Knowledge-based instantiation of full atomic detail into coarse-grain RNA 3D structural models

Frontiers and Challenges of Computing ncRNAs Biogenesis, Function and Modulation

Non-coding RNAs (ncRNAs), generated from nonprotein coding DNA sequences, constitute 98-99% of the human genome. Non-coding RNAs encompass diverse functional classes, including microRNAs, small interfering RNAs, PIWI-interacting RNAs, small nuclear RNAs, small nucleolar RNAs, and long non-coding RNAs. With critical involvement in gene expression and regulation across various biological and physiopathological contexts, such as neuronal disorders, immune responses, cardiovascular diseases, and cancer, non-coding RNAs are emerging as disease biomarkers and therapeutic targets. In this review, after providing an overview of non-coding RNAs' role in cell homeostasis, we illustrate the potential and the challenges of state-of-the-art computational methods exploited to study non-coding RNAs biogenesis, function, and modulation. This can be done by directly targeting them with small molecules or by altering their expression by targeting the cellular engines underlying their biosynthesis. Drawing from applications, also taken from our work, we showcase the significance and role of computer simulations in uncovering fundamental facets of ncRNA mechanisms and modulation. This information may set the basis to advance gene modulation tools and therapeutic strategies to address unmet medical needs.

Quantifying RNA structures and interactions with a unified reduced chain representation model

RNA is a pivotal molecule that plays critical roles in various cellular processes. Quantifying RNA structures and interactions is essential to understanding RNA function and developing RNA-based therapeutics. Using a unified five-bead model and a non-redundant database, this paper investigates the structural features and interactions of five commonly occurring RNA motifs, i.e., double-stranded helices, hairpin loops, internal/bulge loops, multi-branched junctions, and single-stranded terminal tails. Analyzing detailed distributions of RNA local structural features and base-base interactions reveals a preference for helical structures in both local backbone structures and base orientations. The interactions between adjacent bases exhibit motif-specific and sequence-dependent characteristics, reflecting the distinct topological constraints imposed by different loop-helix connection modes and the varying pairing and stacking interactions among different sequences. These findings shed light on the stability of RNA helices, emphasizing their significance in providing dominant base pairing and stacking interactions for RNA structures and stability. The four non-helix motifs encompass unpaired nucleotide loops and exhibit diverse base-base interactions, contributing to the structural diversity observed in RNA. Overall, the complexity of RNA structure arises from the intricate interplay of base-base interactions.

Arena: Rapid and Accurate Reconstruction of Full Atomic RNA Structures From Coarse-grained Models

RNA tertiary structures from experiments or computational predictions often contain missing atoms, which prevent analyses requiring full atomic structures. Current programs for RNA reconstruction can be slow, inaccurate, and/or require specific atoms to be present in the input. We present Arena (Atomic Reconstruction of RNA), which reconstructs a full atomic RNA structure from residues that can have as few as one atom. Arena first fills in missing atoms and then iteratively refines their placement to reduce nonideal geometries. We benchmarked Arena on a dataset of 361 RNA structures, where Arena achieves high accuracy and speed compared to other structure reconstruction programs. For example, Arena was used to reconstruct full atomic structures from a single phosphorus atom per nucleotide to, on average, within 3.63 Å RMSD of the experimental structure, while virtually removing all clashes and running in <3 s, which is 353× and 46× faster than state-of-the-art programs PDBFixer and C2A, respectively. The Arena source code is available at https://github.com/pylelab/Arena and the webserver at https://zhanggroup.org/Arena/.

Modeling the 3D structure and conformational dynamics of very large RNAs using coarse-grained molecular simulations

We describe a computational approach to building and simulating realistic 3D models of very large RNA molecules (>1000 nucleotides) at a resolution of one "bead" per nucleotide. The method starts with a predicted secondary structure and uses several stages of energy minimization and Brownian dynamics (BD) simulation to build 3D models. A key step in the protocol is the temporary addition of a 4 ^th spatial dimension that allows all predicted helical elements to become disentangled from each other in an effectively automated way. We then use the resulting 3D models as input to Brownian dynamics simulations that include hydrodynamic interactions (HIs) that allow the diffusive properties of the RNA to be modelled as well as enabling its conformational dynamics to be simulated. To validate the dynamics part of the method, we first show that when applied to small RNAs with known 3D structures the BD-HI simulation models accurately reproduce their experimental hydrodynamic radii (Rh). We then apply the modelling and simulation protocol to a variety of RNAs for which experimental Rh values have been reported ranging in size from 85 to 3569 nucleotides. We show that the 3D models, when used in BD-HI simulations, produce hydrodynamic radii that are usually in good agreement with experimental estimates for RNAs that do not contain tertiary contacts that persist even under very low salt conditions. Finally, we show that sampling of the conformational dynamics of large RNAs on timescales of 100 µs is computationally feasible with BD-HI simulations.

Advances in RNA 3D Structure Prediction

RNA molecules carry out various cellular functions, and understanding the mechanisms behind their functions requires the knowledge of their 3D structures. Different types of computational methods have been developed to model RNA 3D structures over the past decade. These methods were widely used by researchers although their performance needs to be further improved. Recently, along with these traditional methods, machine-learning techniques have been increasingly applied to RNA 3D structure prediction and show significant improvement in performance. Here we shall give a brief review of the traditional methods and recent related advances in machine-learning approaches for RNA 3D structure prediction.

RNA 3D Structure Prediction Using Coarse-Grained Models

The three-dimensional (3D) structures of Ribonucleic acid (RNA) molecules are essential to understanding their various and important biological functions. However, experimental determination of the atomic structures is laborious and technically difficult. The large gap between the number of sequences and the experimentally determined structures enables the thriving development of computational approaches to modeling RNAs. However, computational methods based on all-atom simulations are intractable for large RNA systems, which demand long time simulations. Facing such a challenge, many coarse-grained (CG) models have been developed. Here, we provide a review of CG models for modeling RNA 3D structures, compare the performance of the different models, and offer insights into potential future developments.

Adventures with RNA graphs

The structure of RNA has been a natural subject for mathematical modeling, inviting many innovative computational frameworks. This single-stranded polynucleotide chain can fold upon itself in numerous ways to form hydrogen-bonded segments, imperfect with single-stranded loops. Illustrating these paired and non-paired interaction networks, known as RNA's secondary (2D) structure, using mathematical graph objects has been illuminating for RNA structure analysis. Building upon such seminal work from the 1970s and 1980s, graph models are now used to study not only RNA structure but also describe RNA's recurring modular units, sample the conformational space accessible to RNAs, predict RNA's three-dimensional folds, and apply the combined aspects to novel RNA design. In this article, we outline the development of the RNA-As-Graphs (or RAG) approach and highlight current applications to RNA structure prediction and design.

F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly

Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications.

Computational Methods for Modeling Aptamers and Designing Riboswitches

Riboswitches, which are located within certain noncoding RNA region perform functions as genetic "switches", regulating when and where genes are expressed in response to certain ligands. Understanding the numerous functions of riboswitches requires computation models to predict structures and structural changes of the aptamer domains. Although aptamers often form a complex structure, computational approaches, such as RNAComposer and Rosetta, have already been applied to model the tertiary (three-dimensional (3D)) structure for several aptamers. As structural changes in aptamers must be achieved within the certain time window for effective regulation, kinetics is another key point for understanding aptamer function in riboswitch-mediated gene regulation. The coarse-grained self-organized polymer (SOP) model using Langevin dynamics simulation has been successfully developed to investigate folding kinetics of aptamers, while their co-transcriptional folding kinetics can be modeled by the helix-based computational method and BarMap approach. Based on the known aptamers, the web server Riboswitch Calculator and other theoretical methods provide a new tool to design synthetic riboswitches. This review will represent an overview of these computational methods for modeling structure and kinetics of riboswitch aptamers and for designing riboswitches.

Base pair probability estimates improve the prediction accuracy of RNA non-canonical base pairs

Prediction of RNA tertiary structure from sequence is an important problem, but generating accurate structure models for even short sequences remains difficult. Predictions of RNA tertiary structure tend to be least accurate in loop regions, where non-canonical pairs are important for determining the details of structure. Non-canonical pairs can be predicted using a knowledge-based model of structure that scores nucleotide cyclic motifs, or NCMs. In this work, a partition function algorithm is introduced that allows the estimation of base pairing probabilities for both canonical and non-canonical interactions. Pairs that are predicted to be probable are more likely to be found in the true structure than pairs of lower probability. Pair probability estimates can be further improved by predicting the structure conserved across multiple homologous sequences using the TurboFold algorithm. These pairing probabilities, used in concert with prior knowledge of the canonical secondary structure, allow accurate inference of non-canonical pairs, an important step towards accurate prediction of the full tertiary structure. Software to predict non-canonical base pairs and pairing probabilities is now provided as part of the RNAstructure software package.

Capturing RNA Folding Free Energy with Coarse-Grained Molecular Dynamics Simulations

We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3-4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).

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.

RNAComposer and RNA 3D structure prediction for nanotechnology

RNAs adopt specific, stable tertiary architectures to perform their activities. Knowledge of RNA tertiary structure is fundamental to understand RNA functions beginning with transcription and ending with turnover. Contrary to advanced RNA secondary structure prediction algorithms, which allow good accuracy when experimental data are integrated into the prediction, tertiary structure prediction of large RNAs still remains a significant challenge. However, the field of RNA tertiary structure prediction is rapidly developing and new computational methods based on different strategies are emerging. RNAComposer is a user-friendly and freely available server for 3D structure prediction of RNA up to 500 nucleotide residues. RNAComposer employs fully automated fragment assembly based on RNA secondary structure specified by the user. Importantly, this method allows incorporation of distance restraints derived from the experimental data to strengthen the 3D predictions. The potential and limitations of RNAComposer are discussed and an application to RNA design for nanotechnology is presented.

It's a loop world - single strands in RNA as structural and functional elements

Unpaired regions in RNA molecules - loops - are centrally involved in defining the characteristic three-dimensional (3D) architecture of RNAs and are of high interest in RNA engineering and design. Loops adopt diverse, but specific conformations stabilised by complex tertiary structural interactions that provide structural flexibility to RNA structures that would otherwise not be possible if they only consisted of the rigid A-helical shapes usually formed by canonical base pairing. By participating in sequence-non-local contacts, they furthermore contribute to stabilising the overall fold of RNA molecules. Interactions between RNAs and other nucleic acids, proteins, or small molecules are also generally mediated by RNA loop structures. Therefore, the function of an RNA molecule is generally dependent on its loops. Examples include intermolecular interactions between RNAs as part of the microRNA processing pathways, ribozymatic activity, or riboswitch-ligand interactions. Bioinformatics approaches have been successfully applied to the identification of novel RNA structural motifs including loops, local and global RNA 3D structure prediction, and structural and conformational analysis of RNAs and have contributed to a better understanding of the sequence-structure-function relationships in RNA loops.

GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies

Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.

Automated 3D RNA structure prediction using the RNAComposer method for riboswitches

Understanding the numerous functions of RNAs depends critically on the knowledge of their three-dimensional (3D) structure. In contrast to the protein field, a much smaller number of RNA 3D structures have been assessed using X-ray crystallography, NMR spectroscopy, and cryomicroscopy. This has led to a great demand to obtain the RNA 3D structures using prediction methods. The 3D structure prediction, especially of large RNAs, still remains a significant challenge and there is still a great demand for high-resolution structure prediction methods. In this chapter, we describe RNAComposer, a method and server for the automated prediction of RNA 3D structures based on the knowledge of secondary structure. Its applications are supported by other automated servers: RNA FRABASE and RNApdbee, developed to search and analyze secondary and 3D structures. Another method, RNAlyzer, offers new way to analyze and visualize quality of RNA 3D models. Scope and limitations of RNAComposer in application for an automated prediction of riboswitches' 3D structure will be presented and discussed. Analysis of the cyclic di-GMP-II riboswitch from Clostridium acetobutylicum (PDB ID 3Q3Z) as an example allows for 3D structure prediction of related riboswitches from Clostridium difficile 4, Bacillus halodurans 1, and Thermus aquaticus Y5.1 of yet unknown structures.

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Small molecule compounds targeting miRNAs for cancer therapy

One of the most fascinating discoveries in molecular oncology has been that cancer represents a disease in which genetic alterations in protein-coding, but also in non-coding genes complement each other. MicroRNAs (miRNAs) are a type of non-coding RNA (ncRNA) transcripts that can regulate gene expression primarily by disrupting messenger RNA (mRNA) translation and/or stability, or alternatively by modulating the transcription of target mRNAs. For the last decade, miRNAs have shown to be pivotal characters of every single one of the cancer hallmarks. Profiling studies have proven the significance of identifying over-expressed miRNAs (oncomiRs) causative of the activation of oncogenic pathways that lead to malignancy. Due to their crucial role in cancer, it has become a challenge to develop efficient miRNA-inhibiting strategies such as antagomiRs, locked nucleic acids or antisense oligonucleotides. However, to this date, the accessible delivery agents and their pharmacokinetic/pharmacodynamic properties are not ideal. Thus there is an urgent, unmet need to develop miRNA-based inhibitory therapeutics. Herein we present a novel therapeutic strategy that is only at the tip of the iceberg: the use of small molecule inhibitors to target specific miRNAs (SMIRs). Furthermore we describe several high-throughput techniques to screen for SMIRs both in vitro and in silico. Finally we take you through the journey that has led to discovering the handful of SMIRs that have been validated to this date.

Evolutionary Algorithm in the Optimization of a Coarse-Grained Force Field

Simulations using residue-scale coarse-grained models of biomolecules are less computationally demanding than simulations employing full-atomistic force fields. However, the coarse-grained models are often difficult and tedious to parametrize for certain applications. Therefore, a systematic and objective method to help develop or adapt the coarse-grained models is needed. We present an automatic method that implements an evolutionary algorithm to find a set of optimal force field parameters for a one-bead coarse-grained model. In addition to an optimized force field, parameter correlations and significance of the potential energy terms can be determined. The method is applied to two classes of problems: the dynamics of an RNA helix and the RNA structure prediction.

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

A model for the structure of satellite tobacco mosaic virus

Satellite tobacco mosaic virus (STMV) is an icosahedral T=1 single-stranded RNA virus with a genome containing 1058 nucleotides. X-ray crystallography revealed a structure containing 30 double-helical RNA segments, with each helix having nine base pairs and an unpaired nucleotide at the 3' end of each strand. Based on this structure, Larson and McPherson proposed a model of 30 hairpin-loop elements occupying the edges of the icosahedron and connected by single-stranded regions. More recently, Schroeder et al. have combined the results of chemical probing with a novel helix searching algorithm to propose a specific secondary structure for the STMV genome, compatible with the Larson-McPherson model. Here we report an all-atom model of STMV, using the complete protein and RNA sequences and the Schroeder RNA secondary structure. As far as we know, this is the first all-atom model for the complete structure of any virus (100% of the atoms) using the natural genomic sequence.

Automated 3D structure composition for large RNAs

Understanding the numerous functions that RNAs play in living cells depends critically on knowledge of their three-dimensional structure. Due to the difficulties in experimentally assessing structures of large RNAs, there is currently great demand for new high-resolution structure prediction methods. We present the novel method for the fully automated prediction of RNA 3D structures from a user-defined secondary structure. The concept is founded on the machine translation system. The translation engine operates on the RNA FRABASE database tailored to the dictionary relating the RNA secondary structure and tertiary structure elements. The translation algorithm is very fast. Initial 3D structure is composed in a range of seconds on a single processor. The method assures the prediction of large RNA 3D structures of high quality. Our approach needs neither structural templates nor RNA sequence alignment, required for comparative methods. This enables the building of unresolved yet native and artificial RNA structures. The method is implemented in a publicly available, user-friendly server RNAComposer. It works in an interactive mode and a batch mode. The batch mode is designed for large-scale modelling and accepts atomic distance restraints. Presently, the server is set to build RNA structures of up to 500 residues.

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.

RNA-Puzzles: a CASP-like evaluation of RNA three-dimensional structure prediction

We report the results of a first, collective, blind experiment in RNA three-dimensional (3D) structure prediction, encompassing three prediction puzzles. The goals are to assess the leading edge of RNA structure prediction techniques; compare existing methods and tools; and evaluate their relative strengths, weaknesses, and limitations in terms of sequence length and structural complexity. The results should give potential users insight into the suitability of available methods for different applications and facilitate efforts in the RNA structure prediction community in ongoing efforts to improve prediction tools. We also report the creation of an automated evaluation pipeline to facilitate the analysis of future RNA structure prediction exercises.

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.

RNA structure prediction: an overview of methods

RNA is now appreciated to serve numerous cellular roles, and understanding RNA structure is important for understanding a mechanism of action. This contribution discusses the methods available for predicting RNA structure. Secondary structure is the set of the canonical base pairs, and secondary structure can be accurately determined by comparative sequence analysis. Secondary structure can also be predicted. The most commonly used method is free energy minimization. The accuracy of structure prediction is improved either by using experimental mapping data or by predicting a structure conserved in a set of homologous sequences. Additionally, tertiary structure, the three-dimensional arrangement of atoms, can be modeled with guidance from comparative analysis and experimental techniques. New approaches are also available for predicting tertiary structure.

Simbios: an NIH national center for physics-based simulation of biological structures

Physics-based simulation provides a powerful framework for understanding biological form and function. Simulations can be used by biologists to study macromolecular assemblies and by clinicians to design treatments for diseases. Simulations help biomedical researchers understand the physical constraints on biological systems as they engineer novel drugs, synthetic tissues, medical devices, and surgical interventions. Although individual biomedical investigators make outstanding contributions to physics-based simulation, the field has been fragmented. Applications are typically limited to a single physical scale, and individual investigators usually must create their own software. These conditions created a major barrier to advancing simulation capabilities. In 2004, we established a National Center for Physics-Based Simulation of Biological Structures (Simbios) to help integrate the field and accelerate biomedical research. In 6 years, Simbios has become a vibrant national center, with collaborators in 16 states and eight countries. Simbios focuses on problems at both the molecular scale and the organismal level, with a long-term goal of uniting these in accurate multiscale simulations.

Fast flexible modeling of RNA structure using internal coordinates

Modeling the structure and dynamics of large macromolecules remains a critical challenge. Molecular dynamics (MD) simulations are expensive because they model every atom independently, and are difficult to combine with experimentally derived knowledge. Assembly of molecules using fragments from libraries relies on the database of known structures and thus may not work for novel motifs. Coarse-grained modeling methods have yielded good results on large molecules but can suffer from difficulties in creating more detailed full atomic realizations. There is therefore a need for molecular modeling algorithms that remain chemically accurate and economical for large molecules, do not rely on fragment libraries, and can incorporate experimental information. RNABuilder works in the internal coordinate space of dihedral angles and thus has time requirements proportional to the number of moving parts rather than the number of atoms. It provides accurate physics-based response to applied forces, but also allows user-specified forces for incorporating experimental information. A particular strength of RNABuilder is that all Leontis-Westhof basepairs can be specified as primitives by the user to be satisfied during model construction. We apply RNABuilder to predict the structure of an RNA molecule with 160 bases from its secondary structure, as well as experimental information. Our model matches the known structure to 10.2 Angstroms RMSD and has low computational expense.

Automated RNA tertiary structure prediction from secondary structure and low-resolution restraints

A novel protocol for all-atom RNA tertiary structure prediction is presented that uses restrained molecular mechanics and simulated annealing. The restraints are from secondary structure, covariation analysis, coaxial stacking predictions for helices in junctions, and, when available, cross-linking data. Results are demonstrated on the Alu domain of the mammalian signal recognition particle RNA, the Saccharomyces cerevisiae phenylalanine tRNA, the hammerhead ribozyme, the hepatitis C virus internal ribosomal entry site, and the P4-P6 domain of the Tetrahymena thermophila group I intron. The predicted structure is selected from a pool of decoy structures with a score that maximizes radius of gyration and base-base contacts, which was empirically found to select higher quality decoys. This simple ab initio approach is sufficient to make good predictions of the structure of RNAs compared to current crystal structures using both root mean square deviation and the accuracy of base-base contacts.

Identification of TTA codon containing genes in Frankia and exploration of the role of tRNA in regulating these genes

The TTA codon, one of the six available codons for the amino acid leucine, is the rarest codon among the high GC genomes of Actinobacteria including Frankia. This codon has been implicated in various regulatory mechanisms involving secondary metabolism and morphological development. TTA-mediated gene regulation is well documented in Streptomyces coelicolor, but that role has not been investigated in other Actinobacteria including Frankia. Among the various Actinomycetes with a GC content of more than 70%, Frankia genomes had the highest percentages of TTA-containing genes ranging from 5.2 to 10.68% of the genome. In contrast, TTA-bearing genes comprised 1.7, 3.4 and 4.1% of the Streptomyces coelicolor, S. avermitilis and Nocardia farcinia genomes, respectively. We analyzed their functional role, evolutionary significance, horizontal acquisition and the codon-anticodon interaction. The TTA-bearing genes were found to be well represented in metabolic genes involved in amino acid transport and secondary metabolism. A reciprocal Blast search reveal that many of the TTA-bearing genes have orthologs in the other Frankia genomes, and some of these orthologous genes also have a TTA codon in them. The gene expression level of TTA-containing genes was estimated by the use of the codon adaption index (CAI), and the CAI values were found to have a positive correlation with the GC3 (GC content at the 3rd codon position). A full-atomic 3D model of the leucine tRNA recognizing the TTA (UUA) codon was generated and utilized for in silico docking to determine binding affinity in codon-anticodon interaction. We found a proficient codon-anticodon interaction for this codon which is perhaps why so many genes hold on to this rare codon without compromising their translational efficiency.

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.

Probing mechanism and transition state of RNA refolding

Kinetics and the atomic detail of RNA refolding are only poorly understood. It has been proposed that conformations with transient base pairing interaction are populated during RNA refolding, but a detailed description of those states is lacking. By NMR and CD spectroscopy, we examined the refolding of a bistable RNA and the influence of urea, Mg(2+), and spermidine on its refolding kinetics. The bistable RNA serves as a model system and exhibits two almost equally stable ground-state conformations. We designed a photolabile caged RNA to selectively stabilize one of the two ground-state conformations and trigger RNA refolding by in situ light irradiation in the NMR spectrometer. We can show that the refolding kinetics of the bistable RNA is modulated by urea, Mg(2+), and spermidine by different mechanisms. From a statistical analysis based on elementary rate constants, we deduce the required number of base pairs that need to be destabilized during the refolding transition and propose a model for the transition state of the folding reaction.

Elucidating the higher-order structure of biopolymers by structural probing and mass spectrometry: MS3D

Chemical probing represents a very versatile alternative for studying the structure and dynamics of substrates that are intractable by established high-resolution techniques. The implementation of MS-based strategies for the characterization of probing products has not only extended the range of applicability to virtually all types of biopolymers but has also paved the way for the introduction of new reagents that would not have been viable with traditional analytical platforms. As the availability of probing data is steadily increasing on the wings of the development of dedicated interpretation aids, powerful computational approaches have been explored to enable the effective utilization of such information to generate valid molecular models. This combination of factors has contributed to making the possibility of obtaining actual 3D structures by MS-based technologies (MS3D) a reality. Although approaches for achieving structure determination of unknown targets or assessing the dynamics of known structures may share similar reagents and development trajectories, they clearly involve distinctive experimental strategies, analytical concerns and interpretation paradigms. This Perspective offers a commentary on methods aimed at obtaining distance constraints for the modeling of full-fledged structures while highlighting common elements, salient distinctions and complementary capabilities exhibited by methods used in dynamics studies. We discuss critical factors to be addressed for completing effective structural determinations and expose possible pitfalls of chemical methods. We survey programs developed for facilitating the interpretation of experimental data and discuss possible computational strategies for translating sparse spatial constraints into all-atom models. Examples are provided to illustrate how the concerted application of very diverse probing techniques can lead to the solution of actual biological systems.

Three-dimensional structures of RNA obtained by means of knowledge-based interaction potentials

We derive a set of effective potentials describing the interaction between pairs of nucleotides that belong to an RNA molecule. Such interaction potentials are then used as the main constituents of a simplified simulation model, which is tested in the description of small secondary structure motifs. Our simulated RNA hairpins are consistent with the experimental structures obtained by NMR.