W0445

Sources of Variation of Torsion Angles in High-Resolution Protein Structures: Mean Value, Statistical Error, Positional Uncertainty and Structure Difference. Glenn Butterfoss and Jan Hermans*, Dept. of Biochemistry and Biophysics, School of Medicine, Univ. of North Carolina, Chapel Hill, NC 27599-7260.

In this paper we sort the variation of the values of dihedral angles in proteins into categories, by analyzing distributions in a database of structures determined at a resolution of 1.8 Å or better (Lovell et al., Proteins: Struct. Funct. Genet. 50, 437-450, 2003). The first analysis uses the torsion angle for the C^α-C^β bond (χ₁) of "straight" side chains (Gln, Glu, Arg and Lys). Extrapolation to low B-factors sets a low value of 70 on the mean square deviation of χ₁ related to structural differences. Extrapolation to high resolution gives a value of 120, while over the entire database the MSD is 180. (The angle is measured in degrees.) The assumption of three independent sources gives 8.4° as the "intrinsic" RMSD due to structural differences between proteins, 7° due to structural uncertainty related to thermal disorder, and 8° due to statistical error. Intrinsic RMSDs for torsion angles in other side chains estimated using instances with atomic B-values below 20, from a low of 6.5° for χ₁ of some rotamers of Ile to a high of 30° for χ₂ of the gauche^– rotamer of Phe. Those aspects of the distributions not related to statistical error or structural uncertainty have a clear basis in the energies of model compounds computed with high-level quantum-mechanics. For example, mean side chain torsion angles correlate well with those of minimum-energy rotamers of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme, and a striking correlation exists between the distribution of the C-S torsion angle (χ₃) of Met and the exponential of the torsion energy, exp(-βE) of the model compound CH₃CH₂-SCH₃.