Do conformational biases of simple helical junctions influence RNA folding stability and specificity?

Topological constraints of RNA pseudoknotted and loop-kissing motifs: applications to three-dimensional structure prediction

An RNA global fold can be described at the level of helix orientations and relatively flexible loop conformations that connect the helices. The linkage between the helices plays an essential role in determining the structural topology, which restricts RNA local and global folds, especially for RNA tertiary structures involving cross-linked base pairs. We quantitatively analyze the topological constraints on RNA 3D conformational space, in particular, on the distribution of helix orientations, for pseudoknots and loop-loop kissing structures. The result shows that a viable conformational space is predominantly determined by the motif type, helix size, and loop size, indicating a strong topological coupling between helices and loops in RNA tertiary motifs. Moreover, the analysis indicates that (cross-linked) tertiary contacts can cause much stronger topological constraints on RNA global fold than non-cross-linked base pairs. Furthermore, based on the topological constraints encoded in the 2D structure and the 3D templates, we develop a 3D structure prediction approach. This approach can be further combined with structure probing methods to expand the capability of computational prediction for large RNA folds.

The roles of structural dynamics in the cellular functions of RNAs

RNAs fold into 3D structures that range from simple helical elements to complex tertiary structures and quaternary ribonucleoprotein assemblies. The functions of many regulatory RNAs depend on how their 3D structure changes in response to a diverse array of cellular conditions. In this Review, we examine how the structural characterization of RNA as dynamic ensembles of conformations, which form with different probabilities and at different timescales, is improving our understanding of RNA function in cells. We discuss the mechanisms of gene regulation by microRNAs, riboswitches, ribozymes, post-transcriptional RNA modifications and RNA-binding proteins, and how the cellular environment and processes such as liquid-liquid phase separation may affect RNA folding and activity. The emerging RNA-ensemble-function paradigm is changing our perspective and understanding of RNA regulation, from in vitro to in vivo and from descriptive to predictive.

Probing excited conformational states of nucleic acids by nitrogen CEST NMR spectroscopy

Characterizing low-populated and short-lived excited conformational states has become increasingly important for understanding mechanisms of RNA function. Interconversion between RNA ground and excited conformational states often involves base pairing rearrangements that lead to changes in the hydrogen-bond network. Here, we present two 15N chemical exchange saturation transfer (CEST) NMR experiments that utilize protonated and non-protonated nitrogens, which are key hydrogen-bond donors and acceptors, for characterizing excited conformational states in RNA. We demonstrated these approaches on the B. Cereus fluoride riboswitch, where 15N CEST profiles complement 13C CEST profiles in depicting a potential pathway for ligand-dependent allosteric regulation of the excited conformational state of the fluoride riboswitch.

Salt Dependence of A-Form RNA Duplexes: Structures and Implications

The biological functions of RNA range from gene regulation through catalysis and depend critically on its structure and flexibility. Conformational variations of flexible, non-base-paired components, including RNA hinges, bulges, or single-stranded tails, are well documented. Recent work has also identified variations in the structure of ubiquitous, base-paired duplexes found in almost all functional RNAs. Duplexes anchor the structures of folded RNAs, and their surface features are recognized by partner molecules. To date, no consistent picture has been obtained that describes the range of conformations assumed by RNA duplexes. Here, we apply wide angle, solution X-ray scattering (WAXS) to quantify these variations, by sampling length scales characteristic of helical geometries under different solution conditions. To identify the radius, helical rise, twist, and length of dsRNA helices, we exploit molecular dynamics generated structures, explicit solvent models, and ensemble optimization methods. Our results quantify the substantial and salt-dependent deviations of double-stranded (ds) RNA duplexes from the assumed canonical A-form conformation. Recent experiments underscore the need to properly describe the structures of RNA duplexes when interpreting the salt dependence of RNA conformations.

3D structure stability of the HIV-1 TAR RNA in ion solutions: A coarse-grained model study

As an extremely common structural motif, RNA hairpins with bulge loops [e.g., the human immunodeficiency virus type 1 (HIV-1) transactivation response (TAR) RNA] can play essential roles in normal cellular processes by binding to proteins and small ligands, which could be very dependent on their three-dimensional (3D) structures and stability. Although the structures and conformational dynamics of the HIV-1 TAR RNA have been extensively studied, there are few investigations on the thermodynamic stability of the TAR RNA, especially in ion solutions, and the existing studies also have some divergence on the unfolding process of the RNA. Here, we employed our previously developed coarse-grained model with implicit salt to predict the 3D structure, stability, and unfolding pathway for the HIV-1 TAR RNA over a wide range of ion concentrations. As compared with the extensive experimental/theoretical results, the present model can give reliable predictions on the 3D structure stability of the TAR RNA from the sequence. Based on the predictions, our further comprehensive analyses on the stability of the TAR RNA as well as its variants revealed that the unfolding pathway of an RNA hairpin with a bulge loop is mainly determined by the relative stability between different states (folded state, intermediate state, and unfolded state) and the strength of the coaxial stacking between two stems in folded structures, both of which can be apparently modulated by the ion concentrations as well as the sequences.

Why Does RNA Collapse? The Importance of Water in a Simulation Study of Helix-Junction-Helix Systems

Using computer simulations, we consider the balance of thermodynamic forces that collapse RNA. A model helix-junction-helix (HJH) construct is used to investigate the transition from an extended to a collapsed conformation. Conventional Molecular Dynamics and Milestoning Simulations are used to study the free energy profile of the process for two ion concentrations. We illustrate that HJH folds to a collapsed state with two types of counterions (Mg²⁺ and K⁺). By dissecting the free energy landscape into energetic and entropic contributions, we illustrate that the electrostatic forces between the RNA and the mobile ions do not drive the RNA to a collapsed state. Instead, entropy gains from water expulsion near the neighborhood of the RNA provide the stabilization free energy that tilt HJH into more compact structures. Further simulations of a three-helix hammerhead ribozyme show a similar behavior and support the idea of collapse due to increased gain in water entropy.

Conformations of an RNA Helix-Junction-Helix Construct Revealed by SAXS Refinement of MD Simulations

RNA is involved in a broad range of biological processes that extend far beyond translation. Many of RNA's recently discovered functions rely on folding to a specific conformation or transitioning between conformations. The RNA structure contains rigid, short basepaired regions connected by more flexible linkers. Studies of model constructs such as small helix-junction-helix (HJH) motifs are useful in understanding how these elements work together to determine RNA conformation. Here, we reveal the full ensemble of solution structures assumed by a model RNA HJH. We apply small-angle x-ray scattering and an ensemble optimization method to selectively refine models generated by all-atom molecular dynamics simulations. The expectation of a broad distribution of helix orientations, at and above physiological ionic strength, is not met. Instead, this analysis shows that the HJH structures are dominated by two distinct conformations at moderate to high ionic strength. Atomic structures, selected from the molecular dynamics simulations, reveal strong base-base interactions in the junction that critically constrain the conformational space available to the HJH molecule and lead to a surprising re-extension at high salt. These results are corroborated by comparison with previous single-molecule fluorescence resonance energy transfer experiments on the same constructs.

How the Conformations of an Internal Junction Contribute to Fold an RNA Domain

Like proteins, some RNAs fold to compact structures. We can model functional RNAs as a series of short, rigid, base-paired elements, connected by non-base-paired nucleotides that serve as junctions. These connecting regions bend and twist, facilitating the formation of tertiary contacts that stabilize compact states. Here, we explore the roles of salt and junction sequence in determining the structures of a ubiquitous connector: an asymmetric internal loop. We focus on the J5/5a junction from the widely studied P4-P6 domain of the Tetrahymena ribozyme. Following the addition of magnesium ions to fold P4-P6, this junction bends dramatically, bringing the two halves of the RNA domain together for tertiary contact engagement. Using single-molecule fluorescence resonance energy transfer (smFRET), we examine the role of sequence and salt on model RNA constructs that contain these junction regions. We explore the wild-type J5/5a junction as well as two sequence variants. These junctions display distinct, salt-dependent conformations. Small-angle X-ray scattering (SAXS) measurements verify that these effects persist in the full-length P4-P6 domain. These measurements underscore the importance of junction sequence and interactions with ions in facilitating RNA folding.

The Story of RNA Folding, as Told in Epochs

The past decades have witnessed tremendous developments in our understanding of RNA biology. At the core of these advances have been studies aimed at discerning RNA structure and at understanding the forces that influence the RNA folding process. It is easy to take the present state of understanding for granted, but there is much to be learned by considering the path to our current understanding, which has been tortuous, with the birth and death of models, the adaptation of experimental tools originally developed for characterization of protein structure and catalysis, and the development of novel tools for probing RNA. In this review we tour the stages of RNA folding studies, considering them as "epochs" that can be generalized across scientific disciplines. These epochs span from the discovery of catalytic RNA, through biophysical insights into the putative primordial RNA World, to characterization of structured RNAs, the building and testing of models, and, finally, to the development of models with the potential to yield generalizable predictive and quantitative models for RNA conformational, thermodynamic, and kinetic behavior. We hope that this accounting will aid others as they navigate the many fascinating questions about RNA and its roles in biology, in the past, present, and future.

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-Throughput Investigation of Diverse Junction Elements in RNA Tertiary Folding

RNAs fold into defined tertiary structures to function in critical biological processes. While quantitative models can predict RNA secondary structure stability, we are still unable to predict the thermodynamic stability of RNA tertiary structure. Here, we probe conformational preferences of diverse RNA two-way junctions to develop a predictive model for the formation of RNA tertiary structure. We quantitatively measured tertiary assembly energetics of >1,000 of RNA junctions inserted in multiple structural scaffolds to generate a "thermodynamic fingerprint" for each junction. Thermodynamic fingerprints enabled comparison of junction conformational preferences, revealing principles for how sequence influences 3-dimensional conformations. Utilizing fingerprints of junctions with known crystal structures, we generated ensembles for related junctions that predicted their thermodynamic effects on assembly formation. This work reveals sequence-structure-energetic relationships in RNA, demonstrates the capacity for diverse compensation strategies within tertiary structures, and provides a path to quantitative modeling of RNA folding energetics based on "ensemble modularity."

Structure modeling of RNA using sparse NMR constraints

RNAs fold into distinct molecular conformations that are often essential for their functions. Accurate structure modeling of complex RNA motifs, including ubiquitous non-canonical base pairs and pseudoknots, remains a challenge. Here, we present an NMR-guided all-atom discrete molecular dynamics (DMD) platform, iFoldNMR, for rapid and accurate structure modeling of complex RNAs. We show that sparse distance constraints from imino resonances, which can be readily obtained from routine NMR experiments and easier to compile than laborious assignments of non-solvent-exchangeable protons, are sufficient to direct a DMD search for low-energy RNA conformers. Benchmarking on a set of RNAs with complex folds spanning up to 56 nucleotides in length yields structural models that recapitulate experimentally determined structures with all-heavy-atom RMSDs ranging from 2.4 to 6.5 Å. This platform represents an efficient approach for high-throughput RNA structure modeling and will facilitate analysis of diverse, newly discovered functional RNAs.

Tuning RNA folding and function through rational design of junction topology

Structured RNAs such as ribozymes must fold into specific 3D structures to carry out their biological functions. While it is well-known that architectural features such as flexible junctions between helices help guide RNA tertiary folding, the mechanisms through which junctions influence folding remain poorly understood. We combine computational modeling with single molecule Förster resonance energy transfer (smFRET) and catalytic activity measurements to investigate the influence of junction design on the folding and function of the hairpin ribozyme. Coarse-grained simulations of a wide range of junction topologies indicate that differences in sterics and connectivity, independent of stacking, significantly affect tertiary folding and appear to largely explain previously observed variations in hairpin ribozyme stability. We further use our simulations to identify stabilizing modifications of non-optimal junction topologies, and experimentally validate that a three-way junction variant of the hairpin ribozyme can be stabilized by specific insertion of a short single-stranded linker. Combined, our multi-disciplinary study further reinforces that junction sterics and connectivity are important determinants of RNA folding, and demonstrates the potential of coarse-grained simulations as a tool for rationally tuning and optimizing RNA folding and function.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔG_align, the probability of aligning tertiary contact partners, and ΔG_tert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔG_HJH) or from changes in the electrostatic environment (ΔG_+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔG_tert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔG_tert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

Resolving sugar puckers in RNA excited states exposes slow modes of repuckering dynamics

Recent studies have shown that RNAs exist in dynamic equilibrium with short-lived low-abundance 'excited states' that form by reshuffling base pairs in and around non-canonical motifs. These conformational states are proposed to be rich in non-canonical motifs and to play roles in the folding and regulatory functions of non-coding RNAs but their structure proves difficult to characterize given their transient nature. Here, we describe an approach for determining sugar pucker conformation in RNA excited states through nuclear magnetic resonance measurements of C1΄ and C4΄ rotating frame spin relaxation (R1ρ) in uniformly 13C/15N labeled RNA samples. Application to HIV-1 TAR exposed slow modes of sugar repuckering dynamics at the μs and ms timescale accompanying transitions between non-helical (C2΄-endo) to helical (C3΄-endo) conformations during formation of two distinct excited states. In contrast, we did not obtain any evidence for slow sugar repuckering dynamics for nucleotides in a variety of structural contexts that do not undergo non-helical to helical transitions. Our results outline a route for significantly improving the conformational characterization of RNA excited states and suggest that slow modes of repuckering dynamics gated by transient changes in secondary structure are quite common in RNA.

Tuning RNA Flexibility with Helix Length and Junction Sequence

The increasing awareness of RNA's central role in biology calls for a new understanding of how RNAs, like proteins, recognize biological partners. Because RNA is inherently flexible, it assumes a variety of conformations. This conformational flexibility can be a critical aspect of how RNA attracts and binds molecular partners. Structurally, RNA consists of rigid basepaired duplexes, separated by flexible non-basepaired regions. Here, using an RNA system consisting of two short helices, connected by a single-stranded (non-basepaired) junction, we explore the role of helix length and junction sequence in determining the range of conformations available to a model RNA. Single-molecule Förster resonance energy transfer reports on the RNA conformation as a function of either mono- or divalent ion concentration. Electrostatic repulsion between helices dominates at low salt concentration, whereas junction sequence effects determine the conformations at high salt concentration. Near physiological salt concentrations, RNA conformation is sensitive to both helix length and junction sequence, suggesting a means for sensitively tuning RNA conformations.

Kinetic and thermodynamic framework for P4-P6 RNA reveals tertiary motif modularity and modulation of the folding preferred pathway

The past decade has seen a wealth of 3D structural information about complex structured RNAs and identification of functional intermediates. Nevertheless, developing a complete and predictive understanding of the folding and function of these RNAs in biology will require connection of individual rate and equilibrium constants to structural changes that occur in individual folding steps and further relating these steps to the properties and behavior of isolated, simplified systems. To accomplish these goals we used the considerable structural knowledge of the folded, unfolded, and intermediate states of P4-P6 RNA. We enumerated structural states and possible folding transitions and determined rate and equilibrium constants for the transitions between these states using single-molecule FRET with a series of mutant P4-P6 variants. Comparisons with simplified constructs containing an isolated tertiary contact suggest that a given tertiary interaction has a stereotyped rate for breaking that may help identify structural transitions within complex RNAs and simplify the prediction of folding kinetics and thermodynamics for structured RNAs from their parts. The preferred folding pathway involves initial formation of the proximal tertiary contact. However, this preference was only ∼10 fold and could be reversed by a single point mutation, indicating that a model akin to a protein-folding contact order model will not suffice to describe RNA folding. Instead, our results suggest a strong analogy with a modified RNA diffusion-collision model in which tertiary elements within preformed secondary structures collide, with the success of these collisions dependent on whether the tertiary elements are in their rare binding-competent conformations.

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.

Probing the kinetic and thermodynamic consequences of the tetraloop/tetraloop receptor monovalent ion-binding site in P4-P6 RNA by smFRET

Structured RNA molecules play roles in central biological processes and understanding the basic forces and features that govern RNA folding kinetics and thermodynamics can help elucidate principles that underlie biological function. Here we investigate one such feature, the specific interaction of monovalent cations with a structured RNA, the P4-P6 domain of the Tetrahymena ribozyme. We employ single molecule FRET (smFRET) approaches as these allow determination of folding equilibrium and rate constants over a wide range of stabilities and thus allow direct comparisons without the need for extrapolation. These experiments provide additional evidence for specific binding of monovalent cations, Na+ and K+, to the RNA tetraloop-tetraloop receptor (TL-TLR) tertiary motif. These ions facilitate both folding and unfolding, consistent with an ability to help order the TLR for binding and further stabilize the tertiary contact subsequent to attainment of the folding transition state.

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

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

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.

MD Simulations of tRNA and Aminoacyl-tRNA Synthetases: Dynamics, Folding, Binding, and Allostery

While tRNA and aminoacyl-tRNA synthetases are classes of biomolecules that have been extensively studied for decades, the finer details of how they carry out their fundamental biological functions in protein synthesis remain a challenge. Recent molecular dynamics (MD) simulations are verifying experimental observations and providing new insight that cannot be addressed from experiments alone. Throughout the review, we briefly discuss important historical events to provide a context for how far the field has progressed over the past few decades. We then review the background of tRNA molecules, aminoacyl-tRNA synthetases, and current state of the art MD simulation techniques for those who may be unfamiliar with any of those fields. Recent MD simulations of tRNA dynamics and folding and of aminoacyl-tRNA synthetase dynamics and mechanistic characterizations are discussed. We highlight the recent successes and discuss how important questions can be addressed using current MD simulations techniques. We also outline several natural next steps for computational studies of AARS:tRNA complexes.

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.

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.

Dynamic motions of the HIV-1 frameshift site RNA

The HIV-1 frameshift site (FS) plays a critical role in viral replication. During translation, the HIV-1 FS transitions from a 3-helix to a 2-helix junction RNA secondary structure. The 2-helix junction structure contains a GGA bulge, and purine-rich bulges are common motifs in RNA secondary structure. Here, we investigate the dynamics of the HIV-1 FS 2-helix junction RNA. Interhelical motions were studied under different ionic conditions using NMR order tensor analysis of residual dipolar couplings. In 150 mM potassium, the RNA adopts a 43°(±4°) interhelical bend angle (β) and displays large amplitude, anisotropic interhelical motions characterized by a 0.52(±0.04) internal generalized degree of order (GDOint) and distinct order tensor asymmetries for its two helices (η = 0.26(±0.04) and 0.5(±0.1)). These motions are effectively quenched by addition of 2 mM magnesium (GDOint = 0.87(±0.06)), which promotes a near-coaxial conformation (β = 15°(±6°)) of the two helices. Base stacking in the bulge was investigated using the fluorescent purine analog 2-aminopurine. These results indicate that magnesium stabilizes extrahelical conformations of the bulge nucleotides, thereby promoting coaxial stacking of helices. These results are highly similar to previous studies of the HIV transactivation response RNA, despite a complete lack of sequence similarity between the two RNAs. Thus, the conformational space of these RNAs is largely determined by the topology of their interhelical junctions.

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.

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.

Many-body effect in ion binding to RNA

Ion-mediated electrostatic interactions play an important role in RNA folding stability. For a RNA in a solution with higher Mg(2+) ion concentration, more counterions in the solution can bind to the RNA, causing a strong many-body coupling between the bound ions. The many-body effect can change the effective potential of mean force between the tightly bound ions. This effect tends to dampen ion binding and lower RNA folding stability. Neglecting the many-body effect leads to a systematic error (over-estimation) of RNA folding stability at high Mg(2+) ion concentrations. Using the tightly bound ion model combined with a conformational ensemble model, we investigate the influence of the many-body effect on the ion-dependent RNA folding stability. Comparisons with the experimental data indicate that including the many-body effect led to much improved predictions for RNA folding stability at high Mg(2+) ion concentrations. The results suggest that the many-body effect can be important for RNA folding in high concentrations of multivalent ions. Further investigation showed that the many-body effect can influence the spatial distribution of the tightly bound ions and the effect is more pronounced for compact RNA structures and structures prone to the formation of local clustering of ions.

Understanding nucleic acid-ion interactions

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Hierarchy of RNA functional dynamics

RNA dynamics play a fundamental role in many cellular functions. However, there is no general framework to describe these complex processes, which typically consist of many structural maneuvers that occur over timescales ranging from picoseconds to seconds. Here, we classify RNA dynamics into distinct modes representing transitions between basins on a hierarchical free-energy landscape. These transitions include large-scale secondary-structural transitions at >0.1-s timescales, base-pair/tertiary dynamics at microsecond-to-millisecond timescales, stacking dynamics at timescales ranging from nanoseconds to microseconds, and other "jittering" motions at timescales ranging from picoseconds to nanoseconds. We review various modes within these three different tiers, the different mechanisms by which they are used to regulate function, and how they can be coupled together to achieve greater functional complexity.

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.

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.

NMR studies of nucleic acid dynamics

Nucleic acid structures have to satisfy two diametrically opposite requirements; on one hand they have to adopt well-defined 3D structures that can be specifically recognized by proteins; on the other hand, their structures must be sufficiently flexible to undergo very large conformational changes that are required during key biochemical processes, including replication, transcription, and translation. How do nucleic acids introduce flexibility into their 3D structure without losing biological specificity? Here, I describe the development and application of NMR spectroscopic techniques in my laboratory for characterizing the dynamic properties of nucleic acids that tightly integrate a broad set of NMR measurements, including residual dipolar couplings, spin relaxation, and relaxation dispersion with sample engineering and computational approaches. This approach allowed us to obtain fundamental new insights into directional flexibility in nucleic acids that enable their structures to change in a very specific functional manner.

Role of ion valence in the submillisecond collapse and folding of a small RNA domain

Following the addition of ions to trigger folding, RNA molecules undergo a transition from rigid, extended states to a compact ensemble. Determining the time scale for this collapse provides important insights into electrostatic contributions to RNA folding; however, it can be challenging to isolate the effects of purely nonspecific collapse, e.g., relaxation due to backbone charge compensation, from the concurrent formation of some tertiary contacts. To solve this problem, we decoupled nonspecific collapse from tertiary folding using a single-point mutation to eliminate tertiary contacts in the small RNA subdomain known as tP5abc. Microfluidic mixing with microsecond time resolution and Förster resonance energy transfer detection provides insight into the ionic strength-dependent transition from extended to compact ensembles. Differences in reaction rates are detected when folding is initiated by monovalent or divalent ions, consistent with equilibrium measurements illustrating the enhanced screening of divalent ions relative to monovalent ions at the same ionic strength. Ion-driven collapse is fast, and a comparison of the collapse time of the wild-type and mutant tP5abc suggests that site binding of Mg(2+) occurs on submillisecond time scales.

The functional exchangeability of pk- and k-turns in RNA structure

Ribonuclease P RNA requires a sharply kinked RNA helix to make a loop-receptor interaction that creates the binding site for the substrate. In some forms of the ribozyme, this is accomplished by a k-turn, while others have a different element called the pk-turn. The structure of the pk-turn in RNase P of Thermotoga maritima is globally very similar to a k-turn, but lacks all the standard features of that structure, including long-range hydrogen bonds between the two helical arms. We show here that in an isolated RNA duplex, the pk-turn fails to adopt a tightly kinked structure, but rather is a flexible element. This suggests that the tertiary contacts of RNase P assist its folding into the required kinked structure. We find that we can replace the k-turn of the SAM-I riboswitch with the pk-turn, such that the resulting RNA retains its ability to bind SAM, although with lower affinity. We also find that we can replace the pk-turn of T. maritima RNase P with a standard k-turn (in either orientation) with retention of ribozyme activity. Thus, although the pk-turn cannot intrinsically fold into the kinked structure, it can be induced to fold correctly in context. And the pk-turn and k-turns can substitute functionally for one another.

Ion-mediated RNA structural collapse: effect of spatial confinement

RNAs are negatively charged molecules that reside in cellular environments with macromolecular crowding. Macromolecular confinement can influence the ion effects in RNA folding. In this work, using the recently developed tightly bound ion model for ion fluctuation and correlation, we investigate the effect of confinement on ion-mediated RNA structural collapse for a simple model system. We find that for both Na(+) and Mg(2+), the ion efficiencies in mediating structural collapse/folding are significantly enhanced by the structural confinement. This enhancement of ion efficiency is attributed to the decreased electrostatic free-energy difference between the compact conformation ensemble and the (restricted) extended conformation ensemble due to the spatial restriction.

Salt dependence of the radius of gyration and flexibility of single-stranded DNA in solution probed by small-angle x-ray scattering

Short single-stranded nucleic acids are ubiquitous in biological processes; understanding their physical properties provides insights to nucleic acid folding and dynamics. We used small-angle x-ray scattering to study 8-100 residue homopolymeric single-stranded DNAs in solution, without external forces or labeling probes. Poly-T's structural ensemble changes with increasing ionic strength in a manner consistent with a polyelectrolyte persistence length theory that accounts for molecular flexibility. For any number of residues, poly-A is consistently more elongated than poly-T, likely due to the tendency of A residues to form stronger base-stacking interactions than T residues.

The role of counterion valence and size in GAAA tetraloop-receptor docking/undocking kinetics

For RNA to fold into compact, ordered structures, it must overcome electrostatic repulsion between negatively charged phosphate groups by counterion recruitment. A physical understanding of the counterion-assisted folding process requires addressing how cations kinetically and thermodynamically control the folding equilibrium for each tertiary interaction in a full-length RNA. In this work, single-molecule FRET (fluorescence resonance energy transfer) techniques are exploited to isolate and explore the cation-concentration-dependent kinetics for formation of a ubiquitous RNA tertiary interaction, that is, the docking/undocking of a GAAA tetraloop with its 11-nt receptor. Rate constants for docking (k(dock)) and undocking (k(undock)) are obtained as a function of cation concentration, size, and valence, specifically for the series Na(+), K(+), Mg(2+), Ca(2+), Co(NH(3))(6)(3+), and spermidine(3+). Increasing cation concentration acceleratesk(dock)dramatically but achieves only a slight decrease in k(undock). These results can be kinetically modeled using parallel cation-dependent and cation-independent docking pathways, which allows for isolation of the folding kinetics from the interaction energetics of the cations with the undocked and docked states, respectively. This analysis reveals a preferential interaction of the cations with the transition state and docked state as compared to the undocked RNA, with the ion-RNA interaction strength growing with cation valence. However, the corresponding number of cations that are taken up by the RNA upon folding decreases with charge density of the cation. The only exception to these behaviors is spermidine(3+), whose weaker influence on the docking equilibria with respect to Co(NH(3))(6)(3+) can be ascribed to steric effects preventing complete neutralization of the RNA phosphate groups.

Determining RNA three-dimensional structures using low-resolution data

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

Functional complexity and regulation through RNA dynamics

Changes to the conformation of coding and non-coding RNAs form the basis of elements of genetic regulation and provide an important source of complexity, which drives many of the fundamental processes of life. Although the structure of RNA is highly flexible, the underlying dynamics of RNA are robust and are limited to transitions between the few conformations that preserve favourable base-pairing and stacking interactions. The mechanisms by which cellular processes harness the intrinsic dynamic behaviour of RNA and use it within functionally productive pathways are complex. The versatile functions and ease by which it is integrated into a wide variety of genetic circuits and biochemical pathways suggests there is a general and fundamental role for RNA dynamics in cellular processes.

Entropic origin of Mg2+-facilitated RNA folding

Mg(2+) is essential for the proper folding and function of RNA, though the effect of Mg(2+) concentration on the free energy, enthalpy, and entropy landscapes of RNA folding is unknown. This work exploits temperature-controlled single-molecule FRET methods to address the thermodynamics of RNA folding pathways by probing the intramolecular docking/undocking kinetics of the ubiquitous GAAA tetraloop-receptor tertiary interaction as a function of [Mg(2+)]. These measurements yield the barrier and standard state enthalpies, entropies, and free energies for an RNA tertiary transition, in particular, revealing the thermodynamic origin of [Mg(2+)]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg(2+)] promotes tetraloop-receptor interaction by reducing the entropic barrier (-TΔS(++)(dock)) and the overall entropic penalty (-TΔS(+) (dock)) for docking, with essentially negligible effects on both the activation enthalpy (ΔH(++)(dock)) and overall exothermicity (ΔH(+)(dock)). These observations contrast with the conventional notion that increasing [Mg(2+)] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH(++)(dock)) and ΔH(+)(dock)) with [Mg(2+)]. Instead we propose that higher [Mg(2+)] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.

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.

3D maps of RNA interhelical junctions

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

Topological constraints: using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.

Removal of covalent heterogeneity reveals simple folding behavior for P4-P6 RNA

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior.

Clustering to identify RNA conformations constrained by secondary structure

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