Nuclear Magnetic Resonance of Single-Stranded RNAs and DNAs of CAAU and UCAAUC as Benchmarks for Molecular Dynamics Simulations

RNA Complexes with Nicks and Gaps: Thermodynamic and Kinetic Effects of Coaxial Stacking and Dangling Ends

Multiple RNA strands can interact in solution and assume a large variety of configurations dictated by their potential for base pairing. Although duplex formation from two complementary oligonucleotides has been studied in detail, we still lack a systematic characterization of the behavior of higher order complexes. Here, we focus on the thermodynamic and kinetic effects of an upstream oligonucleotide on the binding of a downstream oligonucleotide to a common template, as we vary the sequence and structure of the contact interface. We show that coaxial stacking in RNA is well correlated with but much more stabilizing than helix propagation over an analogous intact double helix step (median ΔΔG°37 °C ≈ 1.7 kcal/mol). Consequently, approximating coaxial stacking in RNA with the helix propagation term leads to large discrepancies between predictions and our experimentally determined melting temperatures, with an offset of ≈10 °C. Our kinetic study reveals that the hybridization of the downstream probe oligonucleotide is impaired (lower kon) by the presence of the upstream oligonucleotide, with the thermodynamic stabilization coming entirely from an extended lifetime (lower koff) of the bound downstream oligonucleotide, which can increase from seconds to months. Surprisingly, we show that the effect of nicks is dependent on the length of the stacking oligonucleotides, and we discuss the binding of ultrashort (1-4 nt) oligonucleotides that are relevant in the context of the origin of life. The thermodynamic and kinetic data obtained in this work allow for the prediction of the formation and stability of higher-order multistranded complexes.

Hierarchical Assembly of Single-Stranded RNA

Single-stranded RNA (ssRNA) plays a major role in the flow of genetic information-most notably, in the form of messenger RNA (mRNA)-and in the regulation of biological processes. The highly dynamic nature of chains of unpaired nucleobases challenges structural characterizations of ssRNA by experiments or molecular dynamics (MD) simulations alike. Here, we use hierarchical chain growth (HCG) to construct ensembles of ssRNA chains. HCG assembles the structures of protein and nucleic acid chains from fragment libraries created by MD simulations. Applied to homo- and heteropolymeric ssRNAs of different lengths, we find that HCG produces structural ensembles that overall are in good agreement with diverse experiments, including nuclear magnetic resonance (NMR), small-angle X-ray scattering (SAXS), and single-molecule Förster resonance energy transfer (FRET). The agreement can be further improved by ensemble refinement using Bayesian inference of ensembles (BioEn). HCG can also be used to assemble RNA structures that combine base-paired and base-unpaired regions, as illustrated for the 5' untranslated region (UTR) of SARS-CoV-2 RNA.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Simple Adjustment of Intranucleotide Base-Phosphate Interaction in the OL3 AMBER Force Field Improves RNA Simulations

Molecular dynamics (MD) simulations represent an established tool to study RNA molecules. The outcome of MD studies depends, however, on the quality of the force field (ff). Here we suggest a correction for the widely used AMBER OL3 ff by adding a simple adjustment of the nonbonded parameters. The reparameterization of the Lennard-Jones potential for the -H8···O5'- and -H6···O5'- atom pairs addresses an intranucleotide steric clash occurring in the type 0 base-phosphate interaction (0BPh). The nonbonded fix (NBfix) modification of 0BPh interactions (NBfix0BPh modification) was tuned via a reweighting approach and subsequently tested using an extensive set of standard and enhanced sampling simulations of both unstructured and folded RNA motifs. The modification corrects minor but visible intranucleotide clash for the anti nucleobase conformation. We observed that structural ensembles of small RNA benchmark motifs simulated with the NBfix0BPh modification provide better agreement with experiments. No side effects of the modification were observed in standard simulations of larger structured RNA motifs. We suggest that the combination of OL3 RNA ff and NBfix0BPh modification is a viable option to improve RNA MD simulations.

Advances, Applications, and Perspectives in Small-Angle X-ray Scattering of RNA

RNAs exhibit a plethora of functions far beyond transmitting genetic information. Often, RNA functions are entailed in their structure, be it as a regulatory switch, protein binding site, or providing catalytic activity. Structural information is a prerequisite for a full understanding of RNA-regulatory mechanisms. Owing to the inherent dynamics, size, and instability of RNA, its structure determination remains challenging. Methods such as NMR spectroscopy, X-ray crystallography, and cryo-electron microscopy can provide high-resolution structures; however, their limitations make structure determination, even for small RNAs, cumbersome, if at all possible. Although at a low resolution, small-angle X-ray scattering (SAXS) has proven valuable in advancing structure determination of RNAs as a complementary method, which is also applicable to large-sized RNAs. Here, we review the technological and methodological advancements of RNA SAXS. We provide examples of the powerful inclusion of SAXS in structural biology and discuss possible future applications to large RNAs.

Integrating experimental data with molecular simulations to investigate RNA structural dynamics

Conformational dynamics is crucial for ribonucleic acid (RNA) function. Techniques such as nuclear magnetic resonance, cryo-electron microscopy, small- and wide-angle X-ray scattering, chemical probing, single-molecule Förster resonance energy transfer, or even thermal or mechanical denaturation experiments probe RNA dynamics at different time and space resolutions. Their combination with accurate atomistic molecular dynamics (MD) simulations paves the way for quantitative and detailed studies of RNA dynamics. First, experiments provide a quantitative validation tool for MD simulations. Second, available data can be used to refine simulated structural ensembles to match experiments. Finally, comparison with experiments allows for improving MD force fields that are transferable to new systems for which data is not available. Here we review the recent literature and provide our perspective on this field.

Spontaneous binding of single-stranded RNAs to RRM proteins visualized by unbiased atomistic simulations with a rescaled RNA force field

Recognition of single-stranded RNA (ssRNA) by RNA recognition motif (RRM) domains is an important class of protein-RNA interactions. Many such complexes were characterized using nuclear magnetic resonance (NMR) and/or X-ray crystallography techniques, revealing ensemble-averaged pictures of the bound states. However, it is becoming widely accepted that better understanding of protein-RNA interactions would be obtained from ensemble descriptions. Indeed, earlier molecular dynamics simulations of bound states indicated visible dynamics at the RNA-RRM interfaces. Here, we report the first atomistic simulation study of spontaneous binding of short RNA sequences to RRM domains of HuR and SRSF1 proteins. Using a millisecond-scale aggregate ensemble of unbiased simulations, we were able to observe a few dozen binding events. HuR RRM3 utilizes a pre-binding state to navigate the RNA sequence to its partially disordered bound state and then to dynamically scan its different binding registers. SRSF1 RRM2 binding is more straightforward but still multiple-pathway. The present study necessitated development of a goal-specific force field modification, scaling down the intramolecular van der Waals interactions of the RNA which also improves description of the RNA-RRM bound state. Our study opens up a new avenue for large-scale atomistic investigations of binding landscapes of protein-RNA complexes, and future perspectives of such research are discussed.

Conformational Heterogeneity of RNA Stem-Loop Hairpins Bound to FUS-RNA Recognition Motif with Disordered RGG Tail Revealed by Unbiased Molecular Dynamics Simulations

RNA-protein complexes use diverse binding strategies, ranging from structurally well-defined interfaces to completely disordered regions. Experimental characterization of flexible segments is challenging and can be aided by atomistic molecular dynamics (MD) simulations. Here, we used an extended set of microsecond-scale MD trajectories (400 μs in total) to study two FUS-RNA constructs previously characterized by nuclear magnetic resonance (NMR) spectroscopy. The FUS protein contains a well-structured RNA recognition motif domain followed by a presumably disordered RGG tail that binds RNA stem-loop hairpins. Our simulations not only provide several suggestions complementing the experiments but also reveal major methodological difficulties in studies of such complex RNA-protein interfaces. Despite efforts to stabilize the binding via system-specific force-field adjustments, we have observed progressive distortions of the RNA-protein interface inconsistent with experimental data. We propose that the dynamics is so rich that its converged description is not achievable even upon stabilizing the system. Still, after careful analysis of the trajectories, we have made several suggestions regarding the binding. We identify substates in the RNA loops, which can explain the NMR data. The RGG tail localized in the minor groove remains disordered, sampling countless transient interactions with the RNA. There are long-range couplings among the different elements contributing to the recognition, which can lead to allosteric communication throughout the system. Overall, the RNA-FUS systems form dynamical ensembles that cannot be fully represented by single static structures. Thus, albeit imperfect, MD simulations represent a viable tool to investigate dynamic RNA-protein complexes.

Base-specific RNA force field improving the dynamics conformation of nucleotide

RNA plays a key role in numerous biological processes. Traditional experimental methods have difficulties capturing the structure and dynamic conformation of RNA. Thus, Molecular dynamic simulations (MDs) has become an essential complementary for RNA experiment. However, state-of-the-art RNA force fields have two major limitations of overestimation base stacking propensity and generation of a high ratio of intercalated conformations. Therefore, a two-step strategy was used to optimize the parameters of ff99bsc0χOL3 (named BSFF1) to improve these limitations, which as well adjusted the unbonded parameters of nucleobase heavy atoms and added ζ/α grid-based energy correction map energy term with reweighting. MD simulations of tetranucleotides indicate that BSFF1 can significantly decrease the ratio of intercalated conformations. Tests of single-strand RNA and kink-turn show that BSFF1 force field can reproduce more accurate conformers than ff99bsc0χOL3 force field. BSFF1 can also stabilize the conformers of duplex and riboswitch. The successful ab initio folding of tetraloop further supports the performance of BSFF1. These findings confirm that the newly developed force field BSFF1 can improve the conformer sampling of RNA.

Conformational heterogeneity of UCAAUC RNA oligonucleotide from molecular dynamics simulations, SAXS, and NMR experiments

We describe the conformational ensemble of the single-stranded r(UCAAUC) oligonucleotide obtained using extensive molecular dynamics (MD) simulations and Rosetta's FARFAR2 algorithm. The conformations observed in MD consist of A-form-like structures and variations thereof. These structures are not present in the pool generated using FARFAR2. By comparing with available nuclear magnetic resonance (NMR) measurements, we show that the presence of both A-form-like and other extended conformations is necessary to quantitatively explain experimental data. To further validate our results, we measure solution X-ray scattering (SAXS) data on the RNA hexamer and find that simulations result in more compact structures than observed from these experiments. The integration of simulations with NMR via a maximum entropy approach shows that small modifications to the MD ensemble lead to an improved description of the conformational ensemble. Nevertheless, we identify persisting discrepancies in matching experimental SAXS data.

Automatic Learning of Hydrogen-Bond Fixes in the AMBER RNA Force Field

The capability of current force fields to reproduce RNA structural dynamics is limited. Several methods have been developed to take advantage of experimental data in order to enforce agreement with experiments. Here, we extend an existing framework which allows arbitrarily chosen force-field correction terms to be fitted by quantification of the discrepancy between observables back-calculated from simulation and corresponding experiments. We apply a robust regularization protocol to avoid overfitting and additionally introduce and compare a number of different regularization strategies, namely, L1, L2, Kish size, relative Kish size, and relative entropy penalties. The training set includes a GACC tetramer as well as more challenging systems, namely, gcGAGAgc and gcUUCGgc RNA tetraloops. Specific intramolecular hydrogen bonds in the AMBER RNA force field are corrected with automatically determined parameters that we call gHBfix_opt. A validation involving a separate simulation of a system present in the training set (gcUUCGgc) and new systems not seen during training (CAAU and UUUU tetramers) displays improvements regarding the native population of the tetraloop as well as good agreement with NMR experiments for tetramers when using the new parameters. Then, we simulate folded RNAs (a kink–turn and L1 stalk rRNA) including hydrogen bond types not sufficiently present in the training set. This allows a final modification of the parameter set which is named gHBfix21 and is suggested to be applicable to a wider range of RNA systems.

RNA-Specific Force Field Optimization with CMAP and Reweighting

RNA plays a key role in a variety of cell activities. However, it is difficult to capture its structure dynamics by the traditional experimental methods because of the inherent limitations. Molecular dynamics simulation has become a valuable complement to the experimental methods. Previous studies have indicated that the current force fields cannot accurately reproduce the conformations and structural dynamics of RNA. Therefore, an RNA-specific force field was developed to improve the conformation sampling of RNA. The distribution of ζ/α dihedrals of tetranucleotides was optimized by a reweighting method, and the grid-based energy correction map (CMAP) term was first introduced into the Amber RNA force field of ff99bsc0χOL3, named ff99OL3_CMAP1. Extensive validations of tetranucleotides and tetraloops show that ff99OL3_CMAP1 can significantly decrease the population of an incorrect structure, increase the consistency between the simulation results and experimental values for tetranucleotides, and improve the stability of tetraloops. ff99OL3_CMAP1 can also precisely reproduce the conformation of a duplex and riboswitches. These findings confirm that the newly developed force field ff99OL3_CMAP1 can improve the conformer sampling of RNA.

Nuclear Magnetic Resonance Spectra and AMBER OL3 and ROC-RNA Simulations of UCUCGU Reveal Force Field Strengths and Weaknesses for Single-Stranded RNA

Single-stranded regions of RNA are important for folding of sequences into 3D structures and for design of therapeutics targeting RNA. Prediction of ensembles of 3D structures for single-stranded regions often involves classical mechanical approximations of interactions defined by quantum mechanical calculations on small model systems. Nuclear magnetic resonance (NMR) spectra and molecular dynamics (MD) simulations of short single strands provide tests for how well the approximations model many of the interactions. Here, the NMR spectra for UCUCGU at 2, 15, and 30 °C are compared to simulations with the AMBER force fields, OL3 and ROC-RNA. This is the first such comparison to an oligoribonucleotide containing an internal guanosine nucleotide (G). G is particularly interesting because of its many H-bonding groups, large dipole moment, and proclivity for both syn and anti conformations. Results reveal formation of a G amino to phosphate non-bridging oxygen H-bond. The results also demonstrate dramatic differences in details of the predicted structures. The variations emphasize the dependence of predictions on individual parameters and their balance with the rest of the force field. The NMR data can serve as a benchmark for future force fields.

MD simulations reveal the basis for dynamic assembly of Hfq-RNA complexes

The conserved protein Hfq is a key factor in the RNA-mediated control of gene expression in most known bacteria. The transient intermediates Hfq forms with RNA support intricate and robust regulatory networks. In Pseudomonas, Hfq recognizes repeats of adenine–purine–any nucleotide (ARN) in target mRNAs via its distal binding side, and together with the catabolite repression control (Crc) protein, assembles into a translation–repression complex. Earlier experiments yielded static, ensemble-averaged structures of the complex, but details of its interface dynamics and assembly pathway remained elusive. Using explicit solvent atomistic molecular dynamics simulations, we modeled the extensive dynamics of the Hfq–RNA interface and found implications for the assembly of the complex. We predict that syn/anti flips of the adenine nucleotides in each ARN repeat contribute to a dynamic recognition mechanism between the Hfq distal side and mRNA targets. We identify a previously unknown binding pocket that can accept any nucleotide and propose that it may serve as a ‘status quo’ staging point, providing nonspecific binding affinity, until Crc engages the Hfq–RNA binary complex. The dynamical components of the Hfq–RNA recognition can speed up screening of the pool of the surrounding RNAs, participate in rapid accommodation of the RNA on the protein surface, and facilitate competition among different RNAs. The register of Crc in the ternary assembly could be defined by the recognition of a guanine-specific base–phosphate interaction between the first and last ARN repeats of the bound RNA. This dynamic substrate recognition provides structural rationale for the stepwise assembly of multicomponent ribonucleoprotein complexes nucleated by Hfq–RNA binding.

Effects of Phosphoryl Guanidine Modification of Phosphate Residues on the Structure and Hybridization of Oligodeoxyribonucleotides

Phosphoryl guanidine oligonucleotides (PGOs) are promising tools for biological research and development of biosensors and therapeutics. We performed structural and hybridization analyses of octa-, deca-, and dodecamers with all phosphate residues modified by 1,3-dimethylimidazolidine-2-imine moieties. Similarity of the B-form double helix between native and modified duplexes was noted. In PGO duplexes, we detected a decrease in the proportion of C2'-endo and an increased proportion of C1'-exo sugar conformations of the modified chain. Applicability of the two-state model to denaturation transition of all studied duplexes was proved for the first time. Sequence-dependent effects of this modification on hybridization properties were observed. The thermal stability of PGO complexes is almost native at 100 mM NaCl and slightly increases with decreasing ionic strength. An increase in water activity and dramatic changes in interaction with cations and in solvation of PGOs and their duplexes were noted, resulting in slight elevation of the melting temperature after an ionic-strength decrease from 1 M NaCl down to deionized water. Decreased binding of sodium ions and decreased water solvation were documented for PGOs and their duplexes. In contrast to DNA, the PGO duplex formation leads to a release of several cations. The water shell is significantly more disordered near PGOs and their complexes. Nevertheless, changes in solvation during the formation of native and PGO complexes are similar and indicate that it is possible to develop models for predictive calculations of the thermodynamic properties of phosphoryl guanidine oligomers. Our results may help devise an approach for the rational design of PGOs as novel improved molecular probes and tools for many modern methods involving oligonucleotides.

Fine-Tuning of the AMBER RNA Force Field with a New Term Adjusting Interactions of Terminal Nucleotides

Determination of RNA structural-dynamic properties is challenging for experimental methods. Thus, atomistic molecular dynamics (MD) simulations represent a helpful technique complementary to experiments. However, contemporary MD methods still suffer from limitations of force fields (ffs), including imbalances in the nonbonded ff terms. We have recently demonstrated that some improvement of state-of-the-art AMBER RNA ff can be achieved by adding a new term for H-bonding called gHBfix, which increases tuning flexibility and reduces risk of side-effects. Still, the first gHBfix version did not fully correct simulations of short RNA tetranucleotides (TNs). TNs are key benchmark systems due to availability of unique NMR data, although giving too much weight on improving TN simulations can easily lead to overfitting to A-form RNA. Here we combine the gHBfix version with another term called tHBfix, which separately treats H-bond interactions formed by terminal nucleotides. This allows to refine simulations of RNA TNs without affecting simulations of other RNAs. The approach is in line with adopted strategy of current RNA ffs, where the terminal nucleotides possess different parameters for terminal atoms than the internal nucleotides. Combination of gHBfix with tHBfix significantly improves the behavior of RNA TNs during well-converged enhanced-sampling simulations using replica exchange with solute tempering. TNs mostly populate canonical A-form like states while spurious intercalated structures are largely suppressed. Still, simulations of r(AAAA) and r(UUUU) TNs show some residual discrepancies with primary NMR data which suggests that future tuning of some other ff terms might be useful. Nevertheless, the tHBfix has a clear potential to improve modeling of key biochemical processes, where interactions of RNA single stranded ends are involved.