Structural principles of parallel beta-barrels in proteins.

Eight-stranded beta-sheets in nine protein structures containing "TIM (triose phosphate isomerase) barrels" are shown to be fitted satisfactorily by hyperboloids, the generating lines of which pass through the beta-strands. Simple parameterizations of the hyperboloid model are then used to determine the constraints that govern key parameters, such as the number of strands in the barrel, and to rationalize the remarkable conservation of strand number, observed to be eight, in nearly all the known examples of parallel beta-barrels. It is shown that the requirement to exclude solvent from the barrel interior, while at the same time keeping an upper limit on strand twist and interstrand distance so as to foster extensive hydrogen bonding interactions within the sheet, imposes strong constraints on barrel geometry. A formal description of the relationships between beta-sheet twist, strand number, and barrel dimensions is given here. It could have important implications for studies of protein folding and design.