The anatomy of protein beta-sheet topology

Here, we present a systematic analysis of the open-faced beta-sheet topologies in a set of non-redundant protein domain structures; in particular, we focus on the topological diversity of four-stranded beta-sheet motifs. Of the 96 topologies that are possible for a four-stranded beta-sheet, 42 were identified in known protein structures. Of these, four account for 50% of the structures that we have studied. Two sets of the topologies that were not observed may represent the section of the topological space that is not readily accessible to proteins on either thermodynamic or kinetic grounds. The first set contains topologies with alternating parallel and antiparallel beta-ladders. Their rare occurrence reflects the expectation that it is energetically unfavorable to match different hydrogen bonding patterns. The polypeptide chains in the second set of topologies go through convoluted paths and are expected to experience great kinetic frustrations during the folding processes. A knowledge of the potential causes for the topological preference of small beta-sheets also helps us to understand the topological properties of larger beta-sheet structures which frequently contain four-stranded motifs. The notion that protein topologies can only be taken from a confined and discrete space has important implications for structural genomics.