Conformational and geometrical properties of idealized beta-barrels in proteins

An equation for calculating the distances between the atoms involved in forming an idealized hydrogen bond in a parallel or antiparallel beta-barrel has been derived by adjusting the corresponding data given by Pauling and Corey for a beta-sheet. Based on these distances, a geometrical optimization method was developed, by which one can generate various idealized beta-barrels: parallel or antiparallel, tilted or non-tilted, right-tilted or left-tilted. For each type of idealized beta-barrel thus obtained, the corresponding conformation and characteristic geometric parameters as well as their relationship are analyzed and discussed. Since the strand in a tilted beta-barrel traces a curve rather than a straight line on a cylinder-like surface, a regular chain in which the dihedral angles of each residue are the same cannot form a tilted beta-barrel but only a non-tilted beta-barrel. As observed, the strands of a right-tilted beta-barrel possess a very strong right-handed twist. The radii of the idealized tilted parallel and antiparallel beta-barrels are greater than those of the corresponding non-tilted ones by approximately 1 A and approximately 1.5 A, respectively. Consequently, there is relatively more room for a tilted beta-barrel to accommodate the internal side-chains, suggesting that a conformational change from a non-tilted beta-barrel to a tilted one would ease the repulsion among the crowded internal side-chains so as to make the structure more stable. The values of root-mean-square fits indicate that the idealized right-tilted beta-barrels coincide quite well with the observed beta-barrels in both parallel and antiparallel cases.