Significance of structural changes in proteins: Expected errors in refined protein structures

Abstract

A quantitative expression key to evaluating significant structural differences or induced shifts between any two protein structures is derived. Because crystallography leads to reports of a single (or sometimes dual) position for each atom, the significance of any structural change based on comparison of two structures depends critically on knowing the expected precision of each median atomic position reported, and on extracting it for each atom, from the information provided in the Protein Data Bank and in the publication. The differences between structures of protein molecules that should be identical, and that are normally distributed, indicating that they are not affected by crystal contacts, were analyzed with respect to many potential indicators of structure precision, so as to extract, essentially by "machine learning" principles, a generally applicable expression involving the highest correlates. Eighteen refined crystal structures from the Protein Data Bank, in which there are multiple molecules in the crystallographic asymmetric unit, were selected and compared. The thermal E factor, the connectivity of the atom, and the ratio of the number of reflections to the number of atoms used in refinement correlate best with the magnitude of the positional differences between regions of the structures that otherwise would be expected to be the same. These results are embodied in a six-parameter equation that can be applied to any crystallographically refined structure to estimate the expected uncertainty in position of each atom. Structure change in a macromolecule can thus be referenced to the expected uncertainty in atomic position as reflected in the variance between otherwise identical structures with the observed values of correlated parameters.

Crystal structure of the HIV-1 integrase catalytic core and C-terminal domains: A model for viral DNA binding

“…Table 1). The catalytic core domain within IN 52-288 forms a symmetric dimer that is very similar to the crystal structure of the isolated catalytic core domain, IN 52-210 (C␣ rms deviation of 0.6 Å between monomers) (30). Each catalytic core domain of the IN 52-288 dimer is linked to the C-terminal domain by residues 195-220 of helix ␣6.…”

The channel architecture of aquaporin 0 at a 2.2-Å resolution

“…The definition of probable error in each atom coordinate is a well defined function of resolution and data to parameter ratio for each structure, as elaborated by R.M.S. and Fauman (36). Any shift below the sum in quadrature of error in the two structures is by definition not detectable.…”

Error Estimates of Protein Structure Coordinates and Deviations from Standard Geometry by Full-Matrix Refinement ofγB- andβB2-Crystallin

“…More recent attempts to estimate errors have included: the 'residue R factor' of Jones et al (1991); the tabulated R indices of Elango & Parthasarathy (1990); the refinement protocol of Carson et al (1994) which uses temperature factors, real-space fit residuals, geometric strains, dihedral angles and shifts from the previous refinement cycle; the 'discriminator' of Sevcik et al (1993) which assesses the likely errors on each atom in terms of its temperature factor divided by its electron density in the final 2IF,,[ -IF,.I map, or U/p where ,o is the electron density; an empirically derived six-parameter equation of Stroud & Fauman (1995), and the use of the diagonal elements of the inverse normal matrix in a final cycle of unrestrained least-squares refinement to give an estimate of the radial errors in atomic positions (Holland et al, 1990).…”