Distance-geometry search method

Dmparison of various methods for searching conformational space has been performed cycloheptadecane (C17H34) [Saunders et al. 1990]. The methods compared were the ematic search, random search (both Cartesian and torsional), distance geometry and ecular dynamics. The number of unique minimum energy conformations found with 1 method within 3 kcal/mol of the global minimum after 30 days of computer processing e determined (the study was performed in 1990 on what would now be considered a / slow computer). The results are shown in Table 9.1. 

Finding the minimum of the hybrid energy function is very complex. Similar to the protein folding problem, the number of degrees of freedom is far too large to allow a complete systematic search in all variables. Systematic search methods need to reduce the problem to a few degrees of freedom (see, e.g.. Ref. 30). Conformations of the molecule that satisfy the experimental bounds are therefore usually calculated with metric matrix distance geometry methods followed by optimization or by optimization methods alone. 

By design, no conformational engine was implemented in DISCO, based on the assumption that at the time, no universal force fields and methods suitable for all types of compounds were available [53]. However, the commercial distributor Tripos provides access to 3D converters and conformational search engines such as Concord and Confort via the Sybyl interface. These algorithms will not be reviewed here as strictly seen they are not part of any pharmacophore identification program. The distance geometry approach has been used... 

T. F. Havel, I. D. Kuntz, and G. M. Crippen, Bull. Math. Biol. 45, 665 (1983). The Theory and Practice of Distance Geometry. See also A. R. Leach, Reviews in Computational Chemistry, Vol. 2, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1991, pp. 1-55. A Survey of Methods for Searching the Conformational Space of Small and Medium-Sized Molecules. 

Optimal filtering was proposed by Altman and Jardetzky (1989) as a heuristic refinement method of structure determination and has also been applied to the dihedral angle space (KoeU et al., 1992). Optimal filtering uses the exclusion paradigm, and during the search aU possible conformations are retained except where they are incompatible with the data. This allows a more systematic search of the allowed conformational space. As in the case of distance geometry, it is a ptire geometric method, and it calculates the mean positions and standard deviations of each atom. The output also needs to be refined to add information fi om the empirical force field. 

In general, five different approaches can be distinguished and are applied to explore the conformational space of a molecule systematic searches, rule-based and data-based approaches (model building), random methods, genetic algorithms, distance geometry, and simulation methods. Some of the basic principles and ideas behind these concepts have already been described in the Secs. 2 and 3 of this article. In the following, the application of these concepts to conformational analysis and searches will be discussed. 

The basic principles of the distance geometry approach have been described in Sec. 3.4. There, it was mentioned that the embedding procedure can produce several molecular geometries that do not violate the preset distance restrictions. Therefore, distance geometry per se can be regarded as a conformational search method. 

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