Molecular shape analysis method

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

An important concern is the efficient detection of local shape changes introduced by chemical changes in remote locations of a molecule. One simple approach [20] applied a truncation method, compatible with the truncation process already used within the shape group methods for molecular shape analysis [41-44]. 

The shape analysis and shape comparisons of electron densities of molecular regions provide information relevant to their interactions. In the next section a brief review of a shape analysis method is given. 

Molecular topology [155-158,190-199] presents a systematic framework for general shape analysis methods applicable, in principle, to all molecules. The same framework is also the basis for special shape analysis methods designed to exploit the typical features of some special, distinguished molecular families, such as the folding properties of polypeptides, proteins, and other chain biomolecules. Molecular topology and the associated topological shape analysis approaches form the basis of the present book. 

Molecular bodies of quantum mechanical electron distributions or some other molecular functions such as electrostatic potentials can be represented on various levels of approximation. These representations have two main components the physical property or model used to define a formal molecular body, and the geometrical or topological method used to describe and analyze the model. If a representation of the molecular body is selected, then the boundaries of these approximate molecular bodies can be regarded as formal molecular surfaces. Hence, the molecular shape analysis problem can be formulated as the shape analysis problem of formal molecular surfaces. 

In multiple shape comparisons, efficient, algorithmic shape analysis methods are of particular importance. The shape group and shape code methods provide a framework for such analysis however, the input information they require, such as the 3D electron densities or electrostatic potentials often involve time consuming calculations. This is the case for large molecules or molecular systems, important in drug design and molecular engineering applications. Efficient calculation and representation of these molecular functions is of special importance in such cases. 

Methods for evaluating the steric misfit are minimal topological difference and -+ molecular shape analysis. 

Burke, B.J. and Hopfinger, A.J. (1993). Advances in Molecular Shape Analysis. In 3D QSAR in Drug Desigru Theory, Methods and Applications. (Kubinyi, H., ed.), ESCOM, Leiden (The Netherlands), pp. 276-306. 

In general, formal molecular fragments that are larger than the conventional functional groups can also be represented by fuzzy moieties of electron densities, dominated by several nuclei. The shapes of molecular fragments with density domains indicating separate identity have important chemical consequences, and these shapes can be characterized by topological shape analysis methods [40]. 

Molecular Field Topology Analysis, Molecular Shape Analysis, quantum-similarity. Shannon Entropy Descriptors, Electronic-Topological method. Compass method. Comparative... 

Whereas the concepts and method described in this contribution are equally applicable to various approximate and more advanced quantum-chemical representations, the basic concepts will be discussed and illustrated within the framework of the conventional Hartree-Fock-Roothaan-Hall SCF LCAO ab initio representation of molecular wave functions and electronic densities, as can be computed, for example, using the Gaussian family of computer programs of Pople and co-workers. The essence of the shape analysis methods will be discussed with respect to some fixed nuclear arrangement K note, however, that the generalizations will involve changes in the nuclear arrangement K. 

The Somoyai function is defined in terms of the electronic density function and the composite nuclear potential, providing a 3D shape representation of the bonding pattern within the molecule under study. Some of the topological techniques of molecular shape analysis have been reviewed, with special emphasis on applications to the Somoyai function. A combination of a family of recently introduced ab initio quality macromolecular electronic density computation methods with the electrostatic Hellmann-Feynman theorem provides a new technique for the computation of forces acting on the nuclei of large molecules. This method of force computation offers a new approach to macromolecular geometry optimization. 

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. 

These techniques often involve statistical treatment of data in a largely retrospective manner which is further limited by the arbitrary choice of common substructures, pharmacophores, binding points, and molecular overlays. In classical QSAR the limitations can be quite severe in that regressions are confined to a series of closely related structures often differing in relatively minor ways. More recent innovations Involve molecular shape analysis (13) and distance geometry methods (14). These techniques represent significant steps toward a true three-dimensional SAR with some predictive... 

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