Evaluating and learning from RNA pseudotorsional space: quantitative validation of a reduced representation for RNA structure

gRNAde: A Geometric Deep Learning Pipeline for 3D RNA Inverse Design

Fundamental to the diverse biological functions of RNA are its 3D structure and conformational flexibility, which enable single sequences to adopt a variety of distinct 3D states. Currently, computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. In this tutorial, we present gRNAde, a geometric RNA design pipeline operating on sets of 3D RNA backbone structures to design sequences that explicitly account for RNA 3D structure and dynamics. gRNAde is a graph neural network that uses an SE (3) equivariant encoder-decoder framework for generating RNA sequences conditioned on backbone structures where the identities of the bases are unknown. We demonstrate the utility of gRNAde for fixed-backbone re-design of existing RNA structures of interest from the PDB, including riboswitches, aptamers, and ribozymes. gRNAde is more accurate in terms of native sequence recovery while being significantly faster compared to existing physics-based tools for 3D RNA inverse design, such as Rosetta.

RNA-TorsionBERT: leveraging language models for RNA 3D torsion angles prediction

MOTIVATION

Predicting the 3D structure of RNA is an ongoing challenge that has yet to be completely addressed despite continuous advancements. RNA 3D structures rely on distances between residues and base interactions but also backbone torsional angles. Knowing the torsional angles for each residue could help reconstruct its global folding, which is what we tackle in this work. This paper presents a novel approach for directly predicting RNA torsional angles from raw sequence data. Our method draws inspiration from the successful application of language models in various domains and adapts them to RNA.

RESULTS

We have developed a language-based model, RNA-TorsionBERT, incorporating better sequential interactions for predicting RNA torsional and pseudo-torsional angles from the sequence only. Through extensive benchmarking, we demonstrate that our method improves the prediction of torsional angles compared to state-of-the-art methods. In addition, by using our predictive model, we have inferred a torsion angle-dependent scoring function, called TB-MCQ, that replaces the true reference angles by our model prediction. We show that it accurately evaluates the quality of near-native predicted structures, in terms of RNA backbone torsion angle values. Our work demonstrates promising results, suggesting the potential utility of language models in advancing RNA 3D structure prediction.

AVAILABILITY AND IMPLEMENTATION

Source code is freely available on the EvryRNA platform: https://evryrna.ibisc.univ-evry.fr/evryrna/RNA-TorsionBERT.

Ramachandran-like Conformational Space for DNA

DNA's ability to exist in a wide variety of structural forms, subforms, and secondary motifs is fundamental to numerous biological processes and has driven the development of biotechnological applications. Major determinants of DNA flexibility are the multiple torsional degrees of freedom around the phosphodiester backbone. This high complexity can be rationalized by using two pseudotorsional angles linking atoms P and C4', from which Ramachandran-like plots can be built. In this contribution, we explore the distribution of η (eta: C4'i-1-Pi-C4'i-Pi+1) and θ (theta: Pi-C4'i-Pi+1-C4'i+1) angles in known experimental structures retrieved from the Protein Data Bank (PDB), subdividing the conformational space into different datasets. After the removal of the canonical/helical conformations typical of the B-form, we find the existence of a conformational map with clearly permitted and forbidden regions. Some of these regions are populated with specific DNA forms, like Z- or A-DNA, or by specific secondary motifs, like G-quadruplexes and junctions. We evaluated the sequence dependency and energy relationship among the high-density regions identified in the η-θ space. Furthermore, we analyzed the effect produced by proteins and cations when bound to DNA, finding that specific proteins produce some nonhelical conformations, while other regions appear to be stabilized by divalent cations.

gRNAde: Geometric Deep Learning for 3D RNA inverse design

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D geometry and conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. gRNAde uses a multi-state Graph Neural Network and autoregressive decoding to generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. (2010), gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Open source code: github.com/chaitjo/geometric-rna-design.

RNAtango: Analysing and comparing RNA 3D structures via torsional angles

RNA molecules, essential for viruses and living organisms, derive their pivotal functions from intricate 3D structures. To understand these structures, one can analyze torsion and pseudo-torsion angles, which describe rotations around bonds, whether real or virtual, thus capturing the RNA conformational flexibility. Such an analysis has been made possible by RNAtango, a web server introduced in this paper, that provides a trigonometric perspective on RNA 3D structures, giving insights into the variability of examined models and their alignment with reference targets. RNAtango offers comprehensive tools for calculating torsion and pseudo-torsion angles, generating angle statistics, comparing RNA structures based on backbone torsions, and assessing local and global structural similarities using trigonometric functions and angle measures. The system operates in three scenarios: single model analysis, model-versus-target comparison, and model-versus-model comparison, with results output in text and graphical formats. Compatible with all modern web browsers, RNAtango is accessible freely along with the source code. It supports researchers in accurately assessing structural similarities, which contributes to the precision and efficiency of RNA modeling.

The pseudotorsional space of RNA

The characterization of the conformational landscape of the RNA backbone is rather complex due to the ability of RNA to assume a large variety of conformations. These backbone conformations can be depicted by pseudotorsional angles linking RNA backbone atoms, from which Ramachandran-like plots can be built. We explore here different definitions of these pseudotorsional angles, finding that the most accurate ones are the traditional η (eta) and θ (theta) angles, which represent the relative position of RNA backbone atoms P and C4'. We explore the distribution of η - θ in known experimental structures, comparing the pseudotorsional space generated with structures determined exclusively by one experimental technique. We found that the complete picture only appears when combining data from different sources. The maps provide a quite comprehensive representation of the RNA accessible space, which can be used in RNA-structural predictions. Finally, our results highlight that protein interactions lead to significant changes in the population of the η - θ space, pointing toward the role of induced-fit mechanisms in protein-RNA recognition.

Long-Distance Movement of Solanum tuberosum Translationally Controlled Tumor Protein (StTCTP) mRNA

Long-distance signaling molecules in plants, including different RNA species, play a crucial role in the development and environmental responses. Among these mobile signals, the Translationally Controlled Tumor Protein (TCTP) mRNA is one of the most abundant. TCTP regulates cell-cycle progression and programmed cell death and is involved in responses to abiotic and biotic stress as well as plant regeneration, among other functions. Considering that the ability to induce plant regeneration is linked to a possible role of TCTP in vegetative propagation and asexual reproduction, we analyzed TCTP overexpression in a solanaceous plant model that can reproduce asexually by regeneration from stolons and tubers. Therefore, in this study, the effect of transient expression of Solanum tuberosum TCTP (StTCTP) on tuber development and vegetative propagation was described. StTCTP mRNA was shown to be transported long-distance. Additionally, transient overexpression of StTCTP resulted in sprouts with a greater diameter compared to control plants. Furthermore, the early stages of tuberization were induced compared to control plants, in which only mature tubers were observed. These results suggest a role of TCTP in vegetative propagation and asexual reproduction.

AMIGOS III: pseudo-torsion angle visualization and motif-based structure comparison of nucleic acids

MOTIVATION

The full description of nucleic acid conformation involves eight torsion angles per nucleotide. To simplify this description, we previously developed a representation of the nucleic acid backbone that assigns each nucleotide a pair of pseudo-torsion angles (eta and theta defined by P and C4' atoms; or eta' and theta' defined by P and C1' atoms). A Java program, AMIGOS II, is currently available for calculating eta and theta angles for RNA and for performing motif searches based on eta and theta angles. However, AMIGOS II lacks the ability to parse DNA structures and to calculate eta' and theta' angles. It also has little visualization capacity for 3D structure, making it difficult for users to interpret the computational results.

RESULTS

We present AMIGOS III, a PyMOL plugin that calculates the pseudo-torsion angles eta, theta, eta' and theta' for both DNA and RNA structures and performs motif searching based on these angles. Compared to AMIGOS II, AMIGOS III offers improved pseudo-torsion angle visualization for RNA and faster nucleic acid worm database generation; it also introduces pseudo-torsion angle visualization for DNA and nucleic acid worm visualization. Its integration into PyMOL enables easy preparation of tertiary structure inputs and intuitive visualization of involved structures.

AVAILABILITY AND IMPLEMENTATION

https://github.com/pylelab/AMIGOSIII.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Developing Community Resources for Nucleic Acid Structures

In this review, we describe the creation of the Nucleic Acid Database (NDB) at Rutgers University and how it became a testbed for the current infrastructure of the RCSB Protein Data Bank. We describe some of the special features of the NDB and how it has been used to enable research. Plans for the next phase as the Nucleic Acid Knowledgebase (NAKB) are summarized.

RNANet: an automatically built dual-source dataset integrating homologous sequences and RNA structures

MOTIVATION

Applied research in machine learning progresses faster when a clean dataset is available and ready to use. Several datasets have been proposed and released over the years for specific tasks such as image classification, speech-recognition and more recently for protein structure prediction. However, for the fundamental problem of RNA structure prediction, information is spread between several databases depending on the level we are interested in: sequence, secondary structure, 3D structure or interactions with other macromolecules. In order to speed-up advances in machine-learning based approaches for RNA secondary and/or 3D structure prediction, a dataset integrating all this information is required, to avoid spending time on data gathering and cleaning.

RESULTS

Here, we propose the first attempt of a standardized and automatically generated dataset dedicated to RNA combining together: RNA sequences, homology information (under the form of position-specific scoring matrices) and information derived by annotation of available 3D structures (including secondary structure, canonical and non-canonical interactions and backbone torsion angles). The data are retrieved from public databases PDB, Rfam and SILVA. The paper describes the procedure to build such dataset and the RNA structure descriptors we provide. Some statistical descriptions of the resulting dataset are also provided.

AVAILABILITY AND IMPLEMENTATION

The dataset is updated every month and available online (in flat-text file format) on the EvryRNA software platform (https://evryrna.ibisc.univ-evry.fr/evryrna/rnanet). An efficient parallel pipeline to build the dataset is also provided for easy reproduction or modification.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection

In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.

RNA Backbone Torsion and Pseudotorsion Angle Prediction Using Dilated Convolutional Neural Networks

RNA three-dimensional structure prediction has been relied on using a predicted or experimentally determined secondary structure as a restraint to reduce the conformational sampling space. However, the secondary-structure restraints are limited to paired bases, and the conformational space of the ribose-phosphate backbone is still too large to be sampled efficiently. Here, we employed the dilated convolutional neural network to predict backbone torsion and pseudotorsion angles using a single RNA sequence as input. The method called SPOT-RNA-1D was trained on a high-resolution training data set and tested on three independent, nonredundant, and high-resolution test sets. The proposed method yields substantially smaller mean absolute errors than the baseline predictors based on random predictions and based on helix conformations according to actual angle distributions. The mean absolute errors for three test sets range from 14°-44° for different angles, compared to 17°-62° by random prediction and 14°-58° by helix prediction. The method also accurately recovers the overall patterns of single or pairwise angle distributions. In general, torsion angles further away from the bases and associated with unpaired bases and paired bases involved in tertiary interactions are more difficult to predict. Compared to the best models in RNA-puzzles experiments, SPOT-RNA-1D yielded more accurate dihedral angles and, thus, are potentially useful as model quality indicators and restraints for RNA structure prediction as in protein structure prediction.

VeriNA3d: an R package for nucleic acids data mining

SUMMARY

veriNA3d is an R package for the analysis of nucleic acids structural data, with an emphasis in complex RNA structures. In addition to single-structure analyses, veriNA3d also implements functions to handle whole datasets of mmCIF/PDB structures that could be retrieved from public/local repositories. Our package aims to fill a gap in the data mining of nucleic acids structures to produce flexible and high throughput analysis of structural databases.

AVAILABILITY AND IMPLEMENTATION

http://mmb.irbbarcelona.org/gitlab/dgallego/veriNA3d.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Coarse-Grained Models of RNA Nanotubes for Large Time Scale Studies in Biomedical Applications

In order to describe the physical properties of large time scale biological systems, coarse-grained models play an increasingly important role. In this paper we develop Coarse-Grained (CG) models for RNA nanotubes and then, by using Molecular Dynamics (MD) simulation, we study their physical properties. Our exemplifications include RNA nanotubes of 40 nm long, equivalent to 10 RNA nanorings connected in series. The developed methodology is based on a coarse-grained representation of RNA nanotubes, where each coarse bead represents a group of atoms. By decreasing computation cost, this allows us to make computations feasible for realistic structures of interest. In particular, for the developed coarse-grained models with three bead approximations, we calculate the histograms for the bond angles and the dihedral angles. From the dihedral angle histograms, we analyze the characteristics of the links used to build the nanotubes. Furthermore, we also calculate the bead distances along the chains of RNA strands in the nanoclusters. The variations in these features with the size of the nanotube are discussed in detail. Finally, we present the results on the calculation of the root mean square deviations for a developed RNA nanotube to demonstrate the equilibration of the systems for drug delivery and other biomedical applications such as medical imaging and tissue engineering.

Conserved Pseudoknots in lncRNA MEG3 Are Essential for Stimulation of the p53 Pathway

Long non-coding RNAs (lncRNAs) are key regulatory molecules, but unlike with other RNAs, the direct link between their tertiary structure motifs and their function has proven elusive. Here we report structural and functional studies of human maternally expressed gene 3 (MEG3), a tumor suppressor lncRNA that modulates the p53 response. We found that, in an evolutionary conserved region of MEG3, two distal motifs interact by base complementarity to form alternative, mutually exclusive pseudoknot structures ("kissing loops"). Mutations that disrupt these interactions impair MEG3-dependent p53 stimulation in vivo and disrupt MEG3 folding in vitro. These findings provide mechanistic insights into regulation of the p53 pathway by MEG3 and reveal how conserved motifs of tertiary structure can regulate lncRNA biological function.

A nucleobase-centered coarse-grained representation for structure prediction of RNA motifs

We introduce the SPlit-and-conQueR (SPQR) model, a coarse-grained (CG) representation of RNA designed for structure prediction and refinement. In our approach, the representation of a nucleotide consists of a point particle for the phosphate group and an anisotropic particle for the nucleoside. The interactions are, in principle, knowledge-based potentials inspired by the $\mathcal {E}$SCORE function, a base-centered scoring function. However, a special treatment is given to base-pairing interactions and certain geometrical conformations which are lost in a raw knowledge-based model. This results in a representation able to describe planar canonical and non-canonical base pairs and base-phosphate interactions and to distinguish sugar puckers and glycosidic torsion conformations. The model is applied to the folding of several structures, including duplexes with internal loops of non-canonical base pairs, tetraloops, junctions and a pseudoknot. For the majority of these systems, experimental structures are correctly predicted at the level of individual contacts. We also propose a method for efficiently reintroducing atomistic detail from the CG representation.

R3D-BLAST2: an improved search tool for similar RNA 3D substructures

Background

RNA molecules have been known to play a variety of significant roles in cells. In principle, the functions of RNAs are largely determined by their three-dimensional (3D) structures. As more and more RNA 3D structures are available in the Protein Data Bank (PDB), a bioinformatics tool, which is able to rapidly and accurately search the PDB database for similar RNA 3D structures or substructures, is helpful to understand the structural and functional relationships of RNAs.

Results

Since its first release in 2011, R3D-BLAST has become a useful tool for searching the PDB database for similar RNA 3D structures and substructures. It was implemented by a structural-alphabet (SA)-based method, which utilizes an SA with 23 structural letters to encode RNA 3D structures into one-dimensional (1D) structural sequences and applies BLAST to the resulting structural sequences for searching similar substructures of RNAs. In this study, we have upgraded R3D-BLAST to develop a new web server named R3D-BLAST2 based on a higher quality SA newly constructed from a representative and sufficiently non-redundant list of RNA 3D structures. In addition, we have modified the kernel program in R3D-BLAST2 so that it can accept an RNA structure in the mmCIF format as an input. The results of our experiments on a benchmark dataset have demonstrated that R3D-BLAST2 indeed performs very well in comparison to its earlier version R3D-BLAST and other similar tools RNA FRABASE, FASTR3D and RAG-3D by searching a larger number of RNA 3D substructures resembling those of the input RNA.

Conclusions

R3D-BLAST2 is a valuable BLAST-like search tool that can more accurately scan the PDB database for similar RNA 3D substructures. It is publicly available at http://genome.cs.nthu.edu.tw/R3D-BLAST2/.

Optimization of RNA 3D structure prediction using evolutionary restraints of nucleotide-nucleotide interactions from direct coupling analysis

Direct coupling analysis of nucleotide coevolution provides a novel approach to identify which nucleotides in an RNA molecule are likely in direct contact, and this information obtained from sequence only can be used to predict RNA 3D structures with much improved accuracy. Here we present an efficient method that incorporates this information into current RNA 3D structure prediction methods, specifically 3dRNA. Our method makes much more accurate RNA 3D structure prediction than the original 3dRNA as well as other existing prediction methods that used the direct coupling analysis. In particular our method demonstrates a significant improvement in predicting multi-branch junction conformations, a major bottleneck for RNA 3D structure prediction. We also show that our method can be used to optimize the predictions by other methods. These results indicate that optimization of RNA 3D structure prediction using evolutionary restraints of nucleotide-nucleotide interactions from direct coupling analysis offers an efficient way for accurate RNA tertiary structure predictions.

Identification of a GUAAY Pentaloop Sequence Involved in a Novel RNA Loop-Helix Interaction

Large RNAs often utilize GNRA tetraloops as structural elements to stabilize the overall tertiary fold. These tetraloop-receptor (TR) interactions have a conserved geometry in which the tetraloop docks into the receptor at an angle of ~15° from the helix containing the receptor. Here, we show that the conserved GUAAY pentaloop found in domain III of group IIB1 introns participates in a novel class of RNA tertiary interaction with a geometry and mode of binding that are significantly different from that found in GNRA TR interactions. This pentaloop is highly conserved within the IIB1 class and interacts with the minor groove of the catalytic domain V. The base planes of the loop and receptor nucleotides are not coplanar and greatly deviate from standard A-minor motifs. The helical axis of the GUAAY stem loop diverges ~70° from the angle of insertion found in a typical GNRA TR interaction. Therefore, the loop architecture and insertion orientation are distinctive, with in vitro splicing data indicating that a GNRA tetraloop is incompatible at this position. The GUAAY pentaloop-receptor motif is also found in the structure of the eukaryotic thiamine pyrophosphate riboswitch in the context of a hexanucleotide loop sequence. We therefore propose, based on phylogenetic, structural, and biochemical data, that the GUAAY pentaloop-receptor interaction represents a novel structural motif that is present in multiple structured RNAs.

iPARTS2: an improved tool for pairwise alignment of RNA tertiary structures, version 2

Since its first release in 2010, iPARTS has become a valuable tool for globally or locally aligning two RNA 3D structures. It was implemented by a structural alphabet (SA)-based approach, which uses an SA of 23 letters to reduce RNA 3D structures into 1D sequences of SA letters and applies traditional sequence alignment to these SA-encoded sequences for determining their global or local similarity. In this version, we have re-implemented iPARTS into a new web server iPARTS2 by constructing a totally new SA, which consists of 92 elements with each carrying both information of base and backbone geometry for a representative nucleotide. This SA is significantly different from the one used in iPARTS, because the latter consists of only 23 elements with each carrying only the backbone geometry information of a representative nucleotide. Our experimental results have shown that iPARTS2 outperforms its previous version iPARTS and also achieves better accuracy than other popular tools, such as SARA, SETTER and RASS, in RNA alignment quality and function prediction. iPARTS2 takes as input two RNA 3D structures in the PDB format and outputs their global or local alignments with graphical display. iPARTS2 is now available online at http://genome.cs.nthu.edu.tw/iPARTS2/.

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

SimRNA: a coarse-grained method for RNA folding simulations and 3D structure prediction

RNA molecules play fundamental roles in cellular processes. Their function and interactions with other biomolecules are dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is laborious and challenging, and therefore, the majority of known RNAs remain structurally uncharacterized. Here, we present SimRNA: a new method for computational RNA 3D structure prediction, which uses a coarse-grained representation, relies on the Monte Carlo method for sampling the conformational space, and employs a statistical potential to approximate the energy and identify conformations that correspond to biologically relevant structures. SimRNA can fold RNA molecules using only sequence information, and, on established test sequences, it recapitulates secondary structure with high accuracy, including correct prediction of pseudoknots. For modeling of complex 3D structures, it can use additional restraints, derived from experimental or computational analyses, including information about secondary structure and/or long-range contacts. SimRNA also can be used to analyze conformational landscapes and identify potential alternative structures.

RNA approaches the B-form in stacked single strand dinucleotide contexts

Duplex RNA adopts an A-form structure, while duplex DNA interconverts between the A- and B-forms depending on the environment. The C2'-endo sugar pucker seen in B-form DNA can occur infrequently in ribose sugars as well, but RNA is not understood to assume B-form conformations. Through analysis of over 45,000 stacked single strand dinucleotide (SSD) crystal structure conformations, this study demonstrates that RNA is capable of adopting a wide conformational range between the canonical A- and B-forms at the localized SSD level, including many B-form-like conformations. It does so through C2'-endo ribose conformations in one or both nucleotides, and B-form-like neighboring base stacking patterns. As chemical reactions on nucleic acids involve localized changes in chemical bonds, the understanding of how enzymes distinguish between DNA and RNA nucleotides is altered by the energetic accessibility of these rare B-form-like RNA SSD conformations. The existence of these conformations also has direct implications in parametrization of molecular mechanics energy functions used extensively to model nucleic acid behavior., 2016. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 65-82, 2016.

Co-evolution of quaternary organization and novel RNA tertiary interactions revealed in the crystal structure of a bacterial protein-RNA toxin-antitoxin system

Genes encoding toxin-antitoxin (TA) systems are near ubiquitous in bacterial genomes and they play key roles in important aspects of bacterial physiology, including genomic stability, formation of persister cells under antibiotic stress, and resistance to phage infection. The CptIN locus from Eubacterium rectale is a member of the recently-discovered Type III class of TA systems, defined by a protein toxin suppressed by direct interaction with a structured RNA antitoxin. Here, we present the crystal structure of the CptIN protein-RNA complex to 2.2 Å resolution. The structure reveals a new heterotetrameric quaternary organization for the Type III TA class, and the RNA antitoxin bears a novel structural feature of an extended A-twist motif within the pseudoknot fold. The retention of a conserved ribonuclease active site as well as traits normally associated with TA systems, such as plasmid maintenance, implicates a wider functional role for Type III TA systems. We present evidence for the co-variation of the Type III component pair, highlighting a distinctive evolutionary process in which an enzyme and its substrate co-evolve.

Lightweight object oriented structure analysis: tools for building tools to analyze molecular dynamics simulations

LOOS (Lightweight Object Oriented Structure-analysis) is a C++ library designed to facilitate making novel tools for analyzing molecular dynamics simulations by abstracting out the repetitive tasks, allowing developers to focus on the scientifically relevant part of the problem. LOOS supports input using the native file formats of most common biomolecular simulation packages, including CHARMM, NAMD, Amber, Tinker, and Gromacs. A dynamic atom selection language based on the C expression syntax is included and is easily accessible to the tool-writer. In addition, LOOS is bundled with over 140 prebuilt tools, including suites of tools for analyzing simulation convergence, three-dimensional histograms, and elastic network models. Through modern C++ design, LOOS is both simple to develop with (requiring knowledge of only four core classes and a few utility functions) and is easily extensible. A python interface to the core classes is also provided, further facilitating tool development.

Modeling of structural, energetic, and dynamic properties of few-atom silver clusters embedded in polynucleotide strands by using molecular dynamics

This work concerns the study of the structural, energetic, and dynamic properties of fluorescent systems composed of silver clusters stabilized by polynucleotide strands. To do so, classical interaction potentials relative to silver, neutral and cationic, were introduced in the AMBER force field. Molecular dynamics simulations allowed analysis of the nature and force of the interactions between the various parts of the nucleic oligomers and the silver clusters. Conformational analyses were necessary to explore the flexibility of the supramolecular assemblies, specifically by radial distribution functions and Ramachandran-type maps.

Automated modeling of RNA 3D structure

This chapter gives an overview over the current methods for automated modeling of RNA structures, with emphasis on template-based methods. The currently used approaches to RNA modeling are presented with a side view on the protein world, where many similar ideas have been used. Two main programs for automated template-based modeling are presented: ModeRNA assembling structures from fragments and MacroMoleculeBuilder performing a simulation to satisfy spatial restraints. Both approaches have in common that they require an alignment of the target sequence to a known RNA structure that is used as a modeling template. As a way to find promising template structures and to align the target and template sequences, we propose a pipeline combining the ParAlign and Infernal programs on RNA family data from Rfam. We also briefly summarize template-free methods for RNA 3D structure prediction. Typically, RNA structures generated by automated modeling methods require local or global optimization. Thus, we also discuss methods that can be used for local or global refinement of RNA structures.

Visualizing the ai5γ group IIB intron

It has become apparent that much of cellular metabolism is controlled by large well-folded noncoding RNA molecules. In addition to crystallographic approaches, computational methods are needed for visualizing the 3D structure of large RNAs. Here, we modeled the molecular structure of the ai5γ group IIB intron from yeast using the crystal structure of a bacterial group IIC homolog. This was accomplished by adapting strategies for homology and de novo modeling, and creating a new computational tool for RNA refinement. The resulting model was validated experimentally using a combination of structure-guided mutagenesis and RNA structure probing. The model provides major insights into the mechanism and regulation of splicing, such as the position of the branch-site before and after the second step of splicing, and the location of subdomains that control target specificity, underscoring the feasibility of modeling large functional RNA molecules.

Solving nucleic acid structures by molecular replacement: examples from group II intron studies

Structured RNA molecules are key players in ensuring cellular viability. It is now emerging that, like proteins, the functions of many nucleic acids are dictated by their tertiary folds. At the same time, the number of known crystal structures of nucleic acids is also increasing rapidly. In this context, molecular replacement will become an increasingly useful technique for phasing nucleic acid crystallographic data in the near future. Here, strategies to select, create and refine molecular-replacement search models for nucleic acids are discussed. Using examples taken primarily from research on group II introns, it is shown that nucleic acids are amenable to different and potentially more flexible and sophisticated molecular-replacement searches than proteins. These observations specifically aim to encourage future crystallographic studies on the newly discovered repertoire of noncoding transcripts.

RNA structural motif recognition based on least-squares distance

RNA structural motifs are recurrent structural elements occurring in RNA molecules. RNA structural motif recognition aims to find RNA substructures that are similar to a query motif, and it is important for RNA structure analysis and RNA function prediction. In view of this, we propose a new method known as RNA Structural Motif Recognition based on Least-Squares distance (LS-RSMR) to effectively recognize RNA structural motifs. A test set consisting of five types of RNA structural motifs occurring in Escherichia coli ribosomal RNA is compiled by us. Experiments are conducted for recognizing these five types of motifs. The experimental results fully reveal the superiority of the proposed LS-RSMR compared with four other state-of-the-art methods.

Urea-induced denaturation of preQ1-riboswitch

Urea, a polar molecule with a large dipole moment, not only destabilizes folded RNA structures but can also enhance the folding rates of large ribozymes. Unlike the mechanism of urea-induced unfolding of proteins, which is well understood, the action of urea on RNA has barely been explored. We performed extensive all-atom molecular dynamics simulations to determine the molecular underpinnings of urea-induced RNA denaturation. Urea displays its denaturing power in both secondary and tertiary motifs of the riboswitch structure. Our simulations reveal that the denaturation of RNA structures is mainly driven by the hydrogen-bonding and stacking interactions of urea with the bases. Through detailed studies of the simulation trajectories, we found that geminate pairs between urea and bases due to hydrogen bonds and stacks persist only ~0.1-1 ns, which suggests that the urea-base interaction is highly dynamic. Most importantly, the early stage of base-pair disruption is triggered by penetration of water molecules into the hydrophobic domain between the RNA bases. The infiltration of water into the narrow space between base pairs is critical in increasing the accessibility of urea to transiently disrupted bases, thus allowing urea to displace inter-base hydrogen bonds. This mechanism--water-induced disruption of base pairs resulting in the formation of a "wet" destabilized RNA followed by solvation by urea--is the exact opposite of the two-stage denaturation of proteins by urea. In the latter case, initial urea penetration creates a dry globule, which is subsequently solvated by water, leading to global protein unfolding. Our work shows that the ability to interact with both water and polar or nonpolar components of nucleotides makes urea a powerful chemical denaturant for nucleic acids.

RNA structure and dynamics: a base pairing perspective

RNA is now known to possess various structural, regulatory and enzymatic functions for survival of cellular organisms. Functional RNA structures are generally created by three-dimensional organization of small structural motifs, formed by base pairing between self-complementary sequences from different parts of the RNA chain. In addition to the canonical Watson-Crick or wobble base pairs, several non-canonical base pairs are found to be crucial to the structural organization of RNA molecules. They appear within different structural motifs and are found to stabilize the molecule through long-range intra-molecular interactions between basic structural motifs like double helices and loops. These base pairs also impart functional variation to the minor groove of A-form RNA helices, thus forming anchoring site for metabolites and ligands. Non-canonical base pairs are formed by edge-to-edge hydrogen bonding interactions between the bases. A large number of theoretical studies have been done to detect and analyze these non-canonical base pairs within crystal or NMR derived structures of different functional RNA. Theoretical studies of these isolated base pairs using ab initio quantum chemical methods as well as molecular dynamics simulations of larger fragments have also established that many of these non-canonical base pairs are as stable as the canonical Watson-Crick base pairs. This review focuses on the various structural aspects of non-canonical base pairs in the organization of RNA molecules and the possible applications of these base pairs in predicting RNA structures with more accuracy.

Fast alignment and comparison of RNA structures

MOTIVATION

To recognize remote relationships between RNA molecules, one must be able to align structures without regard to sequence similarity. We have implemented a method, which is swift [O(n(2))], sensitive and tolerant of large gaps and insertions. Molecules are broken into overlapping fragments, which are characterized by their memberships in a probabilistic classification based on local geometry and H-bonding descriptors. This leads to a probabilistic similarity measure that is used in a conventional dynamic programming method.

RESULTS

Examples are given of database searching, the detection of structural similarities, which would not be found using sequence based methods, and comparisons with a previously published approach.

AVAILABILITY AND IMPLEMENTATION

Source code (C and perl) and binaries for linux are freely available at www.zbh.uni-hamburg.de/fries.

Coarse-grained prediction of RNA loop structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.

RCrane: semi-automated RNA model building

RCrane is a new tool for the partially automated building of RNA crystallographic models into electron-density maps of low or intermediate resolution. This tool helps crystallographers to place phosphates and bases into electron density and then automatically predicts and builds the detailed all-atom structure of the traced nucleotides.

RNA crystals typically diffract to much lower resolutions than protein crystals. This low-resolution diffraction results in unclear density maps, which cause considerable difficulties during the model-building process. These difficulties are exacerbated by the lack of computational tools for RNA modeling. Here, RCrane, a tool for the partially automated building of RNA into electron-density maps of low or intermediate resolution, is presented. This tool works within Coot, a common program for macromolecular model building. RCrane helps crystallographers to place phosphates and bases into electron density and then automatically predicts and builds the detailed all-atom structure of the traced nucleotides. RCrane then allows the crystallographer to review the newly built structure and select alternative backbone conformations where desired. This tool can also be used to automatically correct the backbone structure of previously built nucleotides. These automated corrections can fix incorrect sugar puckers, steric clashes and other structural problems.

Mapping L1 ligase ribozyme conformational switch

L1 ligase (L1L) molecular switch is an in vitro optimized synthetic allosteric ribozyme that catalyzes the regioselective formation of a 5'-to-3' phosphodiester bond, a reaction for which there is no known naturally occurring RNA catalyst. L1L serves as a proof of principle that RNA can catalyze a critical reaction for prebiotic RNA self-replication according to the RNA world hypothesis. L1L crystal structure captures two distinct conformations that differ by a reorientation of one of the stems by around 80Å and are presumed to correspond to the active and inactive state, respectively. It is of great interest to understand the nature of these two states in solution and the pathway for their interconversion. In this study, we use explicit solvent molecular simulation together with a novel enhanced sampling method that utilizes concepts from network theory to map out the conformational transition between active and inactive states of L1L. We find that the overall switching mechanism can be described as a three-state/two-step process. The first step involves a large-amplitude swing that reorients stem C. The second step involves the allosteric activation of the catalytic site through distant contacts with stem C. Using a conformational space network representation of the L1L switch transition, it is shown that the connection between the three states follows different topographical patterns: the stem C swing step passes through a narrow region of the conformational space network, whereas the allosteric activation step covers a much wider region and a more diverse set of pathways through the network.

Discrete RNA libraries from pseudo-torsional space

The discovery that RNA molecules can fold into complex structures and carry out diverse cellular roles has led to interest in developing tools for modeling RNA tertiary structure. While significant progress has been made in establishing that the RNA backbone is rotameric, few libraries of discrete conformations specifically for use in RNA modeling have been validated. Here, we present six libraries of discrete RNA conformations based on a simplified pseudo-torsional notation of the RNA backbone, comparable to phi and psi in the protein backbone. We evaluate the ability of each library to represent single nucleotide backbone conformations, and we show how individual library fragments can be assembled into dinucleotides that are consistent with established RNA backbone descriptors spanning from sugar to sugar. We then use each library to build all-atom models of 20 test folds, and we show how the composition of a fragment library can limit model quality. Despite the limitations inherent in using discretized libraries, we find that several hundred discrete fragments can rebuild RNA folds up to 174 nucleotides in length with atomic-level accuracy (<1.5 Å RMSD). We anticipate that the libraries presented here could easily be incorporated into RNA structural modeling, analysis, or refinement tools.

GeoPCA: a new tool for multivariate analysis of dihedral angles based on principal component geodesics

The GeoPCA package is the first tool developed for multivariate analysis of dihedral angles based on principal component geodesics. Principal component geodesic analysis provides a natural generalization of principal component analysis for data distributed in non-Euclidean space, as in the case of angular data. GeoPCA presents projection of angular data on a sphere composed of the first two principal component geodesics, allowing clustering based on dihedral angles as opposed to Cartesian coordinates. It also provides a measure of the similarity between input structures based on only dihedral angles, in analogy to the root-mean-square deviation of atoms based on Cartesian coordinates. The principal component geodesic approach is shown herein to reproduce clusters of nucleotides observed in an η–θ plot. GeoPCA can be accessed via http://pca.limlab.ibms.sinica.edu.tw.

MINAS--a database of Metal Ions in Nucleic AcidS

Correctly folded into the respective native 3D structure, RNA and DNA are responsible for uncountable key functions in any viable organism. In order to exert their function, metal ion cofactors are closely involved in folding, structure formation and, e.g. in ribozymes, also the catalytic mechanism. The database MINAS, Metal Ions in Nucleic AcidS (http://www.minas.uzh.ch), compiles the detailed information on innersphere, outersphere and larger coordination environment of >70 000 metal ions of 36 elements found in >2000 structures of nucleic acids contained today in the PDB and NDB. MINAS is updated monthly with new structures and offers a multitude of search functions, e.g. the kind of metal ion, metal-ligand distance, innersphere and outersphere ligands defined by element or functional group, residue, experimental method, as well as PDB entry-related information. The results of each search can be saved individually for later use with so-called miniPDB files containing the respective metal ion together with the coordination environment within a 15 Å radius. MINAS thus offers a unique way to explore the coordination geometries and ligands of metal ions together with the respective binding pockets in nucleic acids.

The influence of the local sequence environment on RNA loop structures

RNA folding is assumed to be a hierarchical process. The secondary structure of an RNA molecule, signified by base-pairing and stacking interactions between the paired bases, is formed first. Subsequently, the RNA molecule adopts an energetically favorable three-dimensional conformation in the structural space determined mainly by the rotational degrees of freedom associated with the backbone of regions of unpaired nucleotides (loops). To what extent the backbone conformation of RNA loops also results from interactions within the local sequence context or rather follows global optimization constraints alone has not been addressed yet. Because the majority of base stacking interactions are exerted locally, a critical influence of local sequence on local structure appears plausible. Thus, local loop structure ought to be predictable, at least in part, from the local sequence context alone. To test this hypothesis, we used Random Forests on a nonredundant data set of unpaired nucleotides extracted from 97 X-ray structures from the Protein Data Bank (PDB) to predict discrete backbone angle conformations given by the discretized η/θ-pseudo-torsional space. Predictions on balanced sets with four to six conformational classes using local sequence information yielded average accuracies of up to 55%, thus significantly better than expected by chance (17%-25%). Bases close to the central nucleotide appear to be most tightly linked to its conformation. Our results suggest that RNA loop structure does not only depend on long-range base-pairing interactions; instead, it appears that local sequence context exerts a significant influence on the formation of the local loop structure.

A new way to see RNA

Unlike proteins, the RNA backbone has numerous degrees of freedom (eight, if one counts the sugar pucker), making RNA modeling, structure building and prediction a multidimensional problem of exceptionally high complexity. And yet RNA tertiary structures are not infinite in their structural morphology; rather, they are built from a limited set of discrete units. In order to reduce the dimensionality of the RNA backbone in a physically reasonable way, a shorthand notation was created that reduced the RNA backbone torsion angles to two (η and θ, analogous to φ and ψ in proteins). When these torsion angles are calculated for nucleotides in a crystallographic database and plotted against one another, one obtains a plot analogous to a Ramachandran plot (the η/θ plot), with highly populated and unpopulated regions. Nucleotides that occupy proximal positions on the plot have identical structures and are found in the same units of tertiary structure. In this review, we describe the statistical validation of the η/θ formalism and the exploration of features within the η/θ plot. We also describe the application of the η/θ formalism in RNA motif discovery, structural comparison, RNA structure building and tertiary structure prediction. More than a tool, however, the η/θ formalism has provided new insights into RNA structure itself, revealing its fundamental components and the factors underlying RNA architectural form.

Structural basis of differential ligand recognition by two classes of bis-(3'-5')-cyclic dimeric guanosine monophosphate-binding riboswitches

The bis-(3'-5')-cyclic dimeric guanosine monophosphate (c-di-GMP) signaling pathway regulates biofilm formation, virulence, and other processes in many bacterial species and is critical for their survival. Two classes of c-di-GMP-binding riboswitches have been discovered that bind this second messenger with high affinity and regulate diverse downstream genes, underscoring the importance of RNA receptors in this pathway. We have solved the structure of a c-di-GMP-II riboswitch, which reveals that the ligand is bound as part of a triplex formed with a pseudoknot. The structure also shows that the guanine bases of c-di-GMP are recognized through noncanonical pairings and that the phosphodiester backbone is not contacted by the RNA. Recognition is quite different from that observed in the c-di-GMP-I riboswitch, demonstrating that at least two independent solutions for RNA second messenger binding have evolved. We exploited these differences to design a c-di-GMP analog that selectively binds the c-di-GMP-II aptamer over the c-di-GMP-I RNA. There are several bacterial species that contain both types of riboswitches, and this approach holds promise as an important tool for targeting one riboswitch, and thus one gene, over another in a selective fashion.

Understanding the effects of carbocyclic sugars constrained to north and south conformations on RNA nanodesign

Relatively new types of the modified nucleotides, namely carbocyclic sugars that are constrained to north or south (C2' or C3' exo) conformations, can be used for RNA nanoparticle design to control their structures and stability by rigidifying nucleotides and altering the helical properties of RNA duplexes. Two RNA structures, an RNA dodecamer and an HIV kissing loop complex where several nucleotides were replaced with north or south constrained sugars, were studied by molecular dynamics (MD) simulations. The substituted south constrained nucleotides in the dodecamer widened the major groove and narrowed and deepened the minor groove thus inducing local conformational changes that resemble a B-form DNA helix. In the HIV kissing loop complex, north and south constrained nucleotides were substituted into flanking bases and stems. The modified HIV kissing loop complex showed a lower RMSD value than the normal kissing loop complex. The overall twist angle was also changed and its standard deviation was reduced. In addition, the modified RNA dodecamer and HIV kissing loop complex were characterized by principal component analysis (PCA) and steered molecular dynamics (SMD). PCA results showed that the constrained sugars stabilized the overall motions. The results of the SMD simulations indicated that as the backbone δ angles were increased by elongation, more force was applied to the modified RNA due to the constrained sugar analogues.

Geometric properties of nucleic acids with potential for autobuilding

Algorithms and geometrical properties are described for the automated building of nucleic acids in experimental electron density.

Medium- to high-resolution X-ray structures of DNA and RNA molecules were investigated to find geometric properties useful for automated model building in crystallographic electron-density maps. We describe a simple method, starting from a list of electron-density ‘blobs’, for identifying backbone phosphates and nucleic acid bases based on properties of the local electron-density distribution. This knowledge should be useful for the automated building of nucleic acid models into electron-density maps. We show that the distances and angles involving C1′ and the P atoms, using the pseudo-torsion angles and that describe the …P—C1′—P—C1′… chain, provide a promising basis for building the nucleic acid polymer. These quantities show reasonably narrow distributions with asymmetry that should allow the direction of the phosphate backbone to be established.