Accurate ab initio prediction of NMR chemical shifts of nucleic acids and nucleic acids/protein complexes

MIM-ML: A Novel Quantum Chemical Fragment-Based Random Forest Model for Accurate Prediction of NMR Chemical Shifts of Nucleic Acids

We developed a random forest machine learning (ML) model for the prediction of 1H and 13C NMR chemical shifts of nucleic acids. Our ML model is trained entirely on reproducing computed chemical shifts obtained previously on 10 nucleic acids using a Molecules-in-Molecules (MIM) fragment-based density functional theory (DFT) protocol including microsolvation effects. Our ML model includes structural descriptors as well as electronic descriptors from an inexpensive low-level semiempirical calculation (GFN2-xTB) and trained on a relatively small number of DFT chemical shifts (2080 1H chemical shifts and 1780 13C chemical shifts on the 10 nucleic acids). The ML model is then used to make chemical shift predictions on 8 new nucleic acids ranging in size from 600 to 900 atoms and compared directly to experimental data. Though no experimental data was used in the training, the performance of our model is excellent (mean absolute deviation of 0.34 ppm for 1H chemical shifts and 2.52 ppm for 13C chemical shifts for the test set), despite having some nonstandard structures. A simple analysis suggests that both structural and electronic descriptors are critical for achieving reliable predictions. This is the first attempt to combine ML from fragment-based DFT calculations to predict experimental chemical shifts accurately, making the MIM-ML model a valuable tool for NMR predictions of nucleic acids.

DELTA50: A Highly Accurate Database of Experimental 1H and 13C NMR Chemical Shifts Applied to DFT Benchmarking

Density functional theory (DFT) benchmark studies of ¹H and ¹³C NMR chemical shifts often yield differing conclusions, likely due to non-optimal test molecules and non-standardized data acquisition. To address this issue, we carefully selected and measured ¹H and ¹³C NMR chemical shifts for 50 structurally diverse small organic molecules containing atoms from only the first two rows of the periodic table. Our NMR dataset, DELTA50, was used to calculate linear scaling factors and to evaluate the accuracy of 73 density functionals, 40 basis sets, 3 solvent models, and 3 gauge-referencing schemes. The best performing DFT methodologies for ¹H and ¹³C NMR chemical shift predictions were WP04/6-311++G(2d,p) and ωB97X-D/def2-SVP, respectively, when combined with the polarizable continuum solvent model (PCM) and gauge-independent atomic orbital (GIAO) method. Geometries should be optimized at the B3LYP-D3/6-311G(d,p) level including the PCM solvent model for the best accuracy. Predictions of 20 organic compounds and natural products from a separate probe set had root-mean-square deviations (RMSD) of 0.07 to 0.19 for ¹H and 0.5 to 2.9 for ¹³C. Maximum deviations were less than 0.5 and 6.5 ppm for ¹H and ¹³C, respectively.

Accurate and Cost-Effective NMR Chemical Shift Predictions for Nucleic Acids Using a Molecules-in-Molecules Fragmentation-Based Method

We have developed, implemented, and assessed an efficient protocol for the prediction of NMR chemical shifts of large nucleic acids using our molecules-in-molecules (MIM) fragment-based quantum chemical approach. To assess the performance of our approach, MIM-NMR calculations are calibrated on a test set of three nucleic acids, where the structure is derived from solution-phase NMR studies. For DNA systems with multiple conformers, the one-layer MIM method with trimer fragments (MIM1trimer) is benchmarked to get the lowest energy structure, with an average error of only 0.80 kcal/mol with respect to unfragmented full molecule calculations. The MIMI-NMRdimer calibration with respect to unfragmented full molecule calculations shows a mean absolute deviation (MAD) of 0.06 and 0.11 ppm, respectively, for 1H and 13C nuclei, but the performance with respect to experimental NMR chemical shifts is comparable to the more expensive MIM1-NMR and MIM2-NMR methods with trimer subsystems. To compare with the experimental chemical shifts, a standard protocol is derived using DNA systems with Protein Data Bank (PDB) IDs 1SY8, 1K2K, and 1KR8. The effect of structural minimizations is employed using a hybrid mechanics/semiempirical approach and used for computations in solution with implicit and explicit-implicit solvation models in our MIM1-NMRdimer methodology. To demonstrate the applicability of our protocol, we tested it on seven nucleic acids, including structures with nonstandard residues, heteroatom substitutions (F and B atoms), and side chain mutations with a size ranging from ∼300 to 1100 atoms. The major improvement for predicted MIM1-NMRdimer calculations is obtained from structural minimizations and implicit solvation effects. A significant improvement with the explicit-implicit solvation model is observed only for two smaller nucleic acid systems (1KR8 and 7NBK), where the expensive first solvation shell is replaced by the microsolvation model, in which a single water molecule is added for each solvent-exposed amino and imino protons, along with the implicit solvation. Overall, our target accuracy of ∼0.2-0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for large nucleic acids. The proposed MIM-NMR approach is accurate and cost-effective (linear scaling with system size), and it can aid in the structural assignments of a wide range of complex biomolecules.

Improving IDP theoretical chemical shift accuracy and efficiency through a combined MD/ADMA/DFT and machine learning approach

This work extends the multi-scale computational scheme for the quantum mechanics (QM) calculations of Nuclear Magnetic Resonance (NMR) chemical shifts (CSs) in proteins that lack a well-defined 3D structure. The scheme couples the sampling of an intrinsically disordered protein (IDP) by classical molecular dynamics (MD) with protein fragmentation using the adjustable density matrix assembler (ADMA) and density functional theory (DFT) calculations. In contrast to our early investigation on IDPs (Pavlíková Přecechtělová et al., J. Chem. Theory Comput., 2019, 15, 5642-5658) and the state-of-the art NMR calculations for structured proteins, a partial re-optimization was implemented on the raw MD geometries in vibrational normal mode coordinates to enhance the accuracy of the MD/ADMA/DFT computational scheme. In addition, machine-learning based cluster analysis was performed on the scheme to explore its potential in producing protein structure ensembles (CLUSTER ensembles) that yield accurate CSs at a reduced computational cost. The performance of the cluster-based calculations is validated against results obtained with conventional structural ensembles consisting of MD snapshots extracted from the MD trajectory at regular time intervals (REGULAR ensembles). CS calculations performed with the refined MD/ADMA/DFT framework employed the 6-311++G(d,p) basis set that outperformed IGLO-III calculations with the same density functional approximation (B3LYP) and both explicit and implicit solvation. The partial geometry optimization did not universally improve the agreement of computed CSs with the experiment but substantially decreased errors associated with the ensemble averaging. A CLUSTER ensemble with 50 structures yielded ensemble averages close to those obtained with a REGULAR ensemble consisting of 500 MD frames. The cluster based calculations thus required only a fraction of the computational time.

Computational 1 H and 13 C NMR in structural and stereochemical studies

Present review outlines the advances and perspectives of computational ¹ H and ¹³ C NMR applied to the stereochemical studies of inorganic, organic, and bioorganic compounds, involving in particular natural products, carbohydrates, and carbonium ions. The first part of the review briefly outlines theoretical background of the modern computational methods applied to the calculation of chemical shifts and spin-spin coupling constants at the DFT and the non-empirical levels. The second part of the review deals with the achievements of the computational ¹ H and ¹³ C NMR in the stereochemical investigation of a variety of inorganic, organic, and bioorganic compounds, providing in an abridged form the material partly discussed by the author in a series of parent reviews. Major attention is focused herewith on the publications of the recent years, which were not reviewed elsewhere.

Self-Consistent Parameterization of DNA Residues for the Non-Polarizable AMBER Force Fields

Fixed-charge (non-polarizable) forcefields are accurate and computationally efficient tools for modeling the molecular dynamics of nucleic acid polymers, particularly DNA, well into the µs timescale. The continued utility of these forcefields depends in part on expanding the residue set in step with advancing nucleic acid chemistry and biology. A key step in parameterizing new residues is charge derivation which is self-consistent with the existing residues. As atomic charges are derived by fitting against molecular electrostatic potentials, appropriate structural models are critical. Benchmarking against the existing charge set used in current AMBER nucleic acid forcefields, we report that quantum mechanical models of deoxynucleosides, even at a high level of theory, are not optimal structures for charge derivation. Instead, structures from molecular mechanics minimization yield charges with up to 6-fold lower RMS deviation from the published values, due to the choice of such an approach in the derivation of the original charge set. We present a contemporary protocol for rendering self-consistent charges as well as optimized charges for a panel of nine non-canonical residues that will permit comparison with literature as well as studying the dynamics of novel DNA polymers.

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.

Polarizable continuum models provide an effective electrostatic embedding model for fragment-based chemical shift prediction in challenging systems

Ab initio nuclear magnetic resonance chemical shift prediction provides an important tool for interpreting and assigning experimental spectra, but it becomes computationally prohibitive in large systems. The computational costs can be reduced considerably by fragmentation of the large system into a series of contributions from many smaller subsystems. However, the presence of charged functional groups and the need to partition the system across covalent bonds create complications in biomolecules that typically require the use of large fragments and careful descriptions of the electrostatic environment. The present work shows how a model that combines chemical shielding contributions from non-overlapping monomer and dimer fragments embedded in a polarizable continuum model provides a simple, easy-to-implement, and computationally inexpensive approach for predicting chemical shifts in complex systems. The model's performance proves rather insensitive to the continuum dielectric constant, making the selection of the optimal embedding dielectric less critical. The PCM-embedded fragment model is demonstrated to perform well across systems ranging from molecular crystals to proteins.

Computational 1 H NMR: Part 3. Biochemical studies

This is the third and the last part of three closely interrelated reviews dealing with computation of ¹ H nuclear magnetic resonance chemical shifts and ¹ H-¹ H spin-spin coupling constants. Present review deals with the computation of these parameters in biologically active natural products, carbohydrates, and other molecules of biological origin focusing on stereochemical applications of computational ¹ H nuclear magnetic resonance to these objects.

Chemical shift-based methods in NMR structure determination

Chemical shifts are highly sensitive probes harnessed by NMR spectroscopists and structural biologists as conformational parameters to characterize a range of biological molecules. Traditionally, assignment of chemical shifts has been a labor-intensive process requiring numerous samples and a suite of multidimensional experiments. Over the past two decades, the development of complementary computational approaches has bolstered the analysis, interpretation and utilization of chemical shifts for elucidation of high resolution protein and nucleic acid structures. Here, we review the development and application of chemical shift-based methods for structure determination with a focus on ab initio fragment assembly, comparative modeling, oligomeric systems, and automated assignment methods. Throughout our discussion, we point out practical uses, as well as advantages and caveats, of using chemical shifts in structure modeling. We additionally highlight (i) hybrid methods that employ chemical shifts with other types of NMR restraints (residual dipolar couplings, paramagnetic relaxation enhancements and pseudocontact shifts) that allow for improved accuracy and resolution of generated 3D structures, (ii) the utilization of chemical shifts to model the structures of sparsely populated excited states, and (iii) modeling of sidechain conformations. Finally, we briefly discuss the advantages of contemporary methods that employ sparse NMR data recorded using site-specific isotope labeling schemes for chemical shift-driven structure determination of larger molecules. With this review, we aim to emphasize the accessibility and versatility of chemical shifts for structure determination of challenging biological systems, and to point out emerging areas of development that lead us towards the next generation of tools.

Automated Fragmentation QM/MM Calculation of NMR Chemical Shifts for Protein-Ligand Complexes

In this study, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method was applied for NMR chemical shift calculations of protein-ligand complexes. In the AF-QM/MM approach, the protein binding pocket is automatically divided into capped fragments (within ~200 atoms) for density functional theory (DFT) calculations of NMR chemical shifts. Meanwhile, the solvent effect was also included using the Poission-Boltzmann (PB) model, which properly accounts for the electrostatic polarization effect from the solvent for protein-ligand complexes. The NMR chemical shifts of neocarzinostatin (NCS)-chromophore binding complex calculated by AF-QM/MM accurately reproduce the large-sized system results. The 1H chemical shift perturbations (CSP) between apo-NCS and holo-NCS predicted by AF-QM/MM are also in excellent agreement with experimental results. Furthermore, the DFT calculated chemical shifts of the chromophore and residues in the NCS binding pocket can be utilized as molecular probes to identify the correct ligand binding conformation. By combining the CSP of the atoms in the binding pocket with the Glide scoring function, the new scoring function can accurately distinguish the native ligand pose from decoy structures. Therefore, the AF-QM/MM approach provides an accurate and efficient platform for protein-ligand binding structure prediction based on NMR derived information.

A systematic study on RNA NMR chemical shift calculation based on the automated fragmentation QM/MM approach

¹H, ¹³C and ¹⁵N NMR chemical shift calculations on RNAs were performed using the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach.

AFNMR: automated fragmentation quantum mechanical calculation of NMR chemical shifts for biomolecules

We evaluate the performance of the automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) on the calculation of protein and nucleic acid NMR chemical shifts. The AF-QM/MM approach models solvent effects implicitly through a set of surface charges computed using the Poisson-Boltzmann equation, and it can also be combined with an explicit solvent model through the placement of water molecules in the first solvation shell around the solute; the latter substantially improves the accuracy of chemical shift prediction of protons involved in hydrogen bonding with solvent. We also compare the performance of AF-QM/MM on proteins and nucleic acids with two leading empirical chemical shift prediction programs SHIFTS and SHIFTX2. Although the empirical programs outperform AF-QM/MM in predicting chemical shifts, the differences are in some cases small, and the latter can be applied to chemical shifts on biomolecules which are outside the training set employed by the empirical programs, such as structures containing ligands, metal centers, and non-standard residues. The AF-QM/MM described here is implemented in version 5 of the SHIFTS software, and is fully automated, so that only a structure in PDB format is required as input.

Accurate ab initio calculations of O-HO and O-H(-)O proton chemical shifts: towards elucidation of the nature of the hydrogen bond and prediction of hydrogen bond distances

The inability to determine precisely the location of labile protons in X-ray molecular structures has been a key barrier to progress in many areas of molecular sciences. We report an approach for predicting hydrogen bond distances beyond the limits of X-ray crystallography based on accurate ab initio calculations of O-HO proton chemical shifts, using a combination of DFT and contactor-like polarizable continuum model (PCM). Very good linear correlation between experimental and computed (at the GIAO/B3LYP/6-311++G(2d,p) level of theory) chemical shifts were obtained with a large set of 43 compounds in CHCl3 exhibiting intramolecular O-HO and intermolecular and intramolecular ionic O-H(-)O hydrogen bonds. The calculated OH chemical shifts exhibit a strong linear dependence on the computed (O)HO hydrogen bond length, in the region of 1.24 to 1.85 Å, of -19.8 ppm Å(-1) and -20.49 ppm Å(-1) with optimization of the structures at the M06-2X/6-31+G(d) and B3LYP/6-31+G(d) level of theory, respectively. A Natural Bond Orbitals (NBO) analysis demonstrates a very good linear correlation between the calculated (1)H chemical shifts and (i) the second-order perturbation stabilization energies, corresponding to charge transfer between the oxygen lone pairs and σ antibonding orbital and (ii) Wiberg bond order of the O-HO and O-H(-)O hydrogen bond. Accurate ab initio calculations of O-HO and O-H(-)O (1)H chemical shifts can provide improved structural and electronic description of hydrogen bonding and a highly accurate measure of distances of short and strong hydrogen bonds.

NMR proton chemical shift prediction of C·C mismatches in B-DNA

Accurate prediction of DNA chemical shifts facilitates resonance assignment and allows recognition of different conformational features. Based on the nearest neighbor model and base pair replacement approach, we have determined a set of triplet chemical shift values and correction factors for predicting the proton chemical shifts of B-DNA containing an internal C·C mismatch. Our results provide a reliable chemical shift prediction with an accuracy of 0.07 ppm for non-labile protons and 0.09 ppm for labile protons. In addition, we have also shown that the correction factors for C·C mismatches can be used interchangeably with those for T·T mismatches. As a result, we have generalized a set of correction factors for predicting the flanking residue chemical shifts of pyrimidine·pyrimidine mismatches.