Principles determining the structure of β-sheet barrels in proteins II. The observed structures

In the accompanying paper we derived a set of principles that, we argue, govern the structure of β-sheet barrels. Barrel structures are classified in terms of two integral parameters: the number of strands in the β-sheet, n, and a measure of the stagger in the β-sheet, S. We derived a set of equations that show how the (n, S) values of a barrel structure determine the arrangement of its strands; its general shape; the twist and coiling of the β-sheet, and the arrangement of residues in the barrel interior. This work suggested that there are ten different combinations of n and S that form barrels with good β-sheet geometries and interiors close packed by β-sheet residues. In this paper we demonstrate the validity of these principles. We analyse in detail the observed structures of 39 different β-sheet barrels. These structures include representatives of all the different barrel structures currently known and for which atomic co-ordinates are available. We show that the observed arrangement of the strands, and the extent of the twist and coiling of the β-sheets, are very close to those calculated from the (n, S) values for the barrel. Of the 39 structures, 34 have one of the ten (n, S) values that we expect to form barrels with good β-sheet geometries and interiors close packed by β-sheet residues. The other five have one of two (n, S) values that give good β-sheet geometries but radii so large the β-sheet residues leave cavities at the centre of the barrels. In at least four of these the cavities have a functional role.