Full-matrix refinement of the protein crambin at 0.83 Å and 130 K

This paper describes the first successful full-matrix least-squares (FMLS) refinement of a protein structure. The example used is crambin which is a small hydrophobic protein (4.7 kDa, 46 residues). It proves the feasibility of refining such large molecules by this classic method, routinely applied to small molecules. The final structure with 381 non-H protein atoms (54 protein atoms in alternative positions), 367 H atoms, 162 water molecules (combined occupancy 93) and one disordered ethanol molecule converged to a standard unweighted crystallographic R-factor of R = 9.0% when refined against F with reflections stronger than F > 2σ(F) and R = 9.5% when refined against F². The programs RFINE [Finger & Prince (1975). Natl Bur. Stand. (US) Tech. Note 854. A System of Fortran IV Computer Programs for Crystal Structure Computations] and SHELXL93 [Sheldrick (1993). SHELXL93. Program for Crystal Structure Refinement, Univ. of Göttingen, Germany] were used for FMLS refinement with the high-resolution low-temperature (0.83 Å, 130 K) data set of a mixed-sequence form of crambin. A detailed analysis of the models obtained in FMLS and PROLSQ [restrained least squares or RLS; Teeter, Roe & Heo (1993). J. Mol. Biol. 230, 292–311] refinements with the same data set is presented. The differences between the models obtained by both FMLS and RLS refinements are systematic but negligible and advantages and shortcomings of both methods are discussed. The final structure has very good geometry, fully comparable to the geometry of other structures in this resolution range. Ideal values used in PROLSQ and those by Engh & Huber [Engh & Huber (1991). Acta Cryst. A47, 392–400] differ significantly from this refinement and we recommend a new standard. FMLS refinement constitutes a sensitive tool to detect and model disorder in highly refined protein structures. We describe the modeling of temperature factors by the TLS method [Schomaker & Trueblood (1968). Acta Cryst. B24, 63–76]. Rigid body–TLS refinements led to a better understanding of different modes of vibrations of the molecule. Refinements using F² or F protocols converged and reached slightly different minima. Despite theoretical support for F²-based refinement, we recommend refinement on structure factors.