3D maps of RNA interhelical junctions

Challenges, advances, and opportunities in RNA structural biology by Cryo-EM

RNAs are remarkably versatile molecules that can fold into intricate three-dimensional (3D) structures to perform diverse cellular and viral functions. Despite their biological importance, relatively few RNA 3D structures have been solved, and our understanding of RNA structure-function relationships remains in its infancy. This limitation partly arises from challenges posed by RNA's complex conformational landscape, characterized by structural flexibility, formation of multiple states, and a propensity to misfold. Recently, cryo-electron microscopy (cryo-EM) has emerged as a powerful tool for the visualization of conformationally dynamic RNA-only 3D structures. However, RNA's characteristics continue to pose challenges. We discuss experimental methods developed to overcome these hurdles, including the engineering of modular modifications that facilitate the visualization of small RNAs, improve particle alignment, and validate structural models.

Comprehensive Comparison and Critical Assessment of RNA-Specific Force Fields

Molecular dynamics simulations play a pivotal role in elucidating the dynamic behaviors of RNA structures, offering a valuable complement to traditional methods such as nuclear magnetic resonance or X-ray. Despite this, the current precision of RNA force fields lags behind that of protein force fields. In this work, we systematically compared the performance of four RNA force fields (ff99bsc0χOL3, AMBERDES, ff99OL3_CMAP1, AMBERMaxEnt) across diverse RNA structures. Our findings highlight significant challenges in maintaining stability, particularly with regard to cross-strand and cross-loop hydrogen bonds. Furthermore, we observed the limitations in accurately describing the conformations of nonhelical structural motif, terminal nucleotides, and also base pairing and base stacking interactions by the tested RNA force fields. The identified deficiencies in existing RNA force fields provide valuable insights for subsequent force field development. Concurrently, these findings offer recommendations for selecting appropriate force fields in RNA simulations.

Kinetic Resolution of the Atomic 3D Structures Formed by Ground and Excited Conformational States in an RNA Dynamic Ensemble

Knowing the 3D structures formed by the various conformations populating the RNA free-energy landscape, their relative abundance, and kinetic interconversion rates is required to obtain a quantitative and predictive understanding of how RNAs fold and function at the atomic level. While methods integrating ensemble-averaged experimental data with computational modeling are helping define the most abundant conformations in RNA ensembles, elucidating their kinetic rates of interconversion and determining the 3D structures of sparsely populated short-lived RNA excited conformational states (ESs) remains challenging. Here, we developed an approach integrating Rosetta-FARFAR RNA structure prediction with NMR residual dipolar couplings and relaxation dispersion that simultaneously determines the 3D structures formed by the ground-state (GS) and ES subensembles, their relative abundance, and kinetic rates of interconversion. The approach is demonstrated on HIV-1 TAR, whose six-nucleotide apical loop was previously shown to form a sparsely populated (∼13%) short-lived (lifetime ∼ 45 μs) ES. In the GS, the apical loop forms a broad distribution of open conformations interconverting on the pico-to-nanosecond time scale. Most residues are unpaired and preorganized to bind the Tat-superelongation protein complex. The apical loop zips up in the ES, forming a narrow distribution of closed conformations, which sequester critical residues required for protein recognition. Our work introduces an approach for determining the 3D ensemble models formed by sparsely populated RNA conformational states, provides a rare atomic view of an RNA ES, and kinetically resolves the atomic 3D structures of RNA conformational substates, interchanging on time scales spanning 6 orders of magnitude, from picoseconds to microseconds.

Spherical frame projections for visualising joint range of motion, and a complementary method to capture mobility data

Quantifying joint range of motion (RoM), the reachable poses at a joint, has many applications in research and clinical care. Joint RoM measurements can be used to investigate the link between form and function in extant and extinct animals, to diagnose musculoskeletal disorders and injuries or monitor rehabilitation progress. However, it is difficult to visually demonstrate how the rotations of the joint axes interact to produce joint positions. Here, we introduce the spherical frame projection (SFP), which is a novel 3D visualisation technique, paired with a complementary data collection approach. SFP visualisations are intuitive to interpret in relation to the joint anatomy because they 'trace' the motion of the coordinate system of the distal bone at a joint relative to the proximal bone. Furthermore, SFP visualisations incorporate the interactions of degrees of freedom, which is imperative to capture the full joint RoM. For the collection of such joint RoM data, we designed a rig using conventional motion capture systems, including live audio-visual feedback on torques and sampled poses. Thus, we propose that our visualisation and data collection approach can be adapted for wide use in the study of joint function.

RNAloops: a database of RNA multiloops

MOTIVATION

Knowledge of the 3D structure of RNA supports discovering its functions and is crucial for designing drugs and modern therapeutic solutions. Thus, much attention is devoted to experimental determination and computational prediction targeting the global fold of RNA and its local substructures. The latter include multi-branched loops-functionally significant elements that highly affect the spatial shape of the entire molecule. Unfortunately, their computational modeling constitutes a weak point of structural bioinformatics. A remedy for this is in collecting these motifs and analyzing their features.

RESULTS

RNAloops is a self-updating database that stores multi-branched loops identified in the PDB-deposited RNA structures. A description of each loop includes angular data-planar and Euler angles computed between pairs of adjacent helices to allow studying their mutual arrangement in space. The system enables search and analysis of multiloops, presents their structure details numerically and visually, and computes data statistics.

AVAILABILITY AND IMPLEMENTATION

RNAloops is freely accessible at https://rnaloops.cs.put.poznan.pl.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Refining the RNA Force Field with Small-Angle X-ray Scattering of Helix-Junction-Helix RNA

The growing recognition of the functional and therapeutic roles played by RNA and the difficulties in gaining atomic-level insights by experiments are paving the way for all-atom simulations of RNA. One of the main impediments to the use of all-atom simulations is the imbalance between the energy terms of the RNA force fields. Through exhaustive sampling of an RNA helix-junction-helix (HJH) model using enhanced sampling, we critically assessed the select Amber force fields against small-angle X-ray scattering (SAXS) experiments. The tested AMBER99SB, DES-AMBER, and CUFIX force fields show deviations from measured profiles. First, we identified parameters leading to inconsistencies. Then, as a way to balance the forces governing RNA folding, we adopted strategies to refine hydrogen bonding, backbone, and base-stacking parameters. We validated the modified force field (HB-CUFIX) against SAXS data of the HJH model in different ionic strengths. Moreover, we tested a set of independent RNA systems to cross-validate the force field. Overall, HB-CUFIX demonstrates improved performance in studying thermodynamics and structural properties of realistic RNA motifs.

Rapid and accurate determination of atomistic RNA dynamic ensemble models using NMR and structure prediction

Biomolecules form dynamic ensembles of many inter-converting conformations which are key for understanding how they fold and function. However, determining ensembles is challenging because the information required to specify atomic structures for thousands of conformations far exceeds that of experimental measurements. We addressed this data gap and dramatically simplified and accelerated RNA ensemble determination by using structure prediction tools that leverage the growing database of RNA structures to generate a conformation library. Refinement of this library with NMR residual dipolar couplings provided an atomistic ensemble model for HIV-1 TAR, and the model accuracy was independently supported by comparisons to quantum-mechanical calculations of NMR chemical shifts, comparison to a crystal structure of a substate, and through designed ensemble redistribution via atomic mutagenesis. Applications to TAR bulge variants and more complex tertiary RNAs support the generality of this approach and the potential to make the determination of atomic-resolution RNA ensembles routine.

Determining dynamic ensembles of biomolecules is still challenging. Here the authors present an approach for rapid RNA ensemble determination that combines RNA structure prediction tools and NMR residual dipolar coupling data and use it to determine atomistic ensemble models for a variety of RNAs.

DNA mismatches reveal conformational penalties in protein-DNA recognition

Transcription factors recognize specific genomic sequences to regulate complex gene-expression programs. Although it is well-established that transcription factors bind to specific DNA sequences using a combination of base readout and shape recognition, some fundamental aspects of protein-DNA binding remain poorly understood1,2. Many DNA-binding proteins induce changes in the structure of the DNA outside the intrinsic B-DNA envelope. However, how the energetic cost that is associated with distorting the DNA contributes to recognition has proven difficult to study, because the distorted DNA exists in low abundance in the unbound ensemble3-9. Here we use a high-throughput assay that we term SaMBA (saturation mismatch-binding assay) to investigate the role of DNA conformational penalties in transcription factor-DNA recognition. In SaMBA, mismatched base pairs are introduced to pre-induce structural distortions in the DNA that are much larger than those induced by changes in the Watson-Crick sequence. Notably, approximately 10% of mismatches increased transcription factor binding, and for each of the 22 transcription factors that were examined, at least one mismatch was found that increased the binding affinity. Mismatches also converted non-specific sites into high-affinity sites, and high-affinity sites into 'super sites' that exhibit stronger affinity than any known canonical binding site. Determination of high-resolution X-ray structures, combined with nuclear magnetic resonance measurements and structural analyses, showed that many of the DNA mismatches that increase binding induce distortions that are similar to those induced by protein binding-thus prepaying some of the energetic cost incurred from deforming the DNA. Our work indicates that conformational penalties are a major determinant of protein-DNA recognition, and reveals mechanisms by which mismatches can recruit transcription factors and thus modulate replication and repair activities in the cell10,11.

A coordinate-system-independent method for comparing joint rotational mobilities

Three-dimensional studies of range of motion currently plot joint poses in a 'Euler space' whose axes are angles measured in the joint's three rotational degrees of freedom. Researchers then compute the volume of a pose cloud to measure rotational mobility. However, pairs of poses that are equally different from one another in orientation are not always plotted equally far apart in Euler space. This distortion causes a single joint's mobility to change when measured based on different joint coordinate systems and precludes fair comparison among joints. Here, we present two alternative spaces inspired by a 16th century map projection - cosine-corrected and sine-corrected Euler spaces - that allow coordinate-system-independent comparison of joint rotational mobility. When tested with data from a bird hip joint, cosine-corrected Euler space demonstrated a 10-fold reduction in variation among mobilities measured from three joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function.

A multi-axial RNA joint with a large range of motion promotes sampling of an active ribozyme conformation

Investigating the dynamics of structural elements in functional RNAs is important to better understand their mechanism and for engineering RNAs with novel functions. Previously, we performed rational engineering studies with the Varkud satellite (VS) ribozyme and switched its specificity toward non-natural hairpin substrates through modification of a critical kissing-loop interaction (KLI). We identified functional VS ribozyme variants with surrogate KLIs (ribosomal RNA L88/L22 and human immunodeficiency virus-1 TAR/TAR*), but they displayed ∼100-fold lower cleavage activity. Here, we characterized the dynamics of KLIs to correlate dynamic properties with function and improve the activity of designer ribozymes. Using temperature replica exchange molecular dynamics, we determined that the natural KLI in the VS ribozyme supports conformational sampling of its closed and active state, whereas the surrogate KLIs display more restricted motions. Based on in vitro selection, the cleavage activity of a VS ribozyme variant with the TAR/TAR* KLI could be markedly improved by partly destabilizing the KLI but increasing conformation sampling. We formulated a mechanistic model for substrate binding in which the KLI dynamics contribute to formation of the active site. Our model supports the modular nature of RNA in which subdomain structure and dynamics contribute to define the thermodynamics and kinetics relevant to RNA function.

Characterizing micro-to-millisecond chemical exchange in nucleic acids using off-resonance R1ρ relaxation dispersion

This review describes off-resonance R1ρ relaxation dispersion NMR methods for characterizing microsecond-to-millisecond chemical exchange in uniformly 13C/15N labeled nucleic acids in solution. The review opens with a historical account of key developments that formed the basis for modern R1ρ techniques used to study chemical exchange in biomolecules. A vector model is then used to describe the R1ρ relaxation dispersion experiment, and how the exchange contribution to relaxation varies with the amplitude and frequency offset of an applied spin-locking field, as well as the population, exchange rate, and differences in chemical shifts of two exchanging species. Mathematical treatment of chemical exchange based on the Bloch-McConnell equations is then presented and used to examine relaxation dispersion profiles for more complex exchange scenarios including three-state exchange. Pulse sequences that employ selective Hartmann-Hahn cross-polarization transfers to excite individual 13C or 15N spins are then described for measuring off-resonance R1ρ(13C) and R1ρ(15N) in uniformly 13C/15N labeled DNA and RNA samples prepared using commercially available 13C/15N labeled nucleotide triphosphates. Approaches for analyzing R1ρ data measured at a single static magnetic field to extract a full set of exchange parameters are then presented that rely on numerical integration of the Bloch-McConnell equations or the use of algebraic expressions. Methods for determining structures of nucleic acid excited states are then reviewed that rely on mutations and chemical modifications to bias conformational equilibria, as well as structure-based approaches to calculate chemical shifts. Applications of the methodology to the study of DNA and RNA conformational dynamics are reviewed and the biological significance of the exchange processes is briefly discussed.

Computational Probing of Watson-Crick/Hoogsteen Breathing in a DNA Duplex Containing N1-Methylated Adenine

DNA breathing is a local conformational fluctuation spontaneously occurring in double-stranded DNAs. In particular, the possibility of individual base pairs (bps) in duplex DNA to flip between alternate bp modes, i.e., Watson-Crick (WC)-like and Hoogsteen (HG)-like, at relevant time scales has impacted DNA research fields for many years. In this study, to computationally probe effects of chemical modification on the DNA breathing, we present a free energy landscape of spontaneous thermal transitions between WC and HG bps in a free DNA duplex containing N1-methylated adenine (m1A). For the current free energy computation, a variant of well-tempered metadynamics simulation was extensively performed for a total of 40 μs to produce free energy surfaces. The free energy profile indicated that, upon the chemical modification of adenine, the HG bp (m1A·T) was located in the most favorable conformation (96.7%); however, the canonical WC bp (m1A·T) was distorted into two WC-like bps of WC* (2.8%) and WC** (0.5%). The conformational exchange between these two minor WC-like bps occurs with the first hundred nanoseconds. The transition between WC-like and HG bp features multiple transition pathways displaying various extents of base flipping in combination with glycosidic rotation. Analysis of the simulated ensemble showed that the m1A-induced changes of the backbone and sugar pucker were in a reasonable agreement with previous results inferred from NMR experiments. Also, this study revealed that the formation of the stable HG bp upon the mutation alters the characteristics of dynamic fluctuations of the neighboring WC residues of m1A. We expect this simulation approach to be a robust computational scheme to complement and guide future high-resolution experiments on many outstanding issues of duplex DNA breathing.

Increasing the length of poly-pyrimidine bulges broadens RNA conformational ensembles with minimal impact on stacking energetics

Helical elements separated by bulges frequently undergo transitions between unstacked and coaxially stacked conformations during the folding and function of noncoding RNAs. Here, we examine the dynamic properties of poly-pyrimidine bulges of varying length (n = 1-4, 7) across a range of Mg²⁺ concentrations using HIV-1 TAR RNA as a model system and solution NMR spectroscopy. In the absence of Mg²⁺, helices linked by bulges with n ≥ 3 residues adopt predominantly unstacked conformations (stacked population <15%), whereas one-bulge and two-bulge motifs adopt predominantly stacked conformations (stacked population >74%). In the presence of 3 mM Mg²⁺, the helices predominantly coaxially stack (stacked population >84%), regardless of bulge length, and the midpoint for the Mg²⁺-dependent stacking transition is within threefold regardless of bulge length. In the absence of Mg²⁺, the difference between free energy of interhelical coaxial stacking across the bulge variants is estimated to be ∼2.9 kcal/mol, based on an NMR chemical shift mapping with stacking being more energetically disfavored for the longer bulges. This difference decreases to ∼0.4 kcal/mol in the presence of Mg²⁺ NMR RDCs and resonance intensity data show increased dynamics in the stacked state with increasing bulge length in the presence of Mg²⁺ We propose that Mg²⁺ helps to neutralize the growing electrostatic repulsion in the stacked state with increasing bulge length thereby increasing the number of coaxial conformations that are sampled. Energetically compensated interhelical stacking dynamics may help to maximize the conformational adaptability of RNA and allow a wide range of conformations to be optimally stabilized by proteins and ligands.

High-performance virtual screening by targeting a high-resolution RNA dynamic ensemble

Dynamic ensembles hold great promise in advancing RNA-targeted drug discovery. Here we subjected the transactivation response element (TAR) RNA from human immunodeficiency virus type-1 to experimental high-throughput screening against ~100,000 drug-like small molecules. Results were augmented with 170 known TAR-binding molecules and used to generate sublibraries optimized for evaluating enrichment when virtually screening a dynamic ensemble of TAR determined by combining NMR spectroscopy data and molecular dynamics simulations. Ensemble-based virtual screening scores molecules with an area under the receiver operator characteristic curve of ~0.85-0.94 and with ~40-75% of all hits falling within the top 2% of scored molecules. The enrichment decreased significantly for ensembles generated from the same molecular dynamics simulations without input NMR data and for other control ensembles. The results demonstrate that experimentally determined RNA ensembles can significantly enrich libraries with true hits and that the degree of enrichment is dependent on the accuracy of the ensemble.

Determination of helix orientations in a flexible DNA by multi-frequency EPR spectroscopy

Distance measurements are performed between a pair of spin labels attached to nucleic acids using Pulsed Electron-Electron Double Resonance (PELDOR, also called DEER) spectroscopy which is a complementary tool to other structure determination methods in structural biology. The rigid spin label Ç, when incorporated pairwise into two helical parts of a nucleic acid molecule, allows the determination of both the mutual orientation and the distance between those labels, since Ç moves rigidly with the helix to which it is attached. We have developed a two-step protocol to investigate the conformational flexibility of flexible nucleic acid molecules by multi-frequency PELDOR. In the first step, a library with a broad collection of conformers, which are in agreement with topological constraints, NMR restraints and distances derived from PELDOR, was created. In the second step, a weighted structural ensemble of these conformers was chosen, such that it fits the multi-frequency PELDOR time traces of all doubly Ç-labelled samples simultaneously. This ensemble reflects the global structure and the conformational flexibility of the two-way DNA junction. We demonstrate this approach on a flexible bent DNA molecule, consisting of two short helical parts with a five adenine bulge at the center. The kink and twist motions between both helical parts were quantitatively determined and showed high flexibility, in agreement with a Förster Resonance Energy Transfer (FRET) study on a similar bent DNA motif. The approach presented here should be useful to describe the relative orientation of helical motifs and the conformational flexibility of nucleic acid structures, both alone and in complexes with proteins and other molecules.

Insights into Watson-Crick/Hoogsteen breathing dynamics and damage repair from the solution structure and dynamic ensemble of DNA duplexes containing m1A

In the canonical DNA double helix, Watson-Crick (WC) base pairs (bps) exist in dynamic equilibrium with sparsely populated (∼0.02-0.4%) and short-lived (lifetimes ∼0.2-2.5 ms) Hoogsteen (HG) bps. To gain insights into transient HG bps, we used solution-state nuclear magnetic resonance spectroscopy, including measurements of residual dipolar couplings and molecular dynamics simulations, to examine how a single HG bp trapped using the N1-methylated adenine (m1A) lesion affects the structural and dynamic properties of two duplexes. The solution structure and dynamic ensembles of the duplexes reveals that in both cases, m1A forms a m1A•T HG bp, which is accompanied by local and global structural and dynamic perturbations in the double helix. These include a bias toward the BI backbone conformation; sugar repuckering, major-groove directed kinking (∼9°); and local melting of neighboring WC bps. These results provide atomic insights into WC/HG breathing dynamics in unmodified DNA duplexes as well as identify structural and dynamic signatures that could play roles in m1A recognition and repair.

Inter-helical conformational preferences of HIV-1 TAR-RNA from maximum occurrence analysis of NMR data and molecular dynamics simulations

Detecting conformational heterogeneity in biological macromolecules is a key for the understanding of their biological function. We here provide a comparison between two independent approaches to assess conformational heterogeneity: molecular dynamics simulations, performed without inclusion of any experimental data, and maximum occurrence (MaxOcc) distribution over the topologically available conformational space. The latter only reflects the extent of the averaging and identifies regions which are most compliant with the experimentally measured NMR Residual Dipolar Couplings (RDCs). The analysis was performed for the HIV-1 TAR RNA, consisting of two helical domains connected by a flexible bulge junction, for which four sets of RDCs were available as well as an 8.2 μs all-atom molecular dynamics simulation. A sample and select approach was previously applied to extract from the molecular dynamics trajectory conformational ensembles in agreement with the four sets of RDCs. The MaxOcc analysis performed here identifies the most likely sampled region in the conformational space of the system which, strikingly, overlaps well with the structures independently sampled in the molecular dynamics calculations and even better with the RDC selected ensemble.

Characterizing the bending and flexibility induced by bulges in DNA duplexes

Advances in DNA nanotechnology have stimulated the search for simple motifs that can be used to control the properties of DNA nanostructures. One such motif, which has been used extensively in structures such as polyhedral cages, two-dimensional arrays, and ribbons, is a bulged duplex, that is, two helical segments that connect at a bulge loop. We use a coarse-grained model of DNA to characterize such bulged duplexes. We find that this motif can adopt structures belonging to two main classes: one where the stacking of the helices at the center of the system is preserved, the geometry is roughly straight, and the bulge is on one side of the duplex and the other where the stacking at the center is broken, thus allowing this junction to act as a hinge and increasing flexibility. Small loops favor states where stacking at the center of the duplex is preserved, with loop bases either flipped out or incorporated into the duplex. Duplexes with longer loops show more of a tendency to unstack at the bulge and adopt an open structure. The unstacking probability, however, is highest for loops of intermediate lengths, when the rigidity of single-stranded DNA is significant and the loop resists compression. The properties of this basic structural motif clearly correlate with the structural behavior of certain nano-scale objects, where the enhanced flexibility associated with larger bulges has been used to tune the self-assembly product as well as the detailed geometry of the resulting nanostructures. We further demonstrate the role of bulges in determining the structure of a "Z-tile," a basic building block for nanostructures.

Structural and Dynamic Basis for Low-Affinity, High-Selectivity Binding of L-Glutamine by the Glutamine Riboswitch

Naturally occurring L-glutamine riboswitches occur in cyanobacteria and marine metagenomes, where they reside upstream of genes involved in nitrogen metabolism. By combining X-ray, NMR, and MD, we characterized an L-glutamine-dependent conformational transition in the Synechococcus elongatus glutamine riboswitch from tuning fork to L-shaped alignment of stem segments. This transition generates an open ligand-binding pocket with L-glutamine selectivity enforced by Mg(2+)-mediated intermolecular interactions. The transition also stabilizes the P1 helix through a long-range "linchpin" Watson-Crick G-C pair-capping interaction, while melting a short helix below P1 potentially capable of modulating downstream readout. NMR data establish that the ligand-free glutamine riboswitch in Mg(2+) solution exists in a slow equilibrium between flexible tuning fork and a minor conformation, similar, but not identical, to the L-shaped bound conformation. We propose that an open ligand-binding pocket combined with a high conformational penalty for forming the ligand-bound state provide mechanisms for reducing binding affinity while retaining high selectivity.

Secondary structure encodes a cooperative tertiary folding funnel in the Azoarcus ribozyme

A requirement for specific RNA folding is that the free-energy landscape discriminate against non-native folds. While tertiary interactions are critical for stabilizing the native fold, they are relatively non-specific, suggesting additional mechanisms contribute to tertiary folding specificity. In this study, we use coarse-grained molecular dynamics simulations to explore how secondary structure shapes the tertiary free-energy landscape of the Azoarcus ribozyme. We show that steric and connectivity constraints posed by secondary structure strongly limit the accessible conformational space of the ribozyme, and that these so-called topological constraints in turn pose strong free-energy penalties on forming different tertiary contacts. Notably, native A-minor and base-triple interactions form with low conformational free energy, while non-native tetraloop/tetraloop–receptor interactions are penalized by high conformational free energies. Topological constraints also give rise to strong cooperativity between distal tertiary interactions, quantitatively matching prior experimental measurements. The specificity of the folding landscape is further enhanced as tertiary contacts place additional constraints on the conformational space, progressively funneling the molecule to the native state. These results indicate that secondary structure assists the ribozyme in navigating the otherwise rugged tertiary folding landscape, and further emphasize topological constraints as a key force in RNA folding.

Unveiling Inherent Degeneracies in Determining Population-Weighted Ensembles of Interdomain Orientational Distributions Using NMR Residual Dipolar Couplings: Application to RNA Helix Junction Helix Motifs

A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general approach for exploring degeneracies in ensemble determination for different types of experimental data.

Slowdown of Interhelical Motions Induces a Glass Transition in RNA

RNA function depends crucially on the details of its dynamics. The simplest RNA dynamical unit is a two-way interhelical junction. Here, for such a unit--the transactivation response RNA element--we present evidence from molecular dynamics simulations, supported by nuclear magnetic resonance relaxation experiments, for a dynamical transition near 230 K. This glass transition arises from the freezing out of collective interhelical motional modes. The motions, resolved with site-specificity, are dynamically heterogeneous and exhibit non-Arrhenius relaxation. The microscopic origin of the glass transition is a low-dimensional, slow manifold consisting largely of the Euler angles describing interhelical reorientation. Principal component analysis over a range of temperatures covering the glass transition shows that the abrupt slowdown of motion finds its explanation in a localization transition that traps probability density into several disconnected conformational pools over the low-dimensional energy landscape. Upon temperature increase, the probability density pools then flood a larger basin, akin to a lakes-to-sea transition. Simulations on transactivation response RNA are also used to backcalculate inelastic neutron scattering data that match previous inelastic neutron scattering measurements on larger and more complex RNA structures and which, upon normalization, give temperature-dependent fluctuation profiles that overlap onto a glass transition curve that is quasi-universal over a range of systems and techniques.

Predicting RNA 3D structure using a coarse-grain helix-centered model

A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a fine-grain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.

New insights into Hoogsteen base pairs in DNA duplexes from a structure-based survey

Hoogsteen (HG) base pairs (bps) provide an alternative pairing geometry to Watson-Crick (WC) bps and can play unique functional roles in duplex DNA. Here, we use structural features unique to HG bps (syn purine base, HG hydrogen bonds and constricted C1'-C1' distance across the bp) to search for HG bps in X-ray structures of DNA duplexes in the Protein Data Bank. The survey identifies 106 A•T and 34 G•C HG bps in DNA duplexes, many of which are undocumented in the literature. It also uncovers HG-like bps with syn purines lacking HG hydrogen bonds or constricted C1'-C1' distances that are analogous to conformations that have been proposed to populate the WC-to-HG transition pathway. The survey reveals HG preferences similar to those observed for transient HG bps in solution by nuclear magnetic resonance, including stronger preferences for A•T versus G•C bps, TA versus GG steps, and also suggests enrichment at terminal ends with a preference for 5'-purine. HG bps induce small local perturbations in neighboring bps and, surprisingly, a small but significant degree of DNA bending (∼14°) directed toward the major groove. The survey provides insights into the preferences and structural consequences of HG bps in duplex DNA.

Noncanonical secondary structure stabilizes mitochondrial tRNA(Ser(UCN)) by reducing the entropic cost of tertiary folding

Mammalian mitochondrial tRNA(Ser(UCN)) (mt-tRNA(Ser)) and pyrrolysine tRNA (tRNA(Pyl)) fold to near-canonical three-dimensional structures despite having noncanonical secondary structures with shortened interhelical loops that disrupt the conserved tRNA tertiary interaction network. How these noncanonical tRNAs compensate for their loss of tertiary interactions remains unclear. Furthermore, in human mt-tRNA(Ser), lengthening the variable loop by the 7472insC mutation reduces mt-tRNA(Ser) concentration in vivo through poorly understood mechanisms and is strongly associated with diseases such as deafness and epilepsy. Using simulations of the TOPRNA coarse-grained model, we show that increased topological constraints encoded by the unique secondary structure of wild-type mt-tRNA(Ser) decrease the entropic cost of folding by ∼2.5 kcal/mol compared to canonical tRNA, offsetting its loss of tertiary interactions. Further simulations show that the pathogenic 7472insC mutation disrupts topological constraints and hence destabilizes the mutant mt-tRNA(Ser) by ∼0.6 kcal/mol relative to wild-type. UV melting experiments confirm that insertion mutations lower mt-tRNA(Ser) melting temperature by 6-9 °C and increase the folding free energy by 0.8-1.7 kcal/mol in a largely sequence- and salt-independent manner, in quantitative agreement with our simulation predictions. Our results show that topological constraints provide a quantitative framework for describing key aspects of RNA folding behavior and also provide the first evidence of a pathogenic mutation that is due to disruption of topological constraints.

From static to dynamic: the need for structural ensembles and a predictive model of RNA folding and function

To understand RNA, it is necessary to move beyond a descriptive categorization towards quantitative predictions of its molecular conformations and functional behavior. An incisive approach to understanding the function and folding of biological RNA systems involves characterizing small, simple components that are largely responsible for the behavior of complex systems including helix-junction-helix elements and tertiary motifs. State-of-the-art methods have permitted unprecedented insight into the conformational ensembles of these elements revealing, for example, that conformations of helix-junction-helix elements are confined to a small region of the ensemble, that this region is highly dependent on the junction's topology, and that the correct alignment of tertiary motifs may be a rare conformation on the overall folding landscape. Further characterization of RNA components and continued development of experimental and computational methods with the goal of quantitatively predicting RNA folding and functional behavior will be critical to understanding biological RNA systems.

Efficient in silico exploration of RNA interhelical conformations using Euler angles and WExplore

HIV-1 TAR RNA is a two-helix bulge motif that plays a critical role in HIV viral replication and is an important drug target. However, efforts at designing TAR inhibitors have been challenged by its high degree of structural flexibility, which includes slow large-amplitude reorientations of its helices with respect to one another. Here, we use the recently introduced algorithm WExplore in combination with Euler angles to achieve unprecedented sampling of the TAR conformational ensemble. Our ensemble achieves similar agreement with experimental NMR data when compared with previous TAR computational studies, and is generated at a fraction of the computational cost. It clearly emerges from configuration space network analysis that the intermittent formation of the A22-U40 base pair acts as a reversible switch that enables sampling of interhelical conformations that would otherwise be topologically disallowed. We find that most previously determined ligand-bound structures are found in similar location in the network, and we use a sample-and-select approach to guide the construction of a set of novel conformations which can serve as the basis for future drug development efforts. Collectively, our findings demonstrate the utility of WExplore in combination with suitable order parameters as a method for exploring RNA conformational space.

Insights into domain-domain motions in proteins and RNA from solution NMR

Many multidomain proteins and ribonucleic acids consist of domains that autonomously fold and that are linked together by flexible junctions. This architectural design allows domains to sample a wide range of positions with respect to one another, yet do so in a way that retains structural specificity, since the number of sampled conformations remains extremely small compared to the total conformations that would be sampled if the domains were connected by an infinitely long linker. This “tuned” flexibility in interdomain conformation is in turn used in many biochemical processes.

There is great interest in characterizing the dynamic properties of multidomain systems, and moving beyond conventional descriptions in terms of static structures, toward the characterization of population-weighted ensembles describing a distribution of many conformations sampled in solution. There is also great interest in understanding the design principles and underlying physical and chemical interactions that specify the nature of interdomain flexibility. NMR spectroscopy is one of the most powerful techniques for characterizing motions in complex biomolecules and has contributed greatly toward our basic understanding of dynamics in proteins and nucleic acids and its role in folding, recognition, and signaling.

Here, we review methods that have been developed in our laboratories to address these challenges. Our approaches are based on the ability of one domain of the molecule to self-align in a magnetic field, or to dominate the overall orientation of the molecule, so that the conformational freedom of other domains can be assessed by their degree of alignment induced by the aligned part. In turn, this self-alignment ability can be intrinsic or can be caused by tagging appropriate constructs to the molecule of interest. In general, self-alignment is due to magnetic susceptibility anisotropy. Nucleic acids with elongated helices have this feature, as well as several paramagnetic metal centers that can be found in, or attached to, a protein domain.

Recognition of nucleic acid junctions using triptycene-based molecules

The modulation of nucleic acids by small molecules is an essential process across the kingdoms of life. Targeting nucleic acids with small molecules represents a significant challenge at the forefront of chemical biology. Nucleic acid junctions are ubiquitous structural motifs in nature and in designed materials. Herein, we describe a new class of structure-specific nucleic acid junction stabilizers based on a triptycene scaffold. Triptycenes provide significant stabilization of DNA and RNA three-way junctions, providing a new scaffold for the development of nucleic acid junction binders with enhanced recognition properties. Additionally, we report cytotoxicity and cell uptake data in two human ovarian carcinoma cell lines.

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA's allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA's helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA's different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.

Structural dynamics of a single-stranded RNA-helix junction using NMR

Many regulatory RNAs contain long single strands (ssRNA) that adjoin secondary structural elements. Here, we use NMR spectroscopy to study the dynamic properties of a 12-nucleotide (nt) ssRNA tail derived from the prequeuosine riboswitch linked to the 3' end of a 48-nt hairpin. Analysis of chemical shifts, NOE connectivity, (13)C spin relaxation, and residual dipolar coupling data suggests that the first two residues (A25 and U26) in the ssRNA tail stack onto the adjacent helix and assume an ordered conformation. The following U26-A27 step marks the beginning of an A6-tract and forms an acute pivot point for substantial motions within the tail, which increase toward the terminal end. Despite substantial internal motions, the ssRNA tail adopts, on average, an A-form helical conformation that is coaxial with the helix. Our results reveal a surprising degree of structural and dynamic complexity at the ssRNA-helix junction, which involves a fine balance between order and disorder that may facilitate efficient pseudoknot formation on ligand recognition.

Measuring similarity between dynamic ensembles of biomolecules

We present a simple and general approach termed REsemble for quantifying population overlap and structural similarity between ensembles. This approach captures improvements in the quality of ensembles determined using increasing input experimental data--improvements that go undetected when conventional methods for comparing ensembles are used--and reveals unexpected similarities between RNA ensembles determined using NMR and molecular dynamics simulations.

From a structural average to the conformational ensemble of a DNA bulge

Direct experimental measurements of conformational ensembles are critical for understanding macromolecular function, but traditional biophysical methods do not directly report the solution ensemble of a macromolecule. Small-angle X-ray scattering interferometry has the potential to overcome this limitation by providing the instantaneous distance distribution between pairs of gold-nanocrystal probes conjugated to a macromolecule in solution. Our X-ray interferometry experiments reveal an increasing bend angle of DNA duplexes with bulges of one, three, and five adenosine residues, consistent with previous FRET measurements, and further reveal an increasingly broad conformational ensemble with increasing bulge length. The distance distributions for the AAA bulge duplex (3A-DNA) with six different Au-Au pairs provide strong evidence against a simple elastic model in which fluctuations occur about a single conformational state. Instead, the measured distance distributions suggest a 3A-DNA ensemble with multiple conformational states predominantly across a region of conformational space with bend angles between 24 and 85 degrees and characteristic bend directions and helical twists and displacements. Additional X-ray interferometry experiments revealed perturbations to the ensemble from changes in ionic conditions and the bulge sequence, effects that can be understood in terms of electrostatic and stacking contributions to the ensemble and that demonstrate the sensitivity of X-ray interferometry. Combining X-ray interferometry ensemble data with molecular dynamics simulations gave atomic-level models of representative conformational states and of the molecular interactions that may shape the ensemble, and fluorescence measurements with 2-aminopurine-substituted 3A-DNA provided initial tests of these atomistic models. More generally, X-ray interferometry will provide powerful benchmarks for testing and developing computational methods.

Coarse grained models reveal essential contributions of topological constraints to the conformational free energy of RNA bulges

Recent studies have shown that simple stereochemical constraints encoded at the RNA secondary structure level significantly restrict the orientation of RNA helices across two-way junctions and yield physically reasonable distributions of RNA 3D conformations. Here we develop a new coarse-grain model, TOPRNA, that is optimized for exploring detailed aspects of these topological constraints in complex RNA systems. Unlike prior models, TOPRNA effectively treats RNAs as collections of semirigid helices linked by freely rotatable single strands, allowing us to isolate the effects of secondary structure connectivity and sterics on 3D structure. Simulations of bulge junctions show that TOPRNA captures new aspects of topological constraints, including variations arising from deviations in local A-form structure, translational displacements of the helices, and stereochemical constraints imposed by bulge-linker nucleotides. Notably, these aspects of topological constraints define free energy landscapes that coincide with the distribution of bulge conformations in the PDB. Our simulations also quantitatively reproduce NMR RDC measurements made on HIV-1 TAR at low salt concentrations, although not for different TAR mutants or at high salt concentrations. Our results confirm that topological constraints are an important determinant of bulge conformation and dynamics and demonstrate the utility of TOPRNA for studying the topological constraints of complex RNAs.

Graph-based sampling for approximating global helical topologies of RNA

A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.

WExplore: hierarchical exploration of high-dimensional spaces using the weighted ensemble algorithm

As most relevant motions in biomolecular systems are inaccessible to conventional molecular dynamics simulations, algorithms that enhance sampling of rare events are indispensable. Increasing interest in intrinsically disordered systems and the desire to target ensembles of protein conformations (rather than single structures) in drug development motivate the need for enhanced sampling algorithms that are not limited to "two-basin" problems, and can efficiently determine structural ensembles. For systems that are not well-studied, this must often be done with little or no information about the dynamics of interest. Here we present a novel strategy to determine structural ensembles that uses dynamically defined sampling regions that are organized in a hierarchical framework. It is based on the weighted ensemble algorithm, where an ensemble of copies of the system ("replicas") is directed to new regions of configuration space through merging and cloning operations. The sampling hierarchy allows for a large number of regions to be defined, while using only a small number of replicas that can be balanced over multiple length scales. We demonstrate this algorithm on two model systems that are analytically solvable and examine the 10-residue peptide chignolin in explicit solvent. The latter system is analyzed using a configuration space network, and novel hydrogen bonds are found that facilitate folding.

A method of determining RNA conformational ensembles using structure-based calculations of residual dipolar couplings

We describe a method of determining the conformational fluctuations of RNA based on the incorporation of nuclear magnetic resonance (NMR) residual dipolar couplings (RDCs) as replica-averaged structural restraints in molecular dynamics simulations. In this approach, the alignment tensor required to calculate the RDCs corresponding to a given conformation is estimated from its shape, and multiple replicas of the RNA molecule are simulated simultaneously to reproduce in silico the ensemble-averaging procedure performed in the NMR measurements. We provide initial evidence that with this approach it is possible to determine accurately structural ensembles representing the conformational fluctuations of RNA by applying the reference ensemble test to the trans-activation response element of the human immunodeficiency virus type 1.

Advances in the determination of nucleic acid conformational ensembles

Conformational changes in nucleic acids play a key role in the way genetic information is stored, transferred, and processed in living cells. Here, we describe new approaches that employ a broad range of experimental data, including NMR-derived chemical shifts and residual dipolar couplings, small-angle X-ray scattering, and computational approaches such as molecular dynamics simulations to determine ensembles of DNA and RNA at atomic resolution. We review the complementary information that can be obtained from diverse sets of data and the various methods that have been developed to combine these data with computational methods to construct ensembles and assess their uncertainty. We conclude by surveying RNA and DNA ensembles determined using these methods, highlighting the unique physical and functional insights obtained so far.

Network Theory Tools for RNA Modeling

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

A general method for constructing atomic-resolution RNA ensembles using NMR residual dipolar couplings: the basis for interhelical motions revealed

The ability to modulate alignment and measure multiple independent sets of NMR residual dipolar couplings (RDCs) has made it possible to characterize internal motions in proteins at atomic resolution and with time scale sensitivity ranging from picoseconds up to milliseconds. The application of such methods to the study of RNA dynamics, however, remains fundamentally limited by the inability to modulate alignment and by strong couplings between internal and overall motions that complicate the quantitative interpretation of RDCs. Here, we address this problem by showing that RNA alignment can be generally modulated, in a controlled manner, by variable elongation of A-form helices and that the information contained within the measured RDCs can be extracted even in the presence of strong couplings between motions and overall alignment via structure-based prediction of alignment. Using this approach, four RDC data sets, and a broad conformational pool obtained from a 8.2 μs molecular dynamics simulation, we successfully construct and validate an atomic resolution ensemble of human immunodeficiency virus type I transactivation response element RNA. This ensemble reveals local motions in and around the bulge involving changes in stacking and hydrogen-bonding interactions, which are undetectable by traditional spin relaxation and drive global changes in interhelical orientation. This new approach broadens the scope of using RDCs in characterizing the dynamics of nucleic acids.

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

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