantification of the steric and electrostatic fields surrounding a molecule (7). A further refinement of field analysis, which merges statistical and molecular modeling techniques, is the COMparative Molecular Field Analysis method (COMFA) of Cramer (8). These latter approaches seek to encode information about more than just steric bulk or form. They express multivariate information about the structure, so they might be considered multidimensional shape descriptors. 

The purpose of this book is to acquaint the reader with the topological methods of the description and analysis of shapes, in particular, the three-dimensional shapes of molecules. The topological approach is generally applicable to all aspects of shape in chemistry, hence the title of the book appears justified, although our focus will be on the central shape problem in chemistry on molecular shape. 

The distribution of electrostatic potential o over molecular surfaces is a useful model for the analysis of chemical reactivity and steric effects. i The shape group method can be adapted to this model, by using values of the electrostatic potential to define the truncations on the molecular surface, The shape description obtained can be used in correlations with biochemical activity. [Note that the analysis of electrostatic isopotential surfaces, whenever closed, can be accomplished by the same method used with isodensity surfaces. The characterization of potential surfaces is relevant to interpreting molecular recognition processes. O i ]... 

The shape group method (SGM), reviewed in ref. [2], has been proposed for the analysis of three-dimensional shape properties of formal molecular bodies. For example, by choosing the electronic charge isodensity contours G(a) (of various density values a) as the physical property P for shape representation, and by taking the family of Betti numbers b as the topological tool for shape description [2], the similarity of the geometrical shapes of two molecules, A and B, is transformed into an equivalence of their topological shape, expressed as... 

A molecule contains a nuclear distribution and an electronic distribution there is nothing else in a molecule. The nuclear arrangement is fully reflected in the electronic density distribution, consequently, the electronic density and its changes are sufficient to derive all information on all molecular properties. Molecular bodies are the fuzzy bodies of electronic charge density distributions consequently, the shape and shape changes of these fuzzy bodies potentially describe all molecular properties. Modern computational methods of quantum chemistry provide practical means to describe molecular electron distributions, and sufficiently accurate quantum chemical representations of the fuzzy molecular bodies are of importance for many reasons. A detailed analysis and understanding of "static" molecular properties such as "equilibrium" structure, and the more important dynamic properties such as vibrations, conformational changes and chemical reactions are hardly possible without a description of the molecule itself that implies a description of molecular bodies. 

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