PyKnot: a PyMOL tool for the discovery and analysis of knots in proteins

AlphaKnot 2.0: a web server for the visualization of proteins' knotting and a database of knotted AlphaFold-predicted models

The availability of 3D protein models is rapidly increasing with the development of structure prediction algorithms. With the expanding availability of data, new ways of analysis, especially topological analysis, of those predictions are becoming necessary. Here, we present the updated version of the AlphaKnot service that provides a straightforward way of analyzing structure topology. It was designed specifically to determine knot types of the predicted structure models, however, it can be used for all structures, including the ones solved experimentally. AlphaKnot 2.0 provides the user's ability to obtain the knowledge necessary to assess the topological correctness of the model. Both probabilistic and deterministic knot detection methods are available, together with various visualizations (including a trajectory of simplification steps to highlight the topological complexities). Moreover, the web server provides a list of proteins similar to the queried model within AlphaKnot's database and returns their knot types for direct comparison. We pre-calculated the topology of high-quality models from the AlphaFold Database (4th version) and there are now more than 680.000 knotted models available in the AlphaKnot database. AlphaKnot 2.0 is available at https://alphaknot.cent.uw.edu.pl/.

PyProtif: a PyMol plugin to retrieve and visualize protein motifs for structural studies

Proteins often possess several motifs and the ones with similar motifs were found to have similar biochemical properties and thus related biological functions. Thereby, multiple databases were developed to store information on such motifs in proteins. For instance, PDBsum stores the results of Promotif's generated structural motifs and Pfam stores pre-computed patterns of functional domains. In addition to the fact that all this stored information is extremely useful, we can further augment its importance if we ought to integrate these motifs into visualization software. In this work, we have developed PyProtif, a plugin for the PyMOL molecular visualization program, which automatically retrieves protein structural and functional motifs from different databases and integrates them in PyMOL for visualization and analyses. Through an expendable menu and a user-friendly interface, the plugin grants the users the ability to study simultaneously multiple proteins and to select and manipulate each motif separately. Thus, this plugin will be of great interest for structural, evolutionary and classification studies of proteins.

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.

Quantifying steric hindrance and topological obstruction to protein structure superposition

BACKGROUND

In computational structural biology, structure comparison is fundamental for our understanding of proteins. 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. 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. 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.

RESULTS

To distinguish such cases, we analyze the linear interpolation between two aligned and superimposed backbones. We quantify the amount of steric clashes and find all self-intersections in a linear backbone interpolation. 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. 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. Either the algorithm finds a self-avoiding path or it returns a smallest set of essential self-intersections. Each of these indicates a significant difference between the folds of the aligned protein structures. 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. We also find examples of homologous proteins that are differently threaded, and we find many distinct folds connected by longer but simple deformations. TM-align is one of the most restrictive alignment programs. With standard parameters, it only aligns residues superimposed within 5 Ångström distance. We find 42165 topological obstructions between aligned parts in 142068 TM-alignments. Thus, this restrictive alignment procedure still allows topological dissimilarity of the aligned parts.

CONCLUSIONS

Based 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.

A Scalable Computational Approach for Simulating Complexes of Multiple Chromosomes

Significant efforts have been recently made to obtain the three-dimensional (3D) structure of the genome with the goal of understanding how structures may affect gene regulation and expression. Chromosome conformational capture techniques such as Hi-C, have been key in uncovering the quantitative information needed to determine chromatin organization. Complementing these experimental tools, co-polymers theoretical methods are necessary to determine the ensemble of three-dimensional structures associated to the experimental data provided by Hi-C maps. Going beyond just structural information, these theoretical advances also start to provide an understanding of the underlying mechanisms governing genome assembly and function. Recent theoretical work, however, has been focused on single chromosome structures, missing the fact that, in the full nucleus, interactions between chromosomes play a central role in their organization. To overcome this limitation, MiChroM (Minimal Chromatin Model) has been modified to become capable of performing these multi-chromosome simulations. It has been upgraded into a fast and scalable software version, which is able to perform chromosome simulations using GPUs via OpenMM Python API, called Open-MiChroM. To validate the efficiency of this new version, analyses for GM12878 individual autosomes were performed and compared to earlier studies. This validation was followed by multi-chain simulations including the four largest human chromosomes (C1-C4). These simulations demonstrated the full power of this new approach. Comparison to Hi-C data shows that these multiple chromosome interactions are essential for a more accurate agreement with experimental results. Without any changes to the original MiChroM potential, it is now possible to predict experimentally observed inter-chromosome contacts. This scalability of Open-MiChroM allow for more audacious investigations, looking at interactions of multiple chains as well as moving towards higher resolution chromosomes models.

ISL Induces Apoptosis and Autophagy in Hepatocellular Carcinoma via Downregulation of PI3K/AKT/mTOR Pathway in vivo and in vitro

Aims

Isoliquiritigenin (ISL), a flavonoid from Glycyrrhiza glabra, has previously been reported to have anti-tumor effects in vivo and in vitro. However, the mechanisms whereby ISL exerts its anticancer effects remain poorly understood in hepatocellular carcinoma (HCC).

Purpose

In the present study, we investigated the anticancer efficacy and associated mechanisms of ISL in HCC MHCC97-H and SMMC7721 cells.

Results

We found that ISL inhibited cell viability and proliferation and induced apoptosis in a dose- and time-dependent manner in liver cancer lines. Furthermore, ISL could activate autophagy in HCC cells, and the autophagy inhibitor HCQ enhances ISL-induced apoptosis in HCC cells. Additionally, ISL induced apoptosis and autophagy through inhibition of the PI3K/Akt/mTOR pathway. Most importantly, in a xenograft tumor model in nude mice, data showed that the administration of ISL decreased tumor growth and concurrently promoted the expression of LC3-II and cleaved-caspase-3. Interestingly, we found that ISL inhibits mTOR by docking onto the ATP-binding pocket of mTOR (ie, it competes with ATP). We thus suggest that mTOR is a potential target for ISL inhibition of hepatocellular carcinoma development, which could be of interest for future investigations.

Conclusion

Taken together, the results reveal that ISL effectively inhibited proliferation and induced apoptosis in HCC through autophagy induction in vivo and in vitro, probably via the PI3K/Akt/mTOR pathway. ISL may be a potential therapeutic agent for hepatocellular carcinoma.

PyVibMS: a PyMOL plugin for visualizing vibrations in molecules and solids

Visualizing vibrational motions calculated with different ab initio packages requires dedicated post-processing tools. Here, we present a PyMOL plugin called PyVibMS for visualizing the vibrational motions for both molecular and solid systems calculated by mainstream quantum chemical computer programs including Gaussian, Q-Chem, VASP, and CRYSTAL. Benefiting from the continuing development of the PyMOL platform, PyVibMS provides powerful functionalities and user-friendly interface. PyVibMS was written in Python and its open-source nature makes it flexible and sustainable. As an example, the motions of the Konkoli-Cremer local vibrational modes are shown in this work for the first time. PyVibMS is freely available at https://github.com/smutao/PyVibMS . Graphical abstract In this work, a PyMOL plugin named PyVibMS is developed to visualize molecular and lattice vibrations.

PyLink: a PyMOL plugin to identify links

SUMMARY

Links are generalization of knots, that consist of several components. They appear in proteins, peptides and other biopolymers with disulfide bonds or ions interactions giving rise to the exceptional stability. Moreover because of this stability such biopolymers are the target of commercial and medical use (including anti-bacterial and insecticidal activity). Therefore, topological characterization of such biopolymers, not only provides explanation of their thermodynamical or mechanical properties, but paves the way to design templates in pharmaceutical applications. However, distinction between links and trivial topology is not an easy task. Here, we present PyLink-a PyMOL plugin suited to identify three types of links and perform comprehensive topological analysis of proteins rich in disulfide or ion bonds. PyLink can scan for the links automatically, or the user may specify their own components, including closed loops with several bridges and ion interactions. This creates the possibility of designing new biopolymers with desired properties.

AVAILABILITY AND IMPLEMENTATION

The PyLink plugin, manual and tutorial videos are available at http://pylink.cent.uw.edu.pl.

On folding of entangled proteins: knots, lassos, links and θ-curves

Around 6% of protein structures deposited in the PDB are entangled, forming knots, slipknots, lassos, links, and θ-curves. In each of these cases, the protein backbone weaves through itself in a complex way, and at some point passes through a closed loop, formed by other regions of the protein structure. Such a passing can be interpreted as crossing a topological barrier. How proteins overcome such barriers, and therefore different degrees of frustration, challenged scientists and has shed new light on the field of protein folding. In this review, we summarize the current knowledge about the free energy landscape of proteins with non-trivial topology. We describe identified mechanisms which lead proteins to self-tying. We discuss the influence of excluded volume, such as crowding and chaperones, on tying, based on available data. We briefly discuss the diversity of topological complexity of proteins and their evolution. We also list available tools to investigate non-trivial topology. Finally, we formulate intriguing and challenging questions at the boundary of biophysics, bioinformatics, biology, and mathematics, which arise from the discovery of entangled proteins.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

iPBAvizu: a PyMOL plugin for an efficient 3D protein structure superimposition approach

Background

Protein 3D structure is the support of its function. Comparison of 3D protein structures provides insight on their evolution and their functional specificities and can be done efficiently via protein structure superimposition analysis. Multiple approaches have been developed to perform such task and are often based on structural superimposition deduced from sequence alignment, which does not take into account structural features. Our methodology is based on the use of a Structural Alphabet (SA), i.e. a library of 3D local protein prototypes able to approximate protein backbone. The interest of a SA is to translate into 1D sequences into the 3D structures.

Results

We used Protein blocks (PB), a widely used SA consisting of 16 prototypes, each representing a conformation of the pentapeptide skeleton defined in terms of dihedral angles. Proteins are described using PB from which we have previously developed a sequence alignment procedure based on dynamic programming with a dedicated PB Substitution Matrix. We improved the procedure with a specific two-step search: (i) very similar regions are selected using very high weights and aligned, and (ii) the alignment is completed (if possible) with less stringent parameters. Our approach, iPBA, has shown to perform better than other available tools in benchmark tests. To facilitate the usage of iPBA, we designed and implemented iPBAvizu, a plugin for PyMOL that allows users to run iPBA in an easy way and analyse protein superimpositions.

Conclusions

iPBAvizu is an implementation of iPBA within the well-known and widely used PyMOL software. iPBAvizu enables to generate iPBA alignments, create and interactively explore structural superimposition, and assess the quality of the protein alignments.

Knot_pull-python package for biopolymer smoothing and knot detection

SUMMARY

The biggest hurdle in studying topology in biopolymers is the steep learning curve for actually seeing the knots in structure visualization. Knot_pull is a command line utility designed to simplify this process-it presents the user with a smoothing trajectory for provided structures (any number and length of protein, RNA or chromatin chains in PDB, CIF or XYZ format), and calculates the knot type (including presence of any links, and slipknots when a subchain is specified).

AVAILABILITY AND IMPLEMENTATION

Knot_pull works under Python >=2.7 and is system independent. Source code and documentation are available at http://github.com/dzarmola/knot_pull under GNU GPL license and include also a wrapper script for PyMOL for easier visualization. Examples of smoothing trajectories can be found at: https://www.youtube.com/watch?v=IzSGDfc1vAY.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Searching the Optimal Folding Routes of a Complex Lasso Protein

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.

Chain organization of human interphase chromosome determines the spatiotemporal dynamics of chromatin loci

We investigate spatiotemporal dynamics of human interphase chromosomes by employing a heteropolymer model that incorporates the information of human chromosomes inferred from Hi-C data. Despite considerable heterogeneities in the chromosome structures generated from our model, chromatins are organized into crumpled globules with space-filling (SF) statistics characterized by a single universal scaling exponent (ν = 1/3), and this exponent alone can offer a quantitative account of experimentally observed, many different features of chromosome dynamics. The local chromosome structures, whose scale corresponds to that of topologically associated domains (∼ 0.1 − 1 Mb), display dynamics with a fast relaxation time (≲ 1 − 10 sec); in contrast, the long-range spatial reorganization of the entire chromatin (≳O(102) Mb) occurs on a much slower time scale (≳ hour), providing the dynamic basis of cell-to-cell variability and glass-like behavior of chromosomes. Biological activities, modeled using stronger isotropic white noises added to active loci, accelerate the relaxation dynamics of chromatin domains associated with the low frequency modes and induce phase segregation between the active and inactive loci. Surprisingly, however, they do not significantly change the dynamics at local scales from those obtained under passive conditions. Our study underscores the role of chain organization of chromosome in determining the spatiotemporal dynamics of chromatin loci.

Chromosomes are giant chain molecules made of hundreds of megabase-long DNA intercalated with proteins. Structure and dynamics of interphase chromatin in space and time hold the key to understanding the cell type-dependent gene regulation. In this study, we establish that the crumpled and space-filling (SF) organization of chromatin fiber in the chromosome territory, characterized by a single scaling exponent, is sufficient to explain the complex spatiotemporal hierarchy in chromatin dynamics as well as the subdiffusive motion of the chromatin loci. While seemingly a daunting problem at a first glance, our study shows that relatively simple principles, rooted in polymer physics, can be used to grasp the essence of dynamical properties of the interphase chromatin.

KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers

The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .

Design principles for rapid folding of knotted DNA nanostructures

Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be threaded through previously formed loops in an exactly defined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology, only the one with the folding pathway designed according to the ‘free-end' rule folds efficiently into the target structure. Besides high folding yield on slow annealing, this design also folds rapidly on temperature quenching and dilution from chemical denaturant. This strategy could be used to design folding of other knotted programmable polymers such as RNA or proteins.

Driven by complementary base pairing, artificial single-chain DNA is capable of forming complex 3D architectures if an appropriate folding pathway can be realised. Here, the authors describe the design principles for rapidly folding structures, exemplified through fabrication of a nanosized square pyramid.

KnotProt: a database of proteins with knots and slipknots

The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its subchains. The pattern visible in the matrix gives the knotting fingerprint of a given protein and permits users to determine, for example, the minimal length of the knotted regions (knot's core size) or the depth of a knot, i.e. how many amino acids can be removed from either end of the cataloged protein structure before converting it from a knot to a different type of knot. In addition, the database presents extensive information about the biological functions, families and fold types of proteins with non-trivial knotting. As an additional feature, the KnotProt database enables users to submit protein or polymer chains and generate their knotting fingerprints.

Genome-wide structural modelling of TCR-pMHC interactions

Background

The adaptive immune response is antigen-specific and triggered by pathogen recognition through T cells. Although the interactions and mechanisms of TCR-peptide-MHC (TCR-pMHC) have been studied over three decades, the biological basis for these processes remains controversial. As an increasing number of high-throughput binding epitopes and available TCR-pMHC complex structures, a fast genome-wide structural modelling of TCR-pMHC interactions is an emergent task for understanding immune interactions and developing peptide vaccines.

Results

We first constructed the PPI matrices and iMatrix, using 621 non-redundant PPI interfaces and 398 non-redundant antigen-antibody interfaces, respectively, for modelling the MHC-peptide and TCR-peptide interfaces, respectively. The iMatrix consists of four knowledge-based scoring matrices to evaluate the hydrogen bonds and van der Waals forces between sidechains or backbones, respectively. The predicted energies of iMatrix are high correlated (Pearson's correlation coefficient is 0.6) to 70 experimental free energies on antigen-antibody interfaces. To further investigate iMatrix and PPI matrices, we inferred the 701,897 potential peptide antigens with significant statistic from 389 pathogen genomes and modelled the TCR-pMHC interactions using available TCR-pMHC complex structures. These identified peptide antigens keep hydrogen-bond energies and consensus interactions and our TCR-pMHC models can provide detailed interacting models and crucial binding regions.

Conclusions

Experimental results demonstrate that our method can achieve high precision for predicting binding affinity and potential peptide antigens. We believe that iMatrix and our template-based method can be useful for the binding mechanisms of TCR-pMHC complexes and peptide vaccine designs.

Knot localization in proteins

The backbones of proteins form linear chains. In the case of some proteins, these chains can be characterized as forming linear open knots. The knot type of the full chain reveals only limited information about the entanglement of the chain since, for example, subchains of an unknotted protein can form knots and subchains of a knotted protein can form different types of knots than the entire protein. To understand fully the entanglement within the backbone of a given protein, a complete analysis of the knotting within all of the subchains of that protein is necessary. In the present article, we review efforts to characterize the full knotting complexity within individual proteins and present a matrix that conveys information about various aspects of protein knotting. For a given protein, this matrix identifies the precise localization of knotted regions and shows the knot types formed by all subchains. The pattern in the matrix can be considered as a knotting fingerprint of that protein. We observe that knotting fingerprints of distantly related knotted proteins are strongly conserved during evolution and discuss how some characteristic motifs in the knotting fingerprints are related to the structure of the knotted regions and their possible biological role.