Basic design features of the parallel alpha beta barrel, a ubiquitous protein-folding motif

Basic design features of the beta-sheet portion in parallel alpha beta barrels in known protein structures are analysed in the context of a model of a regular hyperboloid. A formal description of the relationships between beta-sheet twist, number of strands in the sheet and barrel dimensions is derived, and the underlying physical principles are rationalized. Results suggest that the major constraints on the geometry of the beta-sheet portion of the barrel come from the requirements to have optimal H-bonding interactions between beta-strands and to closely pack amino acid side-chains in the barrel interior so as to exclude bulk water. In addition, we show how the hyperboloid model and the ensuing formalism can serve to derive useful geometric and graphic tools for computer-aided protein design de novo. We then illustrate how these tools are used to determine that the requirement to have a closed regular eight-stranded beta-sheet surface imposes no particular constraints on the geometry (phi, psi angles) of the polypeptide backbone. Understanding the role of the amino acid sequence in determining the observed structures remains a major challenge. Detailed comparisons of known alpha beta-barrel structures (and amino acid sequence) with each other, and with polypeptide fragments from other protein crystal structures, reveal only a limited number of common sequence-structure motifs. These belong to characteristic alpha beta 1 and alpha beta 3 loop families previously described in alpha beta proteins, and occur at least once in nearly all the alpha beta-barrel structures examined.