Remarks about protein structure precision

• Published in: Acta crystallographica. Section D, Biological crystallography. Vol. 55; no. 3; pp. 583 - 601
• Main Author: Cruickshank, D. W. J.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.03.1999
• Subjects: full-matrix least-squares method; Protein Conformation; protein structure precision; X-Ray Diffraction
• ISSN: 1399-0047; 0907-4449; 1399-0047
• DOI: 10.1107/S0907444998012645

Full‐matrix least squares is taken as the basis for an examination of protein structure precision. A two‐atom protein 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. Data of 0.94 Å resolution for the 237‐residue protein concanavalin A are used in unrestrained and restrained full‐matrix inversions to provide standard uncertainties 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 between σ(r) and σ(l). Other full‐matrix inversions are reported. Such inversions require massive calculations. Several approximate methods are examined and compared critically. These include a Fourier map formula [Cruickshank (1949). Acta Cryst.2, 65–82], Luzzati plots [Luzzati (1952). Acta Cryst.5, 802–810] and a new diffraction‐component precision index (DPI). The DPI estimate of σ(r, Bavg) is given by a simple formula. It uses R or Rfree and is based on a very rough approximation to the least‐squares method. Many examples show its usefulness as a precision comparator for high‐ and low‐resolution structures. The effect of restraints as resolution varies is examined. More regular use of full‐matrix inversion is urged to establish positional precision and hence the precision of non‐dictionary distances in both high‐ and low‐resolution structures. Failing this, parameter blocks for representative residues and their neighbours should be inverted to gain a general idea of σ(r) as a function of B. The whole discussion is subject to some caveats about the effects of disordered regions in the crystal.