Absence of knots in known RNA structures

lociPARSE: a locality-aware invariant point attention model for scoring RNA 3D structures

A scoring function that can reliably assess the accuracy of a 3D RNA structural model in the absence of experimental structure is not only important for model evaluation and selection but also useful for scoring-guided conformational sampling. However, high-fidelity RNA scoring has proven to be difficult using conventional knowledge-based statistical potentials and currently-available machine learning-based approaches. Here we present lociPARSE, a locality-aware invariant point attention architecture for scoring RNA 3D structures. Unlike existing machine learning methods that estimate superposition-based root mean square deviation (RMSD), lociPARSE estimates Local Distance Difference Test (lDDT) scores capturing the accuracy of each nucleotide and its surrounding local atomic environment in a superposition-free manner, before aggregating information to predict global structural accuracy. Tested on multiple datasets including CASP15, lociPARSE significantly outperforms existing statistical potentials (rsRNASP, cgRNASP, DFIRE-RNA, and RASP) and machine learning methods (ARES and RNA3DCNN) across complementary assessment metrics. lociPARSE is freely available at https://github.com/Bhattacharya-Lab/lociPARSE.

Knotted artifacts in predicted 3D RNA structures

Unlike proteins, RNAs deposited in the Protein Data Bank do not contain topological knots. Recently, admittedly, the first trefoil knot and some lasso-type conformations have been found in experimental RNA structures, but these are still exceptional cases. Meanwhile, algorithms predicting 3D RNA models have happened to form knotted structures not so rarely. Interestingly, machine learning-based predictors seem to be more prone to generate knotted RNA folds than traditional methods. A similar situation is observed for the entanglements of structural elements. In this paper, we analyze all models submitted to the CASP15 competition in the 3D RNA structure prediction category. We show what types of topological knots and structure element entanglements appear in the submitted models and highlight what methods are behind the generation of such conformations. We also study the structural aspect of susceptibility to entanglement. We suggest that predictors take care of an evaluation of RNA models to avoid publishing structures with artifacts, such as unusual entanglements, that result from hallucinations of predictive algorithms.

Discovery of a trefoil knot in the RydC RNA: Challenging previous notions of RNA topology

Knots are very common in polymers, including DNA and protein molecules. Yet, no genuine knot has been identified in natural RNA molecules to date. Upon re-examining experimentally determined RNA 3D structures, we discovered a trefoil knot 31, the most basic non-trivial knot, in the RydC RNA. This knotted RNA is a member of a small family of short bacterial RNAs, whose secondary structure is characterized by an H-type pseudoknot. Molecular dynamics simulations suggest a folding pathway of the RydC RNA that starts with a native twisted loop. Based on sequence analyses and computational RNA 3D structure predictions, we postulate that this trefoil knot is a conserved feature of all RydC-related RNAs. The first discovery of a knot in a natural RNA molecule introduces a novel perspective on RNA 3D structure formation and on fundamental research on the relationship between function and spatial structure of biopolymers.

RNAspider: a webserver to analyze entanglements in RNA 3D structures

Advances in experimental and computational techniques enable the exploration of large and complex RNA 3D structures. These, in turn, reveal previously unstudied properties and motifs not characteristic for small molecules with simple architectures. Examples include entanglements of structural elements in RNA molecules and knot-like folds discovered, among others, in the genomes of RNA viruses. Recently, we presented the first classification of entanglements, determined by their topology and the type of entangled structural elements. Here, we introduce RNAspider - a web server to automatically identify, classify, and visualize primary and higher-order entanglements in RNA tertiary structures. The program applies to evaluate RNA 3D models obtained experimentally or by computational prediction. It supports the analysis of uncommon topologies in the pseudoknotted RNA structures. RNAspider is implemented as a publicly available tool with a user-friendly interface and can be freely accessed at https://rnaspider.cs.put.poznan.pl/.

Entanglements of structure elements revealed in RNA 3D models

Computational methods to predict RNA 3D structure have more and more practical applications in molecular biology and medicine. Therefore, it is crucial to intensify efforts to improve the accuracy and quality of predicted three-dimensional structures. A significant role in this is played by the RNA-Puzzles initiative that collects, evaluates, and shares RNAs built computationally within currently nearly 30 challenges. RNA-Puzzles datasets, subjected to multi-criteria analysis, allow revealing the strengths and weaknesses of computer prediction methods. Here, we study the issue of entangled RNA fragments in the predicted RNA 3D structure models. By entanglement, we mean an arrangement of two structural elements such that one of them passes through the other. We propose the classification of entanglements driven by their topology and components. It distinguishes two general classes, interlaces and lassos, and subclasses characterized by element types-loops, dinucleotide steps, open single-stranded fragments-and puncture multiplicity. Our computational pipeline for entanglement detection, applied for 1,017 non-redundant models from RNA-Puzzles, has shown the frequency of different entanglements and allowed identifying 138 structures with intersected assemblies.

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.

RNApdbee 2.0: multifunctional tool for RNA structure annotation

In the field of RNA structural biology and bioinformatics, an access to correctly annotated RNA structure is of crucial importance, especially in the secondary and 3D structure predictions. RNApdbee webserver, introduced in 2014, primarily aimed to address the problem of RNA secondary structure extraction from the PDB files. Its new version, RNApdbee 2.0, is a highly advanced multifunctional tool for RNA structure annotation, revealing the relationship between RNA secondary and 3D structure given in the PDB or PDBx/mmCIF format. The upgraded version incorporates new algorithms for recognition and classification of high-ordered pseudoknots in large RNA structures. It allows analysis of isolated base pairs impact on RNA structure. It can visualize RNA secondary structures—including that of quadruplexes—with depiction of non-canonical interactions. It also annotates motifs to ease identification of stems, loops and single-stranded fragments in the input RNA structure. RNApdbee 2.0 is implemented as a publicly available webserver with an intuitive interface and can be freely accessed at http://rnapdbee.cs.put.poznan.pl/

Topological Sieving of Rings According to Their Rigidity

We present a novel mechanism for resolving the mechanical rigidity of nanoscopic circular polymers that flow in a complex environment. The emergence of a regime of negative differential mobility induced by topological interactions between the rings and the substrate is the key mechanism for selective sieving of circular polymers with distinct flexibilities. A simple model accurately describes the sieving process observed in molecular dynamics simulations and yields experimentally verifiable analytical predictions, which can be used as a reference guide for improving filtration procedures of circular filaments. The topological sieving mechanism we propose ought to be relevant also in probing the microscopic details of complex substrates.

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 .

Molecular Knots

The first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small-molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including chirality, strong and selective ion binding, and catalytic activity. As the number and complexity of accessible molecular knot topologies increases, it will become increasingly useful for chemists to adopt the knot terminology employed by other disciplines. Here we give an overview of synthetic strategies towards molecular knots and outline the principles of knot, braid, and tangle theory appropriate to chemistry and molecular structure.

Contact Statistics Highlight Distinct Organizing Principles of Proteins and RNA

Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have territorial organization with signatures pointing to metastability, we analyzed the biomolecular structures deposited in the Protein Data Bank and found that the intrachain contact probabilities, P(s) as a function of the arc length s, decay in power-law ∼s(-γ) over the intermediate range of s, 10 ≲ s ≲ 110. We found that the contact probability scaling exponent is γ ≈ 1.11 for large RNA (N > 110), γ ≈ 1.41 for small-sized RNA (N < 110), and γ ≈ 1.65 for proteins. Given that Gaussian statistics is expected for a fully equilibrated chain in polymer melts, the deviation of γ-value from γ = 1.5 for the subchains of large RNA in the native state suggests that the chain configuration of RNA is not fully equilibrated. It is visually clear that folded structures of large-sized RNA (N ≳ 110) adopt crumpled structures, partitioned into modular multidomains assembled by proximal sequences along the chain, whereas the polypeptide chain of folded proteins looks better mixed with the rest of the structure. Our finding of γ ≈ 1 for large RNA might be an ineluctable consequence of the hierarchical ordering of the secondary to tertiary elements in the folding process.

Synthesizing topological structures containing RNA

Though knotting and entanglement have been observed in DNA and proteins, their existence in RNA remains an enigma. Synthetic RNA topological structures are significant for understanding the physical and biological properties pertaining to RNA topology, and these properties in turn could facilitate identifying naturally occurring topologically nontrivial RNA molecules. Here we show that topological structures containing single-stranded RNA (ssRNA) free of strong base pairing interactions can be created either by configuring RNA-DNA hybrid four-way junctions or by template-directed synthesis with a single-stranded DNA (ssDNA) topological structure. By using a constructed ssRNA knot as a highly sensitive topological probe, we find that Escherichia coli DNA topoisomerase I has low RNA topoisomerase activity and that the R173A point mutation abolishes the unknotting activity for ssRNA, but not for ssDNA. Furthermore, we discover the topological inhibition of reverse transcription (RT) and obtain different RT-PCR patterns for an ssRNA knot and circle of the same sequence.

A Knot Polynomial Invariant for Analysis of Topology of RNA Stems and Protein Disulfide Bonds

Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are not taken into account in conventional knot polynomials. In this study, we develop a new class of knot polynomials specifically designed to study RNA molecules, which considers stem regions. We demonstrate that our knot polynomials have direct structural relation with RNA molecules, and can be used to classify the topology of RNA secondary structures. Furthermore, we point out that these knot polynomials can be used to model the topological effects of disulfide bonds in protein molecules.

The elusive quest for RNA knots

Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs.

How to fold intricately: using theory and experiments to unravel the properties of knotted proteins

Over the years, advances in experimental and computational methods have helped us to understand the role of thermodynamic, kinetic and active (chaperone-aided) effects in coordinating the folding steps required to achieving a knotted native state. Here, we review such developments by paying particular attention to the complementarity of experimental and computational studies. Key open issues that could be tackled with either or both approaches are finally pointed out.

Multiple folding pathways of proteins with shallow knots and co-translational folding

We study the folding process in the shallowly knotted protein MJ0366 within two variants of a structure-based model. We observe that the resulting topological pathways are much richer than identified in previous studies. In addition to the single knot-loop events, we find novel, and dominant, two-loop mechanisms. We demonstrate that folding takes place in a range of temperatures and the conditions of most successful folding are at temperatures which are higher than those required for the fastest folding. We also demonstrate that nascent conditions are more favorable to knotting than off-ribosome folding.

Molecular knots in biology and chemistry

Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.

Knotted proteins: A tangled tale of Structural Biology

Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

Two Adhesive Sites Can Enhance the Knotting Probability of DNA

Self-entanglement, or knotting, is entropically favored in long polymers. Relatively short polymers such as proteins can knot as well, but in this case the entanglement is mainly driven by fine-tuned, sequence-specific interactions. The relation between the sequence of a long polymer and its topological state is here investigated by means of a coarse-grained model of DNA. We demonstrate that the introduction of two adhesive regions along the sequence of a self-avoiding chain substantially increases the probability of forming a knot.