Stepping through an RNA structure: A novel approach to conformational analysis

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.

Sarcin/Ricin Domain RNA Retains Its Structure Better Than A-RNA in Adaptively Biased Molecular Dynamics Simulations

Less than one in thirty of the RNA sequences transcribed in humans are translated into protein. The noncoding RNA (ncRNA) functions in catalysis, structure, regulation, and more. However, for the most part, these functions are poorly characterized. RNA is modular and described by motifs that include helical A-RNA with canonical Watson-Crick base-pairing as well as structures with only noncanonical base pairs. Understanding the structure and dynamics of motifs will aid in deciphering functions of specific ncRNAs. We present computational studies on a standard sarcin/ricin domain (SRD), citrus bark cracking viroid SRD, as well as A-RNA. We have applied enhanced molecular dynamics techniques that construct an inverse free-energy surface (iFES) determined by collective variables that monitor base-pairing and backbone conformation. Each SRD RNA is flanked on each side by A-RNA, allowing comparison of the behavior of these motifs in the same molecule. The RNA iFESs have single peaks, indicating that the combined motifs should denature as a single cohesive unit, rather than by regional melting. Local root-mean-square deviation (RMSD) analysis and communication propensity (CProp, variance in distances between residue pairs) reveal distinct motif properties. Our analysis indicates that the standard SRD is more stable than the viroid SRD, which is more stable than A-RNA. Base pairs at SRD to A-RNA transitions have limited flexibility. Application of CProp reveals extraordinary stiffness of the SRD, allowing residues on opposite sides of the motif to sense each other's motions.

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.

Molecular insights into binding dynamics of tandem RNA recognition motifs (tRRMs) of human antigen R (HuR) with mRNA and the effect of point mutations in impaired HuR-mRNA recognition

Human antigen R (HuR) is a key regulatory protein with prominent roles in RNA metabolism and post-transcriptional gene regulation. Many studies have shown the involvement of HuR in plethora of human diseases, which are often manifestations of impaired HuR-RNA interactions. However, the inherent complexities of highly flexible protein-RNA interactions have limited our understanding of the structural basis of HuR-RNA recognition. In this study, we dissect the underlying molecular mechanism of interaction between N-terminal tandem RNA-recognition motifs (tRRMs) of HuR and mRNA using molecular dynamics simulation. We have also explored the effect of point mutations (T90A, R97A and R136A) of three reported critical residues in HuR-mRNA binding specificity. Our findings show that N-terminal tRRMs exhibit conformational stability upon RNA binding. We further show that R136A and R97A mutants significantly lose their binding affinity owing to the loss of critical interactions with mRNA. This may be attributed to the larger domain rearrangements in the mutant complexes, especially the β2β3 loops in both the tRRMs, leading to unfavourable conformations and loss of binding affinity. We have identified critical binding residues in tRRMs of HuR, contributing favourable binding energy in mRNA recognition. This study contributes significantly to understand the molecular mechanism of RNA recognition by tandem RRMs and provides a platform to modulate binding affinities through mutations. This may further guide in future structure-based drug-therapies targeting impaired HuR-RNA interactions.Communicated by Ramaswamy H. Sarma.

Thermodynamics of unfolding mechanisms of mouse mammary tumor virus pseudoknot from a coarse-grained loop-entropy model

Pseudoknotted RNA molecules play important biological roles that depend on their folded structure. To understand the underlying principles that determine their thermodynamics and folding/unfolding mechanisms, we carried out a study on a variant of the mouse mammary tumor virus pseudoknotted RNA (VPK), a widely studied model system for RNA pseudoknots. Our method is based on a coarse-grained discrete-state model and the algorithm of PK3D (pseudoknot structure predictor in three-dimensional space), with RNA loops explicitly constructed and their conformational entropic effects incorporated. Our loop entropy calculations are validated by accurately capturing previously measured melting temperatures of RNA hairpins with varying loop lengths. For each of the hairpins that constitutes the VPK, we identified alternative conformations that are more stable than the hairpin structures at low temperatures and predicted their populations at different temperatures. Our predictions were validated by thermodynamic experiments on these hairpins. We further computed the heat capacity profiles of VPK, which are in excellent agreement with available experimental data. Notably, our model provides detailed information on the unfolding mechanisms of pseudoknotted RNA. Analysis of the distribution of base-pairing probability of VPK reveals a cooperative unfolding mechanism instead of a simple sequential unfolding of first one stem and then the other. Specifically, we find a simultaneous "loosening" of both stems as the temperature is raised, whereby both stems become partially melted and co-exist during the unfolding process.

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.

Structural alphabets for conformational analysis of nucleic acids available at dnatco.datmos.org

A detailed description of the dnatco.datmos.org web server implementing the universal structural alphabet of nucleic acids is presented. It is capable of processing any mmCIF- or PDB-formatted files containing DNA or RNA molecules; these can either be uploaded by the user or supplied as the wwPDB or PDB-REDO structural database access code. The web server performs an assignment of the nucleic acid conformations and presents the results for the intuitive annotation, validation, modeling and refinement of nucleic acids.

Ensemble Allosteric Model for the Modified Wobble Hypothesis

The residue 2-thiouridine (s²U) provides a remarkable example for the "modified wobble" hypothesis, which postulates that some post-transcriptional modifications at the wobble position of tRNAs restrict recognition of degenerate codons. Through extensive molecular dynamics simulations using our χ_IDRP force field parameters, we demonstrate how this modification shifts the conformational ensemble from a predominantly disordered, as in the case of an RNA pentamer (GUUUC), to a substantially ordered population in Gs²UUUC. Our simulations clearly showed that the van der Waals interaction of sulfur played a major role in driving the disorder-to-order transition. The conformational redistribution and the slowing down of the transition between the clusters within the population in the presence of s²U suggest ensemble allostery to be a key mechanism that may play a general role in the functioning of the wobble modifications of tRNAs.

3D-NuS: A Web Server for Automated Modeling and Visualization of Non-Canonical 3-Dimensional Nucleic Acid Structures

The inherent conformational flexibility of nucleic acids facilitates the formation of a range of conformations such as duplex, triplex, quadruplex, etc. that play crucial roles in biological processes. Elucidation of the influence of non-canonical base pair mismatches on DNA/RNA structures at different sequence contexts to understand the mismatch repair, misregulation of alternative splicing mechanisms and the sequence-dependent effect of RNA-DNA hybrid in relevance to antisense strategy demand their three-dimensional structural information. Furthermore, structural insights about nucleic acid triplexes, which are generally not tractable to structure determination by X-ray crystallography or NMR techniques, are essential to establish their biological function(s). A web server, namely 3D-NuS (http://iith.ac.in/3dnus/), has been developed to generate energy-minimized models of 80 different types of triplexes, 64 types of G-quadruplexes, left-handed Z-DNA/RNA duplexes, and RNA-DNA hybrid duplex along with inter- and intramolecular DNA or RNA duplexes comprising a variety of mismatches and their chimeric forms for any user-defined sequence and length. It also generates an ensemble of conformations corresponding to the modeled structure. These structures may serve as good starting models for docking proteins and small molecules with nucleic acids, NMR structure determination, cryo-electron microscope modeling, DNA/RNA nanotechnology applications and molecular dynamics simulation studies.

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.

Embracing proteins: structural themes in aptamer-protein complexes

Understanding the structural rules that govern specific, high-affinity binding characteristic of aptamer-protein interactions is important in view of the increasing use of aptamers across many applications. From the modest number of 16 aptamer-protein structures currently available, trends are emerging. The flexible phosphodiester backbone allows folding into precise three-dimensional structures using known nucleic acid motifs as scaffolds that orient specific functional groups for target recognition. Still, completely novel motifs essential for structure and function are found in modified aptamers with diversity-enhancing side chains. Aptamers and antibodies, two classes of macromolecules used as affinity reagents with entirely different backbones and composition, recognize protein epitopes of similar size and with comparably high shape complementarity.

Identification of possible siRNA molecules for TDP43 mutants causing amyotrophic lateral sclerosis: In silico design and molecular dynamics study

The DNA binding protein, TDP43 is a major protein involved in amyotrophic lateral sclerosis and other neurological disorders such as frontotemporal dementia, Alzheimer disease, etc. In the present study, we have designed possible siRNAs for the glycine rich region of tardbp mutants causing ALS disorder based on a systematic theoretical approach including (i) identification of respective codons for all mutants (reported at the protein level) based on both minimum free energy and probabilistic approaches, (ii) rational design of siRNA, (iii) secondary structure analysis for the target accessibility of siRNA, (iii) determination of the ability of siRNA to interact with mRNA and the formation/stability of duplex via molecular dynamics study for a period of 15ns and (iv) characterization of mRNA-siRNA duplex stability based on thermo-physical analysis. The stable GC-rich siRNA expressed strong binding affinity towards mRNA and forms stable duplex in A-form. The linear dependence between the thermo-physical parameters such as Tm, GC content and binding free energy revealed the ability of the identified siRNAs to interact with mRNA in comparable to that of the experimentally reported siRNAs. Hence, this present study proposes few siRNAs as the possible gene silencing agents in RNAi therapy based on the in silico approach.

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.

Crystal structure of group II intron domain 1 reveals a template for RNA assembly

Although the importance of large noncoding RNAs is increasingly appreciated, our understanding of their structures and architectural dynamics remains limited. In particular, we know little about RNA folding intermediates and how they facilitate the productive assembly of RNA tertiary structures. Here, we report the crystal structure of an obligate intermediate that is required during the earliest stages of group II intron folding. Composed of domain 1 from the Oceanobacillus iheyensis group II intron (266 nucleotides), this intermediate retains native-like features but adopts a compact conformation in which the active site cleft is closed. Transition between this closed and the open (native) conformation is achieved through discrete rotations of hinge motifs in two regions of the molecule. The open state is then stabilized by sequential docking of downstream intron domains, suggesting a 'first come, first folded' strategy that may represent a generalizable pathway for assembly of large RNA and ribonucleoprotein 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.

Computational Methods for RNA Structure Validation and Improvement

With increasing recognition of the roles RNA molecules and RNA/protein complexes play in an unexpected variety of biological processes, understanding of RNA structure-function relationships is of high current importance. To make clean biological interpretations from three-dimensional structures, it is imperative to have high-quality, accurate RNA crystal structures available, and the community has thoroughly embraced that goal. However, due to the many degrees of freedom inherent in RNA structure (especially for the backbone), it is a significant challenge to succeed in building accurate experimental models for RNA structures. This chapter describes the tools and techniques our research group and our collaborators have developed over the years to help RNA structural biologists both evaluate and achieve better accuracy. Expert analysis of large, high-resolution, quality-conscious RNA datasets provides the fundamental information that enables automated methods for robust and efficient error diagnosis in validating RNA structures at all resolutions. The even more crucial goal of correcting the diagnosed outliers has steadily developed toward highly effective, computationally based techniques. Automation enables solving complex issues in large RNA structures, but cannot circumvent the need for thoughtful examination of local details, and so we also provide some guidance for interpreting and acting on the results of current structure validation for RNA.

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.

The role of nucleobase interactions in RNA structure and dynamics

The intricate network of interactions observed in RNA three-dimensional structures is often described in terms of a multitude of geometrical properties, including helical parameters, base pairing/stacking, hydrogen bonding and backbone conformation. We show that a simple molecular representation consisting in one oriented bead per nucleotide can account for the fundamental structural properties of RNA. In this framework, canonical Watson-Crick, non-Watson-Crick base-pairing and base-stacking interactions can be unambiguously identified within a well-defined interaction shell. We validate this representation by performing two independent, complementary tests. First, we use it to construct a sequence-independent, knowledge-based scoring function for RNA structural prediction, which compares favorably to fully atomistic, state-of-the-art techniques. Second, we define a metric to measure deviation between RNA structures that directly reports on the differences in the base–base interaction network. The effectiveness of this metric is tested with respect to the ability to discriminate between structurally and kinetically distant RNA conformations, performing better compared to standard techniques. Taken together, our results suggest that this minimalist, nucleobase-centric representation captures the main interactions that are relevant for describing RNA structure and dynamics.

Stabilization of hairpins and bulged secondary structures of nucleic acids by single incorporation of α,β-D-CNA featuring a gauche(+) alpha torsional angle

A constrained dinucleotide unit featuring a gauche(+) alpha torsional angle configuration was used to stabilize DNA hairpin or bulged structures.

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.

The DNA and RNA sugar-phosphate backbone emerges as the key player. An overview of quantum-chemical, structural biology and simulation studies

Knowledge of geometrical and physico-chemical properties of the sugar-phosphate backbone substantially contributes to the comprehension of the structural dynamics, function and evolution of nucleic acids. We provide a side by side overview of structural biology/bioinformatics, quantum chemical and molecular mechanical/simulation studies of the nucleic acids backbone. We highlight main features, advantages and limitations of these techniques, with a special emphasis given to their synergy. The present status of the research is then illustrated by selected examples which include classification of DNA and RNA backbone families, benchmark structure-energy quantum chemical calculations, parameterization of the dihedral space of simulation force fields, incorporation of arsenate into DNA, sugar-phosphate backbone self-cleavage in small RNA enzymes, and intricate geometries of the backbone in recurrent RNA building blocks. Although not apparent from the current literature showing limited overlaps between the QM, simulation and bioinformatics studies of the nucleic acids backbone, there in fact should be a major cooperative interaction between these three approaches in studies of the sugar-phosphate backbone.

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.

NASSAM: a server to search for and annotate tertiary interactions and motifs in three-dimensional structures of complex RNA molecules

Similarities in the 3D patterns of RNA base interactions or arrangements can provide insights into their functions and roles in stabilization of the RNA 3D structure. Nucleic Acids Search for Substructures and Motifs (NASSAM) is a graph theoretical program that can search for 3D patterns of base arrangements by representing the bases as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph’s nodes while the edges are the inter-pseudo-atomic distances. The input files for NASSAM are PDB formatted 3D coordinates. This web server can be used to identify matches of base arrangement patterns in a query structure to annotated patterns that have been reported in the literature or that have possible functional and structural stabilization implications. The NASSAM program is freely accessible without any login requirement at http://mfrlab.org/grafss/nassam/.

Statistical mechanical modeling of RNA folding: from free energy landscape to tertiary structural prediction

In spite of the success of computational methods for predicting RNA secondary structure, the problem of predicting RNA tertiary structure folding remains. Low-resolution structural models show promise as they allow for rigorous statistical mechanical computation for the conformational entropies, free energies, and the coarse-grained structures of tertiary folds. Molecular dynamics refinement of coarse-grained structures leads to all-atom 3D structures. Modeling based on statistical mechanics principles also has the unique advantage of predicting the full free energy landscape, including local minima and the global free energy minimum. The energy landscapes combined with the 3D structures form the basis for quantitative predictions of RNA functions. In this chapter, we present an overview of statistical mechanical models for RNA folding and then focus on a recently developed RNA statistical mechanical model -- the Vfold model. The main emphasis is placed on the physics underpinning the models, the computational strategies, and the connections to RNA biology.

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.

A procedure to validate and correct the 13C chemical shift calibration of RNA datasets

Chemical shifts reflect the structural environment of a certain nucleus and can be used to extract structural and dynamic information. Proper calibration is indispensable to extract such information from chemical shifts. Whereas a variety of procedures exist to verify the chemical shift calibration for proteins, no such procedure is available for RNAs to date. We present here a procedure to analyze and correct the calibration of (13)C NMR data of RNAs. Our procedure uses five (13)C chemical shifts as a reference, each of them found in a narrow shift range in most datasets deposited in the Biological Magnetic Resonance Bank. In 49 datasets we could evaluate the (13)C calibration and detect errors or inconsistencies in RNA (13)C chemical shifts based on these chemical shift reference values. More than half of the datasets (27 out of those 49) were found to be improperly referenced or contained inconsistencies. This large inconsistency rate possibly explains that no clear structure-(13)C chemical shift relationship has emerged for RNA so far. We were able to recalibrate or correct 17 datasets resulting in 39 usable (13)C datasets. 6 new datasets from our lab were used to verify our method increasing the database to 45 usable datasets. We can now search for structure-chemical shift relationships with this improved list of (13)C chemical shift data. This is demonstrated by a clear relationship between ribose (13)C shifts and the sugar pucker, which can be used to predict a C2'- or C3'-endo conformation of the ribose with high accuracy. The improved quality of the chemical shift data allows statistical analysis with the potential to facilitate assignment procedures, and the extraction of restraints for structure calculations of RNA.

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.

Structure and stability of RNA/RNA kissing complex: with application to HIV dimerization initiation signal

We develop a statistical mechanical model to predict the structure and folding stability of the RNA/RNA kissing-loop complex. One of the key ingredients of the theory is the conformational entropy for the RNA/RNA kissing complex. We employ the recently developed virtual bond-based RNA folding model (Vfold model) to evaluate the entropy parameters for the different types of kissing loops. A benchmark test against experiments suggests that the entropy calculation is reliable. As an application of the model, we apply the model to investigate the structure and folding thermodynamics for the kissing complex of the HIV-1 dimerization initiation signal. With the physics-based energetic parameters, we compute the free energy landscape for the HIV-1 dimer. From the energy landscape, we identify two minimal free energy structures, which correspond to the kissing-loop dimer and the extended-duplex dimer, respectively. The results support the two-step dimerization process for the HIV-1 replication cycle. Furthermore, based on the Vfold model and energy minimization, the theory can predict the native structure as well as the local minima in the free energy landscape. The root-mean-square deviations (RMSDs) for the predicted kissing-loop dimer and extended-duplex dimer are ~3.0 Å. The method developed here provides a new method to study the RNA/RNA kissing complex.

Novel base triples in RNA structures revealed by graph theoretical searching methods

Background

Highly hydrogen bonded base interactions play a major part in stabilizing the tertiary structures of complex RNA molecules, such as transfer-RNAs, ribozymes and ribosomal RNAs.

Results

We describe the graph theoretical identification and searching of highly hydrogen bonded base triples, where each base is involved in at least two hydrogen bonds with the other bases. Our approach correlates theoretically predicted base triples with literature-based compilations and other actual occurrences in crystal structures. The use of ‘fuzzy’ search tolerances has enabled us to discover a number of triple interaction types that have not been previously recorded nor predicted theoretically.

Conclusions

Comparative analyses of different ribosomal RNA structures reveal several conserved base triple motifs in 50S rRNA structures, indicating an important role in structural stabilization and ultimately RNA function.

Nonparametric clustering for studying RNA conformations

The local conformation of RNA molecules is an important factor in determining their catalytic and binding properties. The analysis of such conformations is particularly difficult due to the large number of degrees of freedom, such as the measured torsion angles per residue and the interatomic distances among interacting residues. In this work, we use a nearest-neighbor search method based on the statistical mechanical Potts model to find clusters in the RNA conformational space. The proposed technique is mostly automatic and may be applied to problems, where there is no prior knowledge on the structure of the data space in contrast to many other clustering techniques. Results are reported for both single residue conformations, where the parameter set of the data space includes four to seven torsional angles, and base pair geometries, where the data space is reduced to two dimensions. Moreover, new results are reported for base stacking geometries. For the first two cases, i.e., single residue conformations and base pair geometries, we get a very good match between the results of the proposed clustering method and the known classifications with only few exceptions. For the case of base stacking geometries, we validate our classification with respect to geometrical constraints and describe the content, and the geometry of the new clusters.

A conditional random fields method for RNA sequence-structure relationship modeling and conformation sampling

Accurate tertiary structures are very important for the functional study of non-coding RNA molecules. However, predicting RNA tertiary structures is extremely challenging, because of a large conformation space to be explored and lack of an accurate scoring function differentiating the native structure from decoys. The fragment-based conformation sampling method (e.g. FARNA) bears shortcomings that the limited size of a fragment library makes it infeasible to represent all possible conformations well. A recent dynamic Bayesian network method, BARNACLE, overcomes the issue of fragment assembly. In addition, neither of these methods makes use of sequence information in sampling conformations. Here, we present a new probabilistic graphical model, conditional random fields (CRFs), to model RNA sequence–structure relationship, which enables us to accurately estimate the probability of an RNA conformation from sequence. Coupled with a novel tree-guided sampling scheme, our CRF model is then applied to RNA conformation sampling. Experimental results show that our CRF method can model RNA sequence–structure relationship well and sequence information is important for conformation sampling. Our method, named as TreeFolder, generates a much higher percentage of native-like decoys than FARNA and BARNACLE, although we use the same simple energy function as BARNACLE.

Contact:zywang@ttic.edu; j3xu@ttic.edu

Supplementary Information:Supplementary data are available at Bioinformatics online.

Prevalence of syn nucleobases in the active sites of functional RNAs

Biological RNAs, like their DNA counterparts, contain helical stretches, which have standard Watson-Crick base pairs in the anti conformation. Most functional RNAs also adopt geometries with far greater complexity such as bulges, loops, and multihelical junctions. Occasionally, nucleobases in these regions populate the syn conformation wherein the base resides close to or over the ribose sugar, which leads to a more compact state. The importance of the syn conformation to RNA function is largely unknown. In this study, we analyze 51 RNAs with tertiary structure, including aptamers, riboswitches, ribozymes, and ribosomal RNAs, for number, location, and properties of syn nucleobases. These RNAs represent the set of nonoverlapping, moderate- to high-resolution structures available at present. We find that syn nucleobases are much more common among purines than pyrimidines, and that they favor C2'-endo-like conformations especially among those nucleobases in the intermediate syn conformation. Strikingly, most syn nucleobases participate in tertiary stacking and base-pairing interactions: Inspection of RNA structures revealed that the majority of the syn nucleobases are in regions assigned to function, with many syn nucleobases interacting directly with a ligand or ribozyme active site. These observations suggest that judicious placement of conformationally restricted nucleotides biased into the syn conformation could enhance RNA folding and catalysis. Such changes could also be useful for locking RNAs into functionally competent folds for use in X-ray crystallography and NMR.

3D maps of RNA interhelical junctions

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.

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.

Physics-based de novo prediction of RNA 3D structures

Current experiments on structural determination cannot keep up the pace with the steadily emerging RNA sequences and new functions. This underscores the request for an accurate model for RNA three-dimensional (3D) structural prediction. Although considerable progress has been made in mechanistic studies, accurate prediction for RNA tertiary folding from sequence remains an unsolved problem. The first and most important requirement for the prediction of RNA structure from physical principles is an accurate free energy model. A recently developed three-vector virtual bond-based RNA folding model ("Vfold") has allowed us to compute the chain entropy and predict folding free energies and structures for RNA secondary structures and simple pseudoknots. Here we develop a free energy-based method to predict larger more complex RNA tertiary folds. The approach is based on a multiscaling strategy: from the nucleotide sequence, we predict the two-dimensional (2D) structures (defined by the base pairs and tertiary contacts); based on the 2D structure, we construct a 3D scaffold; with the 3D scaffold as the initial state, we combine AMBER energy minimization and PDB-based fragment search to predict the all-atom structure. A key advantage of the approach is the statistical mechanical calculation for the conformational entropy of RNA structures, including those with cross-linked loops. Benchmark tests show that the model leads to significant improvements in RNA 3D structure prediction.

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.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.