Calculation of structural behavior of indirect NMR spin-spin couplings in the backbone of nucleic acids

Systematic QM/MM Study for Predicting 31P NMR Chemical Shifts of Adenosine Nucleotides in Solution and Stages of ATP Hydrolysis in a Protein Environment

NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.

Evaluating Geometric Definitions of Stacking for RNA Dinucleoside Monophosphates Using Molecular Mechanics Calculations

RNA modulation via small molecules is a novel approach in pharmacotherapies, where the determination of the structural properties of RNA motifs is considered a promising way to develop drugs capable of targeting RNA structures to control diseases. However, due to the complexity and dynamic nature of RNA molecules, the determination of RNA structures using experimental approaches is not always feasible, and computational models employing force fields can provide important insight. The quality of the force field will determine how well the predictions are compared to experimental observables. Stacking in nucleic acids is one such structural property, originating mainly from London dispersion forces, which are quantum mechanical and are included in molecular mechanics force fields through nonbonded interactions. Geometric descriptions are utilized to decide if two residues are stacked and hence to calculate the stacking free energies for RNA dinucleoside monophosphates (DNMPs) through statistical mechanics for comparison with experimental thermodynamics data. Here, we benchmark four different stacking definitions using molecular dynamics (MD) trajectories for 16 RNA DNMPs produced by two different force fields (RNA-IL and ff99OL3) and show that our stacking definition better correlates with the experimental thermodynamics data. While predictions within an accuracy of 0.2 kcal/mol at 300 K were observed in RNA CC, CU, UC, AG, GA, and GG, stacked states of purine-pyrimidine and pyrimidine-purine DNMPs, respectively, were typically underpredicted and overpredicted. Additionally, population distributions of RNA UU DNMPs were poorly predicted by both force fields, implying a requirement for further force field revisions. We further discuss the differences predicted by each RNA force field. Finally, we show that discrete path sampling (DPS) calculations can provide valuable information and complement the MD simulations. We propose the use of experimental thermodynamics data for RNA DNMPs as benchmarks for testing RNA force fields.

The Ad-MD method to calculate NMR shift including effects due to conformational dynamics: The 31 P NMR shift in DNA

A method for averaging of NMR parameters by molecular dynamics (MD) has been derived from the method of statistical averaging in MD snapshots, benchmarked and applied to structurally dynamic interpretation of the ³¹ P NMR shift (δ_31P ) in DNA phosphates. The method employs adiabatic dependence of an NMR parameter on selected geometric parameter(s) that is weighted by MD-calculated probability distribution(s) for the geometric parameter(s) (Ad-MD method). The usage of Ad-MD for polymers is computationally convenient when one pre-calculated structural dependence of an NMR parameter is employed for all chemically equivalent units differing only in dynamic behavior. The Ad-MD method is benchmarked against the statistical averaging method for δ_31P in the model phosphates featuring distinctively different structures and dynamic behavior. The applicability of Ad-MD is illustrated by calculating ³¹ P NMR spectra in the Dickerson-Drew DNA dodecamer. δ_31P was calculated with the B3LYP/IGLO-III/PCM(water) and the probability distributions for the torsion angles adjacent to the phosphorus atoms in the DNA phosphates were calculated using the OL15 force field.

Recent advances in computational 31 P NMR: Part 2. Spin-spin coupling constants

This is the second part of two closely related reviews dealing with the computation of ³¹ P nuclear magnetic resonance (NMR) parameters in a wide range of phosphorous containing compounds. The first part of this review concentrated primarily on the computation of ³¹ P NMR chemical shifts, whereas the second part concerns the calculation of spin-spin coupling constants involving phosphorus nucleus, focusing primarily on their stereochemical dependencies and stereodynamic behavior in particular classes of organophosphorus compounds. This review is dedicated to the Full Member of the Russian Academy of Sciences Professor Boris A. Trofimov in view of his invaluable contribution to the field of synthesis, NMR, and computation studies of organophosphorus compounds.

Structural interpretation of the 31P NMR chemical shifts in thiophosphate and phosphate: key effects due to spin–orbit and explicit solvent

Structural interpretation of the ³¹P NMR shifts measured in different molecules including thiophosphate or phosphate group was obtained by means of theoretical calculations including the effects of geometry, molecular dynamics, solvent, relativistic effects and the effect of NMR reference.

The benchmark of 31P NMR parameters in phosphate: a case study on structurally constrained and flexible phosphate

A benchmark for structural interpretation of the ³¹P NMR shift and the ²J_P,C spin–spin coupling in the phosphate group was obtained by means of theoretical calculations and measurements in diethylphosphate and 5,5-dimethyl-2-hydroxy-1,3,2-dioxaphosphinane 2-oxide.

Empirical Corrections to the Amber RNA Force Field with Target Metadynamics

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

Automatic workflow for the classification of local DNA conformations

Background

A growing number of crystal and NMR structures reveals a considerable structural polymorphism of DNA architecture going well beyond the usual image of a double helical molecule. DNA is highly variable with dinucleotide steps exhibiting a substantial flexibility in a sequence-dependent manner. An analysis of the conformational space of the DNA backbone and the enhancement of our understanding of the conformational dependencies in DNA are therefore important for full comprehension of DNA structural polymorphism.

Results

A detailed classification of local DNA conformations based on the technique of Fourier averaging was published in our previous work. However, this procedure requires a considerable amount of manual work. To overcome this limitation we developed an automatic classification method consisting of the combination of supervised and unsupervised approaches. A proposed workflow is composed of k-NN method followed by a non-hierarchical single-pass clustering algorithm. We applied this workflow to analyze 816 X-ray and 664 NMR DNA structures released till February 2013. We identified and annotated six new conformers, and we assigned four of these conformers to two structurally important DNA families: guanine quadruplexes and Holliday (four-way) junctions. We also compared populations of the assigned conformers in the dataset of X-ray and NMR structures.

Conclusions

In the present work we developed a machine learning workflow for the automatic classification of dinucleotide conformations. Dinucleotides with unassigned conformations can be either classified into one of already known 24 classes or they can be flagged as unclassifiable. The proposed machine learning workflow permits identification of new classes among so far unclassifiable data, and we identified and annotated six new conformations in the X-ray structures released since our previous analysis. The results illustrate the utility of machine learning approaches in the classification of local DNA conformations.

The DNA and RNA sugar-phosphate backbone emerges as the key player. An overview of quantum-chemical, structural biology and simulation studies

Knowledge of geometrical and physico-chemical properties of the sugar-phosphate backbone substantially contributes to the comprehension of the structural dynamics, function and evolution of nucleic acids. We provide a side by side overview of structural biology/bioinformatics, quantum chemical and molecular mechanical/simulation studies of the nucleic acids backbone. We highlight main features, advantages and limitations of these techniques, with a special emphasis given to their synergy. The present status of the research is then illustrated by selected examples which include classification of DNA and RNA backbone families, benchmark structure-energy quantum chemical calculations, parameterization of the dihedral space of simulation force fields, incorporation of arsenate into DNA, sugar-phosphate backbone self-cleavage in small RNA enzymes, and intricate geometries of the backbone in recurrent RNA building blocks. Although not apparent from the current literature showing limited overlaps between the QM, simulation and bioinformatics studies of the nucleic acids backbone, there in fact should be a major cooperative interaction between these three approaches in studies of the sugar-phosphate backbone.

Correlating the 31P NMR chemical shielding tensor and the 2J(P,C) spin-spin coupling constants with torsion angles ζ and α in the backbone of nucleic acids

Determination of nucleic acid (NA) structure with NMR spectroscopy is limited by the lack of restraints on conformation of NA phosphate. In this work, the (31)P chemical shielding tensor, the Γ(P,C5'H5'1) and Γ(P,C5'H5'2) cross-correlated relaxation rates, and the (2)J(P,C3'), (2)J(P,C5'), and (3)J(P,C4') coupling constants were calculated in dependence on NA backbone torsion angles ζ and α. While the orientation of the (31)P chemical shielding tensor was almost independent of the NA phosphate conformation, the principal tensor components varied by up to ~40 ppm. This variation and the dependence of the phosphate geometry on torsion angles ζ and α had only a minor influence on the calculated Γ(P,C5'H5'1) and Γ(P,C5'H5'2) cross-correlated relaxation rates, and therefore, the so-called rigid tensor approximation was here validated. For the first time, the (2)J(P,C) spin-spin coupling constants were correlated with the conformation of NA phosphate. Although each of the two J-couplings was significantly modulated by both torsions ζ and α, the (2)J(P,C3') coupling could be structurally assigned to torsion ζ and the (2)J(P,C5') coupling to torsion α. We propose qualitative rules for their structural interpretation as loose restraints on torsion angles ζ and α. The (3)J(P,C4') coupling assigned to torsion angle β was found dependent also on torsions ζ and α, implying that the uncertainty in determination of β with standard Karplus curves could be as large as ~25°. The calculations provided a unified picture of NMR parameters applicable for the determination of NA phosphate conformation.

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.

Observed and calculated 1H and 13C chemical shifts induced by the in situ oxidation of model sulfides to sulfoxides and sulfones

A series of model sulfides was oxidized in the NMR sample tube to sulfoxides and sulfones by the stepwise addition of meta-chloroperbenzoic acid in deuterochloroform. Various methods of quantum chemical calculations have been tested to reproduce the observed (1)H and (13)C chemical shifts of the starting sulfides and their oxidation products. It has been shown that the determination of the energy-minimized conformation is a very important condition for obtaining realistic data in the subsequent calculation of the NMR chemical shifts. The correlation between calculated and observed chemical shifts is very good for carbon atoms (even for the 'cheap' DFT B3LYP/6-31G* method) and somewhat less satisfactory for hydrogen atoms. The calculated chemical shifts induced by oxidation (the Delta delta values) agree even better with the experimental values and can also be used to determine the oxidation state of the sulfur atom (-S-, -SO-, -SO(2)-).

The metal-binding sites of glycose phosphates

In aqueous solution, the reducing sugar phosphates D-arabinose 5-phosphate, D-ribose 5-phosphate, D-fructose 1,6-bisphosphate, D-fructose 6-phosphate, D-glucose 6-phosphate and D-mannose 6-phosphate provide metal-binding sites at their glycose core on reaction with Pd(II)(en) or M(III)(tacn) residues (M = Ga, Co; en = ethylenediamine, tacn = 1,4,7-triazacyclononane). The individual species were detected by one- and two-dimensional NMR spectroscopy. The coordination patterns are related to the metal-binding modes of the respective parent glycoses. In detail, ribo- and arabinofuranose phosphate favour kappaO(1,3) coordination, whereas the ketofuranose core of fructose phosphate and fructose bisphosphate provides the kappaO(2,3) chelator thus maintaining the configuration of the respective major solution anomer. On palladium excess, D-fructose 6-phosphate is metallated twice in a unique kappaO(1,3):kappaO(2,4) metallation pattern. Dimetallation is also found for the aldohexose phosphates. A mixed glycose-core-phosphate chelation was detected for Pd(II)(en) and M(III)(tacn) residues with M = Al, Ga in the pH range just above the physiological pH for the D-fructose 1,6-bisphosphate ligand. The results are discussed in relation to D-fructose-1,6-bisphosphate-metabolism in class-II aldolases.

Structure and dynamics of the ApA, ApC, CpA, and CpC RNA dinucleoside monophosphates resolved with NMR scalar spin-spin couplings

The measured NMR scalar coupling constants (J-couplings) in the XpY, (X,Y = adenine (A) or cytosine (C)) RNA dinucleoside monophosphates (DMPs) were assigned to the backbone (alpha, beta, gamma, delta, epsilon, zeta) and glycosidic (chi) torsion angles in order to resolve the global structure of the DMP molecules. The experimental J-couplings were correlated with the theoretical J-couplings obtained as the dynamical averages of the Karplus equations relevant to the torsion angles. The dynamical information was captured using the molecular dynamics (MD) calculation method. The individual conformational flexibility of the four DMP molecules was thus consistently probed with the NMR J-couplings. The calculated structure and flexibility of the DMP molecules depend on the sequence considered with respect to the 5' and 3' end of the DMP molecules (5'-XpY-3'). The dynamical characteristics of the two nucleosides are not equivalent even for the ApA and CpC homologues. An enhancement of the sampling in the MD calculations was achieved using five different starting structural motives classified previously for the RNA backbone in the solid phase (Richardson et al. RNA 2008, 14, 465-481). The initial structures were selected on the basis of a database search for RNA oligonucleotides. Frequent interconversions between the conformers during the MD calculations were actually observed. The structural interpretation of the NMR spectroscopic data based on the MD simulations combined with the Karplus equations indicates that the dominant conformation of the DMP molecules in solution corresponds to the A-RNA form. For 52% of the total simulation time (1000 ns), the zeta(g-)-alpha(g-)-gamma(g+) backbone topology corresponding to the canonical A-RNA form was observed, with roughly equally populated C2'- and C3'-endo sugar puckers interconverting on the nanosecond time scale. However, other noncanonical patterns were also found and thus indicate their relatively high potential to be populated in the dynamical regime. For approximately 72% of the time portion when the A-RNA of the zeta-alpha-gamma combination occurred, the nucleobases were classified as being mutually stacked. The geometries of the nucleobases classified in this work as stacked were significantly more populated for the DMP molecules with adenosine at the 3' end (ApA and CpA DMPs) than the ApC or CpC RNA molecules with C at the 3' end.

Geometrical and electronic structure variability of the sugar-phosphate backbone in nucleic acids

The anionic sugar-phosphate backbone of nucleic acids substantially contributes to their structural flexibility. To model nucleic acid structure and dynamics correctly, the potentially sampled substates of the sugar-phosphate backbone must be properly described. However, because of the complexity of the electronic distribution in the nucleic acid backbone, its representation by classical force fields is very challenging. In this work, the three-dimensional potential energy surfaces with two independent variables corresponding to rotations around the alpha and gamma backbone torsions are studied by means of high-level ab initio methods (B3LYP/6-31+G*, MP2/6-31+G*, and MP2 complete basis set limit levels). The ability of the AMBER ff99 [Wang, J. M.; Cieplak, P.; Kollman, P. A. J. Comput. Chem. 2000, 21, 1049-1074] and parmbsc0 [Perez, A.; Marchan, I.; Svozil, D.; Sponer, J.; Cheatham, T. E.; Laughten, C. A.; Orozco, M. Biophys. J. 2007, 92, 3817-3829] force fields to describe the various alpha/gamma conformations of the DNA backbone accurately is assessed by comparing the results with those of ab initio quantum chemical calculations. Two model systems differing in structural complexity were used to describe the alpha/gamma energetics. The simpler one, SPM, consisting of a sugar and methyl group linked through a phosphodiester bond was used to determine higher-order correlation effects covered by the CCSD(T) method. The second, more complex model system, SPSOM, includes two deoxyribose residues (without the bases) connected via a phosphodiester bond. It has been shown by means of a natural bond orbital analysis that the SPSOM model provides a more realistic representation of the hyperconjugation network along the C5'-O5'-P-O3'-C3' linkage. However, we have also shown that quantum mechanical investigations of this model system are nontrivial because of the complexity of the SPSOM conformational space. A comparison of the ab initio data with the ff99 potential energy surface clearly reveals an incorrect ff99 force-field description in the regions where the gamma torsion is in the trans conformation. An explanation is proposed for why the alpha/gamma flips are eliminated so successfully when the parmbsc0 force-field modification is used.