Distance Geometry DG

The procedure of DG calculations can be subdivided in three separated steps [119-121]. At first, holonomic matrices (see below for explanahon) with pairwise distance upper and lower limits are generated from the topology of the molecule of interest. These limits can be further restrained by NOE-derived distance information which are obtained from NMR experiments. In a second step, random distances within the upper and lower limit are selected and are stored in a metric matrix. This operation is called metrization. Finally, all distances are converted into a complex geometry by mathematical operations. Hereby, the matrix-based distance space is projected into a Gartesian coordinate space (embedding). 

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If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

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... 

The conformational influence of Saa2, Saa3, and Saa4 on the peptide backbone of three cyclic peptides 27-29 (Figure 1) has been investigated in more detail by NMR spectroscopy, distance geometry (DG), and subsequent molecular dynamic (MD) calculations.1451... 

Other simple geometrical descriptors are interatomic distances between pairs of atoms s and t. Interatomic distances are devided into intramolecular interatomic distances, i.e. distances between any pair of atoms (s, t) within the molecule, and intermo-lecular interatomic distances, i.e. distances between atoms of a molecule and atoms of a receptor structure, a reference compound or another molecule. While classical computational chemistry describes molecular geometry in terms of three-dimensional Cartesian coordinates or internal coordinates, the -> distance geometry (DG) method takes the interatomic distances as the fundamental coordinates of molecules, exploiting their close relationship to experimental quantities and molecular energies. 

Numerical methods. Quantum mechanical calculations, molecular mechanics, and distance geometry (DG) are summarized under numerical methods because they are based on extensive numerical optimization procedures often requiring substantial computation times (QMMM > DG). Although quantum mechanical or molecular mechanics programs need a reasonable starting... 

Blaney has described his impressive applications of distance geometry (DG) to ligand docking active site is first defined by overlapping... 

Cluster the lattice folding results [197] and/or calculate a mean structure by means of distance geometry (DG). 

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