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

Protein superfolds are characterised as frustration-free topologies: A case study of pure parallel β-sheet topologies

A protein superfold is a type of protein fold that is observed in at least three distinct, non-homologous protein families. Structural classification studies have revealed a limited number of prevalent superfolds alongside several infrequent occurring folds, and in α/β type superfolds, the C-terminal β-strand tends to favor the edge of the β-sheet, while the N-terminal β-strand is often found in the middle. The reasons behind these observations, whether they are due to evolutionary sampling bias or physical interactions, remain unclear. This article offers a physics-based explanation for these observations, specifically for pure parallel β-sheet topologies. Our investigation is grounded in several established structural rules that are based on physical interactions. We have identified "frustration-free topologies" which are topologies that can satisfy all the rules simultaneously. In contrast, topologies that cannot are termed "frustrated topologies." Our findings reveal that frustration-free topologies represent only a fraction of all theoretically possible patterns, these topologies strongly favor positioning the C-terminal β-strand at the edge of the β-sheet and the N-terminal β-strand in the middle, and there is significant overlap between frustration-free topologies and superfolds. We also used a lattice protein model to thoroughly investigate sequence-structure relationships. Our results show that frustration-free structures are highly designable, while frustrated structures are poorly designable. These findings suggest that superfolds are highly designable due to their lack of frustration, and the preference for positioning C-terminal β-strands at the edge of the β-sheet is a direct result of frustration-free topologies. These insights not only enhance our understanding of sequence-structure relationships but also have significant implications for de novo protein design.

Exploration of novel αβ-protein folds through de novo design

A fundamental question in protein evolution is whether nature has exhaustively sampled nearly all possible protein folds throughout evolution, or whether a large fraction of the possible folds remains unexplored. To address this question, we defined a set of rules for β-sheet topology to predict novel αβ-folds and carried out a systematic de novo protein design exploration of the novel αβ-folds predicted by the rules. The designs for all eight of the predicted novel αβ-folds with a four-stranded β-sheet, including a knot-forming one, folded into structures close to the design models. Further, the rules predicted more than 10,000 novel αβ-folds with five- to eight-stranded β-sheets; this number far exceeds the number of αβ-folds observed in nature so far. This result suggests that a vast number of αβ-folds are possible, but have not emerged or have become extinct due to evolutionary bias.

The Structural Rule Distinguishing a Superfold: A Case Study of Ferredoxin Fold and the Reverse Ferredoxin Fold

Superfolds are folds commonly observed among evolutionarily unrelated multiple superfamilies of proteins. Since discovering superfolds almost two decades ago, structural rules distinguishing superfolds from the other ordinary folds have been explored but remained elusive. Here, we analyzed a typical superfold, the ferredoxin fold, and the fold which reverses the N to C terminus direction from the ferredoxin fold as a case study to find the rule to distinguish superfolds from the other folds. Though all the known structural characteristics for superfolds apply to both the ferredoxin fold and the reverse ferredoxin fold, the reverse fold has been found only in a single superfamily. The database analyses in the present study revealed the structural preferences of αβ- and βα-units; the preferences separate two α-helices in the ferredoxin fold, preventing their collision and stabilizing the fold. In contrast, in the reverse ferredoxin fold, the preferences bring two helices near each other, inducing structural conflict. The Rosetta folding simulations suggested that the ferredoxin fold is physically much more realizable than the reverse ferredoxin fold. Therefore, we propose that minimal structural conflict or minimal frustration among secondary structures is the rule to distinguish a superfold from ordinary folds. Intriguingly, the database analyses revealed that a most stringent structural rule in proteins, the right-handedness of the βαβ-unit, is broken in a set of structures to prevent the frustration, suggesting the proposed rule of minimum frustration among secondary structural units is comparably strong as the right-handedness rule of the βαβ-unit.