FREE-ENERGY DETERMINANTS OF SECONDARY STRUCTURE FORMATION .2. ANTIPARALLEL BETA-SHEETS

The factors that determine the stability of antiparallel beta-she ets are considered via a theoretical analysis of conformational free energ ies. A series of idealized model polyalanine beta-sheets are built wit h constraints such that the angular geometry of hydrogen bonding varie s in the range observed in proteins while hydrogen bonding distance re mains fixed. The conformations of the sheets generated in this way hav e a broad distribution of twist angles ranging from highly twisted lef t-handed to highly twisted right-handed orientations. The association free energies of the sheets are calculated with a gas phase CHARMM pot ential and EDPB/gamma solvation models. Left-handed structures are fou nd to be less stable than right handed structures due to intrachain st eric hindrance in isolated left-handed strands. This explains why anti parallel beta-sheets in proteins are invariably twisted in the right-h anded direction. The free energy surface for right-handed sheets shows particular preference for conformations ranging from flat to those th at exhibit a pronounced right-handed twist. This suggests that antipar allel beta-sheets can adopt a variety of right-handed conformations, a result that is consistent with observations on known proteins. In par allel with our study of alpha-helices we find that van der Waals and h ydrophobic interactions are the primary factor stabilizing polyalanine beta-sheets, while electrostatic interactions including hydrogen bond ing are found to be destabilizing. However, in contrast to helices, th e net change in conformational free energy involving only backbone-bac kbone interactions (including beta-carbons) is not sufficient to overc ome the loss in configurational entropy that accompanies sheet formati on. Rather we suggest that cross-strand non-polar side-chain-sidechain interactions are essential for sheet formation, explaining why large non-polar amino acids have the greatest sheet forming propensities. Th us, sheet propensities involve pairwise interactions and are expected to be context dependent, as has been observed in recent experiments. ( C) 1995 Academic Press Limited