Free-energy landscape of a hyperstable RNA tetraloop

Energy landscapes of homopolymeric RNAs revealed by deep unsupervised learning

Conformational dynamics of RNA plays important roles in a variety of cellular functions such as transcriptional regulation, catalysis, scaffolding, and sensing. Recently, RNAs with low-complexity sequences have been shown to phase separate and form condensate phases similar to lowcomplexity protein domains. The affinity for phase separation and the material characteristics of RNA condensates are strongly dependent on sequence composition and patterning. We hypothesize that differences in the affinities for RNA phase separation can be uncovered by studying sequence-dependent conformational dynamics of single RNA chains. To this end, we have employed atomistic simulations and deep dimensionality reduction techniques to map temperature-dependent conformational free energy landscapes for 20 base-long homopolymeric RNA sequences: poly(U), poly(G), poly(C), and poly(A). The energy landscapes of homopolymeric RNAs reveal a plethora of metastable states with qualitatively different populations stemming from differences in base chemistry. Through detailed analysis of base, phosphate, and sugar interactions, we show that experimentally observed temperature-driven shifts in metastable state populations align with experiments on RNA phase transitions. Specifically, we find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability, mirroring the propensity of RNA to form condensates. To conclude, this work shows that at least for homopolymeric RNA sequences the single-chain conformational dynamics contains sufficient information for predicting and quantifying condensate forming affinities of RNAs. Thus, we anticipate that atomically detailed studies of temeprature -dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Characterizing the Folding Transition-State Ensembles in the Energy Landscape of an RNA Tetraloop

Molecular dynamics (MD) simulations have become increasingly powerful and can now describe the folding/unfolding of small biomolecules in atomic detail. However, a major challenge in MD simulations is to represent the complex energy landscape of biomolecules using a small number of reaction coordinates. In this study, we investigate the folding pathways of an RNA tetraloop, gcGCAAgc, using five classical MD simulations with a combined simulation time of approximately 120 μs. Our approach involves analyzing the tetraloop dynamics, including the folding transition state ensembles, using the energy landscape visualization method (ELViM). The ELViM is an approach that uses internal distances to compare any two conformations, allowing for a detailed description of the folding process without requiring root mean square alignment of structures. This method has previously been applied to describe the energy landscape of disordered β-amyloid peptides and other proteins. The ELViM results in a non-linear projection of the multidimensional space, providing a comprehensive representation of the tetraloop's energy landscape. Our results reveal four distinct transition-state regions and establish the paths that lead to the folded tetraloop structure. This detailed analysis of the tetraloop's folding process has important implications for understanding RNA folding, and the ELViM approach can be used to study other biomolecules.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

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.

Exploring the multiple conformational states of RNA genome through interhelical dynamics and network analysis

The structural variation of RNA is often very transient and can be easily missed in experiments. Molecular dynamics simulation studies along with network analysis can be an effective tool to identify prominent conformations of such dynamic biomolecular systems. Here we describe a method to effectively sample different RNA conformations at six different temperatures based on the changes in the interhelical orientations. This method gives the information about prominent states of the RNA as well as the probability of the existence of different conformations and their interconnections during the process of evolution. In the case of the SARS-CoV-2 genome, the change of prominent structures was found to be faster at 333 K as compared to higher temperatures due to the formation of the non-native base pairs. ΔΔG calculated between 288 K and 363 K are found to be 10.31 kcal/mol (88 nt) considering the contribution from the multiple states of the RNA which agrees well with the experimentally reported denaturation energy for E. coli α mRNA pseudoknot (∼16 kcal/mol, 112 nt) determined by calorimetry/UV hyperchromicity and human telomerase RNA telomerase (4.5-6.6 kcal/mol, 54 nt) determined by FRET analysis.

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.

TPP Riboswitch Populates Holo-Form-like Structure Even in the Absence of Cognate Ligand at High Mg2+ Concentration

Riboswitches are noncoding RNA that regulate gene expression by folding into specific three-dimensional structures (holo-form) upon binding by their cognate ligand in the presence of Mg²⁺. Riboswitch functioning is also hypothesized to be under kinetic control requiring large cognate ligand concentrations. We ask the question under thermodynamic conditions, can the riboswitches populate structures similar to the holo-form only in the presence of Mg²⁺ and absence of cognate ligand binding. We addressed this question using thiamine pyrophosphate (TPP) riboswitch as a model system and computer simulations using a coarse-grained model for RNA. The folding free energy surface (FES) shows that with the initial increase in Mg²⁺ concentration ([Mg²⁺]), the aptamer domain (AD) of TPP riboswitch undergoes a barrierless collapse in its dimensions. On further increase in [Mg²⁺], intermediates separated by barriers appear on the FES, and one of the intermediates has a TPP ligand-binding competent structure. We show that site-specific binding of the Mg²⁺ aids in the formation of tertiary contacts. For [Mg²⁺] greater than physiological concentration, AD folds into a structure similar to the crystal structure of the TPP holo-form even in the absence of the TPP ligand. The folding kinetics shows that TPP AD populates an intermediate due to the misalignment of two arms present in the structure, which acts as a kinetic trap, leading to larger folding timescales. The predictions of the intermediate structures from the simulations are amenable for experimental verification.

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.

Temperature-Dependent Conformational Evolution of SARS CoV-2 RNA Genome Using Network Analysis

Understanding the dynamics of the SARS CoV-2 RNA genome and its dependence on temperature is necessary to fight the current COVID-19 crisis. Computationally, the handling of large data is a major challenge in the elucidation of the structures of RNA. This work presents network analysis as an important tool to see the conformational evolution and the most dominant structures of the RNA genome at six different temperatures. It effectively distinguished different communities of RNA having structural variation. It is found that at higher temperatures (348 K and above), 80% of the RNA structure is destroyed in both the SPC/E and mTIP3P water models. The thermal denaturation free energy change ΔΔG value calculated for the long-lived structure at higher temperatures of 348 and 363 K ranges from 2.58 to 2.78 kcal/mol for the SPC/E water model, which agrees well with the experimentally reported thermal denaturation free energy range of 2.874 kcal/mol of SARS CoV-NP at normal pH. At higher temperatures, the stability of RNA conformation is found to be due to the existence of non-native base pairs in the SPC/E water model.

Deciphering nucleotide modification-induced structure and stability changes

Nucleotide modification in RNA controls a bevy of biological processes, including RNA degradation, gene expression, and gene editing. In turn, misregulation of modified nucleotides is associated with a host of chronic diseases and disorders. However, the molecular mechanisms driving these processes remain poorly understood. To partially address this knowledge gap, we used alchemical and temperature replica exchange molecular dynamics (TREMD) simulations on an RNA duplex and an analogous hairpin to probe the structural effects of modified and/or mutant nucleotides. The simulations successfully predict the modification/mutation-induced relative free energy change for complementary duplex formation, and structural analyses highlight mechanisms driving stability changes. Furthermore, TREMD simulations for a hairpin-forming RNA with and without modification provide reliable estimations of the energy landscape. Illuminating the impact of methylated and/or mutated nucleotides on the structure-function relationship and the folding energy landscape, the simulations provide insights into modification-induced alterations to the folding mechanics of the hairpin. The results here may be biologically significant as hairpins are widespread structure motifs that play critical roles in gene expression and regulation. Specifically, the tetraloop of the probed hairpin is phylogenetically abundant, and the stem mirrors a miRNA seed region whose modification has been implicated in epilepsy pathogenesis.

Modeling the Influenza A NP-vRNA-Polymerase Complex in Atomic Detail

Seasonal flu is an acute respiratory disease that exacts a massive toll on human populations, healthcare systems and economies. The disease is caused by an enveloped Influenza virus containing eight ribonucleoprotein (RNP) complexes. Each RNP incorporates multiple copies of nucleoprotein (NP), a fragment of the viral genome (vRNA), and a viral RNA-dependent RNA polymerase (POL), and is responsible for packaging the viral genome and performing critical functions including replication and transcription. A complete model of an Influenza RNP in atomic detail can elucidate the structural basis for viral genome functions, and identify potential targets for viral therapeutics. In this work we construct a model of a complete Influenza A RNP complex in atomic detail using multiple sources of structural and sequence information and a series of homology-modeling techniques, including a motif-matching fragment assembly method. Our final model provides a rationale for experimentally-observed changes to viral polymerase activity in numerous mutational assays. Further, our model reveals specific interactions between the three primary structural components of the RNP, including potential targets for blocking POL-binding to the NP-vRNA complex. The methods developed in this work open the possibility of elucidating other functionally-relevant atomic-scale interactions in additional RNP structures and other biomolecular complexes.

On the Adaptability of the Chemical Reaction of Hairpin Ribozyme to High Pressures

The discovery of RNA enzymes, ribozymes, provided strong support to the RNA world hypothesis suggesting that early life evolved from RNAs able to both store genetic information and catalyze biochemical reactions. Moreover, evidence is accumulating that primitive life might have emerged in deep-sea environments and, thus, at high hydrostatic pressures. If true, ribozymes should be able to function under those pressures. In this work, we ask if and possibly how ribozymes could function at high pressures. To this end, we specifically focus on the chemical reaction steps of the self-cleavage catalysis of hairpin ribozyme by employing extensive QM/MM metadynamics simulations. We find that the reaction scenario at high pressures is vastly different than that at ambient conditions, yet the rate-limiting reaction barrier and, thus, the reaction rate are only marginally affected. Therefore, the results indeed suggest that ribozymes would function at high pressures but by following a vastly different reaction scenario.

Probing the operability regime of an engineered ribocomputing unit in terms of dynamic range maintenance with extracellular changes and time

Synthetic biology aims at engineering gene regulatory circuits to end with cells (re)programmed on purpose to implement novel functions or discover natural behaviors. However, one overlooked question is whether the resulting circuits perform as intended in variety of environments or with time. Here, we considered a recently engineered genetic system that allows programming the cell to work as a minimal computer (arithmetic logic unit) in order to analyze its operability regime. This system involves transcriptional and post-transcriptional regulations. In particular, we studied the analog behavior of the system, the effect of physicochemical changes in the environment, the impact on cell growth rate of the heterologous expression, and the ability to maintain the arithmetic functioning over time. Conclusively, our results suggest 1) that there are wide input concentration ranges that the system can correctly process, the resulting outputs being predictable with a simple mathematical model, 2) that the engineered circuitry is quite sensitive to temperature effects, 3) that the expression of heterologous small RNAs is costly for the cell, not only of heterologous proteins, and 4) that a proper genetic reorganization of the system to reduce the amount of heterologous DNA in the cell can improve its evolutionary stability.

Pressure dependence of vibrational optical activity of model biomolecules. A computational study

Change of molecular properties with pressure is an attracting means to regulate molecular reactivity or biological activity. However, the effect is usually small and so far explored rather scarcely. To obtain a deeper insight and estimate the sensitivity of vibrational optical activity spectra to pressure-induced conformational changes, we investigate small model molecules. The Ala-Ala dipeptide, isomaltose disaccharide and adenine-uracil dinucleotide were chosen to represent three different biomolecular classes. The pressure effects were modeled by molecular dynamics and density functional theory simulations. The dinucleotide was found to be the most sensitive to the pressure, whereas for the disaccharide the smallest changes are predicted. Pressure-induced relative intensity changes in vibrational circular dichroism and Raman optical activity spectra are predicted to be 2-3-times larger than for non-polarized IR and Raman techniques.

Kinetic Mechanism of RNA Helix-Terminal Basepairing-A Kinetic Minima Network Analysis

RNA functions are often kinetically controlled. The folding kinetics of RNAs involves global structural changes and local nucleotide movement, such as base flipping. The most elementary step in RNA folding is the closing and opening of a basepair. By integrating molecular dynamics simulation, master equation, and kinetic Monte Carlo simulation, we investigate the kinetics mechanism of RNA helix-terminal basepairing. The study reveals a six-state folding scheme with three dominant folding pathways of tens, hundreds, and thousands of nanoseconds of folding timescales, respectively. The overall kinetics is rate limited by the detrapping of a misfolded state with the overall folding time of 10^-5 s. Moreover, the analysis examines the different roles of the various driving forces, such as the basepairing and stacking interactions and the ion binding/dissociation effects on structural changes. The results may provide useful insights for developing a basepair opening/closing rate model and further kinetics models of large RNAs.

Mechanistic role of nucleobases in self-cleavage catalysis of hairpin ribozyme at ambient versus high-pressure conditions

Ribozymes catalyze the site-specific self-cleavage of intramolecular phosphodiester bonds. Initially thought to act as metalloenzymes, they are now known to be functional even in the absence of divalent metal ions and specific nucleobases directly participate in the self-cleavage reaction. Here, we use extensive replica exchange molecular dynamics simulations to probe the precise mechanistic role of nucleobases by simulating precatalytic reactant and active precursor states of a hairpin ribozyme along its reaction path at ambient as well as high-pressure conditions. The results provide novel key insights into the self-cleavage of ribozymes. We find that deprotonation of the hydroxyl group is crucial and might be the penultimate step to the self-cleavage. The G8 nucleobase is found to stabilize the activated precursor into inline arrangement for facile nucleophilic attack of the scissile phosphate only after deprotonation of the hydroxyl group. The protonated A38 nucleobase, in contrast, mainly acts a proton donor to the O5'-oxygen leaving group that eventually leads to the self-cleavage. Indeed, systematic high-pressure simulations of catalytically relevant states confirm these findings and, moreover, provide support to the role of ribozymes as piezophilic biocatalysts with regard to their relevance in early life under extreme conditions in the realm of RNA world hypothesis.

Perspective: Identification of collective variables and metastable states of protein dynamics

The statistical analysis of molecular dynamics simulations requires dimensionality reduction techniques, which yield a low-dimensional set of collective variables (CVs) {x _i } = x that in some sense describe the essential dynamics of the system. Considering the distribution P( x ) of the CVs, the primal goal of a statistical analysis is to detect the characteristic features of P( x ), in particular, its maxima and their connection paths. This is because these features characterize the low-energy regions and the energy barriers of the corresponding free energy landscape ΔG( x ) = -k _B T ln P( x ), and therefore amount to the metastable states and transition regions of the system. In this perspective, we outline a systematic strategy to identify CVs and metastable states, which subsequently can be employed to construct a Langevin or a Markov state model of the dynamics. In particular, we account for the still limited sampling typically achieved by molecular dynamics simulations, which in practice seriously limits the applicability of theories (e.g., assuming ergodicity) and black-box software tools (e.g., using redundant input coordinates). We show that it is essential to use internal (rather than Cartesian) input coordinates, employ dimensionality reduction methods that avoid rescaling errors (such as principal component analysis), and perform density based (rather than k-means-type) clustering. Finally, we briefly discuss a machine learning approach to dimensionality reduction, which highlights the essential internal coordinates of a system and may reveal hidden reaction mechanisms.

RNA as a Complex Polymer with Coupled Dynamics of Ions and Water in the Outer Solvation Sphere

We unravel the internal and collective modes of a widely studied 58-nucleotide rRNA fragment in solvent using atomically detailed molecular dynamics simulations. The variation of lifetimes for water hydrogen bonds with nucleotide groups indicates heterogeneity of water dynamics on the RNA surface. The time scales of interactions of the discrete water molecules with RNA nucleotides extend from several hundred picoseconds to a few nanoseconds. We determine all of the association sites and the spatial distribution of residence times for Mg²⁺, K⁺, and water molecules in those sites. We provide insights into the population of Mg²⁺ and K⁺ ions and water molecules in the outer sphere and how their fluctuations are intricately linked with the kinetics of the 58-mer. We find that many of the long-lived Mg²⁺ sites identified from the simulations agree with the locations of ions in the X-ray structure. We determine the excess ion atmosphere around the rRNA and compare it with experimental data. We investigate the collective behavior of RNA, ions, and water, by performing a joint principle component analysis for the Cartesian coordinates of the RNA phosphorus atoms and for the occupation counts of the association sites. Our results indicate that the 58-mer system is a complex polymer, composed of RNA that is encased by a fluctuating network of associated counterions, co-ions, and water.

Concentration-dependent and configuration-dependent interactions of monovalent ions with an RNA tetraloop

Monovalent salt solutions have strongly coupled interactions with biopolymers, from large polyelectrolytes to small RNA oligomers. High salt concentrations have been known to induce transitions in the structure of RNA, producing non-canonical configurations and even driving RNA to precipitate out of solution. Using all-atom molecular dynamics simulations, we model a monovalent salt species (KCL) at high concentrations (0.1-3m) and calculate the equilibrium distributions of water and ions around a small tetraloop-forming RNA oligomer in a variety of structural arrangements: folded A-RNA (canonical) and Z-RNA (non-canonical) tetraloops and unfolded configurations. From these data, we calculate the ion preferential binding coefficients and Donnan coefficients for the RNA oligomer as a function of concentration and structure. We find that cation accumulation is highest around non-canonical Z-RNA configurations at concentrations below 0.5m, while unfolded configurations accumulate the most co-ions in all concentrations. By contrast, canonical A-RNA structures consistently show the lowest accumulations for all ion species. Water distributions vary markedly with RNA configuration but show little dependency on KCL concentration. Based on Donnan coefficient calculations, the net charge of the solution at the surface of the RNA decreases linearly as a function of salt concentration and becomes net-neutral near 2.5-3m KCL for folded configurations, while unfolded configurations still show a positive solution charge. Our findings show that all-atom molecular dynamics can describe the equilibrium distributions of monovalent salt in the presence of small RNA oligomers at KCL concentrations where ion correlation effects become important. Furthermore, these results provide valuable insights into the distributions of water and ions near the RNA oligomer surface as a function of structural configuration.

Principal component analysis on a torus: Theory and application to protein dynamics

A dimensionality reduction method for high-dimensional circular data is developed, which is based on a principal component analysis (PCA) of data points on a torus. Adopting a geometrical view of PCA, various distance measures on a torus are introduced and the associated problem of projecting data onto the principal subspaces is discussed. The main idea is that the (periodicity-induced) projection error can be minimized by transforming the data such that the maximal gap of the sampling is shifted to the periodic boundary. In a second step, the covariance matrix and its eigendecomposition can be computed in a standard manner. Adopting molecular dynamics simulations of two well-established biomolecular systems (Aib₉ and villin headpiece), the potential of the method to analyze the dynamics of backbone dihedral angles is demonstrated. The new approach allows for a robust and well-defined construction of metastable states and provides low-dimensional reaction coordinates that accurately describe the free energy landscape. Moreover, it offers a direct interpretation of covariances and principal components in terms of the angular variables. Apart from its application to PCA, the method of maximal gap shifting is general and can be applied to any other dimensionality reduction method for circular data.

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.

Emergency Services of Viral RNAs: Repair and Remodeling

Reproduction of RNA viruses is typically error-prone due to the infidelity of their replicative machinery and the usual lack of proofreading mechanisms. The error rates may be close to those that kill the virus. Consequently, populations of RNA viruses are represented by heterogeneous sets of genomes with various levels of fitness. This is especially consequential when viruses encounter various bottlenecks and new infections are initiated by a single or few deviating genomes. Nevertheless, RNA viruses are able to maintain their identity by conservation of major functional elements. This conservatism stems from genetic robustness or mutational tolerance, which is largely due to the functional degeneracy of many protein and RNA elements as well as to negative selection. Another relevant mechanism is the capacity to restore fitness after genetic damages, also based on replicative infidelity. Conversely, error-prone replication is a major tool that ensures viral evolvability. The potential for changes in debilitated genomes is much higher in small populations, because in the absence of stronger competitors low-fit genomes have a choice of various trajectories to wander along fitness landscapes. Thus, low-fit populations are inherently unstable, and it may be said that to run ahead it is useful to stumble. In this report, focusing on picornaviruses and also considering data from other RNA viruses, we review the biological relevance and mechanisms of various alterations of viral RNA genomes as well as pathways and mechanisms of rehabilitation after loss of fitness. The relationships among mutational robustness, resilience, and evolvability of viral RNA genomes are discussed.

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.

Exploring RNA structure and dynamics through enhanced sampling simulations

RNA function is intimately related to its structural dynamics. Molecular dynamics simulations are useful for exploring biomolecular flexibility but are severely limited by the accessible timescale. Enhanced sampling methods allow this timescale to be effectively extended in order to probe biologically relevant conformational changes and chemical reactions. Here, we review the role of enhanced sampling techniques in the study of RNA systems. We discuss the challenges and promises associated with the application of these methods to force-field validation, exploration of conformational landscapes and ion/ligand-RNA interactions, as well as catalytic pathways. Important technical aspects of these methods, such as the choice of the biased collective variables and the analysis of multi-replica simulations, are examined in detail. Finally, a perspective on the role of these methods in the characterization of RNA dynamics is provided.

Insilico direct folding of thrombin-binding aptamer G-quadruplex at all-atom level

The reversible folding of the thrombin-binding DNA aptamer G-quadruplexes (GQs) (TBA-15) starting from fully unfolded states was demonstrated using a prolonged time scale (10-12 μs) parallel tempering metadynamics (PTMetaD) simulation method in conjunction with a modified version of the AMBER bsc1 force field. For unbiased descriptions of the folding free energy landscape of TBA-15, this force field was minimally modified. From this direct folding simulation using the modified bsc1 force field, reasonably converged free energy landscapes were obtained in K+-rich aqueous solution (150 mM), providing detailed atomistic pictures of GQ folding mechanisms for TBA-15. This study found that the TBA folding occurred via multiple folding pathways with two major free energy barriers of 13 and 15 kcal/mol in the presence of several intermediate states of G-triplex variants. The early formation of these intermediates was associated with a single K+ ion capturing. Interestingly, these intermediate states appear to undergo facile transitions among themselves through relatively small energy barriers.

Pressure modulates the self-cleavage step of the hairpin ribozyme

The ability of certain RNAs, denoted as ribozymes, to not only store genetic information but also catalyse chemical reactions gave support to the RNA world hypothesis as a putative step in the development of early life on Earth. This, however, might have evolved under extreme environmental conditions, including the deep sea with pressures in the kbar regime. Here we study pressure-induced effects on the self-cleavage of hairpin ribozyme by following structural changes in real-time. Our results suggest that compression of the ribozyme leads to an accelerated transesterification reaction, being the self-cleavage step, although the overall process is retarded in the high-pressure regime. The results reveal that favourable interactions between the reaction site and neighbouring nucleobases are strengthened under pressure, resulting therefore in an accelerated self-cleavage step upon compression. These results suggest that properly engineered ribozymes may also act as piezophilic biocatalysts in addition to their hitherto known properties.

Noncanonical α/γ Backbone Conformations in RNA and the Accuracy of Their Description by the AMBER Force Field

The sugar-phosphate backbone of RNA can exist in diverse rotameric substates, giving RNA molecules enormous conformational variability. The most frequent noncanonical backbone conformation in RNA is α/γ = t/t, which is derived from the canonical backbone by a crankshaft motion and largely preserves the standard geometry of the RNA duplex. A similar conformation also exists in DNA, where it has been extensively studied and shown to be involved in DNA-protein interactions. However, the function of the α/γ = t/t conformation in RNA is poorly understood. Here, we present molecular dynamics simulations of several prototypical RNA structures obtained from X-ray and NMR experiments, including canonical and mismatched RNA duplexes, UUCG and GAGA tetraloops, Loop E, the sarcin-ricin loop, a parallel guanine quadruplex, and a viral pseudoknot. The stability of various noncanonical α/γ backbone conformations was analyzed with two AMBER force fields, ff99bsc0χ_OL3 and ff99bsc0χ_OL3 with the recent εζ_OL1 and β_OL1 corrections for DNA. Although some α/γ substates were stable with seemingly well-described equilibria, many were unstable in our simulations. Notably, the most frequent noncanonical conformer α/γ = t/t was unstable in both tested force fields. Possible reasons for this instability are discussed. Our work reveals a potentially important artifact in RNA force fields and highlights a need for further force field refinement.

Revisiting GNRA and UNCG folds: U-turns versus Z-turns in RNA hairpin loops

When thinking about RNA three-dimensional structures, coming across GNRA and UNCG tetraloops is perceived as a boon since their folds have been extensively described. Nevertheless, analyzing loop conformations within RNA and RNP structures led us to uncover several instances of GNRA and UNCG loops that do not fold as expected. We noticed that when a GNRA does not assume its "natural" fold, it adopts the one we typically associate with a UNCG sequence. The same folding interconversion may occur for loops with UNCG sequences, for instance within tRNA anticodon loops. Hence, we show that some structured tetranucleotide sequences starting with G or U can adopt either of these folds. The underlying structural basis that defines these two fold types is the mutually exclusive stacking of a backbone oxygen on either the first (in GNRA) or the last nucleobase (in UNCG), generating an oxygen-π contact. We thereby propose to refrain from using sequences to distinguish between loop conformations. Instead, we suggest using descriptors such as U-turn (for "GNRA-type" folds) and a newly described Z-turn (for "UNCG-type" folds). Because tetraloops adopt for the largest part only two (inter)convertible turns, we are better able to interpret from a structural perspective loop interchangeability occurring in ribosomes and viral RNA. In this respect, we propose a general view on the inclination for a given sequence to adopt (or not) a specific fold. We also suggest how long-noncoding RNAs may adopt discrete but transient structures, which are therefore hard to predict.

Equilibrium Denaturation and Preferential Interactions of an RNA Tetraloop with Urea

Urea is an important organic cosolute with implications in maintaining osmotic stress in cells and differentially stabilizing ensembles of folded biomolecules. We report an equilibrium study of urea-induced denaturation of a hyperstable RNA tetraloop through unbiased replica exchange molecular dynamics. We find that, in addition to destabilizing the folded state, urea smooths the RNA free energy landscape by destabilizing specific configurations, and forming favorable interactions with RNA nucleobases. A linear concentration-dependence of the free energy (m-value) is observed, in agreement with the results of other RNA hairpins and proteins. Additionally, analysis of the hydrogen-bonding and stacking interactions within RNA primarily show temperature-dependence, while interactions between RNA and urea primarily show concentration-dependence. Our findings provide valuable insight into the effects of urea on RNA folding and describe the thermodynamics of a basic RNA hairpin as a function of solution chemistry.

Simultaneous NMR characterisation of multiple minima in the free energy landscape of an RNA UUCG tetraloop

RNA molecules in solution tend to undergo structural fluctuations of relatively large amplitude and to populate a range of different conformations some of which with low populations. It is still very challenging, however, to characterise the structures of these low populated states and to understand their functional roles. In the present study, we address this problem by using NMR residual dipolar couplings (RDCs) as structural restraints in replica-averaged metadynamics (RAM) simulations. By applying this approach to a 14-mer RNA hairpin containing the prototypical UUCG tetraloop motif, we show that it is possible to construct the free energy landscape of this RNA molecule. This free energy landscapes reveals the surprisingly rich dynamics of the UUCG tetraloop and identifies the multiple substates that exist in equilibrium owing to thermal fluctuations. The approach that we present is general and can be applied to the study of the free energy landscapes of other RNA or RNA-protein systems.

The Chloroplast SRP Systems of Chaetosphaeridium globosum and Physcomitrella patens as Intermediates in the Evolution of SRP-Dependent Protein Transport in Higher Plants

The bacterial signal recognition particle (SRP) mediates the cotranslational targeting of membrane proteins and is a high affinity complex consisting of a SRP54 protein subunit (Ffh) and an SRP RNA. The chloroplast SRP (cpSRP) pathway has adapted throughout evolution to enable the posttranslational targeting of the light harvesting chlorophyll a/b binding proteins (LHCPs) to the thylakoid membrane. In spermatophytes (seed plants), the cpSRP lacks the SRP RNA and is instead formed by a high affinity interaction of the conserved 54-kD subunit (cpSRP54) with the chloroplast-specific cpSRP43 protein. This heterodimeric cpSRP recognizes LHCP and delivers it to the thylakoid membrane. However, in contrast to spermatophytes, plastid SRP RNAs were identified within all streptophyte lineages and in all chlorophyte branches. Furthermore, it was shown that cpSRP43 does not interact with cpSRP54 in chlorophytes (e.g., Chlamydomonas reinhardtii). In this study, we biochemically characterized the cpSRP system of the charophyte Chaetosphaeridium globosum and the bryophyte Physcomitrella patens. Interaction studies demonstrate low affinity binding of cpSRP54 to cpSRP43 (Kd ~10 μM) in Chaetosphaeridium globosum and Physcomitrella patens as well as relatively low affinity binding of cpSRP54 to cpSRP RNA (Kd ~1 μM) in Physcomitrella patens. CpSRP54/cpSRP43 complex formation in charophytes is supported by the finding that specific alterations in the second chromodomain of cpSRP43, that are conserved within charophytes and absent in land plants, do not interfere with cpSRP54 binding. Furthermore, our data show that the elongated apical loop structure of the Physcomitrella patens cpSRP RNA contributes to the low binding affinity between cpSRP54 and the cpSRP RNA.

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.