Distance geometry possible conformations

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... 

Finally, Burkhard Luy, Andreas Frank and Horst Kessler discuss Conformational Analysis of Drugs by Nuclear Magnetic Resonance Spectroscopy . The determination and refinement of molecular conformations comprehends three main methods distance geometry (DG), molecular dynamics (MD) and simulated anneahng (SA). In principle, it is possible to exclusively make use of DG, MD or... 

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. 

Distance geometry methods tend to be faster than molecular mechanics methods and they are easier to parameterize. On the other hand, they are less accurate and the generated conformations can be rather crude because the distance matrix describes conformational properties only in a coarse manner as, for example, there is no possibility to describe multiple energy minima of torsional angles. Thus, the cyclohexane chair and boat conformations would be considered to be equally reasonable. 

All possible conformers lie between these upper and lower distance bounds—the task of distance geometry is to convert or embed this usually uncertain distance information into accurate three-dimensional Cartesian coordinates. Crippen and HavePi solved the problem for the case of an exact distance matrix, where all distances are known. Much additional effort has gone into finding efficient and practical methods for solving the general problem of a distance bounds matrix, where only a subset of the distances is known exactly. This remains a very difficult problem for large molecules with more than 1000 atoms. 

One of the most important uses of distance geometry is for deriving conformations that are consistent with experimental distance information, especially distances obtained from NMR experiments. The NMR spectroscopist has at his or her disposal a range of experiments that can provide a wealth of information about the conformation of a molecule. Two of the most commonly used NMR experiments that provide such conformationally dependent information are the 2D-NOESY (nuclear Overhauser enhancement spectroscopy) and the 2D-COSY (correlated spectroscopy) experiments [Derome 1987]. NOESY provides information about the distances between atoms which are close together in space but may be separated by many bonds. The strength of the NOESY signal is inversely proportional to the sixth power of the distance and so by analysing the nuclear Overhauser spectrum it is possible... 

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