Distance geometry refinement

Model building, in which molecular structure is represented by experimental data as input and this structure is manipulated with use of stereochemical rules. This includes computer graphics and distance geometry refinement. 

The greatest value of molecular dynamic simulations is that they complement and help to explain existing data for designing new experiments. The simulations are increasingly useful for structural refinement of models generated from NMR, distance geometry, and X-ray data. 

The first step of the structure refinement is the appHcation of distance geometry (DG) calculations which do not use an energy function but only experimentally derived distances and restraints which follow directly from the constitution, the so-caUed holonomic constraints. Those constraints are, for example, distances between geminal protons, which normally are in the range between 1.7 and 1.8 A, or the distance between vicinal protons, which can not exceed 3.1 A when protons are in anti-periplanar orientation. 

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... 

Some investigators would argue that the results of distance geometry are only initial structures and that biases should disappear after thorough MD or other energetic refinement. In this case, one should bear in mind that one may then suffer from biases in the molecular mechanics force field. The most serious of these is the tendency for structures to become too compact if simulations are conducted in vacuo. The obvious solution here is to perform simulations in the presence of explicit solvent, although this is computationally expensive. 

K. M. Banks, D. R. Hare, and B. R. Reid, Biochemistry, 28,6996 (1989). Three-Dimensional Solution Structure of a DNA Duplex Containing the Bel I Restriction Sequence Two-Dimensional NMR Studies, Distance Geometry Calculations, and Refinement by Back-Calculation of the NOESY Spectrum. 

Considering the generally poor ability of prediction methods, including those that are based on GAs, to provide accurate predictions based on sequence alone, the next studies [51-53] explored the possibility of including experimental data in the prediction scheme. In Ref. [51], distance constraints derived from NMR experiments were used to calculate the three-dimensional structure of proteins with the help of a GA for structure refinement. In this case, of course, the method is not a prediction scheme, but rather is used as a computational tool, like distance geometry algorithms, to identify a structure or structures which are compatible with the distance constraints. 

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).

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