Topological knots and links in proteins

Pawel Dabrowski-Tumanski, Joanna I. Sulkowska
<span title="2017-03-09">2017</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
Twenty years after their discovery, knots in proteins are now quite well understood. They are believed to be functionally advantageous and provide extra stability to protein chains. In this work, we go one step further and search for links-entangled structures, more complex than knots, which consist of several components. We derive conditions that proteins need to meet to be able to form links. We search through the entire Protein Data Bank and identify several sequentially nonhomologous chains
more &raquo; ... that form a Hopf link and a Solomon link. We relate topological properties of these proteins to their function and stability and show that the link topology is characteristic of eukaryotes only. We also explain how the presence of links affects the folding pathways of proteins. Finally, we define necessary conditions to form Borromean rings in proteins and show that no structure in the Protein Data Bank forms a link of this type. folding | catenanes | slipknot | lasso | disulphide bridge K notted proteins have been identified in all kingdoms of life, in organisms separated even by 1 billion years of evolution (1-5). High conservation (5) of knotted motifs and their location (usually) in enzymatic active sites indicates that knots are crucial for protein function. Over 1,300 knotted or slipknotted (shoelace-type) structures, including the trefoil (31), figure-eight (41), three-twist (52), and Stevedore's (61) knots (4, 6, 7), have been deposited in the Protein Data Bank (PDB) to date according to KnotProt (8). Mathematically, a knot is defined as an embedding of a circle into a 3D space. A link is a generalization of a knot, defined as an embedding of a finite set of circles. The simplest examples of links are, e.g., the Hopf link and the Solomon link ( Fig. 1 , Center). Links have been found in DNA (9, 10) and have been synthesized in template synthesis (11, 12) . In proteins, the first attempts to identify links were made by Mislow (13, 14) . In his approach, however, the link-forming loops were defined either by including interaction with a metal ion (noncovalent loop) or by at least two disulfide bonds for each (covalent) loop. The links formed by covalent loops, each closed by one disulfide bridge only, were considered "unlikely to lead to knots or links" (ref. 14, p. 4,202) by Mislow and therefore hardly examined. Moreover, all of the structures were scanned only by "visual examination of their 3D structures" (ref. 14, p. 4,202). To date, the only known simple protein links are designed p53 protein catenanes (15) (with the backbones of both chains artificially closed, forming linked loops) and a thermophilic two-chain complex (16) (with linked loops formed by the backbones closed via disulfide bridges). However, the discovery of a wide class of complex lasso proteins (17, 18), in which a chain pierces a covalently closed loop (Fig. 1) , opens a unique possibility of defining and identifying links. Such links (or more formally, pretzelanes) are defined using covalent loops closed by disulfide bridges in a single-protein chain (compare Fig. 1) . Therefore, 20 years after the discovery of knotted proteins, it is time to reformulate Mansfield's (1) question and ask, Are there links in proteins? In this paper, we propose a general method to identify and classify links in proteins and discuss their biological role. The existence of proteins with stable links changes our view on the complexity of proteins and leads to many intriguing questions never asked before: Are links conserved evolutionarily to provide unique features of proteins? Do they exist in all kingdoms? How do they fold? In this paper, we answer these questions, and, in addition, we find relations between proteins with links based on comparing their evolutionary, sequential, and functional properties. Search for Links To identify stable links in proteins, we analyzed their structure and used the method of spanning the (triangulated) minimal surface (17, 18) . A segment of a protein chain forms a covalent loop if the ends of the segment are connected by a covalent bond (e.g., disulfide bridges). Such a covalent loop can be pierced by a protein tail, thereby forming a complex lasso structure (17) (Fig. 2) . A link is formed when the piercing tail is itself a part of another covalent loop. To identify links and their types, we analyze sequential numbers (indexes) of loop-forming cysteines and piercing residues (Fig. 2) . The indexes of the cysteines are known from the protein structure, whereas indexes of loop-piercing residues can be determined from minimal surface analysis used in the classification of lasso proteins (17, 18) . This method is general and can be applied to various intramolecular contacts. Using the above method, we performed a comprehensive survey of the more than 115,000 chains deposited in the PDB as of May 2016, taking into account all known covalent interactions (e.g., cysteine, amide, ester, thioester, or carbon-carbon bonds). We found that links are formed in as many as 159 structures, of which 129 form the Hopf link and 35 form the Solomon link. The classification of these proteins according to their topological complexity, sequence similarity, and biological function is shown in Datasets S1 and S2, and exemplary linked protein are shown in Fig. 1 . In what follows we discuss conclusions that follow from this review. Conservation of Links and Artificial Structures To investigate the structural importance of links in proteins, we analyzed their conservation in clusters of 30% sequential homology. We found that links are strictly conserved for all homologs (representative structures are presented in SI Appendix, Figs. S1-S3). The nonconservation of topology in a homology cluster can be therefore viewed as a trace of a structure failure. Indeed, Significance Twenty years after a discovery of knotted proteins, we found that some single-protein chains can form links, which have even more complex structures than knots. We derive conditions that proteins need to meet to form links. We search through the entire Protein Data Bank and identify several chains that form a Hopf link and a Solomon link. The link motif has not been recognized before; however, it is clearly of important functional significance in proteins. In this article, we relate topological properties of proteins with links to their function and stability and show that the link topology is characteristic of eukaryotes only.
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