Computational approaches to 3D modeling of RNA

Automated identification of RNA 3D modules with discriminative power in RNA structural alignments

Recent progress in predicting RNA structure is moving towards filling the ‘gap’ in 2D RNA structure prediction where, for example, predicted internal loops often form non-canonical base pairs. This is increasingly recognized with the steady increase of known RNA 3D modules. There is a general interest in matching structural modules known from one molecule to other molecules for which the 3D structure is not known yet. We have created a pipeline, metaRNAmodules, which completely automates extracting putative modules from the FR3D database and mapping of such modules to Rfam alignments to obtain comparative evidence. Subsequently, the modules, initially represented by a graph, are turned into models for the RMDetect program, which allows to test their discriminative power using real and randomized Rfam alignments. An initial extraction of 22 495 3D modules in all PDB files results in 977 internal loop and 17 hairpin modules with clear discriminatory power. Many of these modules describe only minor variants of each other. Indeed, mapping of the modules onto Rfam families results in 35 unique locations in 11 different families. The metaRNAmodules pipeline source for the internal loop modules is available at http://rth.dk/resources/mrm.

Network Theory Tools for RNA Modeling

An introduction into the usage of graph or network theory tools for the study of RNA molecules is presented. By using vertices and edges to define RNA secondary structures as tree and dual graphs, we can enumerate, predict, and design RNA topologies. Graph connectivity and associated Laplacian eigenvalues relate to biological properties of RNA and help understand RNA motifs as well as build, by computational design, various RNA target structures. Importantly, graph theoretical representations of RNAs reduce drastically the conformational space size and therefore simplify modeling and prediction tasks. Ongoing challenges remain regarding general RNA design, representation of RNA pseudoknots, and tertiary structure prediction. Thus, developments in network theory may help advance RNA biology.

Predicting helical topologies in RNA junctions as tree graphs

RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires knowledge of their tertiary structures. Though computational RNA folding approaches exist, they often require manual manipulation and expert intuition; predicting global long-range tertiary contacts remains challenging. Here we develop a computational approach and associated program module (RNAJAG) to predict helical arrangements/topologies in RNA junctions. Our method has two components: junction topology prediction and graph modeling. First, junction topologies are determined by a data mining approach from a given secondary structure of the target RNAs; second, the predicted topology is used to construct a tree graph consistent with geometric preferences analyzed from solved RNAs. The predicted graphs, which model the helical arrangements of RNA junctions for a large set of 200 junctions using a cross validation procedure, yield fairly good representations compared to the helical configurations in native RNAs, and can be further used to develop all-atom models as we show for two examples. Because junctions are among the most complex structural elements in RNA, this work advances folding structure prediction methods of large RNAs. The RNAJAG module is available to academic users upon request.

Towards 3D structure prediction of large RNA molecules: an integer programming framework to insert local 3D motifs in RNA secondary structure

Motivation: The prediction of RNA 3D structures from its sequence only is a milestone to RNA function analysis and prediction. In recent years, many methods addressed this challenge, ranging from cycle decomposition and fragment assembly to molecular dynamics simulations. However, their predictions remain fragile and limited to small RNAs. To expand the range and accuracy of these techniques, we need to develop algorithms that will enable to use all the structural information available. In particular, the energetic contribution of secondary structure interactions is now well documented, but the quantification of non-canonical interactions—those shaping the tertiary structure—is poorly understood. Nonetheless, even if a complete RNA tertiary structure energy model is currently unavailable, we now have catalogues of local 3D structural motifs including non-canonical base pairings. A practical objective is thus to develop techniques enabling us to use this knowledge for robust RNA tertiary structure predictors.

Results: In this work, we introduce RNA-MoIP, a program that benefits from the progresses made over the last 30 years in the field of RNA secondary structure prediction and expands these methods to incorporate the novel local motif information available in databases. Using an integer programming framework, our method refines predicted secondary structures (i.e. removes incorrect canonical base pairs) to accommodate the insertion of RNA 3D motifs (i.e. hairpins, internal loops and k-way junctions). Then, we use predictions as templates to generate complete 3D structures with the MC-Sym program. We benchmarked RNA-MoIP on a set of 9 RNAs with sizes varying from 53 to 128 nucleotides. We show that our approach (i) improves the accuracy of canonical base pair predictions; (ii) identifies the best secondary structures in a pool of suboptimal structures; and (iii) predicts accurate 3D structures of large RNA molecules.

Availability:RNA-MoIP is publicly available at: http://csb.cs.mcgill.ca/RNAMoIP.

Contact:jeromew@cs.mcgill.ca

Polymorphisms within the COL5A1 3'-UTR that alters mRNA structure and the MIR608 gene are associated with Achilles tendinopathy

COL5A1 encodes for the α1 chain of type V collagen, an important regulator of fibril assembly in tendons, ligaments and other connective tissues. A polymorphism (rs12722) within the functional COL5A1 3'-untranslated region (UTR) has been shown to associate with chronic Achilles tendinopathy and other exercise-related phenotypes. The COL5A1 3'-UTR contains several putative cis-acting elements including a functional Hsa-miR-608 binding site. The aim of this study was to determine whether previously uncharacterized polymorphisms within a functional region of the COL5A1 3'-UTR or the MIR608 gene are associated with chronic Achilles tendinopathy. The effect of these COL5A1 3'-UTR polymorphisms on the 3'-UTR predicted mRNA secondary structure was also investigated. One hundred and sixty Caucasian chronic Achilles tendinopathic and 342 control participants were genotyped for the COL5A1 3'-UTR markers rs71746744, rs16399 and rs1134170, as well as marker rs4919510 within MIR608. All four genetic markers were independently associated with chronic Achilles tendinopathy. The COL5A1 polymorphisms appear to alter the predicted secondary structure of the 3'-UTR. We propose that the secondary structure plays a role in the regulation of the COL5A1 mRNA stability and by implication type V collagen production.

An algorithmic game-theory approach for coarse-grain prediction of RNA 3D structure

We present a new approach for the prediction of the coarse-grain 3D structure of RNA molecules. We model a molecule as being made of helices and junctions. Those junctions are classified into topological families that determine their preferred 3D shapes. All the parts of the molecule are then allowed to establish long-distance contacts that induce a 3D folding of the molecule. An algorithm relying on game theory is proposed to discover such long-distance contacts that allow the molecule to reach a Nash equilibrium. As reported by our experiments, this approach allows one to predict the global shape of large molecules of several hundreds of nucleotides that are out of reach of the state-of-the-art methods.

Candidate RNA structures for domain 3 of the foot-and-mouth-disease virus internal ribosome entry site

The foot-and-mouth-disease virus (FMDV) utilizes non-canonical translation initiation for viral protein synthesis, by forming a specific RNA structure called internal ribosome entry site (IRES). Domain 3 in FMDV IRES is phylogenetically conserved and highly structured; it contains four-way junctions where intramolecular RNA–RNA interactions serve as a scaffold for the RNA to fold for efficient IRES activity. Although the 3D structure of domain 3 is crucial to exploring and deciphering the initiation mechanism of translation, little is known. Here, we employ a combination of various modeling approaches to propose candidate tertiary structures for the apical region of domain 3, thought to be crucial for IRES function. We begin by modeling junction topology candidates and build atomic 3D models consistent with available experimental data. We then investigate each of the four candidate 3D structures by molecular dynamics simulations to determine the most energetically favorable configurations and to analyze specific tertiary interactions. Only one model emerges as viable containing not only the specific binding site for the GNRA tetraloop but also helical arrangements which enhance the stability of domain 3. These collective findings, together with available experimental data, suggest a plausible theoretical tertiary structure of the apical region in FMDV IRES domain 3.

Uniqueness, advantages, challenges, solutions, and perspectives in therapeutics applying RNA nanotechnology

The field of RNA nanotechnology is rapidly emerging. RNA can be manipulated with the simplicity characteristic of DNA to produce nanoparticles with a diversity of quaternary structures by self-assembly. Additionally RNA is tremendously versatile in its function and some RNA molecules display catalytic activities much like proteins. Thus, RNA has the advantage of both worlds. However, the instability of RNA has made many scientists flinch away from RNA nanotechnology. Other concerns that have deterred the progress of RNA therapeutics include the induction of interferons, stimulation of cytokines, and activation of other immune systems, as well as short pharmacokinetic profiles in vivo. This review will provide some solutions and perspectives on the chemical and thermodynamic stability, in vivo half-life and biodistribution, yield and production cost, in vivo toxicity and side effect, specific delivery and targeting, as well as endosomal trapping and escape.

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.

Computational analysis of noncoding RNAs

Noncoding RNAs have emerged as important key players in the cell. Understanding their surprisingly diverse range of functions is challenging for experimental and computational biology. Here, we review computational methods to analyze noncoding RNAs. The topics covered include basic and advanced techniques to predict RNA structures, annotation of noncoding RNAs in genomic data, mining RNA-seq data for novel transcripts and prediction of transcript structures, computational aspects of microRNAs, and database resources.

Uniqueness, advantages, challenges, solutions, and perspectives in therapeutics applying RNA nanotechnology

The field of RNA nanotechnology is rapidly emerging. RNA can be manipulated with the simplicity characteristic of DNA to produce nanoparticles with a diversity of quaternary structures by self-assembly. Additionally RNA is tremendously versatile in its function and some RNA molecules display catalytic activities much like proteins. Thus, RNA has the advantage of both worlds. However, the instability of RNA has made many scientists flinch away from RNA nanotechnology. Other concerns that have deterred the progress of RNA therapeutics include the induction of interferons, stimulation of cytokines, and activation of other immune systems, as well as short pharmacokinetic profiles in vivo. This review will provide some solutions and perspectives on the chemical and thermodynamic stability, in vivo half-life and biodistribution, yield and production cost, in vivo toxicity and side effect, specific delivery and targeting, as well as endosomal trapping and escape.

Hidden coding potential of eukaryotic genomes: nonAUG started ORFs

It is widely considered that the vast majority of eukaryotic mRNAs contain only one open reading frame (ORF) and encode single protein. However, eukaryotic ribosomes can initiate translation at alternative start codons due to leaky scanning or reinitiation mechanisms that provides an opportunity to synthesize several protein products. Recent investigations also demonstrated that alternative translation from nonAUG start codons and AUG codons in a weak nucleotide context could make an important contribution to eukaryotic proteomes. However, accurate prediction of alternative start codons demands detailed investigation of mRNA features influencing their recognition by eukaryotic ribosomes. In this work, we present the results of computational analysis of characteristics of yeast and mammalian mRNAs potentially involved in the recognition of nonAUG start codons. It was found that sequence features of nonAUG started Saccharomyces cerevisiae upstream ORFs (uORFs) were adjusted for efficient translation and these uORFs could frequently encode functional polypeptides. In particular, our initial studies revealed that predicted tertiary structures downstream of nonAUG start sites in mammalian mRNAs were energetically more stable than those predicted for AUG start sites with strong Kozak context. We hypothesize that presence of such stable tertiary structure downstream of nonAUG start sites could be an important factor for the ribosome to recognize noncanonical start codons.

SETTER: web server for RNA structure comparison

The recent discoveries of regulatory non-coding RNAs changed our view of RNA as a simple information transfer molecule. Understanding the architecture and function of active RNA molecules requires methods for comparing and analyzing their 3D structures. While structural alignment of short RNAs is achievable in a reasonable amount of time, large structures represent much bigger challenge. Here, we present the SETTER web server for the RNA structure pairwise comparison utilizing the SETTER (SEcondary sTructure-based TERtiary Structure Similarity Algorithm) algorithm. The SETTER method divides an RNA structure into the set of non-overlapping structural elements called generalized secondary structure units (GSSUs). The SETTER algorithm scales as O(n²) with the size of a GSSUs and as O(n) with the number of GSSUs in the structure. This scaling gives SETTER its high speed as the average size of the GSSU remains constant irrespective of the size of the structure. However, the favorable speed of the algorithm does not compromise its accuracy. The SETTER web server together with the stand-alone implementation of the SETTER algorithm are freely accessible at http://siret.cz/setter.

Modeling nucleic acids

Nucleic acids are an important class of biological macromolecules that carry out a variety of cellular roles. For many functions, naturally occurring DNA and RNA molecules need to fold into precise three-dimensional structures. Due to their self-assembling characteristics, nucleic acids have also been widely studied in the field of nanotechnology, and a diverse range of intricate three-dimensional nanostructures have been designed and synthesized. Different physical terms such as base-pairing and stacking interactions, tertiary contacts, electrostatic interactions and entropy all affect nucleic acid folding and structure. Here we review general computational approaches developed to model nucleic acid systems. We focus on four key areas of nucleic acid modeling: molecular representation, potential energy function, degrees of freedom and sampling algorithm. Appropriate choices in each of these key areas in nucleic acid modeling can effectively combine to aid interpretation of experimental data and facilitate prediction of nucleic acid structure.

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.

Determining RNA three-dimensional structures using low-resolution data

Knowing the 3-D structure of an RNA is fundamental to understand its biological function. Nowadays X-ray crystallography and NMR spectroscopy are systematically applied to newly discovered RNAs. However, the application of these high-resolution techniques is not always possible, and thus scientists must turn to lower resolution alternatives. Here, we introduce a pipeline to systematically generate atomic resolution 3-D structures that are consistent with low-resolution data sets. We compare and evaluate the discriminative power of a number of low-resolution experimental techniques to reproduce the structure of the Escherichia coli tRNA(VAL) and P4-P6 domain of the Tetrahymena thermophila group I intron. We test single and combinations of the most accessible low-resolution techniques, i.e. hydroxyl radical footprinting (OH), methidiumpropyl-EDTA (MPE), multiplexed hydroxyl radical cleavage (MOHCA), and small-angle X-ray scattering (SAXS). We show that OH-derived constraints are accurate to discriminate structures at the atomic level, whereas EDTA-based constraints apply to global shape determination. We provide a guide for choosing which experimental techniques or combination of thereof is best in which context. The pipeline represents an important step towards high-throughput low-resolution RNA structure determination.

Dynamic energy landscapes of riboswitches help interpret conformational rearrangements and function

Riboswitches are RNAs that modulate gene expression by ligand-induced conformational changes. However, the way in which sequence dictates alternative folding pathways of gene regulation remains unclear. In this study, we compute energy landscapes, which describe the accessible secondary structures for a range of sequence lengths, to analyze the transcriptional process as a given sequence elongates to full length. In line with experimental evidence, we find that most riboswitch landscapes can be characterized by three broad classes as a function of sequence length in terms of the distribution and barrier type of the conformational clusters: low-barrier landscape with an ensemble of different conformations in equilibrium before encountering a substrate; barrier-free landscape in which a direct, dominant “downhill” pathway to the minimum free energy structure is apparent; and a barrier-dominated landscape with two isolated conformational states, each associated with a different biological function. Sharing concepts with the “new view” of protein folding energy landscapes, we term the three sequence ranges above as the sensing, downhill folding, and functional windows, respectively. We find that these energy landscape patterns are conserved in various riboswitch classes, though the order of the windows may vary. In fact, the order of the three windows suggests either kinetic or thermodynamic control of ligand binding. These findings help understand riboswitch structure/function relationships and open new avenues to riboswitch design.

Riboswitches are RNAs that modulate gene expression by ligand-induced conformational changes. However, the way that sequence dictates alternative folding pathways of gene regulation remains unclear. In this study, we mimic transcription by computing energy landscapes which describe accessible secondary structures for a range of sequence lengths. Consistent with experimental evidence, we find that most riboswitch landscapes can be characterized by three broad classes as a function of sequence length in terms of the distribution and barrier type of the conformational clusters: Low-barrier landscape with an ensemble of conformations in equilibrium before encountering a substrate; barrier-free landscape with a dominant “downhill” pathway to the minimum free energy structure; and barrier-dominated landscape with two isolated conformational states with different functions. Sharing concepts with the “new view” of protein folding energy landscapes, we term the three sequence ranges above as the sensing, downhill folding, and functional windows, respectively. We find that these energy landscape patterns are conserved between riboswitch classes, though the order of the windows may vary. In fact, the order of the three windows suggests either kinetic or thermodynamic control of ligand binding. These findings help understand riboswitch structure/function relationships and open new avenues to riboswitch design.

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.

Computational methods for prediction of protein-RNA interactions

Understanding the molecular mechanism of protein-RNA recognition and complex formation is a major challenge in structural biology. Unfortunately, the experimental determination of protein-RNA complexes by X-ray crystallography and nuclear magnetic resonance spectroscopy (NMR) is tedious and difficult. Alternatively, protein-RNA interactions can be predicted by computational methods. Although less accurate than experimental observations, computational predictions can be sufficiently accurate to prompt functional hypotheses and guide experiments, e.g. to identify individual amino acid or nucleotide residues. In this article we review 10 methods for predicting protein-RNA interactions, seven of which predict RNA-binding sites from protein sequences and three from structures. We also developed a meta-predictor that uses the output of top three sequence-based primary predictors to calculate a consensus prediction, which outperforms all the primary predictors. In order to fully cover the software for predicting protein-RNA interactions, we also describe five methods for protein-RNA docking. The article highlights the strengths and shortcomings of existing methods for the prediction of protein-RNA interactions and provides suggestions for their further development.

New insights into the fundamental role of topological constraints as a determinant of two-way junction conformation

Recent studies have shown that topological constraints encoded at the RNA secondary structure level involving basic steric and stereochemical forces can significantly restrict the orientations sampled by helices across two-way RNA junctions. Here, we formulate these topological constraints in greater quantitative detail and use this topological framework to rationalize long-standing but poorly understood observations regarding the basic behavior of RNA two-way junctions. Notably, we show that the asymmetric nature of the A-form helix and the finite length of a bulge provide a physical basis for the experimentally observed directionality and bulge-length amplitude dependence of bulge induced inter-helical bends. We also find that the topologically allowed space can be modulated by variations in sequence, particularly with the addition of non-canonical GU base pairs at the junction, and, surprisingly, by the length of the 5′ and 3′ helices. A survey of two-way RNA junctions in the protein data bank confirms that junction residues have a strong preference to adopt looped-in, non-canonically base-paired conformations, providing a route for extending our bulge-directed framework to internal loop motifs and implying a simplified link between secondary and tertiary structure. Finally, our results uncover a new simple mechanism for coupling junction-induced topological constraints with tertiary interactions.

Predicting coaxial helical stacking in RNA junctions

RNA junctions are important structural elements that form when three or more helices come together in space in the tertiary structures of RNA molecules. Determining their structural configuration is important for predicting RNA 3D structure. We introduce a computational method to predict, at the secondary structure level, the coaxial helical stacking arrangement in junctions, as well as classify the junction topology. Our approach uses a data mining approach known as random forests, which relies on a set of decision trees trained using length, sequence and other variables specified for any given junction. The resulting protocol predicts coaxial stacking within three- and four-way junctions with an accuracy of 81% and 77%, respectively; the accuracy increases to 83% and 87%, respectively, when knowledge from the junction family type is included. Coaxial stacking predictions for the five to ten-way junctions are less accurate (60%) due to sparse data available for training. Additionally, our application predicts the junction family with an accuracy of 85% for three-way junctions and 74% for four-way junctions. Comparisons with other methods, as well applications to unsolved RNAs, are also presented. The web server Junction-Explorer to predict junction topologies is freely available at: http://bioinformatics.njit.edu/junction.

RNA tertiary structure prediction with ModeRNA

Noncoding RNAs perform important roles in the cell. As their function is tightly connected with structure, and as experimental methods are time-consuming and expensive, the field of RNA structure prediction is developing rapidly. Here, we present a detailed study on using the ModeRNA software. The tool uses the comparative modeling approach and can be applied when a structural template is available and an alignment of reasonable quality can be performed. We guide the reader through the entire process of modeling Escherichia coli tRNA(Thr) in a conformation corresponding to the complex with an aminoacyl-tRNA synthetase (aaRS). We describe the choice of a template structure, preparation of input files, and explore three possible modeling strategies. In the end, we evaluate the resulting models using six alternative benchmarks. The ModeRNA software can be freely downloaded from http://iimcb.genesilico.pl/moderna/ under the conditions of the General Public License. It runs under LINUX, Windows and Mac OS. It is also available as a server at http://iimcb.genesilico.pl/modernaserver/. The models and the script to reproduce the study from this article are available at http://www.genesilico.pl/moderna/examples/.

Feature-based 3D motif filtering for ribosomal RNA

MOTIVATION

RNA 3D motifs are recurrent substructures in an RNA subunit and are building blocks of the RNA architecture. They play an important role in binding proteins and consolidating RNA tertiary structures. RNA 3D motif searching consists of two steps: candidate generation and candidate filtering. We proposed a novel method, known as Feature-based RNA Motif Filtering (FRMF), for identifying motifs based on a set of moment invariants and the Earth Mover's Distance in the second step.

RESULTS

A positive set of RNA motifs belonging to six characteristic types, with eight subtypes occurring in HM 50S, is compiled by us. The proposed method is validated on this representative set. FRMF successfully finds most of the positive fragments. Besides the proposed new method and the compiled positive set, we also recognize some new motifs, in particular a π-turn and some non-standard A-minor motifs are found. These newly discovered motifs provide more information about RNA structure conformation.

AVAILABILITY

Matlab code can be downloaded from www.cs.cityu.edu.hk/~yingshen/FRMF.html

CONTACT

cshswong@cityu.edu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

DARS-RNP and QUASI-RNP: new statistical potentials for protein-RNA docking

Background

Protein-RNA interactions play fundamental roles in many biological processes. Understanding the molecular mechanism of protein-RNA recognition and formation of protein-RNA complexes is a major challenge in structural biology. Unfortunately, the experimental determination of protein-RNA complexes is tedious and difficult, both by X-ray crystallography and NMR. For many interacting proteins and RNAs the individual structures are available, enabling computational prediction of complex structures by computational docking. However, methods for protein-RNA docking remain scarce, in particular in comparison to the numerous methods for protein-protein docking.

Results

We developed two medium-resolution, knowledge-based potentials for scoring protein-RNA models obtained by docking: the quasi-chemical potential (QUASI-RNP) and the Decoys As the Reference State potential (DARS-RNP). Both potentials use a coarse-grained representation for both RNA and protein molecules and are capable of dealing with RNA structures with posttranscriptionally modified residues. We compared the discriminative power of DARS-RNP and QUASI-RNP for selecting rigid-body docking poses with the potentials previously developed by the Varani and Fernandez groups.

Conclusions

In both bound and unbound docking tests, DARS-RNP showed the highest ability to identify native-like structures. Python implementations of DARS-RNP and QUASI-RNP are freely available for download at http://iimcb.genesilico.pl/RNP/

Computational approaches to RNA structure prediction, analysis, and design

RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires RNA tertiary structure knowledge. Although modeling approaches for the study of RNA structures and dynamics lag behind efforts in protein folding, much progress has been achieved in the past two years. Here, we review recent advances in RNA folding algorithms, RNA tertiary motif discovery, applications of graph theory approaches to RNA structure and function, and in silico generation of RNA sequence pools for aptamer design. Advances within each area can be combined to impact many problems in RNA structure and function.

RAG: an update to the RNA-As-Graphs resource

Background

In 2004, we presented a web resource for stimulating the search for novel RNAs, RNA-As-Graphs (RAG), which classified, catalogued, and predicted RNA secondary structure motifs using clustering and build-up approaches. With the increased availability of secondary structures in recent years, we update the RAG resource and provide various improvements for analyzing RNA structures.

Description

Our RAG update includes a new supervised clustering algorithm that can suggest RNA motifs that may be "RNA-like". We use this utility to describe RNA motifs as three classes: existing, RNA-like, and non-RNA-like. This produces 126 tree and 16,658 dual graphs as candidate RNA-like topologies using the supervised clustering algorithm with existing RNAs serving as the training data. A comparison of this clustering approach to an earlier method shows considerable improvements. Additional RAG features include greatly expanded search capabilities, an interface to better utilize the benefits of relational database, and improvements to several of the utilities such as directed/labeled graphs and a subgraph search program.

Conclusions

The RAG updates presented here augment the database's intended function - stimulating the search for novel RNA functionality - by classifying available motifs, suggesting new motifs for design, and allowing for more specific searches for specific topologies. The updated RAG web resource offers users a graph-based tool for exploring available RNA motifs and suggesting new RNAs for design.

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.

Clustering to identify RNA conformations constrained by secondary structure

RNA often folds hierarchically, so that its sequence defines its secondary structure (helical base-paired regions connected by single-stranded junctions), which subsequently defines its tertiary fold. To preserve base-pairing and chain connectivity, the three-dimensional conformations that RNA can explore are strongly confined compared to when secondary structure constraints are not enforced. Using three examples, we studied how secondary structure confines and dictates an RNA's preferred conformations. We made use of Macromolecular Conformations by SYMbolic programming (MC-Sym) fragment assembly to generate RNA conformations constrained by secondary structure. Then, to understand the correlations between different helix placements and orientations, we robustly clustered all RNA conformations by employing unique methods to remove outliers and estimate the best number of conformational clusters. We observed that the preferred conformation (as judged by largest cluster size) for each type of RNA junction molecule tested is consistent with its biological function. Further, the improved quality of models in our pruned datasets facilitates subsequent discrimination using scoring functions based either on statistical analysis (knowledge based) or experimental data.

Coarse-grained models to study dynamics of nanoscale biomolecules and their applications to the ribosome

Biopolymers are of dynamic nature and undergo functional motions spanning a large spectrum of timescales. To study the internal dynamics of nano-sized molecular complexes that exceed hundred thousands of atoms with atomic detail is computationally inefficient. Therefore, to achieve both the spatial and temporal scales of biological interest coarse-grained models of macromolecules are often used. By uniting groups of atoms into single interacting centers one decreases the resolution of the system and gets rid of the irrelevant degrees of freedom. This simplification, even though it requires parameterization, makes the studies of biomolecular dynamics computationally tractable and allows us to reach beyond the microsecond time frame. Here, I review the coarse-grained models of macromolecules composed of proteins and nucleic acids. I give examples of one-bead models that were developed to investigate the internal dynamics and focus on their applications to the ribosome--the nanoscale protein synthesis machine.