Pawel Dabrowski-Tumanski

LassoProt: server to analyze biopolymers with lassos

The LassoProt server, http://lassoprot.cent.uw.edu.pl/, enables analysis of biopolymers with entangled configurations called lassos. The server offers various ways of visualizing lasso configurations, as well as their time trajectories, with all the results and plots downloadable. Broad spectrum of applications makes LassoProt a useful tool for biologists, biophysicists, chemists, polymer physicists and mathematicians. The server and our methods have been validated on the whole PDB, and the results constitute the database of proteins with complex lassos, supported with basic biological data. This database can serve as a source of information about protein geometry and entanglement-function correlations, as a reference set in protein modeling, and for many other purposes.

Complex lasso: new entangled motifs in proteins

We identify new entangled motifs in proteins that we call complex lassos. Lassos arise in proteins with disulfide bridges (or in proteins with amide linkages), when termini of a protein backbone pierce through an auxiliary surface of minimal area, spanned on a covalent loop. We find that as much as 18% of all proteins with disulfide bridges in a non-redundant subset of PDB form complex lassos, and classify them into six distinct geometric classes, one of which resembles supercoiling known from DNA. Based on biological classification of proteins we find that lassos are much more common in viruses, plants and fungi than in other kingdoms of life. We also discuss how changes in the oxidation/reduction potential may affect the function of proteins with lassos. Lassos and associated surfaces of minimal area provide new, interesting and possessing many potential applications geometric characteristics not only of proteins, but also of other biomolecules.

Topological knots and links in proteins

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. 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 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.

LinkProt: a database collecting information about biological links

Protein chains are known to fold into topologically complex shapes, such as knots, slipknots or complex lassos. This complex topology of the chain can be considered as an additional feature of a protein, separate from secondary and tertiary structures. Moreover, the complex topology can be defined also as one additional structural level. The LinkProt database (http://linkprot.cent.uw.edu.pl) collects and displays information about protein links — topologically non-trivial structures made by up to four chains and complexes of chains (e.g. in capsids). The database presents deterministic links (with loops closed, e.g. by two disulfide bonds), links formed probabilistically and macromolecular links. The structures are classified according to their topology and presented using the minimal surface area method. The database is also equipped with basic tools which allow users to analyze the topology of arbitrary (bio)polymers.

In Search of Functional Advantages of Knots in Proteins

We analysed the structure of deeply knotted proteins representing three unrelated families of knotted proteins. We looked at the correlation between positions of knotted cores in these proteins and such local structural characteristics as the number of intra-chain contacts, structural stability and solvent accessibility. We observed that the knotted cores and especially their borders showed strong enrichment in the number of contacts. These regions showed also increased thermal stability, whereas their solvent accessibility was decreased. Interestingly, the active sites within these knotted proteins preferentially located in the regions with increased number of contacts that also have increased thermal stability and decreased solvent accessibility. Our results suggest that knotting of polypeptide chains provides a favourable environment for the active sites observed in knotted proteins. Some knotted proteins have homologues without a knot. Interestingly, these unknotted homologues form local entanglements that retain structural characteristics of the knotted cores.

To Tie or Not to Tie? That Is the Question

In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential.

PyLasso: a PyMOL plugin to identify lassos

Summary Entanglement in macromolecules is an important phenomenon and a subject of multidisciplinary research. As recently discovered, around 4% of proteins form new entangled motifs, called lassos. Here we present the PyLasso-a PyMOL plugin to identify and analyse properties of lassos in proteins and other (bio)polymers, as well as in other biological, physical and mathematical systems. The PyLasso is a useful tool for all researchers working on modeling of macromolecules, structure prediction, properties of polymers, entanglement in fluids and fields, etc. Availability and implementation The PyLasso and tutorial videos are available at http://pylasso.cent.uw.edu.pl. Contact jsulkowska@cent.uw.edu.pl.

Prediction of the optimal set of contacts to fold the smallest knotted protein.

Knotted protein chains represent a new motif in protein folds. They have been linked to various diseases, and recent extensive analysis of the Protein Data Bank shows that they constitute 1.5% of all deposited protein structures. Despite thorough theoretical and experimental investigations, the role of knots in proteins still remains elusive. Nonetheless, it is believed that knots play an important role in mechanical and thermal stability of proteins. Here, we perform a comprehensive analysis of native, shadow-specific and non-native interactions which describe free energy landscape of the smallest knotted protein (PDB id 2efv). We show that the addition of shadow-specific contacts in the loop region greatly enhances folding kinetics, while the addition of shadow-specific contacts along the C-terminal region (H3 or H4) results in a new folding route with slower kinetics. By means of direct coupling analysis (DCA) we predict non-native contacts which also can accelerate kinetics. Next, we show that the length of the C-terminal knot tail is responsible for the shape of the free energy barrier, while the influence of the elongation of the N-terminus is not significant. Finally, we develop a concept of a minimal contact map sufficient for 2efv protein to fold and analyze properties of this protein using this map.

GapRepairer: a server to model a structural gap and validate it using topological analysis

Motivation Over 25% of protein structures possess unresolved fragments. On the other hand, approximately 6% of protein chains have non-trivial topology (and form knots, slipknots, lassos and links). As the topology is fundamental for the proper function of proteins, modeling of topologically correct structures is decisive in various fields, including biophysics, biotechnology and molecular biology. However, none of the currently existing tools take into account the topology of the model and those which could be modified to include topology, demand experience in bioinformatics, protein topology and knot theory. Results In this work, we present the GapRepairer-the server that fills the gap in the spectrum of structure modeling methods. Its easy and intuitive interface offers the power of Modeller homology modeling to many non-experts in the field. This server determines the topology of templates and predicted structures. Such information when possible is used by the server to suggest the best model, or it can be used by the user to score models or to design artificially (dis)entangled structures. Availability and implementation GapRepairer server along with tutorials, usage notes, movies and the database of already repaired structures is available at http://gaprepairer.cent.uw.edu.pl. Supplementary information Supplementary data are available at Bioinformatics online.

The exclusive effects of chaperonin on the behavior of proteins with 52 knot.

The folding of proteins with a complex knot is still an unresolved question. Based on representative members of Ubiquitin C-terminal Hydrolases (UCHs) that contain the 52 knot in the native state, we explain how UCHs are able to unfold and refold in vitro reversibly within the structure-based model. In particular, we identify two, topologically different folding/unfolding pathways and corroborate our results with experiment, recreating the chevron plot. We show that confinement effect of chaperonin or weak crowding greatly facilitates folding, simultaneously slowing down the unfolding process of UCHs, compared with bulk conditions. Finally, we analyze the existence of knots in the denaturated state of UCHs. The results of the work show that the crowded environment of the cell should have a positive effect on the kinetics of complex knotted proteins, especially when proteins with deeper knots are found in this family.