Predicting loop-helix tertiary structural contacts in RNA pseudoknots

Deciphering the sequence-dependent unfolding pathways of an RNA pseudoknot with steered molecular dynamics

Programmed ribosomal frameshifting in Simian retrovirus-1 (SRV-1) is sensitive to the mechanical properties of an RNA pseudoknot. Unravelling these mechanical intricacies via unfolding reveals fundamental insights into their structural dynamics. Using constant velocity steered molecular dynamics (CV-SMD) simulations, we explored the unfolding dynamics and the impact of mutations on the unfolding pathway of the pseudoknot. Except for A28C, A/U to C mutations that disrupt base triples between the loop 2 and stem 1 significantly weaken the pseudoknot and make it more susceptible to unfolding. Complementary mutations in 3 base pairs of the stem region (S1) enhanced its susceptibility to disruption except for Mut5 (S2). We quantitatively assessed the variations in unfolding pathways by analysing the opening of distinct Canonical (WC) and non-canonical (NWC) interactions, force-extension curves, and potential mean force profiles (as a guiding decision for planning mutations). These findings offer a quantified perspective, showcasing the potential of utilizing the unfolding pathways of RNA pseudoknots to explore the programmability of RNA structures. This insight proves valuable for designing RNA-PROTACS and RNA-aptamers, allowing for the assessment and manipulation of their biological folding/unfolding processes.

Machine learning in RNA structure prediction: Advances and challenges

RNA molecules play a crucial role in various biological processes, with their functionality closely tied to their structures. The remarkable advancements in machine learning techniques for protein structure prediction have shown promise in the field of RNA structure prediction. In this perspective, we discuss the advances and challenges encountered in constructing machine learning-based models for RNA structure prediction. We explore topics including model building strategies, specific challenges involved in predicting RNA secondary (2D) and tertiary (3D) structures, and approaches to these challenges. In addition, we highlight the advantages and challenges of constructing RNA language models. Given the rapid advances of machine learning techniques, we anticipate that machine learning-based models will serve as important tools for predicting RNA structures, thereby enriching our understanding of RNA structures and their corresponding functions.

Biomotors, viral assembly, and RNA nanobiotechnology: Current achievements and future directions

The International Society of RNA Nanotechnology and Nanomedicine (ISRNN) serves to further the development of a wide variety of functional nucleic acids and other related nanotechnology platforms. To aid in the dissemination of the most recent advancements, a biennial discussion focused on biomotors, viral assembly, and RNA nanobiotechnology has been established where international experts in interdisciplinary fields such as structural biology, biophysical chemistry, nanotechnology, cell and cancer biology, and pharmacology share their latest accomplishments and future perspectives. The results summarized here highlight advancements in our understanding of viral biology and the structure-function relationship of frame-shifting elements in genomic viral RNA, improvements in the predictions of SHAPE analysis of 3D RNA structures, and the understanding of dynamic RNA structures through a variety of experimental and computational means. Additionally, recent advances in the drug delivery, vaccine design, nanopore technologies, biomotor and biomachine development, DNA packaging, RNA nanotechnology, and drug delivery are included in this critical review. We emphasize some of the novel accomplishments, major discussion topics, and present current challenges and perspectives of these emerging fields.

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.

VfoldMCPX: predicting multistrand RNA complexes

Multistrand RNA complexes play a critical role in RNA-related biological processes. The understanding of RNA functions and the rational design of RNA nanostructures require accurate prediction of the structure and folding stability of the complexes, including those containing pseudoknots. Here, we present VfoldMCPX, a new model for predicting two-dimensional (2D) structures and folding stabilities of multistrand RNA complexes. Based on a partition function-based algorithm combined with physical loop free energy parameters, the VfoldMCPX model predicts not only the native structure but also the folding stability of the complex. An important advantage of the model is the ability to treat pseudoknotted structures. Extensive tests on structure predictions show the VfoldMCPX model provides improved accuracy for multistranded RNA complexes, especially for RNA complexes with three or more strands and/or containing pseudoknots. We have developed a freely accessible VfoldMCPX web server at http://rna.physics.missouri.edu/vfoldMCPX2.

rsRNASP: A residue-separation-based statistical potential for RNA 3D structure evaluation

Knowledge-based statistical potentials have been shown to be rather effective in protein 3-dimensional (3D) structure evaluation and prediction. Recently, several statistical potentials have been developed for RNA 3D structure evaluation, while their performances are either still at a low level for the test datasets from structure prediction models or dependent on the "black-box" process through neural networks. In this work, we have developed an all-atom distance-dependent statistical potential based on residue separation for RNA 3D structure evaluation, namely rsRNASP, which is composed of short- and long-ranged potentials distinguished by residue separation. The extensive examinations against available RNA test datasets show that rsRNASP has apparently higher performance than the existing statistical potentials for the realistic test datasets with large RNAs from structure prediction models, including the newly released RNA-Puzzles dataset, and is comparable to the existing top statistical potentials for the test datasets with small RNAs or near-native decoys. In addition, rsRNASP is superior to RNA3DCNN, a recently developed scoring function through 3D convolutional neural networks. rsRNASP and the relevant databases are available to the public.

Vfold2D-MC: A Physics-Based Hybrid Model for Predicting RNA Secondary Structure Folding

Accurate prediction of RNA structure and folding stability has a far-reaching impact on our understanding of RNA functions. Here we develop Vfold2D-MC, a new physics-based model, to predict RNA structure and folding thermodynamics from the sequence. The model employs virtual bond-based coarse-graining of RNA backbone conformation and generates RNA conformations through Monte Carlo sampling of the bond angles and torsional angles of the virtual bonds. Using a coarse-grained statistical potential derived from the known structures, we assign each conformation with a statistical weight. The weighted average over the conformational ensemble gives the entropy and free energy parameters for the hairpin, bulge, and internal loops, and multiway junctions. From the thermodynamic parameters, we predict RNA structures, melting curves, and structural changes from the sequence. Theory-experiment comparisons indicate that Vfold2D-MC not only gives improved structure predictions but also enables the interpretation of thermodynamic results for different RNA structures, including multibranched junctions. This new model sets a promising framework to treat more complicated RNA structures, such as pseudoknotted and intramolecular kissing loops, for which experimental thermodynamic parameters are often unavailable.

Thermostability, Tunability, and Tenacity of RNA as Rubbery Anionic Polymeric Materials in Nanotechnology and Nanomedicine-Specific Cancer Targeting with Undetectable Toxicity

RNA nanotechnology is the bottom-up self-assembly of nanometer-scale architectures, resembling LEGOs, composed mainly of RNA. The ideal building material should be (1) versatile and controllable in shape and stoichiometry, (2) spontaneously self-assemble, and (3) thermodynamically, chemically, and enzymatically stable with a long shelf life. RNA building blocks exhibit each of the above. RNA is a polynucleic acid, making it a polymer, and its negative-charge prevents nonspecific binding to negatively charged cell membranes. The thermostability makes it suitable for logic gates, resistive memory, sensor set-ups, and NEM devices. RNA can be designed and manipulated with a level of simplicity of DNA while displaying versatile structure and enzyme activity of proteins. RNA can fold into single-stranded loops or bulges to serve as mounting dovetails for intermolecular or domain interactions without external linking dowels. RNA nanoparticles display rubber- and amoeba-like properties and are stretchable and shrinkable through multiple repeats, leading to enhanced tumor targeting and fast renal excretion to reduce toxicities. It was predicted in 2014 that RNA would be the third milestone in pharmaceutical drug development. The recent approval of several RNA drugs and COVID-19 mRNA vaccines by FDA suggests that this milestone is being realized. Here, we review the unique properties of RNA nanotechnology, summarize its recent advancements, describe its distinct attributes inside or outside the body and discuss potential applications in nanotechnology, medicine, and material science.

The three-way junction structure of the HIV-1 PBS-segment binds host enzyme important for viral infectivity

HIV-1 reverse transcription initiates at the primer binding site (PBS) in the viral genomic RNA (gRNA). Although the structure of the PBS-segment undergoes substantial rearrangement upon tRNALys3 annealing, the proper folding of the PBS-segment during gRNA packaging is important as it ensures loading of beneficial host factors. DHX9/RNA helicase A (RHA) is recruited to gRNA to enhance the processivity of reverse transcriptase. Because the molecular details of the interactions have yet to be defined, we solved the solution structure of the PBS-segment preferentially bound by RHA. Evidence is provided that PBS-segment adopts a previously undefined adenosine-rich three-way junction structure encompassing the primer activation stem (PAS), tRNA-like element (TLE) and tRNA annealing arm. Disruption of the PBS-segment three-way junction structure diminished reverse transcription products and led to reduced viral infectivity. Because of the existence of the tRNA annealing arm, the TLE and PAS form a bent helical structure that undergoes shape-dependent recognition by RHA double-stranded RNA binding domain 1 (dsRBD1). Mutagenesis and phylogenetic analyses provide evidence for conservation of the PBS-segment three-way junction structure that is preferentially bound by RHA in support of efficient reverse transcription, the hallmark step of HIV-1 replication.

IsRNA1: De Novo Prediction and Blind Screening of RNA 3D Structures

Modeling structures and functions of large ribonucleic acid (RNAs) especially with complicated topologies is highly challenging due to the inefficiency of large conformational sampling and the presence of complicated tertiary interactions. To address this problem, one highly promising approach is coarse-grained modeling. Here, following an iterative simulated reference state approach to decipher the correlations between different structural parameters, we developed a potent coarse-grained RNA model named as IsRNA1 for RNA studies. Molecular dynamics simulations in the IsRNA1 can predict the native structures of small RNAs from a sequence and fold medium-sized RNAs into near-native tertiary structures with the assistance of secondary structure constraints. A large-scale benchmark test on RNA 3D structure prediction shows that IsRNA1 exhibits improved performance for relatively large RNAs of complicated topologies, such as large stem-loop structures and structures containing long-range tertiary interactions. The advantages of IsRNA1 include the consideration of the correlations between the different structural variables, the appropriate characterization of canonical base-pairing and base-stacking interactions, and the better sampling for the backbone conformations. Moreover, a blind screening protocol was developed based on IsRNA1 to identify good structural models from a pool of candidates without prior knowledge of the native structures.

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Computational predictive approaches for interaction and structure of aptamers

Aptamers are short single-strand sequences that can bind to their specific targets with high affinity and specificity. Usually, aptamers are selected experimentally via systematic evolution of ligands by exponential enrichment (SELEX), an evolutionary process that consists of multiple cycles of selection and amplification. The SELEX process is expensive, time-consuming, and its success rates are relatively low. To overcome these difficulties, in recent years, several computational techniques have been developed in aptamer sciences that bring together different disciplines and branches of technologies. In this paper, a complementary review on computational predictive approaches of the aptamer has been organized. Generally, the computational prediction approaches of aptamer have been proposed to carry out in two main categories: interaction-based prediction and structure-based predictions. Furthermore, the available software packages and toolkits in this scope were reviewed. The aim of describing computational methods and tools in aptamer science is that aptamer scientists might take advantage of these computational techniques to develop more accurate and more sensitive aptamers.

Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions

RNA pseudoknots are a kind of minimal RNA tertiary structural motifs, and their three-dimensional (3D) structures and stability play essential roles in a variety of biological functions. Therefore, to predict 3D structures and stability of RNA pseudoknots is essential for understanding their functions. In the work, we employed our previously developed coarse-grained model with implicit salt to make extensive predictions and comprehensive analyses on the 3D structures and stability for RNA pseudoknots in monovalent/divalent ion solutions. The comparisons with available experimental data show that our model can successfully predict the 3D structures of RNA pseudoknots from their sequences, and can also make reliable predictions for the stability of RNA pseudoknots with different lengths and sequences over a wide range of monovalent/divalent ion concentrations. Furthermore, we made comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions. Our analyses for extensive pseudokonts and the wide range of monovalent/divalent ion concentrations verify that the unfolding pathway of RNA pseudoknots is mainly dependent on the relative stability of unfolded intermediate states, and show that the unfolding pathway of RNA pseudoknots can be significantly modulated by their sequences and solution ion conditions.

Ensemble simulations: folding, unfolding and misfolding of a high-efficiency frameshifting RNA pseudoknot

Massive all-atom molecular dynamics simulations were conducted across a distributed computing network to study the folding, unfolding, misfolding and conformational plasticity of the high-efficiency frameshifting double mutant of the 26 nt potato leaf roll virus RNA pseudoknot. Our robust sampling, which included over 40 starting structures spanning the spectrum from the extended unfolded state to the native fold, yielded nearly 120 μs of cumulative sampling time. Conformational microstate transitions on the 1.0 ns to 10.0 μs timescales were observed, with post-equilibration sampling providing detailed representations of the conformational free energy landscape and the complex folding mechanism inherent to the pseudoknot motif. Herein, we identify and characterize two alternative native structures, three intermediate states, and numerous misfolded states, the latter of which have not previously been characterized via atomistic simulation techniques. While in line with previous thermodynamics-based models of a general RNA folding mechanism, our observations indicate that stem-strand-sequence-separation may serve as an alternative predictor of the order of stem formation during pseudoknot folding. Our results contradict a model of frameshifting based on structural rigidity and resistance to mechanical unfolding, and instead strongly support more recent studies in which conformational plasticity is identified as a determining factor in frameshifting efficiency.

Theory and Modeling of RNA Structure and Interactions with Metal Ions and Small Molecules

In addition to continuous rapid progress in RNA structure determination, probing, and biophysical studies, the past decade has seen remarkable advances in the development of a new generation of RNA folding theories and models. In this article, we review RNA structure prediction models and models for ion-RNA and ligand-RNA interactions. These new models are becoming increasingly important for a mechanistic understanding of RNA function and quantitative design of RNA nanotechnology. We focus on new methods for physics-based, knowledge-based, and experimental data-directed modeling for RNA structures and explore the new theories for the predictions of metal ion and ligand binding sites and metal ion-dependent RNA stabilities. The integration of these new methods with theories about the cellular environment effects in RNA folding, such as molecular crowding and cotranscriptional kinetic effects, may ultimately lead to an all-encompassing RNA folding model.

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.

Salt contribution to the flexibility of single-stranded nucleic acid offinite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single-stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse-grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual-bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion-exclusion-volume effect to ion Coulomb correlations. In addition, the predicted Na(+) and Mg(2+)-dependent persistence length l(p)'s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l(p) as a function of [Na(+)], [Mg(2+)] and chain length.

Mimicking Ribosomal Unfolding of RNA Pseudoknot in a Protein Channel

Pseudoknots are a fundamental RNA tertiary structure with important roles in regulation of mRNA translation. Molecular force spectroscopic approaches such as optical tweezers can track the pseudoknot's unfolding intermediate states by pulling the RNA chain from both ends, but the kinetic unfolding pathway induced by this method may be different from that in vivo, which occurs during translation and proceeds from the 5' to 3' end. Here we developed a ribosome-mimicking, nanopore pulling assay for dissecting the vectorial unfolding mechanism of pseudoknots. The pseudoknot unfolding pathway in the nanopore, either from the 5' to 3' end or in the reverse direction, can be controlled by a DNA leader that is attached to the pseudoknot at the 5' or 3' ends. The different nanopore conductance between DNA and RNA translocation serves as a marker for the position and structure of the unfolding RNA in the pore. With this design, we provided evidence that the pseudoknot unfolding is a two-step, multistate, metal ion-regulated process depending on the pulling direction. Most notably, unfolding in both directions is rate-limited by the unzipping of the first helix domain (first step), which is Helix-1 in the 5' → 3' direction and Helix-2 in the 3' → 5' direction, suggesting that the initial unfolding step in either pulling direction needs to overcome an energy barrier contributed by the noncanonical triplex base-pairs and coaxial stacking interactions for the tertiary structure stabilization. These findings provide new insights into RNA vectorial unfolding mechanisms, which play an important role in biological functions including frameshifting.

Coarse-Grained HiRE-RNA Model for ab Initio RNA Folding beyond Simple Molecules, Including Noncanonical and Multiple Base Pairings

HiRE-RNA is a coarse-grained model for RNA structure prediction and the dynamical study of RNA folding. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking, we show that noncanonical and multiple base interactions are necessary to capture the full physical behavior of complex RNAs. In this paper, we give a full account of the model and present results on the folding, stability, and free energy surfaces of 16 systems with 12 to 76 nucleotides of increasingly complex architectures, ranging from monomers to dimers, using a total of 850 μs of simulation time.

RNAssess--a web server for quality assessment of RNA 3D structures

Nowadays, various methodologies can be applied to model RNA 3D structure. Thus, the plausible quality assessment of 3D models has a fundamental impact on the progress of structural bioinformatics. Here, we present RNAssess server, a novel tool dedicated to visual evaluation of RNA 3D models in the context of the known reference structure for a wide range of accuracy levels (from atomic to the whole molecule perspective). The proposed server is based on the concept of local neighborhood, defined as a set of atoms observed within a sphere localized around a central atom of a particular residue. A distinctive feature of our server is the ability to perform simultaneous visual analysis of the model-reference structure coherence. RNAssess supports the quality assessment through delivering both static and interactive visualizations that allows an easy identification of native-like models and/or chosen structural regions of the analyzed molecule. A combination of results provided by RNAssess allows us to rank analyzed models. RNAssess offers new route to a fast and efficient 3D model evaluation suitable for the RNA-Puzzles challenge. The proposed automated tool is implemented as a free and open to all users web server with an user-friendly interface and can be accessed at: http://rnassess.cs.put.poznan.pl/

Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.

Conjoined use of EM and NMR in RNA structure refinement

More than 40% of the RNA structures have been determined using nuclear magnetic resonance (NMR) technique. NMR mainly provides local structural information of protons and works most effectively on relatively small biomacromolecules. Hence structural characterization of large RNAs can be difficult for NMR alone. Electron microscopy (EM) provides global shape information of macromolecules at nanometer resolution, which should be complementary to NMR for RNA structure determination. Here we developed a new energy term in Xplor-NIH against the density map obtained by EM. We conjointly used NMR and map restraints for the structure refinement of three RNA systems — U2/U6 small-nuclear RNA, genome-packing motif (Ψ^CD)₂ from Moloney murine leukemia virus, and ribosome-binding element from turnip crinkle virus. In all three systems, we showed that the incorporation of a map restraint, either experimental or generated from known PDB structure, greatly improves structural precision and accuracy. Importantly, our method does not rely on an initial model assembled from RNA duplexes, and allows full torsional freedom for each nucleotide in the torsion angle simulated annealing refinement. As increasing number of macromolecules can be characterized by both NMR and EM, the marriage between the two techniques would enable better characterization of RNA three-dimensional structures.

Accurate SHAPE-directed RNA secondary structure modeling, including pseudoknots

A pseudoknot forms in an RNA when nucleotides in a loop pair with a region outside the helices that close the loop. Pseudoknots occur relatively rarely in RNA but are highly overrepresented in functionally critical motifs in large catalytic RNAs, in riboswitches, and in regulatory elements of viruses. Pseudoknots are usually excluded from RNA structure prediction algorithms. When included, these pairings are difficult to model accurately, especially in large RNAs, because allowing this structure dramatically increases the number of possible incorrect folds and because it is difficult to search the fold space for an optimal structure. We have developed a concise secondary structure modeling approach that combines SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension) experimental chemical probing information and a simple, but robust, energy model for the entropic cost of single pseudoknot formation. Structures are predicted with iterative refinement, using a dynamic programming algorithm. This melded experimental and thermodynamic energy function predicted the secondary structures and the pseudoknots for a set of 21 challenging RNAs of known structure ranging in size from 34 to 530 nt. On average, 93% of known base pairs were predicted, and all pseudoknots in well-folded RNAs were identified.

Molecular dynamics simulation of RNA pseudoknot unfolding pathway

Many biological functions of RNA molecules are related to their pseudoknot structures. It is significant for predicting the structure and function of RNA that learning about the stability and the process of RNA pseudoknot folding and unfolding. The structural features of mouse mammary tumor virus (MMTV) RNA pseudoknot in different ion concentration, the unfolding process of the RNA pseudoknot, and the two hairpin helices that constitute the RNA pseudoknot were studied with all atom molecule dynamics simulation method in this paper. We found that the higher cation concentration can cause structure of the RNA molecules more stable, and ions played an indispensable role in keeping the structure of RNA molecules stable; the unfolding process of hairpin structure was corresponding to the antiprocess of its folding process. The main pathway of pseudoknot unfolding was that the inner base pair opened first, and then, the two helices, which formed the RNA pseudoknot opened decussately, while the folding pathway of the RNA pseudoknot was a helix folding after formation of the other helix. Therefore, the unfolding process of RNA pseudoknot is different from the antiprocess of its folding process, and the unfolding process of each helix in the RNA pseudoknot is similar to the hairpin structure’s unfolding process, which means that both are the unzipping process.

New models of Tetrahymena telomerase RNA from experimentally derived constraints and modeling

The telomerase ribonucleoprotein complex ensures complete replication of eukaryotic chromosomes. Telomerase RNA (TER) provides the template for replicating the G-rich strand of telomeric DNA, provides an anchor site for telomerase-associated proteins, and participates in catalysis through several incompletely characterized mechanisms. A major impediment toward understanding its nontemplating roles is the absence of high content structural information for TER within the telomerase complex. Here, we used selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) to examine the structure of Tetrahymena TER free in solution and bound to tTERT in the minimal telomerase RNP. We discovered a striking difference in the two conformations and established direct evidence for base triples in the tTER pseudoknot. We then used SHAPE data, previously published FRET data, and biochemical inference to model the structure of tTER using discrete molecular dynamics simulations. The resulting tTER structure was docked with a homology model of the Tetrahymena telomerase reverse transcriptase (tTERT) to characterize the conformational changes of tTER telomerase assembly. Free in solution, tTER appears to contain four pairing regions: stems I, II, and IV, which are present in the commonly accepted structure, and stem III, a large paired region that encompasses the template and pseudoknot domains. Our interpretation of the data and subsequent modeling affords a molecular model for telomerase assemblage in which a large stem III of tTER unwinds to allow proper association of the template with the tTERT active site and formation of the pseudoknot. Additionally, analysis of our SHAPE data and previous enzymatic footprinting allow us to propose a model for stem-loop IV function in which tTERT is activated by binding stem IV in the major groove of the helix-capping loop.

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 3' splice site of influenza A segment 7 mRNA can exist in two conformations: a pseudoknot and a hairpin

The 3′ splice site of influenza A segment 7 is used to produce mRNA for the M2 ion-channel protein, which is critical to the formation of viable influenza virions. Native gel analysis, enzymatic/chemical structure probing, and oligonucleotide binding studies of a 63 nt fragment, containing the 3′ splice site, key residues of an SF2/ASF splicing factor binding site, and a polypyrimidine tract, provide evidence for an equilibrium between pseudoknot and hairpin structures. This equilibrium is sensitive to multivalent cations, and can be forced towards the pseudoknot by addition of 5 mM cobalt hexammine. In the two conformations, the splice site and other functional elements exist in very different structural environments. In particular, the splice site is sequestered in the middle of a double helix in the pseudoknot conformation, while in the hairpin it resides in a two-by-two nucleotide internal loop. The results suggest that segment 7 mRNA splicing can be controlled by a conformational switch that exposes or hides the splice site.

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.

A domain-based model for predicting large and complex pseudoknotted structures

Pseudoknotted structures play important structural and functional roles in RNA cellular functions at the level of transcription, splicing and translation. However, the problem of computational prediction for large pseudoknotted folds remains. Here we develop a domain-based method for predicting complex and large pseudoknotted structures from RNA sequences. The model is based on the observation that large RNAs can be separated into different structural domains. The basic idea is to first identify the domains and then predict the structures for each domain. Assembly of the domain structures gives the full structure. The use of the domain-based approach leads to a reduction of computational time by a factor of about ~N ( 2) for an N-nt sequence. As applications of the model, we predict structures for a variety of RNA systems, such as regions in human telomerase RNA (hTR), internal ribosome entry site (IRES) and HIV genome. The lengths of these sequences range from 200-nt to 400-nt. The results show good agreements with the experiments.

A conserved RNA pseudoknot in a putative molecular switch domain of the 3'-untranslated region of coronaviruses is only marginally stable

The 3'-untranslated region (UTR) of the group 2 coronavirus mouse hepatitis virus (MHV) genome contains a predicted bulged stem-loop (designated P0ab), a conserved cis-acting pseudoknot (PK), and a more distal stem-loop (designated P2). Base-pairing to create the pseudoknot-forming stem (P1(pk)) is mutually exclusive with formation of stem P0a at the base of the bulged stem-loop; as a result, the two structures cannot be present simultaneously. Herein, we use thermodynamic methods to evaluate the ability of individual subdomains of the 3' UTR to adopt a pseudoknotted conformation. We find that an RNA capable of forming only the predicted PK (58 nt; 3' nucleotides 241-185) adopts the P2 stem-loop with little evidence for P1(pk) pairing in 0.1 M KCl and the absence of Mg(2+); as Mg(2+) or 1 M KCl is added, a new thermal unfolding transition is induced and assignable to P1(pk) pairing. The P1(pk) helix is only marginally stable, ΔG(25) ≈ 1.2 ± 0.3 kcal/mol (5.0 mM Mg(2+), 100 mM K(+)), and unfolded at 37°C. Similar findings characterize an RNA 5' extended through the P0b helix only (89 nt; 294-185). In contrast, an RNA capable of forming either the P0a helix or the pseudoknot (97 nt; 301-185) forms no P1(pk) helix. Thermal unfolding simulations are fully consistent with these experimental findings. These data reveal that the PK forms weakly and only when the competing double-hairpin structure cannot form; in the UTR RNA, the double hairpin is the predominant conformer under all solution conditions.

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.

RNA and protein 3D structure modeling: similarities and differences

In analogy to proteins, the function of RNA depends on its structure and dynamics, which are encoded in the linear sequence. While there are numerous methods for computational prediction of protein 3D structure from sequence, there have been very few such methods for RNA. This review discusses template-based and template-free approaches for macromolecular structure prediction, with special emphasis on comparison between the already tried-and-tested methods for protein structure modeling and the very recently developed “protein-like” modeling methods for RNA. We highlight analogies between many successful methods for modeling of these two types of biological macromolecules and argue that RNA 3D structure can be modeled using “protein-like” methodology. We also highlight the areas where the differences between RNA and proteins require the development of RNA-specific solutions.

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Assembly and activation of a kinase ribozyme

RNA activities can be regulated by modulating the relative energies of all conformations in a folding landscape; however, it is often unknown precisely how peripheral elements perturb the overall landscape in the absence of discrete alternative folds (inactive ensemble). This work explores the effects of sequence and secondary structure in governing kinase ribozyme activity. Kin.46 catalyzes thiophosphoryl transfer from ATPγS onto the 5' hydroxyl of polynucleotide substrates, and is regulated 10,000-fold by annealing an effector oligonucleotide to form activator helix P4. Transfer kinetics for an extensive series of ribozyme variants identified several dispensable internal single-stranded segments, in addition to a potential pseudoknot at the active site between segments J1/4 and J3/2 that is partially supported by compensatory rescue. Standard allosteric mechanisms were ruled out, such as formation of discrete repressive structures or docking P4 into the rest of the ribozyme via backbone 2' hydroxyls. Instead, P4 serves both to complete an important structural element (100-fold contribution to the reaction relative to a P4-deleted variant) and to mitigate nonspecific, inhibitory effects of the single-stranded tail (an additional 100-fold contribution to the apparent rate constant, k(obs)). Thermodynamic activation parameters ΔH(‡) and ΔS(‡), calculated from the temperature dependence of k(obs), varied with tail length and sequence. Inhibitory effects of the unpaired tail are largely enthalpic for short tails and are both enthalpic and entropic for longer tails. These results refine the structural view of this kinase ribozyme and highlight the importance of nonspecific ensemble effects in conformational regulation by peripheral elements.

Computing the conformational entropy for RNA folds

We develop a polymer physics-based method to compute the conformational entropy for RNA tertiary folds, namely, conformations consisting of multiple helices connected through (cross-linked) loops. The theory is based on a virtual bond conformational model for the nucleotide chain. A key issue in the calculation of the entropy is how to treat the excluded volume interactions. The weak excluded volume interference between the different loops leads to the decomposition of the whole structure into a number of three-body building blocks, each consisting of a loop and two helices connected to the two ends of the loop. The simple construct of the three-body system allows an accurate computation for the conformational entropy for each building block. The assembly of the building blocks gives the entropy of the whole structure. This approach enables treatment of molten globule-like folds (partially unfolded tertiary structures) for RNAs. Extensive tests against experiments and exact computer enumerations indicate that the method can give accurate results for the entropy. The method developed here provides a solid first step toward a systematic development of a theory for the entropy and free energy landscape for complex tertiary folds for RNAs and proteins.