RNA simulations: probing hairpin unfolding and the dynamics of a GNRA tetraloop

RNA adapts its flexibility to efficiently fold and resist unfolding

Recent studies have demonstrated that the mechanisms through which biopolymers like RNA interconvert between multiple folded structures are critical for their cellular functions. A major obstacle to elucidating these mechanisms is the lack of experimental approaches that can resolve these interconversions between functionally relevant biomolecular structures. Here, using a nano-electronic device with microsecond time resolution, we dissect the complete set of structural rearrangements executed by an ultra-stable RNA, the UUCG stem-loop, at the single-molecule level. We show that the stem-loop samples at least four conformations along two folding pathways leading to two distinct folded structures, only one of which has been previously observed. By modulating its flexibility, the stem-loop can adaptively select between these pathways, enabling it to both fold rapidly and resist unfolding. This paradigm of stabilization through compensatory changes in flexibility broadens our understanding of stable RNA structures and is expected to serve as a general strategy employed by all biopolymers.

Folding@home: Achievements from over 20 years of citizen science herald the exascale era

Simulations of biomolecules have enormous potential to inform our understanding of biology but require extremely demanding calculations. For over 20 years, the Folding@home distributed computing project has pioneered a massively parallel approach to biomolecular simulation, harnessing the resources of citizen scientists across the globe. Here, we summarize the scientific and technical advances this perspective has enabled. As the project's name implies, the early years of Folding@home focused on driving advances in our understanding of protein folding by developing statistical methods for capturing long-timescale processes and facilitating insight into complex dynamical processes. Success laid a foundation for broadening the scope of Folding@home to address other functionally relevant conformational changes, such as receptor signaling, enzyme dynamics, and ligand binding. Continued algorithmic advances, hardware developments such as graphics processing unit (GPU)-based computing, and the growing scale of Folding@home have enabled the project to focus on new areas where massively parallel sampling can be impactful. While previous work sought to expand toward larger proteins with slower conformational changes, new work focuses on large-scale comparative studies of different protein sequences and chemical compounds to better understand biology and inform the development of small-molecule drugs. Progress on these fronts enabled the community to pivot quickly in response to the COVID-19 pandemic, expanding to become the world's first exascale computer and deploying this massive resource to provide insight into the inner workings of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus and aid the development of new antivirals. This success provides a glimpse of what is to come as exascale supercomputers come online and as Folding@home continues its work.

Multiscale Modeling of Phosphate···π Contacts in RNA U-Turns Exposes Differences between Quantum-Chemical and AMBER Force Field Descriptions

Phosphate···π, also called anion···π, contacts occur between nucleobases and anionic phosphate oxygens (OP2) in r(GNRA) and r(UNNN) U-turn motifs (N = A,G,C,U; R = A,G). These contacts were investigated using state-of-the-art quantum-chemical methods (QM) to characterize their physicochemical properties and to serve as a reference to evaluate AMBER force field (AFF) performance. We found that phosphate···π interaction energies calculated with the AFF for dimethyl phosphate···nucleobase model systems are less stabilizing in comparison with double-hybrid DFT and that minimum contact distances are larger for all nucleobases. These distance stretches are also observed in large-scale AFF vs QM/MM computations and classical molecular dynamics (MD) simulations on several r(gcGNRAgc) tetraloop hairpins when compared to experimental data extracted from X-ray/cryo-EM structures (res. ≤ 2.5 Å) using the WebFR3D bioinformatic tool. MD simulations further revealed shifted OP2/nucleobase positions. We propose that discrepancies between the QM and AFF result from a combination of missing polarization in the AFF combined with too large AFF Lennard-Jones (LJ) radii of nucleobase carbon atoms in addition to an exaggerated short-range repulsion of the r^-12 LJ repulsive term. We compared these results with earlier data gathered on lone pair···π contacts in CpG Z-steps occurring in r(UNCG) tetraloops. In both instances, charge transfer calculations do not support any significant n → π* donation effects. We also investigated thiophosphate···π contacts that showed reduced stabilizing interaction energies when compared to phosphate···π contacts. Thus, we challenge suggestions that the experimentally observed enhanced thermodynamic stability of phosphorothioated r(GNRA) tetraloops can be explained by larger London dispersion.

Accelerating the Ensemble Convergence of RNA Hairpin Simulations with a Replica Exchange Structure Reservoir

RNA is a key participant in many biological processes, but studies of RNA using computer simulations lag behind those of proteins, largely due to less-developed force fields and the slow dynamics of RNA. Generating converged RNA ensembles for force field development and other studies remains a challenge. In this study, we explore the ability of replica exchange molecular dynamics to obtain well-converged conformational ensembles for two RNA hairpin systems in an implicit solvent. Even for these small model systems, standard REMD remains computationally costly, but coupling to a pre-generated structure library using the reservoir REMD approach provides a dramatic acceleration of ensemble convergence for both model systems. Such precise ensembles could facilitate RNA force field development and validation and applications of simulation to more complex RNA systems. The advantages and remaining challenges of applying R-REMD to RNA are investigated in detail.

Toward Convergence in Folding Simulations of RNA Tetraloops: Comparison of Enhanced Sampling Techniques and Effects of Force Field Modifications

Atomistic molecular dynamics simulations represent an established technique for investigation of RNA structural dynamics. Despite continuous development, contemporary RNA simulations still suffer from suboptimal accuracy of empirical potentials (force fields, ffs) and sampling limitations. Development of efficient enhanced sampling techniques is important for two reasons. First, they allow us to overcome the sampling limitations, and second, they can be used to quantify ff imbalances provided they reach a sufficient convergence. Here, we study two RNA tetraloops (TLs), namely the GAGA and UUCG motifs. We perform extensive folding simulations and calculate folding free energies (ΔG_fold^°) with the aim to compare different enhanced sampling techniques and to test several modifications of the nonbonded terms extending the AMBER OL3 RNA ff. We demonstrate that replica-exchange solute tempering (REST2) simulations with 12-16 replicas do not show any sign of convergence even when extended to a timescale of 120 μs per replica. However, the combination of REST2 with well-tempered metadynamics (ST-MetaD) achieves good convergence on a timescale of 5-10 μs per replica, improving the sampling efficiency by at least 2 orders of magnitude. Effects of ff modifications on ΔG_fold^° energies were initially explored by the reweighting approach and then validated by new simulations. We tested several manually prepared variants of the gHBfix potential which improve stability of the native state of both TLs by ∼2 kcal/mol. This is sufficient to conveniently stabilize the folded GAGA TL while the UUCG TL still remains under-stabilized. Appropriate adjustment of van der Waals parameters for C-H···O5' base-phosphate interaction may further stabilize the native states of both TLs by ∼0.6 kcal/mol.

The effect of mutation in the stem of the MicroROSE thermometer on its thermosensing ability: insights from molecular dynamics simulation studies

Mutation induced thermosensing ability of MicroROSE thermometer.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

Context-sensitivity of isosteric substitutions of non-Watson-Crick basepairs in recurrent RNA 3D motifs

Sequence variation in a widespread, recurrent, structured RNA 3D motif, the Sarcin/Ricin (S/R), was studied to address three related questions: First, how do the stabilities of structured RNA 3D motifs, composed of non-Watson–Crick (non-WC) basepairs, compare to WC-paired helices of similar length and sequence? Second, what are the effects on the stabilities of such motifs of isosteric and non-isosteric base substitutions in the non-WC pairs? And third, is there selection for particular base combinations in non-WC basepairs, depending on the temperature regime to which an organism adapts? A survey of large and small subunit rRNAs from organisms adapted to different temperatures revealed the presence of systematic sequence variations at many non-WC paired sites of S/R motifs. UV melting analysis and enzymatic digestion assays of oligonucleotides containing the motif suggest that more stable motifs tend to be more rigid. We further found that the base substitutions at non-Watson–Crick pairing sites can significantly affect the thermodynamic stabilities of S/R motifs and these effects are highly context specific indicating the importance of base-stacking and base-phosphate interactions on motif stability. This study highlights the significance of non-canonical base pairs and their contributions to modulating the stability and flexibility of RNA molecules.

Molecular dynamics study of ways of RNA base-pair formation

Base pairing is a fundamental phenomenon in RNA structure and function. However, although there have been considerable recent advances, some important aspects of base-pair formation are still unknown, including the ways of base-pair formation and detailed roles of metal ions. Here we show that base pairs can form through four different ways: stabilizing, bridging, rotating, and shifting. Among them the stabilizing and bridging ways involve direct binding of metal ions while the rotating and shifting ways do not in most cases. Furthermore, we find that the formations of base pairs in different positions of the hairpin stem may adopt different ways.

Interactions between cyclic nucleotides and common cations: an ab initio molecular dynamics study

We present the first, to the best of our knowledge, ab initio molecular dynamics (AIMD) investigation on three aqueous solutions where an abasic cyclic nucleotide model is solvated in the presence of distinct cations (i.e., Na⁺, K⁺ and Mg²⁺). We elucidate the typical modalities of interaction between those ionic species and the nucleotide moiety by first-principles numerical simulations, starting from an inner-shell binding configuration on a time scale of 100 ps (total simulation time of ∼600 ps). Whereas the strong "structure-maker" Mg²⁺ is permanently bound to one of the two oxygen atoms of the phosphate group of the nucleotide model, Na⁺ and K⁺ show binding times τ_b of 65 ps and 10-15 ps, respectively, thus reflecting their chemical nature in aqueous solutions. Furthermore, we qualitatively relate these findings to approximate free-energy barriers of the cations' unbinding obtained by means of exploratory well-tempered metadynamics. With the aim of shedding light on the features of commonly employed force-fields (FFs), classical MD simulations (almost 200 trajectories with a total simulation time of ∼18 μs) using the biomolecular AMBER FF are also reported. By choosing several combinations of the parametrization for the water environment (i.e., TIP3P, SPC/E and OPC) and cations (i.e., Joung-Cheatham, Li-Merz 12-6 and Li-Merz 12-6-4), we found significant differences in the radial distribution functions and residence times compared to the ab initio results. The Na⁺ and K⁺ ions wrongly show quasi-identical radial distribution functions and the Li & Merz 12-6-4 Lennard-Jones parameters for Mg²⁺ were found to be essential in quickly reaching the binding state consistent with AIMD.

Length-Dependent Melting Kinetics of Short DNA Oligonucleotides Using Temperature-Jump IR Spectroscopy

In this work, we utilize Fourier transform infrared and temperature-jump (T-jump) infrared (IR) spectroscopy to investigate the melting thermodynamics and kinetics of a series of five DNA sequences ranging from 6 to 14 base pairs long. IR spectroscopy is well suited for the study of DNA because of its ability to distinguish base-specific information, and the nanosecond time resolution of the T-jump apparatus can access the relevant range of kinetics. Eyring analysis of a two-state model examines both the activation enthalpy and entropy, providing new insights into the energetic driving forces and physical processes behind the association and dissociation while also helping to clarify the commonly observed negative activation energy. Global analysis of the thermodynamic and kinetic data applying a linear dependence of activation barriers on oligo length provides a holistic result by producing reasonable agreement between our data and existing nearest-neighbor (NN) thermodynamic parameters blending the experimental results with established predictive models. By studying the trends in the thermodynamics and kinetics as a function of length, this work demonstrates a direct correlation between the effects additional dinucleotides have on the kinetics and the NN parameters for those dinucleotides. This result further supports the development of a kinetic analogue to the thermodynamic NN parameters.

Effects of flanking regions on HDV cotranscriptional folding kinetics

Hepatitis delta virus (HDV) ribozyme performs the self-cleavage activity through folding to a double pseudoknot structure. The folding of functional RNA structures is often coupled with the transcription process. In this work, we developed a new approach for predicting the cotranscriptional folding kinetics of RNA secondary structures with pseudoknots. We theoretically studied the cotranscriptional folding behavior of the 99-nucleotide (nt) HDV sequence, two upstream flanking sequences, and one downstream flanking sequence. During transcription, the 99-nt HDV can effectively avoid the trap intermediates and quickly fold to the cleavage-active state. It is different from its refolding kinetics, which folds into an intermediate trap state. For all the sequences, the ribozyme regions (from 1 to 73) all fold to the same structure during transcription. However, the existence of the 30-nt upstream flanking sequence can inhibit the ribozyme region folding into the active native state through forming an alternative helix Alt1 with the segments 70-90. The longer upstream flanking sequence of 54 nt itself forms a stable hairpin structure, which sequesters the formation of the Alt1 helix and leads to rapid formation of the cleavage-active structure. Although the 55-nt downstream flanking sequence could invade the already folded active structure during transcription by forming a more stable helix with the ribozyme region, the slow transition rate could keep the structure in the cleavage-active structure to perform the activity.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Effect of GCAA stabilizing loops on three- and four-way intramolecular junctions

Tetraloops are a common way of changing the melting behavior of a DNA or RNA structure without changing the sequence of the stem. Because of the ubiquitous nature of tetraloops, our goal is to understand the effect a GCAA tetraloop, which belongs to the GNRA family of tetraloops, has on the unfolding thermodynamics of intramolecular junctions. Specifically, we have described the melting behavior of intramolecular three-way and four-way junctions where a T₅ loop has been replaced with a GCAA tetraloops in different positions. Their thermodynamic profiles, including Δn_Na⁺ and Δn_W, were analyzed based on the position of the tetraloop. We obtained between -16.7 and -27.5 kcal mol^-1 for all junctions studied. The experimental data indicates the influence of the GCAA tetraloop is primarily dictated by the native unfolding of the junction; if the tetraloop is placed on a stem that unfolds as a single domain when the tetraloop is not present, it will unfold as a single domain when the tetraloop is present but with a higher thermal stability. Conversely, if the tetraloop is placed on a stem which unfolds cooperatively with other stems when the tetraloop is not present, the tetraloop will increase the thermal stability of all the stems in the melting domain. The oligonucleotide structure and not the tetraloop itself affects ion uptake; three-way junctions do not gain an increase in ion uptake, but four-way junctions do. This is not the case for water immobilization, where the position of the tetraloop dictates the amount of water immobilized.

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

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

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.

Nucleobase azide-ethynylribose click chemistry contributes to stabilizing oligonucleotide duplexes and stem-loop structures

The formation of 1,4-disubstituted 1,2,3-triazoles through copper-catalyzed azide-alkyne cycloaddition (CuAAC) in oligonucleotides bearing 1-deoxy-1-ethynyl-β-d-ribofuranose (R^E) can have a positive impact on the stability of oligonucleotide duplexes and stem-loop structures.

How to understand atomistic molecular dynamics simulations of RNA and protein-RNA complexes?

We provide a critical assessment of explicit-solvent atomistic molecular dynamics (MD) simulations of RNA and protein/RNA complexes, written primarily for non-specialists with an emphasis to explain the limitations of MD. MD simulations can be likened to hypothetical single-molecule experiments starting from single atomistic conformations and investigating genuine thermal sampling of the biomolecules. The main advantage of MD is the unlimited temporal and spatial resolution of positions of all atoms in the simulated systems. Fundamental limitations are the short physical time-scale of simulations, which can be partially alleviated by enhanced-sampling techniques, and the highly approximate atomistic force fields describing the simulated molecules. The applicability and present limitations of MD are demonstrated on studies of tetranucleotides, tetraloops, ribozymes, riboswitches and protein/RNA complexes. Wisely applied simulations respecting the approximations of the model can successfully complement structural and biochemical experiments. WIREs RNA 2017, 8:e1405. doi: 10.1002/wrna.1405 For further resources related to this article, please visit the WIREs website.

Intrinsic Base-Pair Rearrangement in the Hairpin Ribozyme Directs RNA Conformational Sampling and Tertiary Interface Formation

Dynamic fluctuations in RNA structure enable conformational changes that are required for catalysis and recognition. In the hairpin ribozyme, the catalytically active structure is formed as an intricate tertiary interface between two RNA internal loops. Substantial alterations in the structure of each loop are observed upon interface formation, or docking. The very slow on-rate for this relatively tight interaction has led us to hypothesize a double conformational capture mechanism for RNA-RNA recognition. We used extensive molecular dynamics simulations to assess conformational sampling in the undocked form of the loop domain containing the scissile phosphate (loop A). We observed several major accessible conformations with distinctive patterns of hydrogen bonding and base stacking interactions in the active-site internal loop. Several important conformational features characteristic of the docked state were observed in well-populated substates, consistent with the kinetic sampling of docking-competent states by isolated loop A. Our observations suggest a hybrid or multistage binding mechanism, in which initial conformational selection of a docking-competent state is followed by induced-fit adjustment to an in-line, chemically reactive state only after formation of the initial complex with loop B.

Free Energy Landscape of GAGA and UUCG RNA Tetraloops

We report the folding thermodynamics of ccUUCGgg and ccGAGAgg RNA tetraloops using atomistic molecular dynamics simulations. We obtain a previously unreported estimation of the folding free energy using parallel tempering in combination with well-tempered metadynamics. A key ingredient is the use of a recently developed metric distance, eRMSD, as a biased collective variable. We find that the native fold of both tetraloops is not the global free energy minimum using the Amberχ_OL3 force field. The estimated folding free energies are 30.2 ± 0.5 kJ/mol for UUCG and 7.5 ± 0.6 kJ/mol for GAGA, in striking disagreement with experimental data. We evaluate the viability of all possible one-dimensional backbone force field corrections. We find that disfavoring the gauche⁺ region of α and ζ angles consistently improves the existing force field. The level of accuracy achieved with these corrections, however, cannot be considered sufficient by judging on the basis of available thermodynamic data and solution experiments.

Free-energy landscape of a hyperstable RNA tetraloop

We report the characterization of the energy landscape and the folding/unfolding thermodynamics of a hyperstable RNA tetraloop obtained through high-performance molecular dynamics simulations at microsecond timescales. Sampling of the configurational landscape is conducted using temperature replica exchange molecular dynamics over three isochores at high, ambient, and negative pressures to determine the thermodynamic stability and the free-energy landscape of the tetraloop. The simulations reveal reversible folding/unfolding transitions of the tetraloop into the canonical A-RNA conformation and the presence of two alternative configurations, including a left-handed Z-RNA conformation and a compact purine Triplet. Increasing hydrostatic pressure shows a stabilizing effect on the A-RNA conformation and a destabilization of the left-handed Z-RNA. Our results provide a comprehensive description of the folded free-energy landscape of a hyperstable RNA tetraloop and highlight the significant advances of all-atom molecular dynamics in describing the unbiased folding of a simple RNA secondary structure motif.

Efficient Generalized Born Models for Monte Carlo Simulations

The Generalized Born Surface Area theory (GBSA) has become a popular method to model the solvation of biomolecules. While efficient in the context of molecular dynamics simulations, GBSA calculations do not integrate well with Monte Carlo simulations because of the nonlocal nature of the Generalized Born energy. We present a method by which Monte Carlo Generalized Born simulations can be made seven to eight times faster on a protein-ligand binding free energy calculation with little or no loss of accuracy. The method can be employed in any type of Monte Carlo or Hybrid Monte Carlo-molecular dynamics simulation and should prove useful in numerous applications.

Influence of Nitroxide Spin Labels on RNA Structure: A Molecular Dynamics Simulation Study

Pulsed electron double resonance (PELDOR) experiments on oligonucleotides provide a distance ruler that allows the measurement of nanometer distances accurately. The technique requires attachment of nitroxide spin labels to the nucleotides, which may possibly perturb its conformation. To study to what extent nitroxide spin labels may affect RNA structure, all-atom molecular dynamics simulations in explicit solvent are performed for six double-labeled RNA duplexes. A new parametrization of the force field for the nitroxide spin label is developed, which leads to intramolecular distances that are in good agreement with experimental results. Comparison of the results for spin-labeled and unlabeled RNA reveals that the conformational effect of the spin label depends significantly on whether the spin label is attached to the major or the minor groove of RNA. While major-groove spin labeling may to some extent affect the conformation of nearby base pairs, minor-groove spin labeling has the advantage of mostly preserving the RNA conformation.

Highly sampled tetranucleotide and tetraloop motifs enable evaluation of common RNA force fields

Recent modifications and improvements to standard nucleic acid force fields have attempted to fix problems and issues that have been observed as longer timescale simulations have become routine. Although previous work has shown the ability to fold the UUCG stem-loop structure, until now no group has attempted to quantify the performance of current force fields using highly converged structural populations of the tetraloop conformational ensemble. In this study, we report the use of multiple independent sets of multidimensional replica exchange molecular dynamics (M-REMD) simulations with different initial conditions to generate well-converged conformational ensembles for the tetranucleotides r(GACC) and r(CCCC), as well as the larger UUCG tetraloop motif. By generating what is to our knowledge the most complete RNA structure ensembles reported to date for these systems, we remove the coupling between force field errors and errors due to incomplete sampling, providing a comprehensive comparison between current top-performing MD force fields for RNA. Of the RNA force fields tested in this study, none demonstrate the ability to correctly identify the most thermodynamically stable structure for all three systems. We discuss the deficiencies present in each potential function and suggest areas where improvements can be made. The results imply that although "short" (nsec-μsec timescale) simulations may stay close to their respective experimental structures and may well reproduce experimental observables, inevitably the current force fields will populate alternative incorrect structures that are more stable than those observed via experiment.

Chemical probing of RNA with the hydroxyl radical at single-atom resolution

While hydroxyl radical cleavage is widely used to map RNA tertiary structure, lack of mechanistic understanding of strand break formation limits the degree of structural insight that can be obtained from this experiment. Here, we determine how individual ribose hydrogens of sarcin/ricin loop RNA participate in strand cleavage. We find that substituting deuterium for hydrogen at a ribose 5'-carbon produces a kinetic isotope effect on cleavage; the major cleavage product is an RNA strand terminated by a 5'-aldehyde. We conclude that hydroxyl radical abstracts a 5'-hydrogen atom, leading to RNA strand cleavage. We used this approach to obtain structural information for a GUA base triple, a common tertiary structural feature of RNA. Cleavage at U exhibits a large 5' deuterium kinetic isotope effect, a potential signature of a base triple. Others had noted a ribose-phosphate hydrogen bond involving the G 2'-OH and the U phosphate of the GUA triple, and suggested that this hydrogen bond contributes to backbone rigidity. Substituting deoxyguanosine for G, to eliminate this hydrogen bond, results in a substantial decrease in cleavage at G and U of the triple. We conclude that this hydrogen bond is a linchpin of backbone structure around the triple.

High-affinity recognition of HIV-1 frameshift-stimulating RNA alters frameshifting in vitro and interferes with HIV-1 infectivity

The life cycle of the human immunodeficiency virus type 1 (HIV-1) has an absolute requirement for ribosomal frameshifting during protein translation in order to produce the polyprotein precursor of the viral enzymes. While an RNA stem-loop structure (the “HIV-1 Frameshift Stimulating Signal”, or HIV-1 FSS) controls the frameshift efficiency and has been hypothesized as an attractive therapeutic target, developing compounds that selectively bind this RNA and interfere with HIV-1 replication has proven challenging. Building on our prior discovery of a “hit” molecule able to bind this stem-loop, we now report the development of compounds displaying high affinity for the HIV-1 FSS. These compounds are able to enhance frameshifting more than 50% in a dual-luciferase assay in human embryonic kidney cells, and they strongly inhibit the infectivity of pseudotyped HIV-1 virions.

Multidimensional Replica Exchange Molecular Dynamics Yields a Converged Ensemble of an RNA Tetranucleotide

A necessary step to properly assess and validate the performance of force fields for biomolecules is to exhaustively sample the accessible conformational space, which is challenging for large RNA structures. Given questions regarding the reliability of modeling RNA structure and dynamics with current methods, we have begun to use RNA tetranucleotides to evaluate force fields. These systems, though small, display considerable conformational variability and complete sampling with standard simulation methods remains challenging. Here we compare and discuss the performance of known variations of replica exchange molecular dynamics (REMD) methods, specifically temperature REMD (T-REMD), Hamiltonian REMD (H-REMD), and multidimensional REMD (M-REMD) methods, which have been implemented in Amber’s accelerated GPU code. Using two independent simulations, we show that M-REMD not only makes very efficient use of emerging large-scale GPU clusters, like Blue Waters at the University of Illinois, but also is critically important in generating the converged ensemble more efficiently than either T-REMD or H-REMD. With 57.6 μs aggregate sampling of a conformational ensemble with M-REMD methods, the populations can be compared to NMR data to evaluate force field reliability and further understand how putative changes to the force field may alter populations to be in more consistent agreement with experiment.

Counterion and polythymidine loop-length-dependent folding and thermodynamic stability of DNA hairpins reveal the unusual counterion-dependent stability of tetraloop hairpins

Stem-loop DNA hairpins containing a 5-base-pair (bp) stem and single-stranded polythymidine loop were investigated using thermodynamic melting analysis and stopped-flow kinetics. These studies revealed the thermodynamic stability and folding kinetics as a function of loop length and counterion concentration. Our results show the unusually high thermodynamic stability for tetraloop or 4 poly(dT) loop hairpin as compared with longer loop length hairpins. Furthermore, this exceptional stability is highly counterion-dependent. For example, in the higher counterion concentration regime of 50 mM NaCl and above, the tetraloop hairpin displays enhanced stability as compared with longer loop length hairpins. However, at lower counterion concentration of 25 mM NaCl and below, the thermal stability of tetraloop hairpin is consistent with the longer loop hairpins. The enhanced stability of tetraloop hairpins at higher counterion concentration can be explained on the basis of the combined entropic effect of loop closure as well as base stacking in the loop regions. The stability of longer loop length hairpins at all counterion concentrations as well as tetraloop hairpin at lower counterion concentration can be explained on the basis of entropic effect of loop closure alone. The thermodynamic parameters at lower and higher counterion concentrations were determined to quantify the enhanced stability of base-stacking effects occurring at higher counterion concentrations. For example, for 100 mM NaCl, excess Gibbs energy and enthalpy due to base stacking within the tetraloops were measured to be -1.2 ± 0.14 and -3.28 ± 0.32 kcal/mol, respectively, whereas, no excess of Gibbs energy and enthalpy was observed for 0, 5, 10, and 25 mM NaCl. These findings suggest significant base-stacking interactions occurring in the loop region of the tetraloop hairpins at higher counterion concentration and less significant base-stacking interactions in the lower counterion concentration regime. We suggest that at higher counterion concentrations, hydrophobic collapse of the nucleotides in the loop may be enhanced due to the increased polarity of the solvent, thereby enhancing base-stacking interactions that contribute to unusually high stability.

RNA structure and dynamics: a base pairing perspective

RNA is now known to possess various structural, regulatory and enzymatic functions for survival of cellular organisms. Functional RNA structures are generally created by three-dimensional organization of small structural motifs, formed by base pairing between self-complementary sequences from different parts of the RNA chain. In addition to the canonical Watson-Crick or wobble base pairs, several non-canonical base pairs are found to be crucial to the structural organization of RNA molecules. They appear within different structural motifs and are found to stabilize the molecule through long-range intra-molecular interactions between basic structural motifs like double helices and loops. These base pairs also impart functional variation to the minor groove of A-form RNA helices, thus forming anchoring site for metabolites and ligands. Non-canonical base pairs are formed by edge-to-edge hydrogen bonding interactions between the bases. A large number of theoretical studies have been done to detect and analyze these non-canonical base pairs within crystal or NMR derived structures of different functional RNA. Theoretical studies of these isolated base pairs using ab initio quantum chemical methods as well as molecular dynamics simulations of larger fragments have also established that many of these non-canonical base pairs are as stable as the canonical Watson-Crick base pairs. This review focuses on the various structural aspects of non-canonical base pairs in the organization of RNA molecules and the possible applications of these base pairs in predicting RNA structures with more accuracy.

Propensities for loop structures of RNA & DNA backbones

RNA oligonucleotides exhibit a large tendency to bend and form a loop conformation which is a major motif contributing to their complex three-dimensional structure. This is in contrast to DNA molecules that predominantly form the double-helix structure. In this paper we investigate by molecular dynamics simulation, as well as, by its combination with the replica-exchange method, the propensity of RNA chains containing the GCUAA pentaloop to form spontaneously a hairpin conformation. The results were then compared with those of analogous hybrid oligonucleotides in which the ribose groups in the loop-region were substituted by deoxyriboses. We find that the RNA oligomers exhibit a marginal excess stability to form loop structures. The equilibrium constant for opening the loop to an extended conformation is twice as large in the hybrid than it is in the RNA chain. Analyses of the hydrogen bonds indicate that the excess stability for forming a hairpin is a result of hydrogen bonds the 2'-hydroxyls in the loop region form with other groups in the loop. Of these hydrogen bonds, the most important is the hydrogen bond donated from the 2'-OH at the first position of the loop to N7 of adenine at the forth position. RNA and DNA backbones are characterized by different backbone dihedral angles and sugar puckering that can potentially facilitate or hamper the hydrogen bonds involving the 2'-OH. Nevertheless, the sugar puckerings of all the pentaloop nucleotides were not significantly different between the two chains displaying the C3'-endo conformation characteristic to the A-form double helix. All of the other backbone dihedrals also did not show any considerable difference in the loop-region except of the δ-dihedral. In this case, the RNA loop exhibited bimodal distributions corresponding to, both, the RNA and DNA backbones, whereas the loop of the hybrid chain behaved mostly as that of a DNA backbone. Thus, it is possible that the behavior of the δ-dihedrals in the loop-region of the RNA adopts conformations that facilitate the intra-nucleotide hydrogen bondings of the 2'-hydroxyls, and consequently renders loop structures in RNA more stable.

Ribose 2'-Hydroxyl Groups Stabilize RNA Hairpin Structures Containing GCUAA Pentaloop

The chemical structure of RNA and DNA is very similar; however, the three-dimensional conformation of these two nucleic acids is very different. Whereas the DNA adopts a repetitive structure of a double-stranded helix, RNA is primarily single stranded with a complex three-dimensional structure in which the hairpin is the most common secondary structure. Apart from the difference between uracil and thymine, the difference in the chemical structure between RNA and DNA is the presence of a hydroxyl group at position 2' of the sugar (ribose) instead of a hydrogen (deoxyribose). In this paper, we present molecular dynamics simulations addressing the contribution of 2'-hydroxyls to the stability of a GCUAA pentaloop motif. The results indicate that the 2'-hydroxyls stabilize the hairpin conformation of the GCUAA pentaloop relative to an analogous oligonucleotide in which the ribose sugars in the loop region were substituted with deoxyriboses. The magnitude of the stabilization was found to be 23.8 ± 4.1 kJ/mol using an alchemical mutations free energy method and 4.2 ± 6.5 kJ/mol using potential of mean force calculations. The latter indicates that in addition to its larger thermodynamic stability the RNA hairpin is also kinetically more stable. We find that the excess stability is a result of intrahairpin hydrogen bonds in the loop region between the 2'-hydroxyls and sugars, bases, and phosphates. The hydrogen bonds with the sugars and phosphates involve predominantly interactions with adjacent nucleotides. However, the hydrogen bonds with the bases involve also interactions between groups on opposite sides of the loop or with the middle base of the loop and are therefore likely to contribute significantly to the stability of the loop. Of these hydrogen bonds, the most frequent is observed between the 2'-hydroxyl at the first position of the pentaloop with N6/N7 of adenine at the forth position, as well as between the 2'-hydroxyl at position -1 with N6 of adenine at the fifth position. Our results contribute to the notion that one of the important roles of the ribose sugars in RNA is to facilitate hairpin formation.

Computational study of unfolding and regulation mechanism of preQ1 riboswitches

Riboswitches are novel RNA regulatory elements. Each riboswitch molecule consists of two domains: aptamer and express platform. The three-dimensional (3D) structure of the aptamer domain, depending on ligand binding or not, controls that of the express platform, which then switches on or off transcriptional or translational process. Here we study the two types of preQ(1) riboswitch aptamers from T. Tengcongensis (denoted as Tte preQ(1) riboswitch for short below) and Bacillus subtilis (denoted as Bsu preQ(1) riboswitch for short below), respectively. The free-state 3D structure of the Tte preQ(1) riboswitch is the same as its bound state but the Bsu preQ(1) riboswitch is not. Therefore, it is very interesting to investigate how these riboswitches realize their different regulation functions. We simulated the unfolding of these two aptamers through all-atom molecular dynamic simulation and found that they have similar unfolding or folding pathways and ligand-binding processes. The main difference between them is the folding intermediate states. The similarity and difference of their unfolding or folding dynamics may suggest their similar regulation mechanisms and account for their different functions, respectively. These results are also useful to understand the regulation mechanism of other riboswitches with free-state 3D structures similar to their bound states.

A kinetic zipper model with intrachain interactions applied to nucleic acid hairpin folding kinetics

Single-stranded DNA and RNA hairpin structures with 4-10 nucleotides (nt) in the loop and 5-8 basepairs (bp) in the stem fold on 10-100 μs timescale. In contrast, theoretical estimate of first contact time of two ends of an ideal semiflexible polymer of similar lengths (with persistence length ~2-nt) is 10-100 ns. We propose that this three-orders-of-magnitude difference between these two timescales is a result of roughness in the folding free energy surface arising from intrachain interactions. We present a statistical mechanical model that explicitly includes all misfolded microstates with nonnative Watson-Crick (WC) and non-WC contacts. Rates of interconversion between different microstates are described in terms of two adjustable parameters: the strength of the non-WC interactions (ΔG(nWC)) and the rate at which a basepair is formed adjacent to an existing basepair (k(bp)(+)). The model accurately reproduces the temperature and loop-length dependence of the measured relaxation rates in temperature-jump studies of a 7-bp stem, single-stranded DNA hairpin with 4-20-nt-long poly(dT) loops, with ΔG(nWC) ≈ -2.4 kcal/mol and k(bp)(+) ≥ (1 ns)(-1), in 100 mM NaCl. Thus, our model provides a microscopic interpretation of the slow hairpin folding times as well as an estimate of the strength of intrachain interactions.

Thermodynamics and kinetics of the hairpin ribozyme from atomistic folding/unfolding simulations

We report a set of atomistic folding/unfolding simulations for the hairpin ribozyme using a Monte Carlo algorithm. The hairpin ribozyme folds in solution and catalyzes self-cleavage or ligation via a specific two-domain structure. The minimal active ribozyme has been studied extensively, showing stabilization of the active structure by cations and dynamic motion of the active structure. Here, we introduce a simple model of tertiary-structure formation that leads to a phase diagram for the RNA as a function of temperature and tertiary-structure strength. We then employ this model to capture many folding/unfolding events and to examine the transition-state ensemble (TSE) of the RNA during folding to its active "docked" conformation. The TSE is compact but with few tertiary interactions formed, in agreement with single-molecule dynamics experiments. To compare with experimental kinetic parameters, we introduce a novel method to benchmark Monte Carlo kinetic parameters to docking/undocking rates collected over many single molecular trajectories. We find that topology alone, as encoded in a biased potential that discriminates between secondary and tertiary interactions, is sufficient to predict the thermodynamic behavior and kinetic folding pathway of the hairpin ribozyme. This method should be useful in predicting folding transition states for many natural or man-made RNA tertiary structures.

Order parameters for macromolecules: application to multiscale simulation

Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10(-14) s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.

Molecular dynamics of ribosomal elongation factors G and Tu

Translation on the ribosome is controlled by external factors. During polypeptide lengthening, elongation factors EF-Tu and EF-G consecutively interact with the bacterial ribosome. EF-Tu binds and delivers an aminoacyl-tRNA to the ribosomal A site and EF-G helps translocate the tRNAs between their binding sites after the peptide bond is formed. These processes occur at the expense of GTP. EF-Tu:tRNA and EF-G are of similar shape, share a common binding site, and undergo large conformational changes on interaction with the ribosome. To characterize the internal motion of these two elongation factors, we used 25 ns long all-atom molecular dynamics simulations. We observed enhanced mobility of EF-G domains III, IV, and V and of tRNA in the EF-Tu:tRNA complex. EF-Tu:GDP complex acquired a configuration different from that found in the crystal structure of EF-Tu with a GTP analogue, showing conformational changes in the switch I and II regions. The calculated electrostatic properties of elongation factors showed no global similarity even though matching electrostatic surface patches were found around the domain I that contacts the ribosome, and in the GDP/GTP binding region.

RNA stability under different combinations of amber force fields and solvation models

The proper matching of force field and solvent is critical to obtain correct result in molecular dynamics simulation of bio-molecules. This problem has been intensively investigated for protein but not for RNA yet. In this paper, we use standard molecular dynamics and replica exchange molecular dynamics to take a series of tests on the RNA stability under different combinations of Amber force field parameters (ff98, ff99 and ff99bsc0) and the general Born implicit solvent models (igb1, igb2 and igb5). It is found that only ff98 and ff99bsc0 with igb1 can keep the native conformations of RNA hairpin and duplex. Our results suggest that ff98 plus igb1 may be reasonable choice for molecular dynamics simulation of RNA dynamics.

Folding kinetics for the conformational switch between alternative RNA structures

Transitions between different conformational states, so-called conformational switching, are intrinsic to RNA catalytic and regulatory functions. Often, conformational switching occurs on time scales of several seconds. In combination with the recent real-time NMR experiments (Wenter et al. Angew. Chem. Int. Ed. 2005, 44, 2600; Wenter et al. ChemBioChem 2006, 7, 417) for the transitions between bistable RNA conformations, we combine the master equation method with the kinetic cluster method to investigate the detailed kinetic mechanism and the factors that govern the folding kinetics. We propose that heat capacity change (ΔC(p)) upon RNA folding may be important for RNA folding kinetics. In addition, we find that, for tetraloop hairpins, noncanonical (tertiary) intraloop interactions are important to determine the folding kinetics. Furthermore, through theory-experiment comparisons, we find that the different rate models for the fundamental steps (i.e., formation/disruption of a base pair or stack) can cause contrasting results in the theoretical predictions.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.

Energetic decomposition with the generalized-born and Poisson-Boltzmann solvent models: lessons from association of G-protein components

Continuum electrostatic models have been shown to be powerful tools in providing insight into the energetics of biomolecular processes. While the Poisson-Boltzmann (PB) equation provides a theoretically rigorous approach to computing electrostatic free energies of solution in such a model, computational cost makes its use for large ensembles of states impractical. The generalized-Born (GB) approximation provides a much faster alternative, although with a weaker theoretical framework. While much attention has been given to how GB recapitulates PB energetics for the overall stability of a biomolecule or the affinity of a complex, little attention has been given to how the contributions of individual functional groups are captured by the two methods. Accurately capturing these individual electrostatic components is essential both for the development of a mechanistic understanding of biomolecular processes and for the design of variant sequences and structures with desired properties. Here, we present a detailed comparison of the group-wise decomposition of both PB and GB electrostatic free energies of binding, using association of various components of the heterotrimeric-G-protein complex as a model. We find that, while net binding free energies are strongly correlated in the two models, the correlations of individual group contributions are highly variable; in some cases, strong correlation is seen, while in others, there is essentially none. Structurally, the GB model seems to capture the magnitude of direct, short-range electrostatic interactions quite well but performs more poorly with moderate-range "action-at-a-distance" interactions--GB has a tendency to overestimate solvent screening over moderate distances, and to underestimate the costs of desolvating charged groups somewhat removed from the binding interface. Despite this, however, GB does seem to be quite effective as a predictor of those groups that will be computed to be most significant in a PB-based model.

Predicting secondary structural folding kinetics for nucleic acids

We report a new computational approach to the prediction of RNA secondary structure folding kinetics. In this approach, each elementary kinetic step is represented as the transformation between two secondary structures that differ by a helix. Based on the free energy landscape analysis, we identify three types of dominant pathways and the rate constants for the kinetic steps: 1), formation; 2), disruption of a helix stem; and 3), helix formation with concomitant partial melting of a competing (incompatible) helix. The third pathway, termed the tunneling pathway, is the low-barrier dominant pathway for the conversion between two incompatible helices. Comparisons with experimental data indicate that this new method is quite reliable in predicting the kinetics for RNA secondary structural folding and structural rearrangements. The approach presented here may provide a robust first step for further systematic development of a predictive theory for the folding kinetics for large RNAs.

Equilibrium conformational dynamics in an RNA tetraloop from massively parallel molecular dynamics

Conformational equilibrium within the ubiquitous GNRA tetraloop motif was simulated at the ensemble level, including 10 000 independent all-atom molecular dynamics trajectories totaling over 110 µs of simulation time. This robust sampling reveals a highly dynamic structure comprised of 15 conformational microstates. We assemble a Markov model that includes transitions ranging from the nanosecond to microsecond timescales and is dominated by six key loop conformations that contribute to fluctuations around the native state. Mining of the Protein Data Bank provides an abundance of structures in which GNRA tetraloops participate in tertiary contact formation. Most predominantly observed in the experimental data are interactions of the native loop structure within the minor groove of adjacent helical regions. Additionally, a second trend is observed in which the tetraloop assumes non-native conformations while participating in multiple tertiary contacts, in some cases involving multiple possible loop conformations. This tetraloop flexibility can act to counterbalance the energetic penalty associated with assuming non-native loop structures in forming tertiary contacts. The GNRA motif has thus evolved not only to readily participate in simple tertiary interactions involving native loop structure, but also to easily adapt tetraloop secondary conformation in order to participate in larger, more complex tertiary interactions.