Error estimates of protein structure coordinates and deviations from standard geometry by full-matrix refinement of γB- and βB2-crystallin

Faster workstations with larger memories are making error estimation from full-matrix least-squares refinement a more practicable technique in protein crystallography. Using minimum variance weighting, estimated standard deviations of atomic positions have been calculated for two eye lens proteins from the inverse of a least-squares normal matrix which was full with respect to the coordinate parameters. gamma B-crystallin, refined at 1.49 Angstrom yielded average errors in atomic positions which ranged from 0.05 Angstrom for main-chain atoms to 0.27 Angstrom for unrestrained water molecules. The second structure used in this work was that of beta B2-crystallin refined at 2.1 Angstrom resolution where the corresponding average errors were 0.08 and 0.35 Angstrom, respectively. The relative errors in atomic positions are dependent on the number and kinds of restraints used in the refinements. It is also shown that minimum variance weighting leads to mean-square deviations from target geometry in the refined structures which are smaller than the variances used in the distance weighting.