Distance geometry systematic searches

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. 

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. 

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

Developing a pharmacophore model using methods such as systematic conformational search, QSAR, distance geometry, and probe interaction calculations. 

Usually the 3-D structure of the enzyme/receptor is not known. In this case, receptor mapping techniques such as CoMFA and conformational analysis techniques such as systematic search and distance geometry are applied to a series of active and inactive structures to obtain a pharmacophore model for use in 3-D database searching. 

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