GLN: a method to reveal unique properties of lasso type topology in proteins

Are there double knots in proteins? Prediction and in vitro verification based on TrmD-Tm1570 fusion from C. nitroreducens

We have been aware of the existence of knotted proteins for over 30 years-but it is hard to predict what is the most complicated knot that can be formed in proteins. Here, we show new and the most complex knotted topologies recorded to date-double trefoil knots (31 #31). We found five domain arrangements (architectures) that result in a doubly knotted structure in almost a thousand proteins. The double knot topology is found in knotted membrane proteins from the CaCA family, that function as ion transporters, in the group of carbonic anhydrases that catalyze the hydration of carbon dioxide, and in the proteins from the SPOUT superfamily that gathers 31 knotted methyltransferases with the active site-forming knot. For each family, we predict the presence of a double knot using AlphaFold and RoseTTaFold structure prediction. In the case of the TrmD-Tm1570 protein, which is a member of SPOUT superfamily, we show that it folds in vitro and is biologically active. Our results show that this protein forms a homodimeric structure and retains the ability to modify tRNA, which is the function of the single-domain TrmD protein. However, how the protein folds and is degraded remains unknown.

Mathematical topology and geometry-based classification of tauopathies

Neurodegenerative diseases, like Alzheimer's, are associated with the presence of neurofibrillary lesions formed by tau protein filaments in the cerebral cortex. While it is known that different morphologies of tau filaments characterize different neurodegenerative diseases, there are few metrics of global and local structure complexity that enable to quantify their structural diversity rigorously. In this manuscript, we employ for the first time mathematical topology and geometry to classify neurodegenerative diseases by using cryo-electron microscopy structures of tau filaments that are available in the Protein Data Bank. By employing mathematical topology metrics (Gauss linking integral, writhe and second Vassiliev measure) we achieve a consistent, but more refined classification of tauopathies, than what was previously observed through visual inspection. Our results reveal a hierarchy of classification from global to local topology and geometry characteristics. In particular, we find that tauopathies can be classified with respect to the handedness of their global conformations and the handedness of the relative orientations of their repeats. Progressive supranuclear palsy is identified as an outlier, with a more complex structure than the rest, reflected by a small, but observable knotoid structure (a diagrammatic structure representing non-trivial topology). This topological characteristic can be attributed to a pattern in the beginning of the R3 repeat that is present in all tauopathies but at different extent. Moreover, by comparing single filament to paired filament structures within tauopathies we find a consistent change in the side-chain orientations with respect to the alpha carbon atoms at the area of interaction.

Non-covalent Lasso Entanglements in Folded Proteins: Prevalence, Functional Implications, and Evolutionary Significance

One-third of protein domains in the CATH database contain a recently discovered tertiary topological motif: non-covalent lasso entanglements, in which a segment of the protein backbone forms a loop closed by non-covalent interactions between residues and is threaded one or more times by the N- or C-terminal backbone segment. Unknown is how frequently this structural motif appears across the proteomes of organisms. And the correlation of these motifs with various classes of protein function and biological processes have not been quantified. Here, using a combination of protein crystal structures, AlphaFold2 predictions, and Gene Ontology terms we show that in E. coli, S. cerevisiae and H. sapiens that 71%, 52% and 49% of globular proteins contain one-or-more non-covalent lasso entanglements in their native fold, and that some of these are highly complex with multiple threading events. Further, proteins containing these tertiary motifs are consistently enriched in certain functions and biological processes across these organisms and depleted in others, strongly indicating an influence of evolutionary selection pressures acting positively and negatively on the distribution of these motifs. Together, these results demonstrate that non-covalent lasso entanglements are widespread and indicate they may be extensively utilized for protein function and subcellular processes, thus impacting phenotype.

Topological links in predicted protein complex structures reveal limitations of AlphaFold

AlphaFold is making great progress in protein structure prediction, not only for single-chain proteins but also for multi-chain protein complexes. When using AlphaFold-Multimer to predict protein‒protein complexes, we observed some unusual structures in which chains are looped around each other to form topologically intertwining links at the interface. Based on physical principles, such topological links should generally not exist in native protein complex structures unless covalent modifications of residues are involved. Although it is well known and has been well studied that protein structures may have topologically complex shapes such as knots and links, existing methods are hampered by the chain closure problem and show poor performance in identifying topologically linked structures in protein‒protein complexes. Therefore, we address the chain closure problem by using sliding windows from a local perspective and propose an algorithm to measure the topological-geometric features that can be used to identify topologically linked structures. An application of the method to AlphaFold-Multimer-predicted protein complex structures finds that approximately 1.72% of the predicted structures contain topological links. The method presented in this work will facilitate the computational study of protein‒protein interactions and help further improve the structural prediction of multi-chain protein complexes.

Nonaffine Mechanics of Entangled Networks Inspired by Intermediate Filaments

Inspired by massive intermediate filament (IF) reorganization in superstretched epithelia, we examine computationally the principles controlling the mechanics of a set of entangled filaments whose ends slide on the cell boundary. We identify an entanglement metric and threshold beyond which random loose networks respond nonaffinely and nonlinearly to stretch by self-organizing into structurally optimal star-shaped configurations. A simple model connecting cellular and filament strains links emergent mechanics to cell geometry, network topology, and filament mechanics. We identify a safety net mechanism in IF networks and provide a framework to harness entanglement in soft fibrous materials.

Is Posttranslational Folding More Efficient Than Refolding from a Denatured State: A Computational Study

The folding of proteins into their native conformation is a complex process that has been extensively studied over the past half-century. The ribosome, the molecular machine responsible for protein synthesis, is known to interact with nascent proteins, adding further complexity to the protein folding landscape. Consequently, it is unclear whether the folding pathways of proteins are conserved on and off the ribosome. The main question remains: to what extent does the ribosome help proteins fold? To address this question, we used coarse-grained molecular dynamics simulations to compare the mechanisms by which the proteins dihydrofolate reductase, type III chloramphenicol acetyltransferase, and d-alanine-d-alanine ligase B fold during and after vectorial synthesis on the ribosome to folding from the full-length unfolded state in bulk solution. Our results reveal that the influence of the ribosome on protein folding mechanisms varies depending on the size and complexity of the protein. Specifically, for a small protein with a simple fold, the ribosome facilitates efficient folding by helping the nascent protein avoid misfolded conformations. However, for larger and more complex proteins, the ribosome does not promote folding and may contribute to the formation of intermediate misfolded states cotranslationally. These misfolded states persist posttranslationally and do not convert to the native state during the 6 μs runtime of our coarse-grain simulations. Overall, our study highlights the complex interplay between the ribosome and protein folding and provides insight into the mechanisms of protein folding on and off the ribosome.

Lasso Proteins-Unifying Cysteine Knots and Miniproteins

Complex lasso proteins are a recently identified class of biological compounds that are present in considerable fraction of proteins with disulfide bridges. In this work, we look at complex lasso proteins as a generalization of well-known cysteine knots and miniproteins (lasso peptides). In particular, we show that complex lasso proteins with the same crucial topological features-cysteine knots and lasso peptides-are antimicrobial proteins, which suggests that they act as a molecular plug. Based on an analysis of the stability of the lasso piercing residue, we also introduce a method to determine which lasso motif is potentially functional. Using this method, we show that the lasso motif in antimicrobial proteins, as well in that in cytokines, is functionally relevant. We also study the evolution of lasso motifs, their conservation, and the usefulness of the lasso fingerprint, which extracts all topologically non-triviality concerning covalent loops. The work is completed by the presentation of extensive statistics on complex lasso proteins to analyze, in particular, the strange propensity for "negative" piercings. We also identify 21 previously unknown complex lasso proteins with an ester and a thioester bridge.

Topoly: Python package to analyze topology of polymers

The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.