Surface comparison mainly address how a protein is seen from and possibly interacts with its exterior. In protein structure comparison either the shapes of proteins’ solvent accessible surfaces or their folded backbones are compared. On the other hand, proteins reuse the same types of folds, but with the growing number of known protein structures, the global view is changing from discrete folds into considering larger parts of fold space as a continuum. Another is that mutations cause plastic deformation that comparison methods should also take into account. One is that even for a fixed sequence of amino acids, some proteins are highly flexible. Aside from the rapid growth of the number of known protein structures, protein structure comparison is challenging for several reasons. Protein shapes are known to be more preserved than their sequences of amino acids: structural comparison of proteins is therefore an important and active area of research with new structural alignment methods reported to double every five years for three decades. Proteins are essential cellular tools and as macroscopic tools, some shapes are preferential for fulfilling specific functions. Conclusionsīased on the data we conclude that our program ProteinAlignmentObstruction provides significant additional information to alignment scores based solely on distances between aligned and superimposed residue pairs. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. TM-align is one of the most restrictive alignment programs. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. As expected, we find at least one essential self-intersection separating most unknotted structures from a knotted structure, and we find even larger motions in proteins connected by obstruction free linear interpolations. Each of these indicates a significant difference between the folds of the aligned protein structures. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. A new path is constructed by altering the linear interpolation using a novel interpretation of Reidemeister moves from knot theory working on three-dimensional curves rather than on knot diagrams. To determine if the self-intersections alter the protein’s backbone curve significantly or not, we present a path-finding algorithm that checks if there exists a self-avoiding path in a neighborhood of the linear interpolation. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. Considering such a linear interpolation, these methods do not differentiate if there is room for the interpolation, if it causes steric clashes, or more severely, if it changes the topology of the compared protein backbone curves. Most methods for structural alignment of protein structures optimize the distances between aligned and superimposed residue pairs, i.e., the distances traveled by the aligned and superimposed residues during linear interpolation. Structure comparison is, e.g., algorithmically the starting point for computational studies of structural evolution and it guides our efforts to predict protein structures from their amino acid sequences. In computational structural biology, structure comparison is fundamental for our understanding of proteins.
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