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.

Motivation: Protein structure alignment is a significant tool to understand evolutionary processes and physicochemical properties of proteins. Important targets of structure alignment are not only monomeric but also oligomeric proteins that sometimes include domain swapping or fusions. Although various protein structural alignment programs have been developed, no method is applicable to any protein pair regardless of the number of chain components and oligomeric states with retaining sequential restrictions: structurally equivalent regions must be aligned in the same order along protein sequences. Results: In this paper, we introduced a new sequential protein structural alignment algorithm MICAN-SQ, which is applicable to protein structures in all oligomeric states. In particular, MICAN-SQ allows the complicated structural alignments of proteins with domain swapping or fusion regions. To validate MICAN-SQ, alignment accuracies were evaluated using curated alignments of monomers and examples of domain swapping, and compared with those of pre-existing protein structural alignment programs. The results of this study show that MICAN-SQ has superior accuracy and robustness in comparison with previous programs and offers limited computational times. We also demonstrate that MICAN-SQ correctly aligns very large complexes and fused proteins. The present computations warrant the consideration of MICAN-SQ for studies of evolutionary and physicochemical properties of monomeric structures and all oligomer types. Availability and implementation: The MICAN program was implemented in C. The source code and executable file can be freely downloaded from http://www.tbp.cse.nagoya-u.ac.jp/MICAN/. Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Protein pairs that have the same secondary structure packing arrangement but have different topologies have attracted much attention in terms of both evolution and physical chemistry of protein structures. Further investigation of such protein relationships would give us a hint as to how proteins can change their fold in the course of evolution, as well as a insight into physico-chemical properties of secondary structure packing. For this purpose, highly accurate sequence order independent structure comparison methods are needed. RESULTS: We have developed a novel protein structure alignment algorithm, MICAN (a structure alignment algorithm that can handle Multiple-chain complexes, Inverse direction of secondary structures, Cα only models, Alternative alignments, and Non-sequential alignments). The algorithm was designed so as to identify the best structural alignment between protein pairs by disregarding the connectivity between secondary structure elements (SSE). One of the key feature of the algorithm is utilizing the multiple vector representation for each SSE, which enables us to correctly treat bent or twisted nature of long SSE. We compared MICAN with other 9 publicly available structure alignment programs, using both reference-dependent and reference-independent evaluation methods on a variety of benchmark test sets which include both sequential and non-sequential alignments. We show that MICAN outperforms the other existing methods for reproducing reference alignments of non-sequential test sets. Further, although MICAN does not specialize in sequential structure alignment, it showed the top level performance on the sequential test sets. We also show that MICAN program is the fastest non-sequential structure alignment program among all the programs we examined here. CONCLUSIONS: MICAN is the fastest and the most accurate program among non-sequential alignment programs we examined here. These results suggest that MICAN is a highly effective tool for automatically detecting non-trivial structural relationships of proteins, such as circular permutations and segment-swapping, many of which have been identified manually by human experts so far. The source code of MICAN is freely download-able at http://www.tbp.cse.nagoya-u.ac.jp/MICAN.