Distance geometry conformational space

Metzler W J, Hare D R and Pardi A 1989 Limited sampling of conformational space by the distance geometry algorithm implications for structures generated from NMR data Bioohemistry 2S 7045-52... 

One way to describe the conformation of a molecule other than by Cartesian or intern coordinates is in terms of the distances between all pairs of atoms. There are N(N - )/ interatomic distances in a molecule, which are most conveniently represented using a N X N S5munetric matrix. In such a matrix, the elements (i, j) and (j, i) contain the distant between atoms i and and the diagonal elements are all zero. Distance geometry explort conformational space by randomly generating many distance matrices, which are the converted into conformations in Cartesian space. The crucial feature about distance geometi (and the reason why it works) is that it is not possible to arbitrarily assign values to ti... 

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. 

Note that although the bounds on the distances satisfy the triangle inequalities, particular choices of distances between these bounds will in general violate them. Therefore, if all distances are chosen within their bounds independently of each other (the method that is used in most applications of distance geometry for NMR strucmre determination), the final distance matrix will contain many violations of the triangle inequalities. The main consequence is a very limited sampling of the conformational space of the embedded structures for very sparse data sets [48,50,51] despite the intrinsic randomness of the tech-... 

Distance Geometry Distance geometry is a well-known technique from the area of structure determination via NMR technology.137,138 Instead of describing a molecule by coordinates in Euclidean space, it is described by a so-called distance matrix containing all interatomic distances in the molecule. Based on distance matrices, a set of allowable conformations can be described in a comprehensive form from a distance interval for each atom pair. 

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. 

W. J. Metzler, D. R. Hare, and A. Pardi, Biochemistry, 28,7045, (1989). Limited Sampling of Conformational Space by the Distance Geometry Algorithm Implications for Structures Generated from NMR Data. 

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. 

Fig. 2. Schematic representation of conformational space exploration efficiencies and their dependency for the different sampling scale with, insufficient (A), nearly sufficient (B), and almost sufficient (C) number of initial structures. In this example, preliminary calculations are distance geometry or torsion angle space algorithms, and refinement is restraint molecular dynamics with same set of NMR-derived structural information. The exploration extents of the refinements are assumed to be similar for selected preliminary calculation s results (i.e., initial structures of the refinement calculations).

---