The register shift rules for βαβ-motifs for de novo protein design

A wide range of de novo design of αβ -proteins has been achieved based on the design rules, which describe secondary structure lengths and loop torsion patterns favorable for design target topologies. This paper proposes design rules for register shifts in βαβ -motifs, which have not been reported previously, but are necessary for determining a target structure of de novo design of αβ -proteins. By analyzing naturally occurring protein structures in a database, we found preferences for register shifts in βαβ -motifs, and derived the following empirical rules: (1) register shifts must not be negative regardless of torsion types for a constituent loop in βαβ -motifs; (2) preferred register shifts strongly depend on the loop torsion types. To explain these empirical rules by physical interactions, we conducted physics-based simulations for systems mimicking a βαβ -motif that contains the most frequently observed loop type in the database. We performed an exhaustive conformational sampling of the loop region, imposing the exclusion volume and hydrogen bond satisfaction condition. The distributions of register shifts obtained from the simulations agreed well with those of the database analysis, indicating that the empirical rules are a consequence of physical interactions, rather than an evolutionary sampling bias. Our proposed design rules will serve as a guide to making appropriate target structures for the de novo design of αβ -proteins.