Detection of protein symmetry and structural rearrangements using secondary structure elements

Many proteins exhibit a degree of internal symmetry in their tertiary structure, including circular permutations. These characteristics play an important role in terms of the functional robustness of proteins against mutations, and are pivotal for the study of protein function and evolution. Proteins exhibiting internal symmetry often demonstrate enhanced functional benefits, such as increased binding affinity due to repeated structural motifs, and evolutionary advantages that may result from gene duplication or fusion events, leading to more robust and adaptable molecular architectures. Similarly, circular permutations have been linked to improved catalytic activity and enhanced thermostability, opening new avenues in the design of enzymes and other functional proteins. In this study, we introduce a novel computational pipeline that leverages secondary structure elements (SSEs) as a compressed yet informative representation of protein structure to detect both symmetry and structural rearrangements effectively. Our method outperforms existing methods, such as Combinatorial Extension with Circular Permutations (CECP) by several orders of magnitude in terms of computational cost and identifies 17,130 circularly related proteins. Additionally, it detects 26,739 proteins associated with indel mutations. Notably, 8855 of these exhibit both circular permutation and indel mutations-highlighting a significant structural co-occurrence between these two types of variation. We also recovered most symmetric proteins identified by the CE-Symm tool and revealed more than 2.5 times as many symmetric proteins in the same dataset. By integrating precise boundary detection, clustering analysis, and rigorous cross-validation against established tools, our framework robustly maps internal structural features. These insights deepen our understanding of protein architecture and provide a structural basis for further investigation into protein evolution, while also informing de novo protein design and engineering.