Leading RNA tertiary interactions: structures, energies, and water insertion of A-minor and P-interactions. A quantum chemical view

Unveiling structural and energetic characterization of the emissive RNA alphabet anchored in the methylthieno[3,4-d]pyrimidine heterocycle core

This study presents a comprehensive theoretical exploration of the fluorescent non-natural emissive nucleobases- mthA, mthG, mthC, and mthU derived from the methylthieno[3,4-d]pyrimidine heterocycle. Our calculations, aligning with experimental findings, reveal that these non-natural bases exert minimal influence on the geometry of classical Watson-Crick base pairs within an RNA duplex, maintaining H-bonding akin to natural bases. In terms of energy, the impact of the modified bases, but for mthG, is also found to be little significant. We delved into an in-depth analysis of the photophysical properties of these non-natural bases. This investigation unveiled a correlation between their absorption/emission peaks and the substantial impact of the modification on the energy levels of the highest unoccupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbital (LUMO). Notably, this alteration in energy levels resulted in a significant reduction of the HOMO-LUMO gap, from approximately 5.4-5.5 eV in the natural bases, to roughly 3.9-4.7 eV in the modified bases. This shift led to a consequential change in absorption and emission spectra towards longer wavelengths, elucidating their bathochromic shift.

The energy landscape of the ribosome

The ribosome is a prototypical assembly that can be used to establish general principles and techniques for the study of biological molecular machines. Motivated by the fact that the dynamics of every biomolecule is governed by an underlying energy landscape, there has been great interest to understand and quantify ribosome energetics. In the present review, we will focus on theoretical and computational strategies for probing the interactions that shape the energy landscape of the ribosome, with an emphasis on more recent studies of the elongation cycle. These efforts include the application of quantum mechanical methods for describing chemical kinetics, as well as classical descriptions to characterize slower (microsecond to millisecond) large-scale (10-100 Å) rearrangements, where motion is described in terms of diffusion across an energy landscape. Together, these studies provide broad insights into the factors that control a diverse range of dynamical processes in this assembly.

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

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

Features and Functions of the A-Minor Motif, the Most Common Motif in RNA Structure

A-minor motifs are RNA tertiary structure motifs that generally involve a canonical base pair and an adenine base forming hydrogen bonds with the minor groove of the base pair. Such motifs are among the most common tertiary interactions in known RNA structures, comparable in number with the non-canonical base pairs. They are often found in functionally important regions of non-coding RNAs and, in particular, play a central role in protein synthesis. Here, we review local variations of the A-minor geometry and discuss difficulties associated with their annotation, as well as various structural contexts and common A-minor co-motifs, and diverse functions of A-minors in various processes in a living cell.

Annotation of the local context of the RNA secondary structure improves the classification and prediction of A-minors

Non-coding RNAs play a crucial role in various cellular processes in living organisms, and RNA functions heavily depend on molecule structures composed of stems, loops, and various tertiary motifs. Among those, the most frequent are A-minor interactions, which are often involved in the formation of more complex motifs such as kink-turns and pseudoknots. We present a novel classification of A-minors in terms of RNA secondary structure where each nucleotide of an A-minor is attributed to the stem or loop, and each pair of nucleotides is attributed to their relative position within the secondary structure. By analyzing classes of A-minors in known RNA structures, we found that the largest classes are mostly homogeneous and preferably localize with known A-minor co-motifs, e.g. tetraloop-tetraloop receptor and coaxial stacking. Detailed analysis of local A-minors within internal loops revealed a novel recurrent RNA tertiary motif, the across-bulged motif. Interestingly, the motif resembles the previously known GAAA/11nt motif but with the local adenines performing the role of the GAAA-tetraloop. By using machine learning, we show that particular classes of local A-minors can be predicted from sequence and secondary structure. The proposed classification is the first step toward automatic annotation of not only A-minors and their co-motifs but various types of RNA tertiary motifs as well.

Replacing thymine with a strongly pairing fifth Base: A combined quantum mechanics and molecular dynamics study

The non-natural ethynylmethylpyridone C-nucleoside (W), a thymidine (T) analogue that can be incorporated in oligonucleotides by automated synthesis, has recently been reported to form a high fidelity base pair with adenosine (A) and to be well accommodated in B-DNA duplexes. The enhanced binding affinity for A of W, as compared to T, makes it an ideal modification for biotechnological applications, such as efficient probe hybridization for the parallel detection of multiple DNA strands. In order to complement the experimental study and rationalize the impact of the non-natural W nucleoside on the structure, stability and dynamics of DNA structures, we performed quantum mechanics (QM) calculations along with molecular dynamics (MD) simulations. Consistently with the experimental study, our QM calculations show that the A:W base pair has an increased stability as compared to the natural A:T pair, due to an additional CH-π interaction. Furthermore, we show that mispairing between W and guanine (G) causes a distortion in the planarity of the base pair, thus explaining the destabilization of DNA duplexes featuring a G:W pair. MD simulations show that incorporation of single or multiple consecutive A:W pairs in DNA duplexes causes minor changes to the intra- and inter-base geometrical parameters, while a moderate widening/shrinking of the major/minor groove of the duplexes is observed. QM calculations applied to selected stacks from the MD simulations also show an increased stacking energy for W, over T, with the neighboring bases.

Occurrence and stability of lone pair-π and OH-π interactions between water and nucleobases in functional RNAs

We identified over 1000 instances of water-nucleobase stacking contacts in a variety of RNA molecules from a non-redundant set of crystal structures with resolution ≤3.0 Å. Such contacts may be of either the lone pair-π (lp-π) or the OH-π type, in nature. The distribution of the distances of the water oxygen from the nucleobase plane peaks at 3.5 Å for A, G and C, and approximately at 3.1-3.2 Å for U. Quantum mechanics (QM) calculations confirm, as expected, that the optimal energy is reached at a shorter distance for the lp-π interaction as compared to the OH-π one (3.0 versus 3.5 Å). The preference of each nucleobase for either type of interaction closely correlates with its electrostatic potential map. Furthermore, QM calculations show that for all the nucleobases a favorable interaction, of either the lp-π or the OH-π type, can be established at virtually any position of the water molecule above the nucleobase skeleton, which is consistent with the uniform projection of the OW atoms over the nucleobases ring we observed in the experimental occurrences. Finally, molecular dynamics simulations of a model system for the characterization of water-nucleobase stacking contacts confirm the stability of these interactions also under dynamic conditions.

Structural and Energetic Impact of Non-natural 7-Deaza-8-azaguanine, 7-Deaza-8-azaisoguanine, and Their 7-Substituted Derivatives on Hydrogen-Bond Pairing with Cytosine and Isocytosine

The impact of 7-deaza-8-azaguanine (DAG) and 7-deaza-8-azaisoguanine (DAiG) modifications on the geometry and stability of the G:C Watson-Crick (cWW) base pair and the G:iC and iG:C reverse Watson-Crick (tWW) base pairs has been characterized theoretically. In addition, the effect on the same base pairs of seven C7-substituted DAG and DAiG derivatives, some of which have been previously experimentally characterized, has been investigated. Calculations indicate that all of these modifications have a negligible impact on the geometry of the above base pairs, and that modification of the heterocycle skeleton has a small impact on the base-pair interaction energies. Instead, base-pair interaction energies are dependent on the nature of the C7 substituent. For the 7-substituted DAG-C cWW systems, a linear correlation between the base-pair interaction energy and the Hammett constant of the 7-substituent is found, with higher interaction energies corresponding to more electron-withdrawing substituents. Therefore, the explored modifications are expected to be accommodated in both parallel and antiparallel nucleic acid duplexes without perturbing their geometry, while the strength of a base pair (and duplex) featuring a DAG modification can, in principle, be tuned by incorporating different substituents at the C7 position.

Theoretical characterization of sulfur-to-selenium substitution in an emissive RNA alphabet: impact on H-bonding potential and photophysical properties

We employ density functional theory (DFT) and time-dependent DFT (TDDFT) calculations to investigate the structural, energetic and optical properties of a new computationally designed RNA alphabet, where the nucleobases, ^tsA, ^tsG, ^tsC, and ^tsU (ts-bases), have been derived by replacing sulfur with selenium in the previously reported tz-bases, based on the isothiazolo[4,3-d]pyrimidine heterocycle core. We find out that the modeled non-natural bases have minimal impact on the geometry and energetics of the classical Watson-Crick base pairs, thus potentially mimicking the natural bases in a RNA duplex in terms of H-bonding. In contrast, our calculations indicate that H-bonded base pairs involving the Hoogsteen edge of purines are destabilized as compared to their natural counterparts. We also focus on the photophysical properties of the non-natural bases and correlate their absorption/emission peaks to the strong impact of the modification on the energy of the lowest unoccupied molecular orbital. It is indeed stabilized by roughly 1.1-1.6 eV as compared to the natural analogues, resulting in a reduction of the gap between the highest occupied and the lowest unoccupied molecular orbital from 5.3-5.5 eV in the natural bases to 3.9-4.2 eV in the modified ones, with a consequent bathochromic shift in the absorption and emission spectra. Overall, our analysis clearly indicates that the newly modelled ts-bases are expected to exhibit better fluorescent properties as compared to the previously reported tz-bases, while retaining similar H-bonding properties. In addition, we show that a new RNA alphabet based on size-extended benzo-homologated ts-bases can also form stable Watson-Crick base pairs with the natural complementary nucleobases.

Energetics and dynamics of the non-natural fluorescent 4AP:DAP base pair

Quantum mechanics and molecular dynamics methods are used to compare the non-natural 4AP–DAP base pair to natural base pairs.

Occurrence and stability of lone pair-π stacking interactions between ribose and nucleobases in functional RNAs

The specific folding pattern and function of RNA molecules lies in various weak interactions, in addition to the strong base-base pairing and stacking. One of these relatively weak interactions, characterized by the stacking of the O4' atom of a ribose on top of the heterocycle ring of a nucleobase, has been known to occur but has largely been ignored in the description of RNA structures. We identified 2015 ribose-base stacking interactions in a high-resolution set of non-redundant RNA crystal structures. They are widespread in structured RNA molecules and are located in structural motifs other than regular stems. Over 50% of them involve an adenine, as we found ribose-adenine contacts to be recurring elements in A-minor motifs. Fewer than 50% of the interactions involve a ribose and a base of neighboring residues, while approximately 30% of them involve a ribose and a nucleobase at least four residues apart. Some of them establish inter-domain or inter-molecular contacts and often implicate functionally relevant nucleotides. In vacuo ribose-nucleobase stacking interaction energies were calculated by quantum mechanics methods. Finally, we found that lone pair-π stacking interactions also occur between ribose and aromatic amino acids in RNA-protein complexes.

Structural and energetic characterization of the emissive RNA alphabet based on the isothiazolo[4,3-d]pyrimidine heterocycle core

We present theoretical characterization of fluorescent non-natural nucleobases, (tz)A, (tz)G, (tz)C, and (tz)U, derived from the isothiazolo[4,3-d]pyrimidine heterocycle. Consistent with the experimental evidence, our calculations show that the non-natural bases have minimal impact on the geometry and stability of the classical Watson-Crick base pairs, allowing them to accurately mimic natural bases in a RNA duplex, in terms of H-bonding. In contrast, our calculations indicate that H-bonded base pairs involving the Hoogsteen edge are destabilized relative to their natural counterparts. Analysis of the photophysical properties of the non-natural bases allowed us to correlate their absorption/emission peaks to the strong impact of the modification on the energy of the lowest unoccupied molecular orbital, LUMO, which is stabilized by roughly 1.0-1.2 eV relative to the natural analogues, while the highest occupied molecular orbital, HOMO, is not substantially affected. As a result, the HOMO-LUMO gap is reduced from 5.3-5.5 eV in the natural bases to 4.0-4.4 eV in the modified ones, with a consequent bathochromic shift in the absorption and emission spectra.

Structural and Energetic Impact of Non-Natural 7-Deaza-8-Azaadenine and Its 7-Substituted Derivatives on H-Bonding Potential with Uracil in RNA Molecules

Non-natural (synthetic) nucleobases, including 7-ethynyl- and 7-triazolyl-8-aza-7-deazaadenine, have been introduced in RNA molecules for targeted applications, and have been characterized experimentally. However, no theoretical characterization of the impact of these modifications on the structure and energetics of the corresponding H-bonded base pair is available. To fill this gap, we performed quantum mechanics calculations, starting with the analysis of the impact of the 8-aza-7-deaza modification of the adenine skeleton, and we moved then to analyze the impact of the specific substituents on the modified 8-aza-7-deazaadenine. Our analysis indicates that, despite of these severe structural modifications, the H-bonding properties of the modified base pair gratifyingly replicate those of the unmodified base pair. Similar behavior is predicted when the same skeleton modifications are applied to guanine when paired to cytosine. To stress further the H-bonding pairing in the modified adenine-uracil base pair, we explored the impact of strong electron donor and electron withdrawing substituents on the C7 position. Also in this case we found minimal impact on the base pair geometry and energy, confirming the validity of this modification strategy to functionalize RNAs without perturbing its stability and biological functionality.

An atlas of RNA base pairs involving modified nucleobases with optimal geometries and accurate energies

Posttranscriptional modifications greatly enhance the chemical information of RNA molecules, contributing to explain the diversity of their structures and functions. A significant fraction of RNA experimental structures available to date present modified nucleobases, with half of them being involved in H-bonding interactions with other bases, i.e. ‘modified base pairs’. Herein we present a systematic investigation of modified base pairs, in the context of experimental RNA structures. To this end, we first compiled an atlas of experimentally observed modified base pairs, for which we recorded occurrences and structural context. Then, for each base pair, we selected a representative for subsequent quantum mechanics calculations, to find out its optimal geometry and interaction energy. Our structural analyses show that most of the modified base pairs are non Watson–Crick like and are involved in RNA tertiary structure motifs. In addition, quantum mechanics calculations quantify and provide a rationale for the impact of the different modifications on the geometry and stability of the base pairs they participate in.

Energies and 2'-Hydroxyl Group Orientations of RNA Backbone Conformations. Benchmark CCSD(T)/CBS Database, Electronic Analysis, and Assessment of DFT Methods and MD Simulations

Sugar-phosphate backbone is an electronically complex molecular segment imparting RNA molecules high flexibility and architectonic heterogeneity necessary for their biological functions. The structural variability of RNA molecules is amplified by the presence of the 2'-hydroxyl group, capable of forming multitude of intra- and intermolecular interactions. Bioinformatics studies based on X-ray structure database revealed that RNA backbone samples at least 46 substates known as rotameric families. The present study provides a comprehensive analysis of RNA backbone conformational preferences and 2'-hydroxyl group orientations. First, we create a benchmark database of estimated CCSD(T)/CBS relative energies of all rotameric families and test performance of dispersion-corrected DFT-D3 methods and molecular mechanics in vacuum and in continuum solvent. The performance of the DFT-D3 methods is in general quite satisfactory. The B-LYP-D3 method provides the best trade-off between accuracy and computational demands. B3-LYP-D3 slightly outperforms the new PW6B95-D3 and MPW1B95-D3 and is the second most accurate density functional of the study. The best agreement with CCSD(T)/CBS is provided by DSD-B-LYP-D3 double-hybrid functional, although its large-scale applications may be limited by high computational costs. Molecular mechanics does not reproduce the fine energy differences between the RNA backbone substates. We also demonstrate that the differences in the magnitude of the hyperconjugation effect do not correlate with the energy ranking of the backbone conformations. Further, we investigated the 2'-hydroxyl group orientation preferences. For all families, we conducted a QM and MM hydroxyl group rigid scan in gas phase and solvent. We then carried out set of explicit solvent MD simulations of folded RNAs and analyze 2'-hydroxyl group orientations of different backbone families in MD. The solvent energy profiles determined primarily by the sugar pucker match well with the distribution data derived from the simulations. The QM and MM energy profiles predict the same 2'-hydroxyl group orientation preferences. Finally, we demonstrate that the high energy of unfavorable and rarely sampled 2'-hydroxyl group orientations can be attributed to clashes between occupied orbitals.

Higher order structural effects stabilizing the reverse Watson-Crick Guanine-Cytosine base pair in functional RNAs

The G:C reverse Watson-Crick (W:W trans) base pair, also known as Levitt base pair in the context of tRNAs, is a structurally and functionally important base pair that contributes to tertiary interactions joining distant domains in functional RNA molecules and also participates in metabolite binding in riboswitches. We previously indicated that the isolated G:C W:W trans base pair is a rather unstable geometry, and that dicationic metal binding to the Guanine base or posttranscriptional modification of the Guanine can increase its stability. Herein, we extend our survey and report on other H-bonding interactions that can increase the stability of this base pair. To this aim, we performed a bioinformatics search of the PDB to locate all the occurencies of G:C trans base pairs. Interestingly, 66% of the G:C trans base pairs in the PDB are engaged in additional H-bonding interactions with other bases, the RNA backbone or structured water molecules. High level quantum mechanical calculations on a data set of representative crystal structures were performed to shed light on the structural stability and energetics of the various crystallographic motifs. This analysis was extended to the binding of the preQ1 metabolite to a preQ1-II riboswitch.

How does hydroxyl introduction influence the double helical structure: the stabilization of an altritol nucleic acid:ribonucleic acid duplex

Altritol nucleic acids (ANAs) are a promising new tool in the development of artificial small interfering ribonucleic acids (siRNAs) for therapeutical applications. To mimic the siRNA:messenger RNA (mRNA) interactions, the crystal structure of the ANA:RNA construct a(CCGUAAUGCC-P):r(GGCAUUACGG) was determined to 1.96 Å resolution which revealed the hybrid to form an A-type helix. As this A-form is a major requirement in the RNAi process, this crystal structure confirms the potential of altritol-modified siRNAs. Moreover, in the ANA strands, a new type of intrastrand interactions was found between the O2' hydroxyl group of one residue and the sugar ring O4' atom of the next residue. These interactions were further investigated by quantum chemical methods. Besides hydration effects, these intrastrand hydrogen bonds may also contribute to the stability of ANA:RNA duplexes.

Understanding the Sequence Preference of Recurrent RNA Building Blocks using Quantum Chemistry: The Intrastrand RNA Dinucleotide Platform

Folded RNA molecules are shaped by an astonishing variety of highly conserved noncanonical molecular interactions and backbone topologies. The dinucleotide platform is a widespread recurrent RNA modular building submotif formed by the side-by-side pairing of bases from two consecutive nucleotides within a single strand, with highly specific sequence preferences. This unique arrangement of bases is cemented by an intricate network of noncanonical hydrogen bonds and facilitated by a distinctive backbone topology. The present study investigates the gas-phase intrinsic stabilities of the three most common RNA dinucleotide platforms - 5'-GpU-3', ApA, and UpC - via state-of-the-art quantum-chemical (QM) techniques. The mean stability of base-base interactions decreases with sequence in the order GpU > ApA > UpC. Bader's atoms-in-molecules analysis reveals that the N2(G)…O4(U) hydrogen bond of the GpU platform is stronger than the corresponding hydrogen bonds in the other two platforms. The mixed-pucker sugar-phosphate backbone conformation found in most GpU platforms, in which the 5'-ribose sugar (G) is in the C2'-endo form and the 3'-sugar (U) in the C3'-endo form, is intrinsically more stable than the standard A-RNA backbone arrangement, partially as a result of a favorable O2'…O2P intra-platform interaction. Our results thus validate the hypothesis of Lu et al. (Lu Xiang-Jun, et al. Nucleic Acids Res. 2010, 38, 4868-4876), that the superior stability of GpU platforms is partially mediated by the strong O2'…O2P hydrogen bond. In contrast, ApA and especially UpC platform-compatible backbone conformations are rather diverse and do not display any characteristic structural features. The average stabilities of ApA and UpC derived backbone conformers are also lower than those of GpU platforms. Thus, the observed structural and evolutionary patterns of the dinucleotide platforms can be accounted for, to a large extent, by their intrinsic properties as described by modern QM calculations. In contrast, we show that the dinucleotide platform is not properly described in the course of atomistic explicit-solvent simulations. Our work also gives methodological insights into QM calculations of experimental RNA backbone geometries. Such calculations are inherently complicated by rather large data and refinement uncertainties in the available RNA experimental structures, which often preclude reliable energy computations.

A-minor tertiary interactions in RNA kink-turns. Molecular dynamics and quantum chemical analysis

The RNA kink-turn is an important recurrent RNA motif, an internal loop with characteristic consensus sequence forming highly conserved three-dimensional structure. Functional arrangement of RNA kink-turns shows a sharp bend in the phosphodiester backbone. Among other signature interactions, kink-turns form A-minor interaction between their two stems. Most kink-turns possess extended A-minor I (A-I) interaction where adenine of the second A•G base pair of the NC-stem interacts with the first canonical pair of the C-stem (i.e., the receptor pair) via trans-sugar-edge/sugar-edge (tSS) and cis-sugar-edge/sugar-edge (cSS) interactions. The remaining kink-turns have less compact A-minor 0 (A-0) interaction with just one tSS contact. We show that kink-turns with A-I in ribosomal X-ray structures keep G═C receptor base pair during evolution while the inverted pair (C═G) is not realized. In contrast, kink-turns with A-0 in the observed structures alternate G═C and C═G base pairs in sequences. We carried out an extended set (~5 μs) of explicit-solvent molecular dynamics simulations of kink-turns to rationalize this structural/evolutionary pattern. The simulations were done using a net-neutral Na(+) cation atmosphere (with ~0.25 M cation concentration) supplemented by simulations with either excess salt KCl atmosphere or inclusion of Mg(2+). The results do not seem to depend on the treatment of ions. The simulations started with X-ray structures of several kink-turns while we tested the response of the simulated system to base substitutions, modest structural perturbations and constraints. The trends seen in the simulations reveal that the A-I/G═C arrangement is preferred over all three other structures. The A-I/C═G triple appears structurally entirely unstable, consistent with the covariation patterns seen during the evolution. The A-0 arrangements tend to shift toward the A-I pattern in simulations, which suggests that formation of the A-0 interaction is likely supported by the surrounding protein and RNA molecules. A-0 may also be stabilized by additional kink-turn nucleotides not belonging to the kink-turn consensus, as shown for the kink-turn from ribosomal Helix 15. Quantum-chemical calculations on all four A-minor triples suggest that there is a different balance of electrostatic and dispersion stabilization in the A-I/G═C and A-I/C═G triples, which may explain different behavior of these otherwise isosteric triples in the context of kink-turns.

Noncanonical hydrogen bonding in nucleic acids. Benchmark evaluation of key base-phosphate interactions in folded RNA molecules using quantum-chemical calculations and molecular dynamics simulations

RNA molecules are stabilized by a wide range of noncanonical interactions that are not present in DNA. Among them, the recently classified base-phosphate (BPh) interactions belong to the most important ones. Twelve percent of nucleotides in the ribosomal crystal structures are involved in BPh interactions. BPh interactions are highly conserved and provide major constraints on RNA sequence evolution. Here we provide assessment of the energetics of BPh interactions using MP2 computations extrapolated to the complete basis set of atomic orbitals and corrected for higher-order electron correlation effects. The reference computations are compared with DFT-D and DFT-D3 approaches, the SAPT method, and the molecular mechanics force field. The computations, besides providing the basic benchmark for the BPh interactions, allow some refinements of the original classification, including identification of some potential doubly bonded BPh patterns. The reference computations are followed by analysis of some larger RNA fragments that consider the context of the BPh interactions. The computations demonstrate the complexity of interaction patterns utilizing the BPh interactions in real RNA structures. The BPh interactions are often involved in intricate interaction networks. We studied BPh interactions of protonated adenine that can contribute to catalysis of hairpin ribozyme, the key BPh interaction in the S-turn motif of the sarcin-ricin loop, which may predetermine the S-turn topology and complex BPh patterns from the glmS riboswitch. Finally, the structural stability of BPh interactions in explicit solvent molecular dynamics simulations is assessed. The simulations well preserve key BPh interactions and allow dissection of structurally/functionally important water-meditated BPh bridges, which could not be considered in earlier bioinformatics classification of BPh interactions.

Quantum chemical studies of nucleic acids: can we construct a bridge to the RNA structural biology and bioinformatics communities?

In this feature article, we provide a side-by-side introduction for two research fields: quantum chemical calculations of molecular interaction in nucleic acids and RNA structural bioinformatics. Our main aim is to demonstrate that these research areas, while largely separated in contemporary literature, have substantial potential to complement each other that could significantly contribute to our understanding of the exciting world of nucleic acids. We identify research questions amenable to the combined application of modern ab initio methods and bioinformatics analysis of experimental structures while also assessing the limitations of these approaches. The ultimate aim is to attain valuable physicochemical insights regarding the nature of the fundamental molecular interactions and how they shape RNA structures, dynamics, function, and evolution.

On the role of the cis Hoogsteen:sugar-edge family of base pairs in platforms and triplets-quantum chemical insights into RNA structural biology

Base pairs belonging to the cis Hoogsteen:sugar-edge (H:S) family play important structural roles in folded RNA molecules. Several of these are present in internal loops, where they are involved in interactions leading to planar dinucleotide platforms which stabilize higher order structures such as base triplets and quartets. We report results of analysis of 30 representative examples spanning 16 possible base pair combinations, with several of them showing multimodality of base pairing geometry. The geometries of 23 of these base pairs were modeled directly from coordinates extracted from RNA crystal structures. The other seven were predicted structures which were modeled on the basis of observed isosteric analogues. After appropriate satisfaction of residual valencies, these structures were relaxed using the B3LYP/6-31G(d,p) method and interaction energies were derived at the RIMP2/aug-cc-pVDZ level of theory. The geometries for each of the studied base pairs have been characterized in terms of the number and nature of H-bonds, rmsd values observed on optimization, base pair geometrical parameters, and sugar pucker analysis. In addition to its evaluation, the nature of intermolecular interaction in these complexes was also analyzed using Morokuma decomposition. The gas phase interaction energies range between -5.2 and -20.6 kcal/mol and, in contrast to the H:S trans base pairs, show enhanced relative importance of the electron correlation component, indicative of the greater role of dispersion energy in stabilization of these base pairs. The rich variety of hydrogen bonding pattern, involving the flexible sugar edge, appears to hold the key to several features of structural motifs, such as planarity and propensity to participate in triplets, observed in this family of base pairs. This work explores these aspects by integrating database analysis, and detailed base pairing geometry analysis at the atomistic level, with ab initio computation of interaction energies. The study, involving alternative classification of base pairs and triplets, provides insights into intrinsic properties of these base pairs and their possible structural and functional roles.

Molecular dynamics and quantum mechanics of RNA: conformational and chemical change we can believe in

Structure and dynamics are both critical to RNA’s vital functions in biology. Numerous techniques can elucidate the structural dynamics of RNA, but computational approaches based on experimental data arguably hold the promise of providing the most detail. In this Account, we highlight areas wherein molecular dynamics (MD) and quantum mechanical (QM) techniques are applied to RNA, particularly in relation to complementary experimental studies.

We have expanded on atomic-resolution crystal structures of RNAs in functionally relevant states by applying explicit solvent MD simulations to explore their dynamics and conformational changes on the submicrosecond time scale. MD relies on simplified atomistic, pairwise additive interaction potentials (force fields). Because of limited sampling, due to the finite accessible simulation time scale and the approximated force field, high-quality starting structures are required.

Despite their imperfection, we find that currently available force fields empower MD to provide meaningful and predictive information on RNA dynamics around a crystallographically defined energy minimum. The performance of force fields can be estimated by precise QM calculations on small model systems. Such calculations agree reasonably well with the Cornell et al. AMBER force field, particularly for stacking and hydrogen-bonding interactions. A final verification of any force field is accomplished by simulations of complex nucleic acid structures.

The performance of the Cornell et al. AMBER force field generally corresponds well with and augments experimental data, but one notable exception could be the capping loops of double-helical stems. In addition, the performance of pairwise additive force fields is obviously unsatisfactory for inclusion of divalent cations, because their interactions lead to major polarization and charge-transfer effects neglected by the force field. Neglect of polarization also limits, albeit to a lesser extent, the description accuracy of other contributions, such as interactions with monovalent ions, conformational flexibility of the anionic sugar−phosphate backbone, hydrogen bonding, and solute polarization by solvent. Still, despite limitations, MD simulations are a valid tool for analyzing the structural dynamics of existing experimental structures. Careful analysis of MD simulations can identify problematic aspects of an experimental RNA structure, unveil structural characteristics masked by experimental constraints, reveal functionally significant stochastic fluctuations, evaluate the structural role of base ionization, and predict structurally and potentially functionally important details of the solvent behavior, including the presence of tightly bound water molecules. Moreover, combining classical MD simulations with QM calculations in hybrid QM/MM approaches helps in the assessment of the plausibility of chemical mechanisms of catalytic RNAs (ribozymes).

In contrast, the reliable prediction of structure from sequence information is beyond the applicability of MD tools. The ultimate utility of computational studies in understanding RNA function thus requires that the results are neither blindly accepted nor flatly rejected, but rather considered in the context of all available experimental data, with great care given to assessing limitations through the available starting structures, force field approximations, and sampling limitations. The examples given in this Account showcase how the judicious use of basic MD simulations has already served as a powerful tool to help evaluate the role of structural dynamics in biological function of RNA.

Elbow flexibility of the kt38 RNA kink-turn motif investigated by free-energy molecular dynamics simulations

Kink-turns (K-turns) are common structural motifs that can introduce sharp kinks into double-stranded RNA, and have been proposed to mediate large-scale motions in the ribosome. K-turns consist of a bulge loop region flanked by trans sugar-Hoogsteen G:A pairs, and the sharp kink conformation is stabilized by A-minor interactions (adenine contacting a G:C basepair in the minor groove). Umbrella-sampling molecular dynamics simulations were used to disrupt an A-minor interaction in the ribosomal kt38 turn and to calculate the associated free-energy change. Coupling of umbrella sampling with replica exchanges between neighboring umbrella-sampling intervals could further improve the convergence of the free-energy calculations. The simulations revealed a coupled A-minor disruption and global opening of the K-turn motif, and allowed us to characterize several intermediate A-minor conformations. The calculated free-energy profile indicated a meta-stable, semi-open structure of slightly higher free energy ( approximately 1 kcal mol(-1)), separated by a small free-energy barrier ( approximately 1.5 kcal mol(-1)) from the closed (highly kinked) form. Both K-turn states are stabilized by distinct variants of the A-minor interaction. Further opening of the K-turn structure required significantly larger free-energy changes. The semi-open form had a reduced kink angle compatible with experimental data on K-turn solution structures, and opening was coupled to a continuous global unwinding of the K-turn motif. The range of free-energy changes associated with kt38 opening and unwinding are compatible with the idea that K-turns may facilitate biologically relevant motions during large-scale ribosome dynamics.

Classification and energetics of the base-phosphate interactions in RNA

Structured RNA molecules form complex 3D architectures stabilized by multiple interactions involving the nucleotide base, sugar and phosphate moieties. A significant percentage of the bases in structured RNA molecules in the Protein Data Bank (PDB) hydrogen-bond with phosphates of other nucleotides. By extracting and superimposing base-phosphate (BPh) interactions from a reduced-redundancy subset of 3D structures from the PDB, we identified recurrent phosphate-binding sites on the RNA bases. Quantum chemical calculations were carried out on model systems representing each BPh interaction. The calculations show that the centers of each cluster obtained from the structure superpositions correspond to energy minima on the potential energy hypersurface. The calculations also show that the most stable phosphate-binding sites occur on the Watson-Crick edge of guanine and the Hoogsteen edge of cytosine. We modified the 'Find RNA 3D' (FR3D) software suite to automatically find and classify BPh interactions. Comparison of the 3D structures of the 16S and 23S rRNAs of Escherichia coli and Thermus thermophilus revealed that most BPh interactions are phylogenetically conserved and they occur primarily in hairpin, internal or junction loops or as part of tertiary interactions. Bases that form BPh interactions, which are conserved in the rRNA 3D structures are also conserved in homologous rRNA sequence alignments.

Trans Hoogsteen/sugar edge base pairing in RNA. Structures, energies, and stabilities from quantum chemical calculations

Trans Hoogsteen/sugar edge (H/SE) RNA base pairs form one of the six families of RNA base pairs that utilize the 2'-hydroxyl group of ribose for base pairing and play key roles in stabilizing folded RNA molecules. Here, we provide a detailed quantum chemical characterization of intrinsic structures and interaction energies of this base pair family, along with the evaluation of solvent screening effects by a continuum solvent approach. We report DFT-optimized geometries and MP2 interaction energies for all 10 crystallographically identified members of the family, for a representative set of them, using complete basis set extrapolation. For 6 of the 10 base pairs, we had to apply geometric constraints to keep the geometries relevant to RNA. We confirm that the remaining, hitherto undetected, possible members of this family do not have appropriate steric features required to establish stable base pairing in the trans H/SE fashion. The interaction patterns in the trans H/SE family are highly diverse, with gas-phase interaction energies in the range from -1 to -17 kcal/mol. Except for the C/rC and G/rG trans H/SE base pairs, the interaction energy is roughly evenly distributed between the HF and correlation components. Thus, in the trans H/SE base pairs, the relative importance of electron correlation is noticeably smaller than in the cis WC/SE or cis and trans SE/SE base pairs, but still larger than in canonical base pairs. The trans H/SE A/rG base pair is the intrinsically most stable member of this family. This base pair is also known as the sheared AG base pair and belongs to the most prominent set of RNA base pairs utilized in molecular building blocks of functional RNAs. For all trans H/SE base pairs that we identified, in addition to conventional base pairing, viable alternative structures were stabilized by amino-acceptor interactions. In the QM calculations, these amino-acceptor complexes appear to be equally as stable as those with common H-bonds, and more importantly, the switch to amino-acceptor interaction does not require any significant geometrical rearrangement of the base pairs. Such interactions are worthy of further investigations, as X-ray crystallography cannot unambiguously distinguish between conventional and amino-acceptor interactions involving the 2'-hydroxyl group, formation of such interactions is usually not considered, and molecular modeling force fields do not include such interactions properly as a result of neglect of aminogroup pyramidalization.

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by Vernizzi, Orland, and Zee [Phys. Rev. Lett. 94, 168103 (2005)]. The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a NxN Hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement, and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of 1/N as being a measure of the concentration of Mg2+ in solution.

The UA_handle: a versatile submotif in stable RNA architectures

Stable RNAs are modular and hierarchical 3D architectures taking advantage of recurrent structural motifs to form extensive non-covalent tertiary interactions. Sequence and atomic structure analysis has revealed a novel submotif involving a minimal set of five nucleotides, termed the UA_handle motif (5'XU/AN(n)X3'). It consists of a U:A Watson-Crick: Hoogsteen trans base pair stacked over a classic Watson-Crick base pair, and a bulge of one or more nucleotides that can act as a handle for making different types of long-range interactions. This motif is one of the most versatile building blocks identified in stable RNAs. It enters into the composition of numerous recurrent motifs of greater structural complexity such as the T-loop, the 11-nt receptor, the UAA/GAN and the G-ribo motifs. Several structural principles pertaining to RNA motifs are derived from our analysis. A limited set of basic submotifs can account for the formation of most structural motifs uncovered in ribosomal and stable RNAs. Structural motifs can act as structural scaffoldings and be functionally and topologically equivalent despite sequence and structural differences. The sequence network resulting from the structural relationships shared by these RNA motifs can be used as a proto-language for assisting prediction and rational design of RNA tertiary structures.

Nature and magnitude of aromatic stacking of nucleic acid bases

This review summarises recent advances in quantum chemical calculations of base-stacking forces in nucleic acids. We explain in detail the very complex relationship between the gas-phase base-stacking energies, as revealed by quantum chemical (QM) calculations, and the highly variable roles of these interactions in nucleic acids. This issue is rarely discussed in quantum chemical and physical chemistry literature. We further extensively discuss methods that are available for base-stacking studies, complexity of comparison of stacking calculations with gas phase experiments, balance of forces in stacked complexes of nucleic acid bases, and the relation between QM and force field descriptions. We also review all recent calculations on base-stacking systems, including details analysis of the B-DNA stacking. Specific attention is paid to the highest accuracy QM calculations, to the decomposition of the interactions, and development of dispersion-balanced DFT methods. Future prospects of computational studies of base stacking are discussed.