Nature of Nucleic Acid−Base Stacking: Nonempirical ab Initio and Empirical Potential Characterization of 10 Stacked Base Dimers. Comparison of Stacked and H-Bonded Base Pairs

Nonparametric clustering for studying RNA conformations

The local conformation of RNA molecules is an important factor in determining their catalytic and binding properties. The analysis of such conformations is particularly difficult due to the large number of degrees of freedom, such as the measured torsion angles per residue and the interatomic distances among interacting residues. In this work, we use a nearest-neighbor search method based on the statistical mechanical Potts model to find clusters in the RNA conformational space. The proposed technique is mostly automatic and may be applied to problems, where there is no prior knowledge on the structure of the data space in contrast to many other clustering techniques. Results are reported for both single residue conformations, where the parameter set of the data space includes four to seven torsional angles, and base pair geometries, where the data space is reduced to two dimensions. Moreover, new results are reported for base stacking geometries. For the first two cases, i.e., single residue conformations and base pair geometries, we get a very good match between the results of the proposed clustering method and the known classifications with only few exceptions. For the case of base stacking geometries, we validate our classification with respect to geometrical constraints and describe the content, and the geometry of the new clusters.

Feasibility study of hydrogen-bonded nucleic acid base pairs in gas and water phases — A theoretical study

To investigate the base pair binding probabilities for nucleic acid bases, numerous models were studied for contacts between adenine, thymine, guanine, cytosine, and uracil using density functional theory (DFT) in combination with the 6–311G* basis set. We obtained an assessment for the energy given by our calculations in gas and aqueous phases, which showed that it should be incorporated into hydrogen bonding and propeller rotational energies. The 42 complexes of base pairs (5 regular and 37 irregular base pairs) were proposed and their hydrogen-bonding (H-bonding) properties were verified. The hydrogen bonds in some irregular base pairs, including CC, UU, and TT (series 1), were stronger than in regular GC and AT base pairs. Also, the strength of the hydrogen bonds in the proposed base pairs, including CU, GG, GU, and TU (series 2), were similar to regular base pairs from an energetic point of view. The propeller rotations revealed a higher rotational barrier energy (6–7.5 kcal/mol; 1 cal = 4.184 J) for irregular base pairs (series 1 and 2) than regular GC and AT ones (1–3 kcal/mol). Nevertheless, the trend in these affinities of the complex contact probabilities and their biological properties were confirmed by our calculations.

DNA base pair hybridization and water-mediated metastable structures studied by molecular dynamics simulations

The base pair hybridization of a DNA segment was studied using molecular dynamics simulation. The results show the obvious correlation between the probability of successful hybridization and the accessible surface area to water of two successive base pairs, including the unpaired base pair adjacent to paired base pair and this adjacent paired base pair. Importantly, two metastable structures in an A-T base pair were discovered by the analysis of the free energy landscape. Both structures involved addition of a water molecule to the linkage between the two nucleobases in one base pair. The existence of the metastable structures provide potential barriers to the Watson-Crick base pair, and numerical simulations show that those potential barriers can be surmounted by thermal fluctuations at higher temperatures. These studies contribute an important step toward the understanding of the mechanism in DNA hybridization, particularly the effect of temperature on DNA hybridization and polymerase chain reaction. These observations are expected to be helpful for facilitating experimental bio/nanotechnology designs involving fast hybridization.

Predicting coaxial helical stacking in RNA junctions

RNA junctions are important structural elements that form when three or more helices come together in space in the tertiary structures of RNA molecules. Determining their structural configuration is important for predicting RNA 3D structure. We introduce a computational method to predict, at the secondary structure level, the coaxial helical stacking arrangement in junctions, as well as classify the junction topology. Our approach uses a data mining approach known as random forests, which relies on a set of decision trees trained using length, sequence and other variables specified for any given junction. The resulting protocol predicts coaxial stacking within three- and four-way junctions with an accuracy of 81% and 77%, respectively; the accuracy increases to 83% and 87%, respectively, when knowledge from the junction family type is included. Coaxial stacking predictions for the five to ten-way junctions are less accurate (60%) due to sparse data available for training. Additionally, our application predicts the junction family with an accuracy of 85% for three-way junctions and 74% for four-way junctions. Comparisons with other methods, as well applications to unsolved RNAs, are also presented. The web server Junction-Explorer to predict junction topologies is freely available at: http://bioinformatics.njit.edu/junction.

Accurate Interaction Energies for Problematic Dispersion-Bound Complexes: Homogeneous Dimers of NCCN, P2, and PCCP

All intermolecular interactions involve London dispersion forces. The accurate treatment of dispersion is essential for the computation of realistic interaction potentials. In general, the most reliable method for computing intermolecular interactions is coupled-cluster singles and doubles with perturbative triples [CCSD(T)] in conjunction with a sufficiently flexible Gaussian atomic orbital basis set, a combination which is not routinely applicable due to its excessive computational demands (CPU time, memory, storage). Recently, many theoretical methods have been developed that attempt to account for dispersion in a more efficient manner. It is well-known that dispersion interactions are more difficult to compute in some systems than others; for example, π-π dispersion is notoriously difficult, while alkane-alkane dispersion is relatively simple to compute. In this work, numerous theoretical methods are tested for their ability to compute reliable interaction energies in particularly challenging systems, namely, the P2, PCCP, and NCCN dimers. Symmetry-adapted perturbation theory (SAPT) is applied to these dimers to demonstrate their sensitivity to the treatment of dispersion. Due to the small size of these systems, highly accurate CCSD(T) potential energy curves could be estimated at the complete basis set limit. Numerous theoretical methods are tested against the reliable CCSD(T) benchmarks. Methods using a treatment of dispersion that relies on time-dependent density functional theory (TDDFT) response functions are found to be the most reliable.

FTIR Spectra of some Pyrimidine Derivatives: AM1, PM3 and Ab Initio Calculations

Abstract. FTIR spectra of some pyrimidine derivatives have been measured experimentally and the observed FTIR vibrational frequencies have been assigned and reported. The different vibrational frequencies have been calculated by the AM1, PM3, and ab initio methods and compared with the experimentally observed frequencies .

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

Accurately modeling unpaired regions of RNA is important for predicting structure, dynamics, and thermodynamics of folded RNA. Comparisons between NMR data and molecular dynamics simulations provide a test of force fields used for modeling. Here, NMR spectroscopy, including NOESY, (1)H-(31)P HETCOR, DQF-COSY, and TOCSY, was used to determine conformational preferences for single-stranded GACC RNA. The spectra are consistent with a conformational ensemble containing major and minor A-form-like structures. In a series of 50 ns molecular dynamics (MD) simulations with the AMBER99 force field in explicit solvent, initial A-form-like structures rapidly evolve to disordered conformations. A set of 50 ns simulations with revised χ torsions (AMBER99χ force field) gives two primary conformations, consistent with the NMR spectra. A single 1.9 μs MD simulation with the AMBER99χ force field showed that the major and minor conformations are retained for almost 68% of the time in the first 700 ns, with multiple transformations from A-form to non-A-form conformations. For the rest of the simulation, random-coil structures and a stable non-A-form conformation inconsistent with NMR spectra were seen. Evidently, the AMBER99χ force field improves structural predictions for single-stranded GACC RNA compared to the AMBER99 force field, but further force field improvements are needed.

Self Consistent-Charge Density-Functional Tight-Binding Method for Simulations of Biological Molecules

We apply a self-consistent charge tight-binding scheme to biomolecules. This method has been shown to give a reliable description of reaction energies, geometries and vibrational frequencies of small organic molecules. We discuss the performance of this method for model peptides and non-bonding interactions in biologically relevant molecular complexes. A comparison with semi-empirical methods and ab initio calculations will be given for DNA base pair H-bonding and stacking interactions.

Molecular dynamics of potential rRNA binders: single-stranded nucleic acids and some analogues

By hindering or "silencing" protein translation in vivo, antisense nucleic acid analogues that hybridize to bacterial rRNA could serve as a promising class of antibacterial compounds. Thus, we performed a comparative analysis of the dynamical properties of modified oligonucleotides based upon a sequence (5')r(UGUUACGACU)(3') that is complementary to bacterial ribosomal A-site RNA. In particular, 25 ns explicit solvent molecular dynamics simulations were computed for the following six single-stranded decamers: (1) the above RNA in unmodified form; (2) the 2'-O-methyl-modified RNA; (3) peptide nucleic acid (PNA) analogues of the above sequence, containing either (a) T or (b) U; and (4) two serine-substituted PNAs. Our results show that 2'-O-methylation attenuates RNA backbone dynamics, thereby preventing interconversion between stacked and unstacked conformations. The PNA analogue is rendered less flexible by replacing uracil with thymine; in addition, we found that derivatizing the PNA backbone with serine leads to enhanced base-stacking interactions. Consistent with known solubility properties of these classes of molecules, both RNAs exhibited greater localization of water molecules than did PNA. In terms of counterions, the initially helical conformation of the 2'-O-methyl RNA exhibits the highest Na(+) density among all the simulated decamers, while Na(+) build-up was most negligible for the neutral PNA systems. Further studies of the conformational and physicochemical properties of such modified single-stranded oligomers may facilitate better design of nucleic acid analogues, particularly those capable of serving as specific, high-affinity ribosomal A-site binders.

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.

Assessment of the Performance of DFT and DFT-D Methods for Describing Distance Dependence of Hydrogen-Bonded Interactions

Noncovalent interactions such as hydrogen bonds, van der Waals forces, and π-π interactions play important roles influencing the structure, stability, and dynamic properties of biomolecules including DNA and RNA base pairs. In an effort to better understand the fundamental physics of hydrogen bonding (H-bonding), we investigate the distance dependence of interaction energies in the prototype bimolecular complexes of formic acid, formamide, and formamidine. Potential energy curves along the H-bonding dissociation coordinate are examined both by establishing reference CCSD(T) interaction energies extrapolated to the complete basis set limit and by assessing the performance of the density functional methods B3LYP, PBE, PBE0, B970, PB86, M05-2X, and M06-2X and empirical dispersion corrected methods B3LYP-D3, PBE-D3, PBE0-D3, B970-D2, BP86-D3, and ωB97X-D, with basis sets 6-311++G(3df,3pd), aug-cc-pVDZ, and aug-cc-pVTZ. Although H-bonding interactions are dominated by electrostatics, it is necessary to properly account for dispersion interactions to obtain accurate energetics. In order to quantitatively probe the nature of hydrogen bonding interactions as a function of distance, we decompose the interaction energy curves into physically meaningful components with symmetry-adapted perturbation theory (SAPT). The SAPT results confirm that the contribution of dispersion and induction are significant at and near equilibrium, although electrostatics dominate. Among the DFT/DFT-D techniques, the best overall results are obtained utilizing counterpoise-corrected ωB97X-D with the aug-cc-pVDZ basis set.

Noncovalent interactions in extended systems described by the effective fragment potential method: theory and application to nucleobase oligomers

The implementation of the effective fragment potential (EFP) method within the Q-CHEM electronic structure package is presented. The EFP method is used to study noncovalent π-π and hydrogen-bonding interactions in DNA strands. Since EFP is a computationally inexpensive alternative to high-level ab initio calculations, it is possible to go beyond the dimers of nucleic acid bases and to investigate the asymptotic behavior of different components of the total interaction energy. The calculations demonstrated that the dispersion energy is a leading component in π-stacked oligomers of all sizes. Exchange-repulsion energy also plays an important role. The contribution of polarization is small in these systems, whereas the magnitude of electrostatics varies. Pairwise fragment interactions (i.e., the sum of dimer binding energies) were found to be a good approximation for the oligomer energy.

Density fitting of intramonomer correlation effects in symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) offers insight into the nature of intermolecular interactions. In addition, accurate energies can be obtained from the wave function-based variant of SAPT provided that intramonomer electron correlation effects are included. We apply density-fitting (DF) approximations to the intramonomer correlation corrections in SAPT. The introduction of this approximation leads to an improvement in the computational cost of SAPT by reducing the scaling of certain SAPT terms, reducing the amount of disk I/O, and avoiding the explicit computation of certain types of MO integrals. We have implemented all the intramonomer correlation corrections to SAPT through second-order under the DF approximation. Additionally, leading third-order terms are also implemented. The accuracy of this truncation of SAPT is tested against the S22 test set of Hobza and co-workers [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. When the intramonomer corrections to dispersion are included in SAPT, a mean absolute deviation of 0.3-0.4 kcal mol(-1) is observed for the S22 test set when using an aug-cc-pVDZ basis. The computations on the adenine-thymine complexes in the S22 test set with an aug-cc-pVDZ basis represent the largest SAPT computations to date that include this degree of intramonomer correlation. Computations of this size can now be performed routinely with our newly developed DF-SAPT program.

The effect of CH3, F and NO2 substituents on the individual hydrogen bond energies in the adenine-thymine and guanine-cytosine base pairs

The substituent effects on the geometrical parameters and the individual hydrogen bond (HB) energies of base pairs such as X-adenine-thymine (X-A-T), X-thymine-adenine (X-T-A), X-guanine-cytosine (X-G-C), and X-cytosine-guanine (X-C-G) have been studied by the quantum mechanical calculations at the B3LYP and MP2 levels with the 6-311++G(d,p) basis set. The electron withdrawing (EW) substituents (F and NO(2)) increase the total binding energy (DeltaE) of X-G-C derivatives and the electron donating (ED) substituent (CH(3)) decreases it when they are introduced in the 8 and 9 positions of G. The effects of substituents are reversed when they are located in the 1, 5, and 6 positions of C, with exception of CH(3) in the 1 position and F in the 5 position, which in both cases the DeltaE value decreases negligibly small. With minor exceptions (X=8-CH(3), 8-F, and 9-NO(2)), both ED and EW substituents increase slightly the DeltaE values of X-A-T derivatives. The individual HB energies (E (HB)s) have been estimated using electron densities that calculated at the hydrogen bond critical points (HBCPs) by the atoms in molecules (AIM) method. Most of changes of individual HBs are in consistent with the ED/EW nature of substituents and the role of atoms entered H-bonding. The remarkable change is observed for NO(2) substituted derivative in each case.

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?

High level ab initio methods have been used to study stacking interactions in ten unique base pair steps both in A-RNA and in B-DNA duplexes. The protocol for selection of geometries based on molecular dynamics (MD) simulations is proposed, and its suitability is demonstrated by comparison with stacking in steps at fiber diffraction geometries. It is shown that fiber diffraction geometries are not sufficiently accurate for interaction energy calculations. In addition, the protocol for selection of geometries based on MD simulations allows for the evaluation of the variability of the intrinsic stacking energies along the MD trajectories. The uncertainty in stacking energies (difference between the most and least stable geometry) due to the dynamical nature of systems can be, in some cases, as large as 3.0 kcal x mol(-1), which is almost 50% of the actual sequence dependence of base stacking energies (the energy difference between the most and least stable sequences). Thus, assessing the relative magnitude of the gas phase stacking energy using a single geometry for each sequence is insufficient to obtain an unambiguous order of gas phase stacking energies in canonical double helices. Though the ordering of ten unique dinucleotide steps cannot be definitive, some general conclusions were drawn. The stacking energies of base pair steps in A-RNA are more evenly separated compared to B-DNA, and their ordering is less sensitive to the dynamics of the system compared to be B-DNA. The most stable step both in B-DNA and A-RNA is the GC/GC [corrected] step that is well separated from the second most stable step CG/CG. [corrected] Also the least stable step (the CC/GG step) is well separated from the rest of the structures. The calculations further show that B-DNA stacking is favorable only marginally (on average by 1.14 kcal x mol(-1) per base pair step) over A-RNA stacking, and this difference vanishes after subtracting the stabilizing van der Waals effect of the thymine 5-methyl group that is absent in RNA. Basically, no correlation between the sequence dependence of gas phase stacking energies and the sequence dependence of DeltaG degrees(37) free energies used in nearest-neighbor models was found either for B-DNA or for A-RNA. This reflects the complexity of the balance of forces that are responsible for the sequence dependence of thermodynamics stability of nucleic acids, which masks the effect of the intrinsic interactions between the stacked base pairs.

On the Structure and Geometry of Biomolecular Binding Motifs (Hydrogen-Bonding, Stacking, X-H···π): WFT and DFT Calculations

The strengths of noncovalent interactions are generally very sensitive to a number of geometric parameters. Among the most important of these parameters is the separation between the interacting moieties (in the case of an intermolecular interaction, this would be the intermolecular separation). Most works seeking to characterize the properties of intermolecular interactions are mainly concerned with binding energies obtained at the potential energy minimum (as determined at some particular level of theory). In this work, in order to extend our understanding of these types of noncovalent interactions, we investigate the distance dependence of several types of intermolecular interactions, these are hydrogen bonds, stacking interactions, dispersion interactions, and X-H···π interactions. There are several methods that have traditionally been used to treat noncovalent interactions as well as many new methods that have emerged within the past three or four years. Here we obtain reference data using estimated CCSD(T) values at the complete basis set limit (using the CBS(T) method); potential energy curves are also produced using several other methods thought to be accurate for intermolecular interactions, these are MP2/cc-pVTZ, MP2/aug-cc-pVDZ, MP2/6-31G*(0.25), SCS(MI)-MP2/cc-pVTZ, estimated MP2.5/CBS, DFT-SAPT/aug-cc-pVTZ, DFT/M06-2X/6-311+G(2df,2p), and DFT-D/TPSS/6-311++G(3df,3pd). The basis set superposition error is systematically considered throughout the study. It is found that the MP2.5 and DFT-SAPT methods, which are both quite computationally intensive, produce potential energy curves that are in very good agreement to those of the reference method. Among the MP2 techniques, which can be said to be of medium computational expense, the best results are obtained with MP2/cc-pVTZ and SCS(MI)-MP2/cc-pVTZ. DFT-D/TPSS/6-311++G(3df,3pd) is the DFT-based method that can be said to give the most well-balanced description of intermolecular interactions.

Effects of the biological backbone on DNA-protein stacking interactions

The pi-pi stacking (face-to-face) interactions between the five natural DNA or RNA nucleobases and the four aromatic amino acids were compared using three different types of dimers: (1) a truncated nucleoside (nucleobase) stacked with a truncated amino acid; (2) a truncated nucleoside (nucleobase) stacked with an extended amino acid; and (3) a nucleoside (extended nucleobase) stacked with a truncated amino acid. Systematic (MP2/6-31G*(0.25)) potential energy surface scans reveal important information about the effects of the deoxyribose sugar and protein backbone on the structure and binding energy between truncated nucleobase and amino acid models that are typically implemented in the literature. Most notably, electrostatic and steric interactions arising from the bulkiness of the biological backbones can change the preferred relative orientations of DNA and protein pi-systems. More importantly, the protein backbone can strengthen the stacking energy (by up to 10 kJ mol(-1)), while the deoxyribose moiety can strengthen or weaken the stacking interaction depending on the positioning of the amino acid relative to the sugar residue. These effects are likely due to additional interactions between the amino acid or nucleobase ring and the backbone in the extended monomer rather than significant changes in the properties of the biological pi-systems upon model extension. Since the present work reveals that all calculated DNA-protein stacking interactions are significant and approach the strength of other noncovalent interactions between biomolecules, both pi-pi and backbone-pi interactions must be considered when attempting to gain a complete picture of DNA-protein binding.

Theoretical insights into the nature of intermolecular interactions in cytosine dimer

In this study we discuss stacking interactions in cytosine dimer in conformations appearing in B-DNA crystals. The variational-perturbational scheme was applied for decomposition of the intermolecular interaction energy at the MP2 level of theory. The significant influence of the mutual orientation of cytosine monomers was observed not only on the total intermolecular interaction energy but also on its components: Different components of intermolecular interaction energy depend in different manner on parameters describing mutual orientation of cytosine monomers.

Probing phenylalanine/adenine pi-stacking interactions in protein complexes with explicitly correlated and CCSD(T) computations

To examine the effects of pi-stacking interactions between aromatic amino acid side chains and adenine bearing ligands in crystalline protein structures, 26 toluene/(N9-methyl)adenine model configurations have been constructed from protein/ligand crystal structures. Full geometry optimizations with the MP2 method cause the 26 crystal structures to collapse to six unique structures. The complete basis set (CBS) limit of the CCSD(T) interaction energies has been determined for all 32 structures by combining explicitly correlated MP2-R12 computations with a correction for higher-order correlation effects from CCSD(T) calculations. The CCSD(T) CBS limit interaction energies of the 26 crystal structures range from -3.19 to -6.77 kcal mol (-1) and average -5.01 kcal mol (-1). The CCSD(T) CBS limit interaction energies of the optimized complexes increase by roughly 1.5 kcal mol (-1) on average to -6.54 kcal mol (-1) (ranging from -5.93 to -7.05 kcal mol (-1)). Corrections for higher-order correlation effects are extremely important for both sets of structures and are responsible for the modest increase in the interaction energy after optimization. The MP2 method overbinds the crystal structures by 2.31 kcal mol (-1) on average compared to 4.50 kcal mol (-1) for the optimized 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.