Shape analysis approaches

We may consider some chemical examples. Several alcohols, including ethanol and ally alcohol, have been studied using the density domain shape analysis approach [2,3], and in all these cases a whole range [a, a"] of density threshold values have been found within which the O and H nuclei of the OH group are completely surrounded by MIDCO s, separating these nuclei from all the other nuclei of the molecule. This criterion, the existence of a MIDCO that separates a group of nuclei from all other nuclei of a molecule, is used for the identification and a detailed characterization of chemical functional groups [1-3]. 

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. 

One practical aspect of the systematic shape analysis approach is of special importance for drug design and molecular engineering applications. Even though the actual relations between molecular shapes and chemical or biochemical properties may be very complex and poorly understood in some cases, for molecular design purposes a detailed understanding is not always necessary. The shape analysis of sequences of molecules of known chemical properties or known biochemical and... 

A shape analysis approach, analogous to macroscopic shape analysis, involves the computation of the Fourier transform of... 

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]. 

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

The absorption curves given by coal macerals approached the horizontal (magnetic field strength) axis more slowly than a Gaussian distribution curve. Shape analysis (16) showed that over much of the curve, the form closely approximated a Lorentzian distribution curve, but both positive and negative deviations were found in the wings of the curves (that is, in various examples, the curves approached the axis either somewhat more or somewhat less rapidly... 

Bursi et al. (2001) reported two methods to calculate the stability of testosterone-like steroids. These were the use of a decision tree and molecular descriptors or quantum mechanical methods. For satisfactory accuracy, Bursi and colleagues (2001) had to use a 3-21G basis set with spin correction and equilibrium geometries. This required 12 hours of computation for reactants and products. Optimization of transition state geometry was also required. The simpler decision tree analysis approach indicated that descriptors such as the volumes and, to a lesser degree, the shape were important. Correlations of calculated and experimental rates of metabolism were reported. 

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]. 

For a shape complementarity analysis of functional groups we shall follow the shape complementarity approach described for molecules in ref. [2],... 

Ehrlich, R., and Full, W. E. (1984), Fourier shape analysis—a multivariate pattern recognition approach, in Beddow, J. K., Ed., Particle Characterization in Technology, Vol. II, Morphological Analysis, CRC Press, Boca Raton, FL. 

The first model, describing the isolated region approach, can be derived easily from the AFDF principle. Molecular regions are described by fuzzy electron densities analogous to densities of complete molecules, and the local shape analysis of regions follows the same principles as the shape analysis of... 

The computation and shape analysis of the interactive RIDCOs of a region R in a macromolecule RM requires the determination of additional contours. This implies that the shape analysis of interacting RIDCOs is computationally more expensive than that of the non-interactive RIDCOs GR M (a). For the suggested approach to the study of host-guest interactions,... 

This observation of Parr and Berk provides the basis for a simple approach to molecular shape analysis and molecular similarity analysis, described below. Although the molecular shapes, as defined by the electronic density, differ somewhat from the shapes of the nuclear potentials, their similarity can be exploited the nuclear potential contour surfaces provide a simple approximation of the shape of molecules. We shall refer to the isopotential surfaces of the nuclear potential contours as NUPCO surfaces. These surfaces have a major advantage the computation of NUPCO s is a trivially simple task as compared to the calculation of electronic densities. Furthermore, nuclear potential is a useful molecular property in its own right, without any reference to electronic density a comparison of NUPCO s of various molecules can provide a valid tool for evaluating molecular similarity. The superposition of potentials of different sets of nuclei can result in similar composite potentials, consequently, the comparison of NUPCO s is better... 

---