Free Energy Determinants of Secondary Structure Formation: II. Antiparallel β-Sheets

The factors that determine the stability of antiparallel beta-sheets are considered via a theoretical analysis of conformational free energies. A series of idealized model polyalanine beta-sheets are built with constraints such that the angular geometry of hydrogen bonding varies in the range observed in proteins while hydrogen bonding distance remains fixed. The conformations of the sheets generated in this way have a broad distribution of twist angles ranging from highly twisted left-handed to highly twisted right-handed orientations. The association free energies of the sheets are calculated with a gas phase CHARMM potential and FDPB/gamma solvation models. Left-handed structures are found to be less stable than right handed structures due to intrachain steric hindrance in isolated left-handed strands. This explains why antiparallel beta-sheets in proteins are invariably twisted in the right-handed direction. The free energy surface for right-handed sheets shows particular preference for conformations ranging from flat to those that exhibit a pronounced right-handed twist. This suggests that antiparallel beta-sheets can adopt a variety of right-handed conformations, a result that is consistent with observations on known proteins. In parallel with our study of alpha-helices we find that van der Waals and hydrophobic interactions are the primary factor stabilizing polyalanine beta-sheets, while electrostatic interactions including hydrogen bonding are found to be destabilizing. However, in contrast to helices, the net change in conformational free energy involving only backbone-backbone interactions (including beta-carbons) is not sufficient to overcome the loss in configurational entropy that accompanies sheet formation. Rather we suggest that cross-strand non-polar side-chain-side-chain interactions are essential for sheet formation, explaining why large non-polar amino acids have the greatest sheet forming propensities. Thus, sheet propensities involve pairwise interactions and are expected to be context dependent, as has been observed in recent experiments.