How anisotropic and isotropic atomic displacement parameters monitor protein covalent bonds rigidity: isotropic B-factors underestimate bond rigidity

Under the assumption that covalent bonds are rigid, it is possible to compare the estimations of rigidity based on anisotropic and isotropic B-factors. This is done by computing the difference of the mean-square displacements (Delta-u) of atoms A and Z along the covalent bond A–Z, which must be close to zero for a rigid bond. The analysis of a high-quality set of protein structures, refined at a resolution better than (or equal to) 0.8 Angstroms, showed that Delta-u is significantly close to zero when anisotropic B-factors are used, with an average 60% Delta-u reduction. This reduction is larger for larger B-factors and this suggests that care should be taken in data-mining procedures that involve isotropic B-factors, especially at lower resolution, when anisotropic B-factors cannot be determined and when the average B-factor increases.