Topological and stereochemical restrictions in beta-sandwich protein structures

Chain topology in beta-structured protein domains and handedness associated with it are discussed. Previously, other workers have shown that by considering just two restrictions--structures that are left-handed and/or have loops that cross can be disregarded--the number of topologies associated with such structures is expected to be severely limited. By way of example, we determine the number of topologies compatible with a six-stranded antiparallel beta-sandwich. Without restriction on the type of strand-strand connection allowed but with elimination of symmetry related structures 360 topologies are possible. If connections between parallel strands are disqualified the number is reduced, 10-fold, to 36. The figure is cut to 24 when structures with loop crossings are eliminated. Handedness in these structures is examined in detail and from this a rationale for the observed predominance of right-handed forms of beta-structures is presented. The 24 structures can be considered as a set of right- and left-handed pairs of 12 topologies. All but two of these pairs can be assigned hands on the basis of existing rules. Six of the structures are found to occur in the Brookhaven Protein Databank and all are right-handed. This study provides a basis for protein design projects which might, for example, attempt the synthesis of unobserved protein topologies. Of the 24 structures in the final set eight are examples of the classic Greek key fold. Thus, the predominance of this motif among all-beta proteins can be attributed in part to these topological constraints. The possible physicochemical origins of the structural selection rules and additional factors which might contribute to the particular favourability of certain structures are also explored.