The energetics of off-rotamer protein side-chain conformations

Non-rotameric ("off-rotamer") conformations are commonly observed for the side-chains of protein crystal structures. This study examines whether such conformations are real or artifactual by comparing the energetics of on and off-rotamer side-chain conformations calculated with the CHARMM energy function. Energy-based predictions of side-chain orientation are carried out by rigid-geometry mapping in the presence of the fixed protein environment for 1709 non-polar side-chains in 24 proteins for which high-resolution (2.0 A or better) structures are available. For on-rotamer conformations, 97.6 % are correctly predicted; i.e. they correspond to the absolute minima of their local side-chain energy maps (generally to within 10 degrees or less). By contrast, for the observed off-rotamer side-chain conformations, 63.8 % are predicted correctly. This difference is statistically significant (P<0.001) and suggests that while most of the observed off-rotamer conformations are real, many of the erroneously predicted ones are likely to be artifacts of the X-ray refinements. Probabilities for off-rotamer conformations of the non-polar side-chains are calculated to be 5.0-6.1 % by adaptive umbrella-sampled molecular dynamics trajectories of individual amino acid residues in vacuum and in the presence of an average protein or aqueous dielectric environment. These results correspond closely to the 5.7 % off-rotamer fraction predicted by the rigid-geometry mapping studies. Since these values are about one-half of the 10.2 % off-rotamer fraction observed in the X-ray structures, they support the conclusion that many of the latter are artifacts. In both the rigid-geometry mapping and the molecular dynamics studies, the discrepancies between the predicted and observed fractions of off-rotamer conformations are largest for leucine residues (approximately 6 % versus 16.6 %). The simulations for the isolated amino acid residues indicate that the real off-rotamer frequency of 5-6 % is consistent with the internal side-chain and local side-chain-backbone energetics and does not originate from shifts due to the protein. The present results suggest that energy-based rotation maps can be used to find side-chain positional artifacts that appear in crystal structures based on refinements in the 2 A resolution range.