Benchmarking AMBER force fields for RNA: comparisons to NMR spectra for single-stranded r(GACC) are improved by revised χ torsions

Comprehensive Assessment of Force-Field Performance in Molecular Dynamics Simulations of DNA/RNA Hybrid Duplexes

Mixed double helices formed by RNA and DNA strands, commonly referred to as hybrid duplexes or hybrids, are essential in biological processes like transcription and reverse transcription. They are also important for their applications in CRISPR gene editing and nanotechnology. Yet, despite their significance, the hybrid duplexes have been seldom modeled by atomistic molecular dynamics methodology, and there is no benchmark study systematically assessing the force-field performance. Here, we present an extensive benchmark study of polypurine tract (PPT) and Dickerson-Drew dodecamer hybrid duplexes using contemporary and commonly utilized pairwise additive and polarizable nucleic acid force fields. Our findings indicate that none of the available force-field choices accurately reproduces all the characteristic structural details of the hybrid duplexes. The AMBER force fields are unable to populate the C3'-endo (north) pucker of the DNA strand and underestimate inclination. The CHARMM force field accurately describes the C3'-endo pucker and inclination but shows base pair instability. The polarizable force fields struggle with accurately reproducing the helical parameters. Some force-field combinations even demonstrate a discernible conflict between the RNA and DNA parameters. In this work, we offer a candid assessment of the force-field performance for mixed DNA/RNA duplexes. We provide guidance on selecting utilizable force-field combinations and also highlight potential pitfalls and best practices for obtaining optimal performance.

Prediction of 3D RNA Structures from Sequence Using Energy Landscapes of RNA Dimers: Application to RNA Tetraloops

Access to the three-dimensional structure of RNA enables an ability to gain a more profound understanding of its biological mechanisms, as well as the ability to design RNA-targeting drugs, which can take advantage of the unique chemical environment imposed by a folded RNA structure. Due to the dynamic and structurally complex properties of RNA, both experimental and traditional computational methods have difficulty in determining RNA's 3D structure. Herein, we introduce TAPERSS (Theoretical Analyses, Prediction, and Evaluation of RNA Structures from Sequence), a physics-based fragment assembly method for predicting 3D RNA structures from sequence. Using a fragment library created using discrete path sampling calculations of RNA dinucleoside monophosphates, TAPERSS can sample the physics-based energy landscapes of any RNA sequence with relatively low computational complexity. We have benchmarked TAPERSS on 21 RNA tetraloops, using a combinatorial algorithm as a proof-of-concept. We show that TAPERSS was successfully able to predict the apo-state structures of all 21 RNA hairpins, with 16 of those structures also having low predicted energies as well. We demonstrate that TAPERSS performs most accurately on GNRA-like tetraloops with mostly stacked loop-nucleotides, while having limited success with more dynamic UNCG and CUYG tetraloops, most likely due to the influence of the RNA force field used to create the fragment library. Moreover, we show that TAPERSS can successfully predict the majority of the experimental non-apo states, highlighting its potential in anticipating biologically significant yet unobserved states. This holds great promise for future applications in drug design and related studies. With discussed improvements and implementation of more efficient sampling algorithms, we believe TAPERSS may serve as a useful tool for a physics-based conformational sampling of large RNA structures.

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.

van der Waals Parameter Scanning with Amber Nucleic Acid Force Fields: Revisiting Means to Better Capture the RNA/DNA Structure through MD

Molecular dynamics simulations can be used in combination with experimental techniques to uncover the intricacies of biomolecular structure, dynamics, and the resulting interactions. However, many noncanonical nucleic acid structures have proven to be challenging to replicate in accurate agreement with experimental data, often attributed to known force field deficiencies. A common force field criticism is the handling of van der Waals (vdW) parameters, which have not been updated since the regular use of Ewald's methods became routine. This work dives into the effects of minute vdW radii shifts on RNA tetranucleotide, B-DNA, and Z-DNA model systems described by commonly used Amber force fields. Using multidimensional replica exchange molecular dynamics (M-REMD), the GACC RNA tetranucleotide demonstrated changes in the structural distribution between the NMR minor and anomalous structure populations based on the O2' vdW radii scanning. However, no significant change in the NMR Major conformation population was observed. There were minimal changes in the B-DNA structure but there were more substantial improvements in Z-DNA structural descriptions, specifically with the Tumuc1 force field. This occurred with both LJbb vdW radii adjustments and incorporation of the CUFIX nonbonded parameter modifications. Though the limited vdW modifications tested did not provide a universal fix to the challenge of simulating the various known nucleic acid structures, they do provide direction and a greater understanding for future force field development efforts.

Dynamics and Function of sRNA/mRNAs Under the Scrutiny of Computational Simulation Methods

Molecular dynamics simulations have proved extremely useful in investigating the functioning of proteins with atomic-scale resolution. Many applications to the study of RNA also exist, and their number increases by the day. However, implementing MD simulations for RNA molecules in solution faces challenges that the MD practitioner must be aware of for the appropriate use of this tool. In this chapter, we present the fundamentals of MD simulations, in general, and the peculiarities of RNA simulations, in particular. We discuss the strengths and limitations of the technique and provide examples of its application to elucidate small RNA's performance.

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.

Structure of pre-miR-31 reveals an active role in Dicer-TRBP complex processing

As an essential posttranscriptional regulator of gene expression, microRNA (miRNA) levels must be strictly maintained. The biogenesis of many miRNAs is mediated by trans-acting protein partners through a variety of mechanisms, including remodeling of the RNA structure. miR-31 functions as an oncogene in numerous cancers, and interestingly, its biogenesis is not known to be regulated by protein-binding partners. Therefore, the intrinsic structural properties of the precursor element of miR-31 (pre-miR-31) can provide a mechanism by which its biogenesis is regulated. We determined the solution structure of pre-miR-31 to investigate the role of distinct structural elements in regulating processing by the Dicer-TRBP complex. We found that the presence or absence of mismatches within the helical stem does not strongly influence Dicer-TRBP processing of the pre-miRNAs. However, both the apical loop size and structure at the Dicing site are key elements for discrimination by the Dicer-TRBP complex. Interestingly, our NMR-derived structure reveals the presence of a triplet of base pairs that link the Dicer cleavage site and the apical loop. Mutational analysis in this region suggests that the stability of the junction region strongly influences processing by the Dicer-TRBP complex. Our results enrich our understanding of the active role that RNA structure plays in regulating miRNA biogenesis, which has direct implications for the control of gene expression.

Benchmarking the Drude Polarizable Force Field Using the r(GACC) Tetranucleotide

Polarizable force fields, in particular, the Drude polarizable force field (Drude FF), may hold the key to more accurately modeling biomolecules with molecular dynamics simulations by explicitly accounting for atomic polarizability. Previous work has shown promising results in simulating duplex nucleic acids and protein structures with excellent agreement with experimental values. However, benchmarking the Drude polarizable force field with highly flexible, single-stranded structures has yet to be achieved. In this work, the r(GACC) tetranucleotide is simulated over a multimicrosecond time scale, starting with various different initial conformations. Despite the starting conformation, including starting from the expected dominant A-form major conformation, the experimental structural distribution is not matched. In fact, the major NMR conformation is never resampled. Instead, the r(GACC) tetranucleotide becomes stabilized in anomalous structures that are inconsistent with the NMR data and that favor base-pairing and electrostatic interactions over base stacking. These structures are maintained for lengthy time scales (>1 μs) themselves, suggesting a misbalance of forces in the Drude polarizable force field itself. This model system is suggestive of the fact that currently the Drude polarizable force field does not appear to produce the sensitive balance of forces required to accurately model other single-stranded or noncanonical RNA structures.

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.

Structure of pre-miR-31 reveals an active role in Dicer processing

As an essential post-transcriptional regulator of gene expression, microRNA (miR) levels must be strictly maintained. The biogenesis of many, but not all, miRs is mediated by trans-acting protein partners through a variety of mechanisms, including remodeling of the RNA structure. miR-31 functions as an oncogene in numerous cancers and interestingly, its biogenesis is not known to be regulated by protein binding partners. Therefore, the intrinsic structural properties of pre-miR-31 can provide a mechanism by which its biogenesis is regulated. We determined the solution structure of the precursor element of miR-31 (pre-miR-31) to investigate the role of distinct structural elements in regulating Dicer processing. We found that the presence or absence of mismatches within the helical stem do not strongly influence Dicer processing of the pre-miR. However, both the apical loop size and structure at the Dicing site are key elements for discrimination by Dicer. Interestingly, our NMR-derived structure reveals the presence of a triplet of base pairs that link the Dicer cleavage site and the apical loop. Mutational analysis in this region suggests that the stability of the junction region strongly influence both Dicer binding and processing. Our results enrich our understanding of the active role that RNA structure plays in regulating Dicer processing which has direct implications for control of gene expression.

Solution Structure of NPSL2, A Regulatory Element in the oncomiR-1 RNA

The miR-17 ∼ 92a polycistron, also known as oncomiR-1, is commonly overexpressed in multiple cancers and has several oncogenic properties. OncomiR-1 encodes six constituent microRNAs (miRs), each enzymatically processed with different efficiencies. However, the structural mechanism that regulates this differential processing remains unclear. Chemical probing of oncomiR-1 revealed that the Drosha cleavage sites of pri-miR-92a are sequestered in a four-way junction. NPSL2, an independent stem loop element, is positioned just upstream of pri-miR-92a and sequesters a crucial part of the sequence that constitutes the basal helix of pri-miR-92a. Disruption of the NPSL2 hairpin structure could promote the formation of a pri-miR-92a structure that is primed for processing by Drosha. Thus, NPSL2 is predicted to function as a structural switch, regulating pri-miR-92a processing. Here, we determined the solution structure of NPSL2 using solution NMR spectroscopy. This is the first high-resolution structure of an oncomiR-1 element. NPSL2 adopts a hairpin structure with a large, but highly structured, apical and internal loops. The 10-bp apical loop contains a pH-sensitive A+·C mismatch. Additionally, several adenosines within the apical and internal loops have elevated pKa values. The protonation of these adenosines can stabilize the NPSL2 structure through electrostatic interactions. Our study provides fundamental insights into the secondary and tertiary structure of an important RNA hairpin proposed to regulate miR biogenesis.

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.

Challenges with Simulating Modified RNA: Insights into Role and Reciprocity of Experimental and Computational Approaches

RNA is critical to a broad spectrum of biological and viral processes. This functional diversity is a result of their dynamic nature; the variety of three-dimensional structures that they can fold into; and a host of post-transcriptional chemical modifications. While there are many experimental techniques to study the structural dynamics of biomolecules, molecular dynamics simulations (MDS) play a significant role in complementing experimental data and providing mechanistic insights. The accuracy of the results obtained from MDS is determined by the underlying physical models i.e., the force-fields, that steer the simulations. Though RNA force-fields have received a lot of attention in the last decade, they still lag compared to their protein counterparts. The chemical diversity imparted by the RNA modifications adds another layer of complexity to an already challenging problem. Insight into the effect of RNA modifications upon RNA folding and dynamics is lacking due to the insufficiency or absence of relevant experimental data. This review provides an overview of the state of MDS of modified RNA, focusing on the challenges in parameterization of RNA modifications as well as insights into relevant reference experiments necessary for their calibration.

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.

Multipolar electrostatics for hairpin and pseudoknots in RNA: Improving the accuracy of force field potential energy function

Molecular dynamics (MD) simulations that rely on force field methods has been widely used to explore the structure and function of RNAs. However, the current commonly used force fields are limited by the electrostatic description offered by atomic charge, dipole and at most quadrupole moments, failing to capture the anisotropic picture of electronic features. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. A multipolar electrostatic model based on high rank multipole moments is described in this work, which allows us to combine polarizability and anisotropy of electron density. RNA secondary structure was taken as a research system, and its substructures including stem, loops (hairpin loop, bulge loop, internal loop, and multi-branch loop), and pseudoknots (H-type and K-type) were investigated, respectively, as well as the hairpin. First, the atom-atom electrostatic properties derived from one chain of a duplex RNA 2MVY in our previous work (Ref. 58) were measured by the pilot RNA systems of hairpin, hairpin loop, stem, and H-type pseudoknot, respectively. The prediction results were not satisfactory. Consequently, to obtain a general set of electrostatic parameters for RNA force fields, the convergence behavior of the atom-atom electrostatic interactions in the pilot RNA systems was explored using high rank atomic multipole moments. The pilot RNA systems were cut into four types of different-sized molecular fragments, and the single nucleotide fragment and nucleotide-paired fragment proved to be the most reasonable systems for base-unpairing regions and base-pairing regions to investigate the convergence behavior of all types of atom-atom electrostatic interactions, respectively. Transferability of the electrostatic properties drawn from the pilot RNA systems to the corresponding test systems was also investigated. Furthermore, the convergence behavior of atomic electrostatic interactions in other substructures including bulge loop, internal loop, multi-branch loop, and K-type pseudoknot was expected to be modeled via the hairpin.

A general RNA force field: comprehensive analysis of energy minima of molecular fragments of RNA

Force fields are actively used to study RNA. Development of accurate force fields relies on a knowledge of how the variation of properties of molecules depends on their structure. Detailed scrutiny of RNA's conformational preferences is needed to guide such development. Towards this end, minimum energy structures for each of a set of 16 small RNA-derived molecules were obtained by geometry optimization at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory. The number of minima computed for a given fragment was found to be related to both its size and flexibility. Atomic electrostatic multipole moments of atoms occurring in the [HO-P(O₃)-CH₂-] fragment of 30 sugar-phosphate-sugar geometries were calculated at the HF/6-31G(d,p) and B3LYP/apc-1 levels of theory, and the transferability of these properties between different conformations was investigated. The atomic multipole moments were found to be highly transferable between different conformations with small standard deviations. These results indicate necessary elements of the development of accurate RNA force fields.

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.

Structural basis for transcriptional start site control of HIV-1 RNA fate

Heterogeneous transcriptional start site usage by HIV-1 produces 5'-capped RNAs beginning with one, two, or three 5'-guanosines (Cap1G, Cap2G, or Cap3G, respectively) that are either selected for packaging as genomes (Cap1G) or retained in cells as translatable messenger RNAs (mRNAs) (Cap2G and Cap3G). To understand how 5'-guanosine number influences fate, we probed the structures of capped HIV-1 leader RNAs by deuterium-edited nuclear magnetic resonance. The Cap1G transcript adopts a dimeric multihairpin structure that sequesters the cap, inhibits interactions with eukaryotic translation initiation factor 4E, and resists decapping. The Cap2G and Cap3G transcripts adopt an alternate structure with an elongated central helix, exposed splice donor residues, and an accessible cap. Extensive remodeling, achieved at the energetic cost of a G-C base pair, explains how a single 5'-guanosine modifies the function of a ~9-kilobase HIV-1 transcript.

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

RNA and DNA are rapidly emerging as targets for therapeutics and as potential frameworks for nanotechnology. Accurate methods for predicting and designing structures and dynamics of nucleic acids would accelerate progress in these and other applications. Suitable approximations for modeling nucleic acids are being developed but require validation against disparate experimental observations. Here, nuclear magnetic resonance spectra for RNA and DNA single strands, CAAU and UCAAUC, are used as benchmarks to test molecular dynamics simulations with AMBER force fields OL3 and ROC-RNA for RNA and BSC1 for DNA. A detailed scheme for making comparisons is also presented. The results reflect recent progress in approximations and reveal remaining challenges.

Improving the Performance of the Amber RNA Force Field by Tuning the Hydrogen-Bonding Interactions

Molecular dynamics (MD) simulations became a leading tool for investigation of structural dynamics of nucleic acids. Despite recent efforts to improve the empirical potentials (force fields, ffs), RNA ffs have persisting deficiencies, which hamper their utilization in quantitatively accurate simulations. Previous studies have shown that at least two salient problems contribute to difficulties in the description of free-energy landscapes of small RNA motifs: (i) excessive stabilization of the unfolded single-stranded RNA ensemble by intramolecular base-phosphate and sugar-phosphate interactions and (ii) destabilization of the native folded state by underestimation of stability of base pairing. Here, we introduce a general ff term (gHBfix) that can selectively fine-tune nonbonding interaction terms in RNA ffs, in particular, the H bonds. The gHBfix potential affects the pairwise interactions between all possible pairs of the specific atom types, while all other interactions remain intact; i.e., it is not a structure-based model. In order to probe the ability of the gHBfix potential to refine the ff nonbonded terms, we performed an extensive set of folding simulations of RNA tetranucleotides and tetraloops. On the basis of these data, we propose particular gHBfix parameters to modify the AMBER RNA ff. The suggested parametrization significantly improves the agreement between experimental data and the simulation conformational ensembles, although our current ff version still remains far from being flawless. While attempts to tune the RNA ffs by conventional reparametrizations of dihedral potentials or nonbonded terms can lead to major undesired side effects, as we demonstrate for some recently published ffs, gHBfix has a clear promising potential to improve the ff performance while avoiding introduction of major new imbalances.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

Computational Investigation of RNA A-Bulges Related to the Microtubule-Associated Protein Tau Causing Frontotemporal Dementia and Parkinsonism

Mutations in the human tau gene result in alternative splicing of the tau protein, which causes frontotemporal dementia and Parkinsonism. One disease mechanism is linked to the stability of a hairpin within the microtubule-associated protein tau (MAPT) mRNA, which contains an A-bulge. Here we employ computational methods to investigate the structural and thermodynamic properties of several A-bulge RNAs with different closing base-pairs. We find that the current amber RNA force field has a preference to overstabilize base-triple over stacked states, even though some of the A-bulges are known to prefer stacked states according to NMR studies. We further determined that if the neighboring base-pairs of A-bulges are AU, this situation can lead to base slippage. However, when the 3'-side of the A-bulge has an UA base-pair, the stacked state is stabilized by an extra interaction that is not observed in the other sequences. We suggest that these A-bulge RNA systems could be used as benchmarks to improve the current RNA force fields.

Improvement of RNA Simulations with Torsional Revisions of the AMBER Force Field

Our current knowledge on the unique roles of RNA in cells makes it vital to investigate the properties of RNA systems using computational methods because of the potential pharmaceutical applications. With the continuous advancement of computer technology, it is now possible to study RNA folding. Molecular mechanics calculations are useful in discovering the structural and thermodynamic properties of RNA systems. Yet, the predictions depend on the quality of the RNA force field, which is a set of parameters describing the potential energy of the system. Torsional parameters are one of the terms in a force field that can be revised using physics-based approaches. This chapter focuses on improvements provided by revisions of torsional parameters of the AMBER (Assisted Model Building with Energy Refinement) RNA force field. The theory behind torsional revisions and re-parameterization of several RNA torsions is briefly described. Applications of the revised torsional parameters to study RNA nucleosides, single-stranded RNA tetramers, and RNA repeat expansions are described in detail. It is concluded that RNA force fields require constant revisions and should be benchmarked against diverse RNA systems such as single strands and internal loops in order to test their qualities.

Assessing Force Field Potential Energy Function Accuracy via a Multipolar Description of Atomic Electrostatic Interactions in RNA

Computational investigations of RNA properties often rely on a molecular mechanical approach to define molecular potential energy. Force fields for RNA typically employ a point charge model of electrostatics, which does not provide a realistic quantum-mechanical picture. In reality, electron distributions around nuclei are not spherically symmetric and are geometry dependent. A multipole expansion method which allows for incorporation of polarizability and anisotropy in a force field is described, and its applicability to modeling the behavior of RNA molecules is investigated. Transferability of the model, critical for force field development, is also investigated.

Conformational ensembles of RNA oligonucleotides from integrating NMR and molecular simulations

RNA molecules are key players in numerous cellular processes and are characterized by a complex relationship between structure, dynamics, and function. Despite their apparent simplicity, RNA oligonucleotides are very flexible molecules, and understanding their internal dynamics is particularly challenging using experimental data alone. We show how to reconstruct the conformational ensemble of four RNA tetranucleotides by combining atomistic molecular dynamics simulations with nuclear magnetic resonance spectroscopy data. The goal is achieved by reweighting simulations using a maximum entropy/Bayesian approach. In this way, we overcome problems of current simulation methods, as well as in interpreting ensemble- and time-averaged experimental data. We determine the populations of different conformational states by considering several nuclear magnetic resonance parameters and point toward properties that are not captured by state-of-the-art molecular force fields. Although our approach is applied on a set of model systems, it is fully general and may be used to study the conformational dynamics of flexible biomolecules and to detect inaccuracies in molecular dynamics force fields.

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.

AMOEBA Polarizable Atomic Multipole Force Field for Nucleic Acids

The AMOEBA polarizable atomic multipole force field for nucleic acids is presented. Valence and electrostatic parameters were determined from high-level quantum mechanical data, including structures, conformational energy, and electrostatic potentials, of nucleotide model compounds. Previously derived parameters for the phosphate group and nucleobases were incorporated. A total of over 35 μs of condensed-phase molecular dynamics simulations of DNA and RNA molecules in aqueous solution and crystal lattice were performed to validate and refine the force field. The solution and/or crystal structures of DNA B-form duplexes, RNA duplexes, and hairpins were captured with an average root-mean-squared deviation from NMR structures below or around 2.0 Å. Structural details, such as base pairing and stacking, sugar puckering, backbone and χ-torsion angles, groove geometries, and crystal packing interfaces, agreed well with NMR and/or X-ray. The interconversion between A- and B-form DNAs was observed in ethanol-water mixtures at 328 K. Crystal lattices of B- and Z-form DNA and A-form RNA were examined with simulations. For the RNA tetraloop, single strand tetramers, and HIV TAR with 29 residues, the simulated conformational states, 3 J-coupling, nuclear Overhauser effect, and residual dipolar coupling data were compared with NMR results. Starting from a totally unstacked/unfolding state, the rCAAU tetranucleotide was folded into A-form-like structures during ∼1 μs molecular dynamics simulations.

Physics-based all-atom modeling of RNA energetics and structure

The database of RNA sequences is exploding, but knowledge of energetics, structures, and dynamics lags behind. All-atom computational methods, such as molecular dynamics, hold promise for closing this gap. New algorithms and faster computers have accelerated progress in improving the reliability and accuracy of predictions. Currently, the methods can facilitate refinement of experimentally determined nuclear magnetic resonance and x-ray structures, but are 'unreliable' for predictions based only on sequence. Much remains to be discovered, however, about the many molecular interactions driving RNA folding and the best way to approximate them quantitatively. The large number of parameters required means that a wide variety of experimental results will be required to benchmark force fields and different approaches. As computational methods become more reliable and accessible, they will be used by an increasing number of biologists, much as x-ray crystallography has expanded. Thus, many fundamental physical principles underlying the computational methods are described. This review presents a summary of the current state of molecular dynamics as applied to RNA. It is designed to be helpful to students, postdoctoral fellows, and faculty who are considering or starting computational studies of RNA. WIREs RNA 2017, 8:e1422. doi: 10.1002/wrna.1422.

RNA force field with accuracy comparable to state-of-the-art protein force fields

The complex and often highly dynamic 3D structures of RNA molecules are central to their diverse cellular functions. Molecular dynamics (MD) simulations have played a major role in characterizing the structure and dynamics of proteins, but the physical models (“force fields”) used for simulating nucleic acids are substantially less accurate overall than those used in protein simulations, creating a major challenge for MD studies of RNA. Here, we report an RNA force field capable of describing the structural and thermodynamic properties of RNA molecules with accuracy comparable to state-of-the-art protein force fields. This force field should facilitate the use of MD simulation as a tool for the study of biologically significant RNA molecules and protein–RNA complexes.

Molecular dynamics (MD) simulation has become a powerful tool for characterizing at an atomic level of detail the conformational changes undergone by proteins. The application of such simulations to RNA structures, however, has proven more challenging, due in large part to the fact that the physical models (“force fields”) available for MD simulations of RNA molecules are substantially less accurate in many respects than those currently available for proteins. Here, we introduce an extensive revision of a widely used RNA force field in which the parameters have been modified, based on quantum mechanical calculations and existing experimental information, to more accurately reflect the fundamental forces that stabilize RNA structures. We evaluate these revised parameters through long-timescale MD simulations of a set of RNA molecules that covers a wide range of structural complexity, including single-stranded RNAs, RNA duplexes, RNA hairpins, and riboswitches. The structural and thermodynamic properties measured in these simulations exhibited dramatically improved agreement with experimentally determined values. Based on the comparisons we performed, this RNA force field appears to achieve a level of accuracy comparable to that of state-of-the-art protein force fields, thus significantly advancing the utility of MD simulation as a tool for elucidating the structural dynamics and function of RNA molecules and RNA-containing biological assemblies.

The impact of base stacking on the conformations and electrostatics of single-stranded DNA

Single-stranded DNA (ssDNA) is notable for its interactions with ssDNA binding proteins (SSBs) during fundamentally important biological processes including DNA repair and replication. Previous work has begun to characterize the conformational and electrostatic properties of ssDNA in association with SSBs. However, the conformational distributions of free ssDNA have been difficult to determine. To capture the vast array of ssDNA conformations in solution, we pair small angle X-ray scattering with novel ensemble fitting methods, obtaining key parameters such as the size, shape and stacking character of strands with different sequences. Complementary ion counting measurements using inductively coupled plasma atomic emission spectroscopy are employed to determine the composition of the ion atmosphere at physiological ionic strength. Applying this combined approach to poly dA and poly dT, we find that the global properties of these sequences are very similar, despite having vastly different propensities for single-stranded helical stacking. These results suggest that a relatively simple mechanism for the binding of ssDNA to non-specific SSBs may be at play, which explains the disparity in binding affinities observed for these systems.

Visualizing single-stranded nucleic acids in solution

Single-stranded nucleic acids (ssNAs) are ubiquitous in many key cellular functions. Their flexibility limits both the number of high-resolution structures available, leaving only a small number of protein-ssNA crystal structures, while forcing solution investigations to report ensemble averages. A description of the conformational distributions of ssNAs is essential to more fully characterize biologically relevant interactions. We combine small angle X-ray scattering (SAXS) with ensemble-optimization methods (EOM) to dynamically build and refine sets of ssNA structures. By constructing candidate chains in representative dinucleotide steps and refining the models against SAXS data, a broad array of structures can be obtained to match varying solution conditions and strand sequences. In addition to the distribution of large scale structural parameters, this approach reveals, for the first time, intricate details of the phosphate backbone and underlying strand conformations. Such information on unperturbed strands will critically inform a detailed understanding of an array of problems including protein-ssNA binding, RNA folding and the polymer nature of NAs. In addition, this scheme, which couples EOM selection with an iteratively refining pool to give confidence in the underlying structures, is likely extendable to the study of other flexible systems.

Improving Computational Predictions of Single-Stranded RNA Tetramers with Revised α/γ Torsional Parameters for the Amber Force Field

With current advancements in RNA based therapeutics, it is becoming crucial to utilize theoretical and computational methods to describe properly the physical properties of RNA molecules. NMR and X-ray crystallography are two powerful techniques for investigating structural properties. However, if the RNA molecules are complex or dynamic, these methods might not be adequate. For computational approaches, the quality of the force field will determine accuracy of our predictions. In this contribution, we revise the α/γ torsional parameters of RNA for amber force field using a model system representing an RNA dimer backbone. Combined with revised χ torsional parameters, previously shown to improve computational predictions, we benchmarked the revised force field on five single-stranded RNA (ssRNA) tetramers, three RNA dodecamer duplexes, and an RNA hairpin. A total of 60 μs of molecular dynamics (MD) simulations were run. We also employ the discrete path sampling (DPS) approach to compare the predictions for the revised amber force field with those for amber10. Our results indicate that the unphysical states observed with amber10 in ssRNA MD simulations are suppressed for the revised amber force field. In line with NMR experimental observations, incorporation of the revised α/γ and χ torsional parameters leads to A-form-like conformational states as the most favorable ssRNA tetramer conformations. Furthermore, the revised force field maintains the A-form geometry in regular RNA duplexes. Our revised amber force field for RNA should therefore improve structural and thermodynamic predictions for challenging RNA systems.

Revised RNA Dihedral Parameters for the Amber Force Field Improve RNA Molecular Dynamics

The backbone dihedral parameters of the Amber RNA force field were improved by fitting using multiple linear regression to potential energies determined by quantum chemistry calculations. Five backbone and four glycosidic dihedral parameters were fit simultaneously to reproduce the potential energies determined by a high-level density functional theory calculation (B97D3 functional with the AUG-CC-PVTZ basis set). Umbrella sampling was used to determine conformational free energies along the dihedral angles, and these better agree with the population of conformations observed in the protein data bank for the new parameters than for the conventional parameters. Molecular dynamics simulations performed on a set of hairpin loops, duplexes and tetramers with the new parameter set show improved modeling for the structures of tetramers CCCC, CAAU, and GACC, and an RNA internal loop of noncanonical pairs, as compared to the conventional parameters. For the tetramers, the new parameters largely avoid the incorrect intercalated structures that dominate the conformational samples from the conventional parameters. For the internal loop, the major conformation solved by NMR is stable with the new parameters, but not with the conventional parameters. The new force field performs similarly to the conventional parameters for the UUCG and GCAA hairpin loops and the [U(UA)6A]2 duplex.

Predicting the Kinetics of RNA Oligonucleotides Using Markov State Models

Nowadays different experimental techniques, such as single molecule or relaxation experiments, can provide dynamic properties of biomolecular systems, but the amount of detail obtainable with these methods is often limited in terms of time or spatial resolution. Here we use state-of-the-art computational techniques, namely, atomistic molecular dynamics and Markov state models, to provide insight into the rapid dynamics of short RNA oligonucleotides, to elucidate the kinetics of stacking interactions. Analysis of multiple microsecond-long simulations indicates that the main relaxation modes of such molecules can consist of transitions between alternative folded states, rather than between random coils and native structures. After properly removing structures that are artificially stabilized by known inaccuracies of the current RNA AMBER force field, the kinetic properties predicted are consistent with the time scales of previously reported relaxation experiments.

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.

Comparative Assessment of Different RNA Tetranucleotides from the DFT-D3 and Force Field Perspective

Classical force field (FF) molecular dynamics (MD) simulations of RNA tetranucleotides have substantial problems in reproducing conformer populations indicated by NMR experiments. To provide more information about the possible sources of errors, we performed quantum mechanical (QM, TPSS-D3/def2-TZVP) and molecular mechanics (MM, AMBER parm99bsc0+χ_OL3) calculations of different r(CCCC), r(GACC), and r(UUUU) conformers obtained from explicit solvent MD simulations. Solvent effects in the static QM and MM calculations were mimicked using implicit solvent models (COSMO and Poisson-Boltzmann, respectively). The comparison of QM and MM geometries and energies revealed that the two methodologies provide qualitatively consistent results in most of the cases. Even though we found some differences, these were insufficient to indicate any systematic corrections of the RNA FF terms that could improve the performance of classical MD in simulating tetranucleotides. On the basis of these findings, we inferred that the overpopulation of intercalated conformers in the MD simulations of RNA tetramers, which were not observed experimentally, might be predominantly caused by imbalanced water-solvent and water-water interactions. Apart from the large-scale QM calculations performed to assess the performance of the AMBER FF, a representative spectrum of faster QM methods was tested.

Computer Folding of RNA Tetraloops: Identification of Key Force Field Deficiencies

The computer-aided folding of biomolecules, particularly RNAs, is one of the most difficult challenges in computational structural biology. RNA tetraloops are fundamental RNA motifs playing key roles in RNA folding and RNA-RNA and RNA-protein interactions. Although state-of-the-art Molecular Dynamics (MD) force fields correctly describe the native state of these tetraloops as a stable free-energy basin on the microsecond time scale, enhanced sampling techniques reveal that the native state is not the global free energy minimum, suggesting yet unidentified significant imbalances in the force fields. Here, we tested our ability to fold the RNA tetraloops in various force fields and simulation settings. We employed three different enhanced sampling techniques, namely, temperature replica exchange MD (T-REMD), replica exchange with solute tempering (REST2), and well-tempered metadynamics (WT-MetaD). We aimed to separate problems caused by limited sampling from those due to force-field inaccuracies. We found that none of the contemporary force fields is able to correctly describe folding of the 5'-GAGA-3' tetraloop over a range of simulation conditions. We thus aimed to identify which terms of the force field are responsible for this poor description of TL folding. We showed that at least two different imbalances contribute to this behavior, namely, overstabilization of base-phosphate and/or sugar-phosphate interactions and underestimated stability of the hydrogen bonding interaction in base pairing. The first artifact stabilizes the unfolded ensemble, while the second one destabilizes the folded state. The former problem might be partially alleviated by reparametrization of the van der Waals parameters of the phosphate oxygens suggested by Case et al., while in order to overcome the latter effect we suggest local potentials to better capture hydrogen bonding interactions.

Empirical Corrections to the Amber RNA Force Field with Target Metadynamics

The computational study of conformational transitions in nucleic acids still faces many challenges. For example, in the case of single stranded RNA tetranucleotides, agreement between simulations and experiments is not satisfactory due to inaccuracies in the force fields commonly used in molecular dynamics simulations. We here use experimental data collected from high-resolution X-ray structures to attempt an improvement of the latest version of the AMBER force field. A modified metadynamics algorithm is used to calculate correcting potentials designed to enforce experimental distributions of backbone torsion angles. Replica-exchange simulations of tetranucleotides including these correcting potentials show significantly better agreement with independent solution experiments for the oligonucleotides containing pyrimidine bases. Although the proposed corrections do not seem to be portable to generic RNA systems, the simulations revealed the importance of the α and ζ backbone angles for the modulation of the RNA conformational ensemble. The correction protocol presented here suggests a systematic procedure for force-field refinement.

Rapid communication capturing the destabilizing effect of dihydrouridine through molecular simulations

The structural effects of the commonly occurring modified nucleoside dihydrouridine (D) observed experimentally in model oligonucleotides include a strong destabilization of the C3'-endo sugar conformation of D, the disruption of stacking interactions of neighboring residues with D and a possible destabilization of the C3'-endo sugar pucker of the 5'-neighboring nucleoside. Our simulations with a combination of a set of parameters for modified RNA residues with the recently developed AMBER FF99χ force field having reoptimized glycosidic torsion angle parameters for standard nucleosides was found to reproduce the destabilizing effect of dihydrouridine better than with the AMBER FF99 force field for nucleic acids for which the parameters for the modified residues were originally developed.

On the Applicability of Elastic Network Models for the Study of RNA CUG Trinucleotide Repeat Overexpansion

Non-coding RNAs play a pivotal role in a number of diseases promoting an aberrant sequestration of nuclear RNA-binding proteins. In the particular case of myotonic dystrophy type 1 (DM1), a multisystemic autosomal dominant disease, the formation of large non-coding CUG repeats set up long-tract hairpins able to bind muscleblind-like proteins (MBNL), which trigger the deregulation of several splicing events such as cardiac troponin T (cTNT) and insulin receptor’s, among others. Evidence suggests that conformational changes in RNA are determinant for the recognition and binding of splicing proteins, molecular modeling simulations can attempt to shed light on the structural diversity of CUG repeats and to understand their pathogenic mechanisms. Molecular dynamics (MD) are widely used to obtain accurate results at atomistic level, despite being very time consuming, and they contrast with fast but simplified coarse-grained methods such as Elastic Network Model (ENM). In this paper, we assess the application of ENM (traditionally applied on proteins) for studying the conformational space of CUG repeats and compare it to conventional and accelerated MD conformational sampling. Overall, the results provided here reveal that ANM can provide useful insights into dynamic rCUG structures at a global level, and that their dynamics depend on both backbone and nucleobase fluctuations. On the other hand, ANM fail to describe local U-U dynamics of the rCUG system, which require more computationally expensive methods such as MD. Given that several limitations are inherent to both methods, we discuss here the usefulness of the current theoretical approaches for studying highly dynamic RNA systems such as CUG trinucleotide repeat overexpansions.

Biochemical Methods To Investigate lncRNA and the Influence of lncRNA:Protein Complexes on Chromatin

Long noncoding RNAs (lncRNAs), defined as nontranslated transcripts greater than 200 nucleotides in length, are often differentially expressed throughout developmental stages, tissue types, and disease states. The identification, visualization, and suppression/overexpression of these sequences have revealed impacts on a wide range of biological processes, including epigenetic regulation. Biochemical investigations on select systems have revealed striking insight into the biological roles of lncRNAs and lncRNA:protein complexes, which in turn prompt even more unanswered questions. To begin, multiple protein- and RNA-centric technologies have been employed to isolate lncRNA:protein and lncRNA:chromatin complexes. LncRNA interactions with the multi-subunit protein complex PRC2, which acts as a transcriptional silencer, represent some of the few cases where the binding affinity, selectivity, and activity of a lncRNA:protein complex have been investigated. At the same time, recent reports of full-length lncRNA secondary structures suggest the formation of complex structures with multiple independent folding domains and pave the way for more detailed structural investigations and predictions of lncRNA three-dimensional structure. This review will provide an overview of the methods and progress made to date as well as highlight new methods that promise to further inform the molecular recognition, specificity, and function of lncRNAs.

Disagreement Between the Structure of the dTpT Thymine Pair Determined by NMR and Molecular Dynamics Simulations Using Amber 14 Force Fields

We report a disagreement between the predicted structures of the dTpT thymine pair (thymidylyl(3' → 5')thymidine) using nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations using the AMBER ff14SB and ff14 + ε/ζOL1 + χOL4 force fields for DNA. The NMR structure was determined using NOE couplings to thymine's H6 and J(HH) couplings between sugar protons. The MD simulation used replica exchange methods to produce converged statistics in a 500 ns trajectory. NMR data indicate that both thymine nucleotides in the pair display an anti conformation of B-DNA, while the MD simulations predict a structure in which the 5'-thymine is flipped into a syn conformation and the 3'-thymine is in an anti conformation. The syn conformation of the 5'-thymine predicted by MD appears by a ∼ 180-deg flip of the glycosidic angle in comparison to the B-form anti structure. Differences in the distortion of the sugar pucker between 5'-thymine and 3'-thymine further highlighted the surprisingly different conformation of the 5'- and 3'-ends. While both MD and NMR indicate the deoxyribose sugars to be primarily in the 2'-endo conformation typical of B-form DNA, the MD simulations predict a more twisted conformation (2'-endo/1'-exo) for the 5'-sugar and significant flexibility of C3' of the 3'-sugar. We conclude that the current AMBER force field does not accurately predict the conformation of single-stranded thymine, in agreement with previous work investigating single-stranded DNA.

Elucidating the Relation between Internal Motions and Dihedral Angles in an RNA Hairpin Using Molecular Dynamics

Molecular dynamics simulations were performed to characterize the internal motions of the ribonucleic acid apical stem loop of human hepatitis B virus. The NMR relaxation rates calculated directly from the trajectory are in good agreement with the experiment. Calculated order parameters follow the experimental pattern. Order parameters lower than 0.8 are observed for nucleotides that are weakly hydrogen bonded to their base pair partner, unpaired, or part of the loop. These residues show slow decay of the internal correlation functions of their base and sugar C-H vectors. Concerted motions around backbone dihedral angles influence the amplitude of motion of the sugar and base C-H vectors. The order parameters for base C-H vectors are also affected by the fluctuation of the glycosidic dihedral angle.

Large-Scale Analysis of 48 DNA and 48 RNA Tetranucleotides Studied by 1 μs Explicit-Solvent Molecular Dynamics Simulations

An understanding of how the conformational behavior of single-stranded DNAs and RNAs depend on sequence is likely to be important for attempts to rationalize the thermodynamics of nucleic acid folding. In an attempt to further our understanding of such sequence dependences, we report here the results of 192 (1 μs) explicit-solvent molecular dynamics (MD) simulations of 48 DNA and 48 RNA tetranucleotide sequences performed using recently reported modifications to the AMBER force field. Each tetranucleotide was simulated starting from two different conformations, a fully natively stacked and a completely unstacked conformation, and populations of the various possible base stacking arrangements were analyzed. The simulations indicate that, for both DNA and RNA, the populations of fully natively stacked conformations increase linearly with increasing numbers of purines in the sequence, while the conformational entropies, computed by two complementary methods, decrease. Despite the comparatively short simulation times, the computed free energies of stacking of the 16 possible combinations of bases in the middle of the sequences are found to be in good correspondence with values reported recently from simulations of dinucleoside monophosphates using the same force field. Finally, consistent with recent reports from other groups, non-native stacking interactions, i.e., between bases that are not adjacent in sequence, are shown to be a recurring feature of the simulations; in particular, stacking interactions of bases in a i:i+2 relationship are shown to occur significantly more frequently when the intervening base is a pyrimidine. Given that the high prevalence of non-native stacking interactions is thought to be unrealistic, it appears that further parametrization work will be required before accurate conformational descriptions of single-stranded nucleic acids can be obtained with current force fields.

Computational study of stability of an H-H-type pseudoknot motif

Motifs in RNA tertiary structures are important to their structural organizations and biological functions. Here we consider an H-H-type pseudoknot (HHpk) motif that consists of two hairpins connected by a junction loop and with kissing interactions between the two hairpin loops. Such a tertiary structural motif is recurrently found in RNA tertiary structures, but is difficult to predict computationally. So it is important to understand the mechanism of its formation and stability. Here we investigate the stability of the HHpk tertiary structure by using an all-atom molecular dynamics simulation. The results indicate that the HHpk tertiary structure is stable. However, it is found that this stability is not due to the helix-helix packing, as is usually expected, but is maintained by the combined action of the kissing hairpin loops and junctions, although the former plays the main role. Stable HHpk motifs may form structural platforms for the molecules to realize their biological functions. These results are useful for understanding the construction principle of RNA tertiary structures and structure prediction.