QM Computations on Complete Nucleic Acids Building Blocks: Analysis of the Sarcin–Ricin RNA Motif Using DFT-D3, HF-3c, PM6-D3H, and MM Approaches

Duplex DNA Retains the Conformational Features of Single Strands: Perspectives from MD Simulations and Quantum Chemical Computations

Molecular dynamics simulations and geometry optimizations carried out at the quantum level as well as by quantum mechanical/molecular mechanics methods predict that short, single-stranded DNA oligonucleotides adopt conformations very similar to those observed in crystallographic double-stranded B-DNA, with rise coordinates close to ≈3.3 Å. In agreement with the experimental evidence, the computational results show that DNA single strands rich in adjacent purine nucleobases assume more regular arrangements than poly-thymine. The preliminary results suggest that single-stranded poly-cytosine DNA should also retain a substantial helical order in solution. A comparison of the structures of single and double helices confirms that the B-DNA motif is a favorable arrangement also for single strands. Indeed, the optimal geometry of the complementary single helices is changed to a very small extent in the formation of the duplex.

B-DNA Structure and Stability: The Role of Nucleotide Composition and Order

We have quantum chemically analyzed the influence of nucleotide composition and sequence (that is, order) on the stability of double-stranded B-DNA triplets in aqueous solution. To this end, we have investigated the structure and bonding of all 32 possible DNA duplexes with Watson-Crick base pairing, using dispersion-corrected DFT at the BLYP-D3(BJ)/TZ2P level and COSMO for simulating aqueous solvation. We find enhanced stabilities for duplexes possessing a higher GC base pair content. Our activation strain analyses unexpectedly identify the loss of stacking interactions within individual strands as a destabilizing factor in the duplex formation, in addition to the better-known effects of partial desolvation. Furthermore, we show that the sequence-dependent differences in the interaction energy for duplexes of the same overall base pair composition result from the so-called "diagonal interactions" or "cross terms". Whether cross terms are stabilizing or destabilizing depends on the nature of the electrostatic interaction between polar functional groups in the pertinent nucleobases.

Chemical reactivity and binding interactions in ribonucleic acid-peptide complexes

The covalent and noncovalent backbone binding interactions in RNA-peptide complexes were studied by DFT methods. Four RNA structures R1(GGCUAGCC), R2(AAUCGAUU), R3(GGGAUCCC), and R4(AAAGCUUU) has been selected for eight protonated peptides (DR, ER, GR, KR, NGR, RR, tmeGnd (tme), and VR) interactions based on an experimental study (Anal Chem. 2019; 91:1659-1664). Chemical reactivity theory is used to study the reactivity of eight peptides with global descriptors. Lower hardness values reflected low stability and high reactivity for the protonated peptides. DR, ER, GR, KR, NGR, RR, and VR show lower value of ω, μ while tme has high value of ω, μ. Larger highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap for ER, GR, and KR showed greater structural stability for peptides. AutoDock and PatchDock results indicated that R1, R2, and R4 retain hairpin structures while interacting with peptide complexes. The calculated binding energies of (R1-R4)-peptide complexes from AutoDock tools are (1.49-11.12) kcal/mol. Results showed that the noncovalent interactions are stronger than the covalent interactions for R1-peptide complexes. The reason might be the transfer of proton from protonated ligand to deprotonated RNA, which has initiated the loss of the ligand. Also it has been observed that proton transfer has become energetically unfavorable in presence of additional hydrogen bonds which is predicted in the experimental results.

Conformational energies and equilibria of cyclic dinucleotides in vacuo and in solution: computational chemistry vs. NMR experiments

Performance of computational methods in modelling cyclic dinucleotides - an important and challenging class of compounds - has been evaluated by two different benchmarks: (1) gas-phase conformational energies and (2) qualitative agreement with NMR observations of the orientation of the χ-dihedral angle in solvent. In gas-phase benchmarks, where CCSD(T) and DLPNO-CCSD(T) methods have been used as the reference, most of the (dispersion corrected) density functional approximations are accurate enough to justify prioritizing computational cost and compatibility with other modelling options as the criterion of choice. NMR experiments of 3'3'-c-di-AMP, 3'3'-c-GAMP, and 3'3'-c-di-GMP show the overall prevalence of the anti-conformation of purine bases, but some population of syn-conformations is observed for guanines. Implicit solvation models combined with quantum-chemical methods struggle to reproduce this behaviour, probably due to a lack of dynamics and explicitly modelled solvent, leading to structures that are too compact. Molecular dynamics simulations overrepresent the syn-conformation of guanine due to the overestimation of an intramolecular hydrogen bond. Our combination of experimental and computational benchmarks provides "error bars" for modelling cyclic dinucleotides in solvent, where such information is generally difficult to obtain, and should help gauge the interpretability of studies dealing with binding of cyclic dinucleotides to important pharmaceutical targets. At the same time, the presented analysis calls for improvement in both implicit solvation models and force-field parameters.

Density functional theory studies on cytosine analogues for inducing double-proton transfer with guanine

To induce double-proton transfer (DPT) with guanine in a biological environment, 12 cytosine analogues (Ca) were formed by atomic substitution. The DPT reactions in the Watson-Crick cytosine-guanine model complex (Ca₀G) and 12 modified cytosine-guanine complexes (Ca_1-12G) were investigated using density functional theory methods at the M06-2X/def2svp level. The intramolecular proton transfers within the analogues are not facile due to high energy barriers. The hydrogen bond lengths of the Ca_1-12G complexes are shorter than those in the Ca₀G complex, which are conducive to DPT reactions. The DPT energy barriers of Ca_1-12G complexes are also lower than that of the Ca₀G complex, in particular, the barriers in the Ca₇G and Ca₁₁G complexes were reduced to -1.33 and -2.02 kcal/mol, respectively, indicating they are significantly more prone to DPT reactions. The DPT equilibrium constants of Ca_1-12G complexes range from 1.60 × 10⁰ to 1.28 × 10⁷, among which the equilibrium constants of Ca₇G and Ca₁₁G are over 1.0 × 10⁵, so their DPT reactions may be adequate. The results demonstrate that those cytosine analogues, especially Ca₇ and Ca₁₁, are capable of inducing DPT with guanine, and then the guanine tautomer will form mismatches with thymine during DNA replication, which may provide new strategies for gene therapy.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

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

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

Prebiotic synthesis of nucleic acids and their building blocks at the atomic level - merging models and mechanisms from advanced computations and experiments

The origin of life on Earth is one of the most fascinating questions of contemporary science. Extensive research in the past decades furnished diverse experimental proposals for the emergence of first informational polymers that could form the basis of the early terrestrial life. Side by side with the experiments, the fast development of modern computational chemistry methods during the last 20 years facilitated the use of in silico modelling tools to complement the experiments. Modern computations can provide unique atomic-level insights into the structural and electronic aspects as well as the energetics of key prebiotic chemical reactions. Many of these insights are not directly obtainable from the experimental techniques and the computations are thus becoming indispensable for proper interpretation of many experiments and for qualified predictions. This review illustrates the synergy between experiment and theory in the origin of life research focusing on the prebiotic synthesis of various nucleic acid building blocks and on the self-assembly of nucleotides leading to the first functional oligonucleotides.

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

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

B-DNA model systems in non-terran bio-solvents: implications for structure, stability and replication

We have computationally analyzed a comprehensive series of Watson–Crick and mismatched B-DNA base pairs, in the gas phase and in several solvents, including toluene, chloroform, ammonia, methanol and water, using dispersion-corrected density functional theory and implicit solvation.

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.

Fragmentation mechanisms of cytosine, adenine and guanine ionized bases

The different fragmentation channels of cytosine, adenine and guanine have been studied through DFT calculations. The electronic structure of bases, their cations, and the fragments obtained by breaking bonds provides a good understanding of the fragmentation process that can complete the experimental approach. The calculations allow assigning various fragments to the given peaks. The comparison between the energy required for the formation of fragments and the peak intensity in the mass spectrum is used. For cytosine and guanine the elimination of the HNCO molecule is a major route of dissociation, while for adenine multiple loss of HCN or HNC can be followed up to small fragments. For cytosine, this corresponds to the initial bond cleavage of N3-C4/N1-C2, which represents the main dissociation route. For guanine the release of HNCO is obtained through the N1-C2/C5-C6 bond cleavage (reverse order also possible) leading to the largest peak of the spectrum. The corresponding energies of 3.5 and 3.9 eV are typically in the range available in the experiments. The loss of NH3 or HCN is also possible but requires more energy. For adenine, fragmentation consists of multiple loss of the HCN molecule and the main route corresponding to HC8N9 loss is followed by the release of HC2N1.

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.

Refinement of the Sugar-Phosphate Backbone Torsion Beta for AMBER Force Fields Improves the Description of Z- and B-DNA

Z-DNA duplexes are a particularly complicated test case for current force fields. We performed a set of explicit solvent molecular dynamics (MD) simulations with various AMBER force field parametrizations including our recent refinements of the ε/ζ and glycosidic torsions. None of these force fields described the ZI/ZII and other backbone substates correctly, and all of them underpredicted the population of the important ZI substate. We show that this underprediction can be attributed to an inaccurate potential for the sugar-phosphate backbone torsion angle β. We suggest a refinement of this potential, β(OL1), which was derived using our recently introduced methodology that includes conformation-dependent solvation effects. The new potential significantly increases the stability of the dominant ZI backbone substate and improves the overall description of the Z-DNA backbone. It also has a positive (albeit small) impact on another important DNA form, the antiparallel guanine quadruplex (G-DNA), and improves the description of the canonical B-DNA backbone by increasing the population of BII backbone substates, providing a better agreement with experiment. We recommend using β(OL1) in combination with our previously introduced corrections, εζ(OL1) and χ(OL4), (the combination being named OL15) as a possible alternative to the current β torsion potential for more accurate modeling of nucleic acids.

A simple and efficient dispersion correction to the Hartree-Fock theory (2): Incorporation of a geometrical correction for the basis set superposition error

One of the most challenging problems in computer-aided drug discovery is the accurate prediction of the binding energy between a ligand and a protein. For accurate estimation of net binding energy ΔEbind in the framework of the Hartree-Fock (HF) theory, it is necessary to estimate two additional energy terms; the dispersion interaction energy (Edisp) and the basis set superposition error (BSSE). We previously reported a simple and efficient dispersion correction, Edisp, to the Hartree-Fock theory (HF-Dtq). In the present study, an approximation procedure for estimating BSSE proposed by Kruse and Grimme, a geometrical counterpoise correction (gCP), was incorporated into HF-Dtq (HF-Dtq-gCP). The relative weights of the Edisp (Dtq) and BSSE (gCP) terms were determined to reproduce ΔEbind calculated with CCSD(T)/CBS or /aug-cc-pVTZ (HF-Dtq-gCP (scaled)). The performance of HF-Dtq-gCP (scaled) was compared with that of B3LYP-D3(BJ)-bCP (dispersion corrected B3LYP with the Boys and Bernadi counterpoise correction (bCP)), by taking ΔEbind (CCSD(T)-bCP) of small non-covalent complexes as 'a golden standard'. As a critical test, HF-Dtq-gCP (scaled)/6-31G(d) and B3LYP-D3(BJ)-bCP/6-31G(d) were applied to the complex model for HIV-1 protease and its potent inhibitor, KNI-10033. The present results demonstrate that HF-Dtq-gCP (scaled) is a useful and powerful remedy for accurately and promptly predicting ΔEbind between a ligand and a protein, albeit it is a simple correction procedure.

Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit

We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields.

Enhanced semiempirical QM methods for biomolecular interactions

Recent successes and failures of the application of 'enhanced' semiempirical QM (SQM) methods are reviewed in the light of the benefits and backdraws of adding dispersion (D) and hydrogen-bond (H) correction terms. We find that the accuracy of SQM-DH methods for non-covalent interactions is very often reported to be comparable to dispersion-corrected density functional theory (DFT-D), while computation times are about three orders of magnitude lower. SQM-DH methods thus open up a possibility to simulate realistically large model systems for problems both in life and materials science with comparably high accuracy.

Towards biochemically relevant QM computations on nucleic acids: controlled electronic structure geometry optimization of nucleic acid structural motifs using penalty restraint functions

Recent developments in dispersion-corrected density functional theory methods allow for the first time the description of large fragments of nucleic acids (hundreds of atoms) with an accuracy clearly surpassing the accuracy of common biomolecular force fields. Such calculations can significantly improve the description of the potential energy surface of nucleic acid molecules, which may be useful for studies of molecular interactions and conformational preferences of nucleic acids, as well as verification and parameterization of other methods. The first of such studies, however, demonstrated that successful applications of accurate QM calculations to larger nucleic acid building blocks are hampered by difficulties in obtaining geometries that are biochemically relevant and are not biased by non-native structural features. We present an approach that can greatly facilitate large-scale QM studies on nucleic acids, namely electronic structure geometry optimization of nucleic acid fragments utilizing a penalty function to restrain key internal coordinates with a specific focus on the torsional backbone angles. This work explores the viability of these restraint optimizations for DFT-D3, PM6-D3H and HF-3c optimizations on a set of examples (a UpA dinucleotide, a DNA G-quadruplex and a B-DNA fragment). Evaluation of different penalty function strengths reveals only a minor system-dependency and reasonable restraint values range from 0.01 to 0.05 Eh rad(-2) for the backbone torsions. Restraints are crucial to perform the QM calculations on biochemically relevant conformations in implicit solvation and gas phase geometry optimizations. The reasons for using restrained instead of constrained or unconstrained optimizations are explained and an open-source external optimizer is provided.

Molecular Dynamics Simulations of Nucleic Acids. From Tetranucleotides to the Ribosome

We present a brief overview of explicit solvent molecular dynamics (MD) simulations of nucleic acids. We explain physical chemistry limitations of the simulations, namely, the molecular mechanics (MM) force field (FF) approximation and limited time scale. Further, we discuss relations and differences between simulations and experiments, compare standard and enhanced sampling simulations, discuss the role of starting structures, comment on different versions of nucleic acid FFs, and relate MM computations with contemporary quantum chemistry. Despite its limitations, we show that MD is a powerful technique for studying the structural dynamics of nucleic acids with a fast growing potential that substantially complements experimental results and aids their interpretation.