Pseudoknots in RNA folding landscapes

ANNaMo: Coarse-grained modeling for folding and assembly of RNA and DNA systems

The folding of RNA and DNA strands plays crucial roles in biological systems and bionanotechnology. However, studying these processes with high-resolution numerical models is beyond current computational capabilities due to the timescales and system sizes involved. In this article, we present a new coarse-grained model for investigating the folding dynamics of nucleic acids. Our model represents three nucleotides with a patchy particle and is parameterized using well-established nearest-neighbor models. Thanks to the reduction of degrees of freedom and to a bond-swapping mechanism, our model allows for simulations at timescales and length scales that are currently inaccessible to more detailed models. To validate the performance of our model, we conducted extensive simulations of various systems: We examined the thermodynamics of DNA hairpins, capturing their stability and structural transitions, the folding of an MMTV pseudoknot, which is a complex RNA structure involved in viral replication, and also explored the folding of an RNA tile containing a k-type pseudoknot. Finally, we evaluated the performance of the new model in reproducing the melting temperatures of oligomers and the dependence on the toehold length of the displacement rate in toehold-mediated displacement processes, a key reaction used in molecular computing. All in all, the successful reproduction of experimental data and favorable comparisons with existing coarse-grained models validate the effectiveness of the new model.

Knotify_V2.0: Deciphering RNA Secondary Structures with H-Type Pseudoknots and Hairpin Loops

Accurately predicting the pairing order of bases in RNA molecules is essential for anticipating RNA secondary structures. Consequently, this task holds significant importance in unveiling previously unknown biological processes. The urgent need to comprehend RNA structures has been accentuated by the unprecedented impact of the widespread COVID-19 pandemic. This paper presents a framework, Knotify_V2.0, which makes use of syntactic pattern recognition techniques in order to predict RNA structures, with a specific emphasis on tackling the demanding task of predicting H-type pseudoknots that encompass bulges and hairpins. By leveraging the expressive capabilities of a Context-Free Grammar (CFG), the suggested framework integrates the inherent benefits of CFG and makes use of minimum free energy and maximum base pairing criteria. This integration enables the effective management of this inherently ambiguous task. The main contribution of Knotify_V2.0 compared to earlier versions lies in its capacity to identify additional motifs like bulges and hairpins within the internal loops of the pseudoknot. Notably, the proposed methodology, Knotify_V2.0, demonstrates superior accuracy in predicting core stems compared to state-of-the-art frameworks. Knotify_V2.0 exhibited exceptional performance by accurately identifying both core base pairing that form the ground truth pseudoknot in 70% of the examined sequences. Furthermore, Knotify_V2.0 narrowed the performance gap with Knotty, which had demonstrated better performance than Knotify and even surpassed it in Recall and F1-score metrics. Knotify_V2.0 achieved a higher count of true positives (tp) and a significantly lower count of false negatives (fn) compared to Knotify, highlighting improvements in Prediction and Recall metrics, respectively. Consequently, Knotify_V2.0 achieved a higher F1-score than any other platform. The source code and comprehensive implementation details of Knotify_V2.0 are publicly available on GitHub.

Accurate prediction of RNA secondary structure including pseudoknots through solving minimum-cost flow with learned potentials

Pseudoknots are key structure motifs of RNA and pseudoknotted RNAs play important roles in a variety of biological processes. Here, we present KnotFold, an accurate approach to the prediction of RNA secondary structure including pseudoknots. The key elements of KnotFold include a learned potential function and a minimum-cost flow algorithm to find the secondary structure with the lowest potential. KnotFold learns the potential from the RNAs with known structures using an attention-based neural network, thus avoiding the inaccuracy of hand-crafted energy functions. The specially designed minimum-cost flow algorithm used by KnotFold considers all possible combinations of base pairs and selects from them the optimal combination. The algorithm breaks the restriction of nested base pairs required by the widely used dynamic programming algorithms, thus enabling the identification of pseudoknots. Using 1,009 pseudoknotted RNAs as representatives, we demonstrate the successful application of KnotFold in predicting RNA secondary structures including pseudoknots with accuracy higher than the state-of-the-art approaches. We anticipate that KnotFold, with its superior accuracy, will greatly facilitate the understanding of RNA structures and functionalities.

Knotify+: Toward the Prediction of RNA H-Type Pseudoknots, Including Bulges and Internal Loops

The accurate "base pairing" in RNA molecules, which leads to the prediction of RNA secondary structures, is crucial in order to explain unknown biological operations. Recently, COVID-19, a widespread disease, has caused many deaths, affecting humanity in an unprecedented way. SARS-CoV-2, a single-stranded RNA virus, has shown the significance of analyzing these molecules and their structures. This paper aims to create a pioneering framework in the direction of predicting specific RNA structures, leveraging syntactic pattern recognition. The proposed framework, Knotify+, addresses the problem of predicting H-type pseudoknots, including bulges and internal loops, by featuring the power of context-free grammar (CFG). We combine the grammar's advantages with maximum base pairing and minimum free energy to tackle this ambiguous task in a performant way. Specifically, our proposed methodology, Knotify+, outperforms state-of-the-art frameworks with regards to its accuracy in core stems prediction. Additionally, it performs more accurately in small sequences and presents a comparable accuracy rate in larger ones, while it requires a smaller execution time compared to well-known platforms. The Knotify+ source code and implementation details are available as a public repository on GitHub.

Nucleic Acid Structure Prediction Including Pseudoknots Through Direct Enumeration of States: A User's Guide to the LandscapeFold Algorithm

Here we detail the LandscapeFold secondary structure prediction algorithm and how it is used. The algorithm was previously described and tested in (Kimchi O et al., Biophys J 117(3):520-532, 2019), though it was not named there. The algorithm directly enumerates all possible secondary structures into which up to two RNA or single-stranded DNA sequences can fold. It uses a polymer physics model to estimate the configurational entropy of structures including complex pseudoknots. We detail each of these steps and ways in which the user can adjust the algorithm as desired. The code is available on the GitHub repository https://github.com/ofer-kimchi/LandscapeFold .

Knotify: An Efficient Parallel Platform for RNA Pseudoknot Prediction Using Syntactic Pattern Recognition

Obtaining valuable clues for noncoding RNA (ribonucleic acid) subsequences remains a significant challenge, acknowledging that most of the human genome transcribes into noncoding RNA parts related to unknown biological operations. Capturing these clues relies on accurate “base pairing” prediction, also known as “RNA secondary structure prediction”. As COVID-19 is considered a severe global threat, the single-stranded SARS-CoV-2 virus reveals the importance of establishing an efficient RNA analysis toolkit. This work aimed to contribute to that by introducing a novel system committed to predicting RNA secondary structure patterns (i.e., RNA’s pseudoknots) that leverage syntactic pattern-recognition strategies. Having focused on the pseudoknot predictions, we formalized the secondary structure prediction of the RNA to be primarily a parsing and, secondly, an optimization problem. The proposed methodology addresses the problem of predicting pseudoknots of the first order (H-type). We introduce a context-free grammar (CFG) that affords enough expression power to recognize potential pseudoknot pattern. In addition, an alternative methodology of detecting possible pseudoknots is also implemented as well, using a brute-force algorithm. Any input sequence may highlight multiple potential folding patterns requiring a strict methodology to determine the single biologically realistic one. We conscripted a novel heuristic over the widely accepted notion of free-energy minimization to tackle such ambiguity in a performant way by utilizing each pattern’s context to unveil the most prominent pseudoknot pattern. The overall process features polynomial-time complexity, while its parallel implementation enhances the end performance, as proportional to the deployed hardware. The proposed methodology does succeed in predicting the core stems of any RNA pseudoknot of the test dataset by performing a 76.4% recall ratio. The methodology achieved a F1-score equal to 0.774 and MCC equal 0.543 in discovering all the stems of an RNA sequence, outperforming the particular task. Measurements were taken using a dataset of 262 RNA sequences establishing a performance speed of 1.31, 3.45, and 7.76 compared to three well-known platforms. The implementation source code is publicly available under knotify github repo.

LaRA 2: parallel and vectorized program for sequence-structure alignment of RNA sequences

BACKGROUND

The function of non-coding RNA sequences is largely determined by their spatial conformation, namely the secondary structure of the molecule, formed by Watson-Crick interactions between nucleotides. Hence, modern RNA alignment algorithms routinely take structural information into account. In order to discover yet unknown RNA families and infer their possible functions, the structural alignment of RNAs is an essential task. This task demands a lot of computational resources, especially for aligning many long sequences, and it therefore requires efficient algorithms that utilize modern hardware when available. A subset of the secondary structures contains overlapping interactions (called pseudoknots), which add additional complexity to the problem and are often ignored in available software.

RESULTS

We present the SeqAn-based software LaRA 2 that is significantly faster than comparable software for accurate pairwise and multiple alignments of structured RNA sequences. In contrast to other programs our approach can handle arbitrary pseudoknots. As an improved re-implementation of the LaRA tool for structural alignments, LaRA 2 uses multi-threading and vectorization for parallel execution and a new heuristic for computing a lower boundary of the solution. Our algorithmic improvements yield a program that is up to 130 times faster than the previous version.

CONCLUSIONS

With LaRA 2 we provide a tool to analyse large sets of RNA secondary structures in relatively short time, based on structural alignment. The produced alignments can be used to derive structural motifs for the search in genomic databases.

RNA-Puzzles toolkit: a computational resource of RNA 3D structure benchmark datasets, structure manipulation, and evaluation tools

Significant improvements have been made in the efficiency and accuracy of RNA 3D structure prediction methods during the succeeding challenges of RNA-Puzzles, a community-wide effort on the assessment of blind prediction of RNA tertiary structures. The RNA-Puzzles contest has shown, among others, that the development and validation of computational methods for RNA fold prediction strongly depend on the benchmark datasets and the structure comparison algorithms. Yet, there has been no systematic benchmark set or decoy structures available for the 3D structure prediction of RNA, hindering the standardization of comparative tests in the modeling of RNA structure. Furthermore, there has not been a unified set of tools that allows deep and complete RNA structure analysis, and at the same time, that is easy to use. Here, we present RNA-Puzzles toolkit, a computational resource including (i) decoy sets generated by different RNA 3D structure prediction methods (raw, for-evaluation and standardized datasets), (ii) 3D structure normalization, analysis, manipulation, visualization tools (RNA_format, RNA_normalizer, rna-tools) and (iii) 3D structure comparison metric tools (RNAQUA, MCQ4Structures). This resource provides a full list of computational tools as well as a standard RNA 3D structure prediction assessment protocol for the community.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Viroid research and its significance for RNA technology and basic biochemistry

Viroids were described 47 years ago as the smallest RNA molecules capable of infecting plants and autonomously self-replicating without an encoded protein. Work on viroids initiated the development of a number of innovative methods. Novel chromatographic and gelelectrophoretic methods were developed for the purification and characterization of viroids; these methods were later used in molecular biology, gene technology and in prion research. Theoretical and experimental studies of RNA folding demonstrated the general biological importance of metastable structures, and nuclear magnetic resonance spectroscopy of viroid RNA showed the partially covalent nature of hydrogen bonds in biological macromolecules. RNA biochemistry and molecular biology profited from viroid research, such as in the detection of RNA as template of DNA-dependent polymerases and in mechanisms of gene silencing. Viroids, the first circular RNA detected in nature, are important for studies on the much wider spectrum of circular RNAs and other non-coding RNAs.

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.

New algorithms to represent complex pseudoknotted RNA structures in dot-bracket notation

Motivation

Understanding the formation, architecture and roles of pseudoknots in RNA structures are one of the most difficult challenges in RNA computational biology and structural bioinformatics. Methods predicting pseudoknots typically perform this with poor accuracy, often despite experimental data incorporation. Existing bioinformatic approaches differ in terms of pseudoknots' recognition and revealing their nature. A few ways of pseudoknot classification exist, most common ones refer to a genus or order. Following the latter one, we propose new algorithms that identify pseudoknots in RNA structure provided in BPSEQ format, determine their order and encode in dot-bracket-letter notation. The proposed encoding aims to illustrate the hierarchy of RNA folding.

Results

New algorithms are based on dynamic programming and hybrid (combining exhaustive search and random walk) approaches. They evolved from elementary algorithm implemented within the workflow of RNA FRABASE 1.0, our database of RNA structure fragments. They use different scoring functions to rank dissimilar dot-bracket representations of RNA structure. Computational experiments show an advantage of new methods over the others, especially for large RNA structures.

Availability and implementation

Presented algorithms have been implemented as new functionality of RNApdbee webserver and are ready to use at http://rnapdbee.cs.put.poznan.pl.

Contact

mszachniuk@cs.put.poznan.pl.

Supplementary information

Supplementary data are available at Bioinformatics online.

RNA structure prediction: from 2D to 3D

We summarize different levels of RNA structure prediction, from classical 2D structure to extended secondary structure and motif-based research toward 3D structure prediction of RNA. We outline the importance of classical secondary structure during all those levels of structure prediction.