Comparison of intrinsic stacking energies of ten unique dinucleotide steps in A-RNA and B-DNA duplexes. Can we determine correct order of stability by quantum-chemical calculations?

Relative stability of different DNA guanine quadruplex stem topologies derived using large-scale quantum-chemical computations

We provide theoretical predictions of the intrinsic stability of different arrangements of guanine quadruplex (G-DNA) stems. Most computational studies of nucleic acids have applied Molecular Mechanics (MM) approaches using simple pairwise-additive force fields. The principle limitation of such calculations is the highly approximate nature of the force fields. In this study, we for the first time apply accurate QM computations (DFT-D3 with large atomic orbital basis sets) to essentially complete DNA building blocks, seven different folds of the cation-stabilized two-quartet G-DNA stem, each having more than 250 atoms. The solvent effects are approximated by COSMO continuum solvent. We reveal sizable differences between MM and QM descriptions of relative energies of different G-DNA stems, which apparently reflect approximations of the DNA force field. Using the QM energy data, we propose correction to earlier free energy estimates of relative stabilities of different parallel, hybrid, and antiparallel G-stem folds based on classical simulations. The new energy ranking visibly improves the agreement between theory and experiment. We predict the 5'-anti-anti-3' GpG dinucleotide step to be the most stable one, closely followed by the 5'-syn-anti-3' step. The results are in good agreement with known experimental structures of 2-, 3-, and 4-quartet G-DNA stems. Besides providing specific results for G-DNA, our study highlights basic limitations of force field modeling of nucleic acids. Although QM computations have their own limitations, mainly the lack of conformational sampling and the approximate description of the solvent, they can substantially improve the quality of calculations currently relying exclusively on force fields.

Backbone-base interactions critical to quantum stabilization of transfer RNA anticodon structure

Transfer RNA (tRNA) anticodons adopt a highly ordered 3'-stack without significant base overlap. Density functional theory at the M06-2X/6-31+G(d,p) level in combination with natural bond orbital analysis was utilized to calculate the intramolecular interactions within the tRNA anticodon that are responsible for stabilizing the stair-stepped conformation. Ten tRNA X-ray crystal structures were obtained from the PDB databank and were trimmed to include only the anticodon bases. Hydrogenic positions were added and optimized for the structures in the stair-stepped conformation. The sugar-phosphate backbone has been retained for these calculations, revealing the role it plays in RNA structural stability. It was found that electrostatic interactions between the sugar-phosphate backbone and the base provide the most stability, rather than the traditionally studied interbase stacking. Base-stacking interactions, though present, were weak and inconsistent. Aqueous solvation was found to have little effect on the intramolecular interactions.

How to understand quantum chemical computations on DNA and RNA systems? A practical guide for non-specialists

In this review primarily written for non-experts we explain basic methodological aspects and interpretation of modern quantum chemical (QM) computations applied to nucleic acids. We introduce current reference QM computations on small model systems consisting of dozens of atoms. Then we comment on recent advance of fast and accurate dispersion-corrected density functional theory methods, which will allow computations of small but complete nucleic acids building blocks in the near future. The qualitative difference between QM and molecular mechanics (MM, force field) computations is discussed. We also explain relation of QM and molecular simulation computations to experiments.

Sequence and conformation effects on ionization potential and charge distribution of homo-nucleobase stacks using M06-2X hybrid density functional theory calculations

DNA is subject to oxidative damage due to radiation or by-products of cellular metabolism, thereby creating electron holes that migrate along the DNA stacks. A systematic computational analysis of the dependence of the electronic properties of nucleobase stacks on sequence and conformation was performed here, on the basis of single- and double-stranded homo-nucleobase stacks of 1-10 bases or 1-8 base pairs in standard A-, B-, and Z-conformation. First, several levels of theory were tested for calculating the vertical ionization potentials of individual nucleobases; the M06-2X/6-31G* hybrid density functional theory method was selected by comparison with experimental data. Next, the vertical ionization potential, and the Mulliken charge and spin density distributions were calculated and considered on all nucleobase stacks. We found that (1) the ionization potential decreases with the number of bases, the lowest being reached by Gua≡Cyt tracts; (2) the association of two single strands into a double-stranded tract lowers the ionization potential significantly (3) differences in ionization potential due to sequence variation are roughly three times larger than those due to conformational modifications. The charge and spin density distributions were found (1) to be located toward the 5'-end for single-stranded Gua-stacks and toward the 3'-end for Cyt-stacks and basically delocalized over all bases for Ade- and Thy-stacks; (2) the association into double-stranded tracts empties the Cyt- and Thy-strands of most of the charge and all the spin density and concentrates them on the Gua- and Ade-strands. The possible biological implications of these results for transcription are discussed.

Theoretical investigation of the coupling between hydrogen-atom transfer and stacking interaction in adenine-thymine dimers

Three different dimers of the adenine-thymine (A-T) base pair are studied to point out the changes of important properties (structure, atomic charge, energy and so on) induced by coupling between the movement of the atoms in the hydrogen bonds and the stacking interaction. The comparison of these results with those for the A-T monomer system explains the role of the stacking interaction in the hydrogen-atom transfer in this biologically important base pair. The results support the idea that this coupling depends on the exact dimer considered and is different for the N-N and N-O hydrogen bonds. In particular, the correlation between the hydrogen transfer and the stacking interaction is more relevant for the N-N bridge than for the N-O one. Also, the two different mechanisms of two-hydrogen transfer (step by step and concerted) can be modified by the stacking interaction between the base pairs.

Quantum-mechanical analysis of the energetic contributions to π stacking in nucleic acids versus rise, twist, and slide

Symmetry-adapted perturbation theory (SAPT) is applied to pairs of hydrogen-bonded nucleobases to obtain the energetic components of base stacking (electrostatic, exchange-repulsion, induction/polarization, and London dispersion interactions) and how they vary as a function of the helical parameters Rise, Twist, and Slide. Computed average values of Rise and Twist agree well with experimental data for B-form DNA from the Nucleic Acids Database, even though the model computations omitted the backbone atoms (suggesting that the backbone in B-form DNA is compatible with having the bases adopt their ideal stacking geometries). London dispersion forces are the most important attractive component in base stacking, followed by electrostatic interactions. At values of Rise typical of those in DNA (3.36 Å), the electrostatic contribution is nearly always attractive, providing further evidence for the importance of charge-penetration effects in π-π interactions (a term neglected in classical force fields). Comparison of the computed stacking energies with those from model complexes made of the "parent" nucleobases purine and 2-pyrimidone indicates that chemical substituents in DNA and RNA account for 20-40% of the base-stacking energy. A lack of correspondence between the SAPT results and experiment for Slide in RNA base-pair steps suggests that the backbone plays a larger role in determining stacking geometries in RNA than in B-form DNA. In comparisons of base-pair steps with thymine versus uracil, the thymine methyl group tends to enhance the strength of the stacking interaction through a combination of dispersion and electrosatic interactions.

Guanine base stacking in G-quadruplex nucleic acids

G-quadruplexes constitute a class of nucleic acid structures defined by stacked guanine tetrads (or G-tetrads) with guanine bases from neighboring tetrads stacking with one another within the G-tetrad core. Individual G-quadruplexes can also stack with one another at their G-tetrad interface leading to higher-order structures as observed in telomeric repeat-containing DNA and RNA. In this study, we investigate how guanine base stacking influences the stability of G-quadruplexes and their stacked higher-order structures. A structural survey of the Protein Data Bank is conducted to characterize experimentally observed guanine base stacking geometries within the core of G-quadruplexes and at the interface between stacked G-quadruplex structures. We couple this survey with a systematic computational examination of stacked G-tetrad energy landscapes using quantum mechanical computations. Energy calculations of stacked G-tetrads reveal large energy differences of up to 12 kcal/mol between experimentally observed geometries at the interface of stacked G-quadruplexes. Energy landscapes are also computed using an AMBER molecular mechanics description of stacking energy and are shown to agree quite well with quantum mechanical calculated landscapes. Molecular dynamics simulations provide a structural explanation for the experimentally observed preference of parallel G-quadruplexes to stack in a 5′–5′ manner based on different accessible tetrad stacking modes at the stacking interfaces of 5′–5′ and 3′–3′ stacked G-quadruplexes.

Novel conformation of an RNA structural switch

The RNA duplex, (5′GACGAGUGUCA)₂, has two conformations in equilibrium. The nuclear magnetic resonance solution structure reveals that the major conformation of the loop, 5′GAGU/3′UGAG, is novel and contains two unusual Watson–Crick/Hoogsteen GG pairs with G residues in the syn conformation, two A residues stacked on each other in the center of the helix with inverted sugars, and two bulged-out U residues. The structure provides a benchmark for testing approaches for predicting local RNA structure and a sequence that allows the design of a unique arrangement of functional groups and/or a conformational switch into nucleic acids.

The Amber ff99 Force Field Predicts Relative Free Energy Changes for RNA Helix Formation

The ability of the Amber ff99 force field to predict relative free energies of RNA helix formation was investigated. The test systems were three hexaloop RNA hairpins with identical loops and varying stems. The potential of mean force of stretching the hairpins from the native state to an extended conformation was calculated with umbrella sampling. Because the hairpins have identical loop sequence, the differences in free energy changes are only from the stem composition. The Amber ff99 force field was able to correctly predict the order of stabilities of the hairpins, although the magnitude of the free energy change is larger than that determined by optical melting experiments. The two measurements cannot be compared directly because the unfolded state in the optical melting experiments is a random coil, while the end state in the umbrella sampling simulations was an elongated chain. The calculations can be compared to reference data by using a thermodynamic cycle. By applying the thermodynamic cycle to the transitions between the hairpins using simulations and nearest neighbor data, agreement was found to be within the sampling error of simulations, thus demonstrating that ff99 force field is able to accurately predict relative free energies of RNA helix formation.

Understanding the role of base stacking in nucleic acids. MD and QM analysis of tandem GA base pairs in RNA duplexes

Preceding NMR experiments show that the conformation of tandem GA base pairs, an important recurrent non-canonical building block in RNA duplexes, is context dependent. The GA base pairs adopt "sheared" N3(G)-N6(A), N2(G)-N7(A) geometry in the r(CGAG)(2) and r(iGGAiC)(2) contexts while switching to "imino" N1(G)-N1(A), O6(G)-N6(A) geometry in the r(GGAC)(2) and r(iCGAiG)(2) contexts (iC and iG stand for isocytosine and isoguanine, respectively). As base stacking is likely to be one of the key sources of the context dependence of the conformation of GA base pairs, we calculated base stacking energies in duplexes containing such base pairs, to see if this dependence can be predicted by stacking energy calculations. When investigating the context dependence of the GA geometry two different conformations of the same duplex were compared (imino vs. sheared). The geometries were generated via explicit solvent MD simulations of the respective RNA duplexes, while the subsequent QM energy calculations focused on base stacking interactions of the four internal base pairs. Geometrical relaxation of nucleobase atoms prior to the stacking energy computations has a non-negligible effect on the results. The stacking energies were derived at the DFT-D/6-311++G(3df,3pd) level. We show a rather good correspondence between the intrinsic gas-phase stacking energies and the NMR-determined GA geometries. The conformation with more favorable gas-phase stacking is in most cases the one observed in experiments. This correlation is not improved when including solvent effects via the COSMO method. On the other side, the stacking calculations do not predict the relative thermodynamic stability of duplex formation for different sequences.

Development of polarizable models for molecular mechanical calculations. 4. van der Waals parametrization

In the previous publications of this series, we presented a set of Thole induced dipole interaction models using four types of screening functions. In this work, we document our effort to refine the van der Waals parameters for the Thole polarizable models. Following the philosophy of AMBER force field development, the van der Waals (vdW) parameters were tuned for the Thole model with linear screening function to reproduce both the ab initio interaction energies and the experimental densities of pure liquids. An in-house genetic algorithm was applied to maximize the fitness of "chromosomes" which is a function of the root-mean-square errors (RMSE) of interaction energy and liquid density. To efficiently explore the vdW parameter space, a novel approach was developed to estimate the liquid densities for a given vdW parameter set using the mean residue-residue interaction energies through interpolation/extrapolation. This approach allowed the costly molecular dynamics simulations be performed at the end of each optimization cycle only and eliminated the simulations during the cycle. Test results show notable improvements over the original AMBER FF99 vdW parameter set, as indicated by the reduction in errors of the calculated pure liquid densities (d), heats of vaporization (H(vap)), and hydration energies. The average percent error (APE) of the densities of 59 pure liquids was reduced from 5.33 to 2.97%; the RMSE of H(vap) was reduced from 1.98 to 1.38 kcal/mol; the RMSE of solvation free energies of 15 compounds was reduced from 1.56 to 1.38 kcal/mol. For the interaction energies of 1639 dimers, the overall performance of the optimized vdW set is slightly better than the original FF99 vdW set (RMSE of 1.56 versus 1.63 kcal/mol). The optimized vdW parameter set was also evaluated for the exponential screening function used in the Amoeba force field to assess its applicability for different types of screening functions. Encouragingly, comparable performance was observed when the optimized vdW set was combined with the Thole Amoeba-like polarizable model, particularly for the interaction energy and liquid density calculations. Thus, the optimized vdW set is applicable to both types of Thole models with either linear or Amoeba-like screening functions.

Can We Accurately Describe the Structure of Adenine Tracts in B-DNA? Reference Quantum-Chemical Computations Reveal Overstabilization of Stacking by Molecular Mechanics

Sequence-dependent local variations of helical parameters, structure, and flexibility are crucial for molecular recognition processes involving B-DNA. A-tracts, i.e., stretches of several consecutive adenines in one strand that are in phase with the DNA helical repeat, mediate significant DNA bending. During the past few decades, there have been intense efforts to understand the sequence dependence of helical parameters in DNA. Molecular dynamics (MD) simulations can provide valuable insights into the molecular mechanism behind the relationship between sequence and structure. However, although recent improvements in empirical force fields have helped to capture many sequence-dependent B-DNA properties, several problems remain, such as underestimation of the helical twist and suspected underestimation of the propeller twist in A-tracts. Here, we employ reference quantum mechanical (QM) calculations, explicit solvent MD, and bioinformatics to analyze the underestimation of propeller twisting of A-tracts in simulations. Although we did not identify a straightforward explanation, we discovered two imbalances in the empirical force fields. The first was overestimation of stacking interactions accompanied by underestimation of base-pairing energy, which we attribute to anisotropic polarizabilities that are not reflected by the isotropic force fields. This may lead to overstacking with potentially important consequences for MD simulations of nucleic acids. The second observed imbalance was steric clash between A(N1) and T(N3) nitrogens of AT base pairs in force-field descriptions, resulting in overestimation of the AT pair stretch in MD simulations. We also substantially extend the available set of benchmark estimated CCSD(T)/CBS data for B-DNA base stacking and provide a code that allows the generation of diverse base-stacking geometries suitable for QM computations with predefined intra- and interbase pair parameters.

A computational proposal for the experimentally observed discriminatory behavior of hypoxanthine, a weak universal nucleobase

A computational model composed of six nucleobases was used to investigate why hypoxanthine does not yield duplexes of equal stability when paired opposite each of the natural DNA nucleobases. The magnitudes of all nearest-neighbor interactions in a DNA helix were calculated, including hydrogen-bonding, intra- and interstrand stacking interactions, as well as 1-3 intrastrand stacking interactions. Although the stacking interactions in DNA relevant arrangements are significant and account for at least one third of the total stabilization energy in our nucleobase complexes, the trends in the magnitude of the stacking interactions cannot explain the relative experimental melting temperatures previously reported in the literature. Furthermore, although the total hydrogen-bonding interactions explain why hypoxanthine preferentially pairs with cytosine, the experimental trend for the remaining nucleobases (A, T, G) is not explained. In fact, the calculated pairing preference of hypoxanthine matches that determined experimentally only when the sum of all types of nearest-neighbor interactions is considered. This finding highlights a strong correlation between the relative magnitude of the total nucleobase-nucleobase interactions and measured melting temperatures for DNA strands containing hypoxanthine despite the potential role of other factors (including hydration, temperature, sugar-phosphate backbone). By considering a large range of sequence combinations, we reveal that the binding preference of hypoxanthine is strongly dependent on the nucleobase sequence, which may explain the varied ability of hypoxanthine to universally bind to the natural bases. As a result, we propose that future work should closely examine the interplay between the dominant nucleobase-nucleobase interactions and the overall strand stability to fully understand how sequence context affects the universal binding properties of modified bases and to aid the design of new molecules with ambiguous pairing properties.

Evaluation of the internal transcribed spacer 2 (ITS2) as a molecular marker for phylogenetic inference using sequence and secondary structure information in blow flies (Diptera: Calliphoridae)

The internal transcribed spacer 2 (ITS2) is a small non-coding region located inside the nuclear ribosomal DNA cluster. ITS2 sequence variability is thought to be appropriate to differentiate species and for phylogenetic reconstructions analyses, which can be further improved if structural information is considered. We evaluated the potential of ITS2 as a molecular marker for phylogenetic inference in Calliphoridae (Diptera: Brachycera) using a broad range of inference methods and different substitution models, accounting or not for structural information. Sequence analyses revealed a hierarchically organized pattern of sequence variation and a small level of nucleotide substitution saturation. Intragenomic variation due to small sequence repeats was found mainly in the most variable domain (IV), but it has no significant impact on the phylogenetic signal at the species level. Inferred secondary structures revealed that GC pairs are more frequently found flanking bulges and loops regions in more conserved domains, thus ensuring structure stability. In the phylogenetic analyses, the use of substitution models accounting for structural information significantly improves phylogenetic inference in both neighbour-joining and Bayesian analyses, although the former provides limited resolution for dealing with highly divergent sequences. For Bayesian analyses, a significant improvement in likelihood was observed when considering structure information, although with small changes in topology and overall support, probably reflecting better evolutionary rates estimates. Based on these findings, ITS2 is a suitable molecular marker for phylogenetic analyses in Calliphoridae, at both species and generic level.

Effect of polymer containing a naphthyl-alanine derivative on the separation selectivity for aromatic compounds in temperature-responsive chromatography

A novel polymer-grafted stationary phase of high-performance liquid chromatography (HPLC) was developed, utilizing a temperature-responsive polymer containing an aromatic moiety. Firstly, we synthesized novel functional polymer poly(N-isopropylacrylamide-co-N-acryloyl-3-(2-naphthyl)-L-alanine methyl ester) [poly(NIPAAm-co-Nap)], which has temperature-responsiveness and selective retention of aromatic compounds by an intermolecular π-π interaction. The polymer exhibited a significant reversible phase transition from hydrophilic to hydrophobic in the vicinity of its lower critical solution temperature. Employing the developed polymer-grafted silica column, temperature-responsive chromatography was conducted using water as a sole mobile phase. A comparison with a conventional ODS column or a homogeneous PNIPAAm-grafted silica column showed that the retention of aromatic compounds was dramatically increased on the poly(NIPAAm-co-Nap)-grafted stationary phase. Introducing the naphthyl-alanine derivative caused a significant effect on the retention selectivity for aromatic compounds.

Computational model for predicting experimental RNA and DNA nearest-neighbor free energy rankings

Hydrogen-bonding, intrastrand base-stacking, and interstrand base-stacking energies were calculated for RNA and DNA dimers at the MP2(full)/6-311G** level of theory. Standard A-form RNA and B-form DNA geometries from average fiber diffraction data were employed for all base monomer and dimer geometries, and all dimer binding energies were obtained via single-point calculations. The effects of water solvation were considered using the PCM model. The resulting dimer binding energies were used to calculate the 10 unique RNA and 10 unique DNA computational nearest-neighbor energies, and the ranking of these computational nearest neighbor energies are in excellent agreement with the ranking of the experimental nearest-neighbor free energies. These results dispel the notion that average fiber diffraction geometries are insufficient for calculating RNA and DNA stacking energies.

Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.

Efficient evaluation of triple excitations in symmetry-adapted perturbation theory via second-order Møller-Plesset perturbation theory natural orbitals

An accurate description of dispersion interactions is required for reliable theoretical studies of many noncovalent complexes. This can be obtained with the wave function-based formulation of symmetry-adapted perturbation theory (SAPT) provided that the contribution of triple excitations to dispersion is included. Unfortunately, this triples dispersion correction limits the applicability of SAPT due to its O(N(7)) scaling. The efficiency of the evaluation of this correction can be greatly improved by removing virtual orbitals from the computation. The error incurred from truncating the virtual space is reduced if second-order Mo̸ller-Plesset perturbation theory (MP2) natural orbitals are used in place of the canonical Hartree-Fock molecular orbitals that are typically used. This approximation is further improved if the triples correction to dispersion is scaled to account for the smaller virtual space. If virtual MP2 natural orbitals are removed according to their occupation numbers, in practice, roughly half of the virtual orbitals can be removed (with the aug-cc-pVDZ basis set) with negligible errors if the remaining triples dispersion contribution is scaled. This typically leads to speedups of 15-20 times for the cases considered here. By combining the truncated virtual space with the frozen core approximation, the triples correction can be evaluated approximately 50 times faster than the canonical computation. These approximations cause less than 1% error (or at most 0.02 kcal mol(-1)) for the cases considered. Truncation of greater fractions of the virtual space is possible for larger basis sets (leading to speedups of over 40 times before additional speedups from the frozen core approximation).

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.

Non-additive interactions of nucleobases in model dinucleotide steps occurring in B-DNA crystals

Non-additivity of base-base interactions in all ten possible model dinucleotide steps were analyzed on MP2/aug-cc-pvDZ quantum chemistry level. Conformations of four nucleobases exactly matched to ones occurring in B-DNA crystals. In most of thw 162 analyzed tetramers both three- and four-body contributions are negligible except for d(GpG) steps. However, in these dinucleotides both contributions are always of opposite signs and in all cases the sum of all non-additive part of intermolecular interactions do not exceed 2.6 kcal mol(-1). This stands for less than 5% of the overall binding energy of dinucleotide steps. Also replacements of guanine with 8-oxoguanine in d(GpG) systems introduces non-additivity of the same magnitude as for canonical dinucleotides. It is observed linear relationships between values of total binding energy obtained in the tetramer basis set and estimated energy exclusively in dimers basis sets with assumption of pairwise additivities. For all analyzed dinucleotides steps there are also linear correlations between amount of non-additive contributions and magnitude of pairs interactions. Based on differences in electrostatic contribution to the total binding energy of four nucleobases and polarity of dinucleotide steps three distinct classes of dinucleotide steps were identified.