De novo design of a non-local [beta]-sheet protein with high stability and accuracy

[beta]-sheet proteins carry out critical functions in biology, and hence are attractive scaffolds for computational protein design. Despite this potential, de novo design of all-[beta]-sheet proteins from first principles lags far behind the design of all-[alpha] or mixed-[alpha][beta] domains owing to their non-local nature and the tendency of exposed [beta]-strand edges to aggregate. Through study of loops connecting unpaired [beta]-strands ([beta]-arches), we have identified a series of structural relationships between loop geometry, side chain directionality and [beta]-strand length that arise from hydrogen bonding and packing constraints on regular [beta]-sheet structures. We use these rules to de novo design jellyroll structures with double-stranded [beta]-helices formed by eight antiparallel [beta]-strands. The nuclear magnetic resonance structure of a hyperthermostable design closely matched the computational model, demonstrating accurate control over the [beta]-sheet structure and loop geometry. Our results open the door to the design of a broad range of non-local [beta]-sheet protein structures.