International Tables for Crystallography
International Tables for Crystallography (2012). Vol. F, ch. 18.5, pp. 499-511 [ doi:10.1107/97809553602060000859 ]
Full-matrix least-squares is taken as the basis for an examination of protein-structure precision. A two-atom model is used to compare the precisions of unrestrained and restrained refinements. In this model, restrained refinement determines a bond length which is the weighted mean of the unrestrained diffraction-only length and the geometric-dictionary length. As a protein example, data with 0.94 Å resolution for concanavalin A are used in unrestrained and restrained full-matrix inversions to provide e.s.d.'s σ(r) for positions and σ(l) for bond lengths. σ(r) is as small as 0.01 Å for atoms with low Debye B values but increases strongly with B. The results emphasize the distinction between unrestrained and restrained refinements and also between σ(r) and σ(l). An unrestrained full-matrix inversion for an immunoglobulin with 1.7 Å data is also discussed. Several approximate methods are examined critically. These include Luzzati plots and the diffraction-component precision index (DPI). The DPI estimate of σ(r, Bavg) is given by a simple formula, which uses R or Rfree and is based on a very rough approximation to the least-squares method. Examples show its usefulness as a precision comparator for high- and low-resolution structures.
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About International Tables for CrystallographyInternational Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of eight volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.