Distance-geometry Algorithms

The amount of computation necessary to try many conformers can be greatly reduced if a portion of the structure is known. One way to determine a portion of the structure experimentally is to obtain some of the internuclear distances from two-dimensional NMR experiments, as predicted by the nuclear Over-hauser effect (NOE). Once a set of distances are determined, they can be used as constraints within a conformation search. This has been particularly effective for predicting protein structure since it is very difficult to obtain crystallographic structures of proteins. It is also possible to define distance constraints based on the average bond lengths and angles, if we assume these are fairly rigid while all conformations are accessible. 

If the molecular motion is faster than the NMR timescale, the distance pre- 

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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... 

Five-carbon fragment to illustrate distance geometry algorithm. 

Restraints due to artifacts may, by chance, be completely consistent with the correct structure of the molecule. However, the majority of incorrect restraints will be inconsistent with the correct structural data (i.e., the correct restraints and information from the force field). Inconsistencies in the data produce distortions in the structure and violations in some restraints. Structural consistency is often taken as the final criterion to identify problematic restraints. It is, for example, the central idea in the bound-smoothing part of distance geometry algorithms, and it is intimately related to the way distance data are usually specified The error bounds are set wide enough that all data are geometrically consistent. 

Define a crude initial structure by either distance geometry algorithms or by model building. The latter starts by defining elements of secundary structure (helices, 3 Sheets) fhom the NMR data. Even starting from an extended structure is feasible (53) ... 

Havel, T. F. The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide-chains a smdy of 1830 independently computed conformations. Biopolymers 1990, 29,1565-1585. 

Figure 3. A typical fragment decomposition for a molecule of moderate coiriplexity. Roughly half of the interatomic distances can be specified in this case by the fragment data. The remaining distances are estimated by the distance geometry algorithm of Crippen (11).

The basis for the determination of solution conformation from NMR data lies in the determination of cross relaxation rates between pairs of protons from cross peak intensities in two-dimensional nuclear Overhauser effect (NOE) experiments. In the event that pairs of protons may be assumed to be rigidly fixed in an isotopically tumbling sphere, a simple inverse sixth power relationship between interproton distances and cross relaxation rates permits the accurate determination of distances. Determination of a sufficient number of interproton distance constraints can lead to the unambiguous determination of solution conformation, as illustrated in the early work of Kuntz, et al. (25). While distance geometry algorithms remain the basis of much structural work done today (1-4), other approaches exist. For instance, those we intend to apply here represent NMR constraints as pseudoenergies for use in molecular dynamics or molecular mechanics programs (5-9). 

Conformations were generated using metric matrix distance geometry algorithm JG (S. Kearsley, Merck Co., unpublished). The conformations were subjected to energy-minimization within... 

W. Braun, C. Bosch, L. R. Brown. N. Go, and K. Wiithrich, Biochim. Biophys. Acta, 667, 377 (1981). Combined Use of Proton-Proton Overhauser Enhancements and a Distance Geometry Algorithm for Determination of Polypeptide Conformations. 

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. 

T. F. Havel, Biopolymers, 29, 1565 (1990). The Sampling Properties of Some Distance Geometry Algorithms Applied to Unconstrained Polypeptide Chains A Study of 1830 Independently Computed Conformations. 

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. 

Distance Geometry Algorithm to Cyclic Oligopeptide Conformation Searches. 

Distance Geometry Algorithm for Conformational Sampling of Cyclic Structures. 

Fig. 9.14- Five-carbon fragment to illustrate distance geometry algorithm...

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