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

Predicted and Experimental NMR Chemical Shifts at Variable Temperatures: The Effect of Protein Conformational Dynamics

NMR chemical shifts provide a sensitive probe of protein structure and dynamics but remain challenging to predict and interpret. We examine the effect of protein conformational distributions on 15N chemical shifts for dihydrofolate reductase (DHFR), comparing QM/MM predicted shifts with experimental shifts in solution as well as frozen distributions. Representative snapshots from MD trajectories exhibit variation in predicted 15N chemical shifts of up to 25 ppm. The average over the fluctuations is in significantly better agreement with room temperature solution experimental values than the prediction for any single optimal conformations. Meanwhile, solid-state NMR (SSNMR) measurements of frozen solutions at 105 K exhibit broad lines whose widths agree well with the widths of distributions of predicted shifts for samples from the trajectory. The backbone torsion angle ψi-1 varies over 60° on the picosecond time scale, compensated by φi. These fluctuations can explain much of the shift variation.

Molecular mechanisms and evolutionary robustness of a color switch in proteorhodopsins

Proteorhodopsins are widely distributed photoreceptors from marine bacteria. Their discovery revealed a high degree of evolutionary adaptation to ambient light, resulting in blue- and green-absorbing variants that correlate with a conserved glutamine/leucine at position 105. On the basis of an integrated approach combining sensitivity-enhanced solid-state nuclear magnetic resonance (ssNMR) spectroscopy and linear-scaling quantum mechanics/molecular mechanics (QM/MM) methods, this single residue is shown to be responsible for a variety of synergistically coupled structural and electrostatic changes along the retinal polyene chain, ionone ring, and within the binding pocket. They collectively explain the observed color shift. Furthermore, analysis of the differences in chemical shift between nuclei within the same residues in green and blue proteorhodopsins also reveals a correlation with the respective degree of conservation. Our data show that the highly conserved color change mainly affects other highly conserved residues, illustrating a high degree of robustness of the color phenotype to sequence variation.

Multitasking Pharmacophores Support Cabotegravir-Based Long-Acting HIV Pre-Exposure Prophylaxis (PrEP)

Cabotegravir is an integrase strand transfer inhibitor (INSTI) for HIV treatment and prevention. Cabotegravir-based long-acting pre-exposure prophylaxis (PrEP) presents an emerging paradigm for infectious disease control. In this scheme, a combination of a high efficacy and low solubility of anti-infection drugs permits the establishment of a pharmaceutical firewall in HIV-vulnerable groups over a long period. Although the structure-activity-relationship (SAR) of cabotegravir as an INSTI is known, the structural determinants of its low solubility have not been identified. In this work, we have integrated multiple experimental and computational methods, namely X-ray diffraction, solid-state NMR (SSNMR) spectroscopy, solution NMR spectroscopy, automated fragmentation (AF)-QM/MM and density functional theory (DFT) calculations, to address this question. The molecular organization of cabotegravir in crystal lattice has been determined. The combination of very-fast magic-angle-sample-spinning (VF MAS) SSNMR and solution NMR, as supported by AF-QM/MM and DFT calculations, permits the identification of structural factors that contribute to the low aqueous solubility of cabotegravir. Our study reveals the multitasking nature of pharmacophores in cabotegravir, which controls the drug solubility and, meanwhile, the biological activity. By unraveling these function-defining molecular features, our work could inspire further development of long-acting HIV PrEP drugs.

Ligand 1 H NMR Chemical Shifts as Accurate Reporters for Protein-Ligand Binding Interfaces in Solution

The availability of high-resolution 3D structural information is crucial for investigating guest-host systems across a wide range of fields. In the context of drug discovery, the information is routinely used to establish and validate structure-activity relationships, grow initial hits from screening campaigns, and to guide molecular docking. For the generation of protein-ligand complex structural information, X-ray crystallography is the experimental method of choice, however, with limited information on protein flexibility. An experimentally verified structural model of the binding interface in the native solution-state would support medicinal chemists in their molecular design decisions. Here we demonstrate that protein-bound ligand 1 H NMR chemical shifts are highly sensitive and accurate probes for the immediate chemical environment of protein-ligand interfaces. By comparing the experimental ligand 1 H chemical shift values with those computed from the X-ray structure using quantum mechanics methodology, we identify significant disagreements for parts of the ligand between the two experimental techniques. We show that quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) ensembles can be used to refine initial X-ray co-crystal structures resulting in a better agreement with experimental 1 H ligand chemical shift values. Overall, our findings highlight the usefulness of ligand 1 H NMR chemical shift information in combination with a QM/MM MD workflow for generating protein-ligand ensembles that accurately reproduce solution structural data.

An RNA excited conformational state at atomic resolution

Sparse and short-lived excited RNA conformational states are essential players in cell physiology, disease, and therapeutic development, yet determining their 3D structures remains challenging. Combining mutagenesis, NMR spectroscopy, and computational modeling, we determined the 3D structural ensemble formed by a short-lived (lifetime ~2.1 ms) lowly-populated (~0.4%) conformational state in HIV-1 TAR RNA. Through a strand register shift, the excited conformational state completely remodels the 3D structure of the ground state (RMSD from the ground state = 7.2 ± 0.9 Å), forming a surprisingly more ordered conformational ensemble rich in non-canonical mismatches. The structure impedes the formation of the motifs recognized by Tat and the super elongation complex, explaining why this alternative TAR conformation cannot activate HIV-1 transcription. The ability to determine the 3D structures of fleeting RNA states using the presented methodology holds great promise for our understanding of RNA biology, disease mechanisms, and the development of RNA-targeting therapeutics.

Calculating 13 C NMR chemical shifts of large molecules using the eXtended ONIOM method at high accuracy with a low cost

Fragmentation-based methods for nuclear magnetic resonance (NMR) chemical shift calculations have become more and more popular in first-principles calculations of large molecules. However, there are many options for a fragmentation-based method to select, such as theoretical methods, fragmentation schemes, the number of levels of theory, etc. It is important to study the optimal combination of the options to achieve a good balance between accuracy and efficiency. Here we investigate different combinations of options used by a fragmentation-based method, the eXtended ONIOM (XO) method, for 13 C chemical shift calculations on a set of organic and biological molecules. We found that: (1) introducing Hartree-Fock exchange into density functional theory (DFT) could reduce the calculation error due to fragmentation in contrast to pure DFT functionals, while a hybrid functional, xOPBE, is generally recommended; (2) fragmentation schemes generated from the molecular tailoring approach (MTA) with small level parameter n, for example, n = 2 and the degree-based fragmentation method (DBFM) with n = 1, are sufficient to achieve satisfactory accuracy; (3) the two-level XO (XO2) NMR calculation is superior to the calculation with only one level of theory, as the second level (i.e., low level) of theory provides a way to well describe the long-range effect. These findings are beneficial to practical applications of fragmentation-based methods for NMR chemical shift calculations of large molecules.

Kinetic Resolution of the Atomic 3D Structures Formed by Ground and Excited Conformational States in an RNA Dynamic Ensemble

Knowing the 3D structures formed by the various conformations populating the RNA free-energy landscape, their relative abundance, and kinetic interconversion rates is required to obtain a quantitative and predictive understanding of how RNAs fold and function at the atomic level. While methods integrating ensemble-averaged experimental data with computational modeling are helping define the most abundant conformations in RNA ensembles, elucidating their kinetic rates of interconversion and determining the 3D structures of sparsely populated short-lived RNA excited conformational states (ESs) remains challenging. Here, we developed an approach integrating Rosetta-FARFAR RNA structure prediction with NMR residual dipolar couplings and relaxation dispersion that simultaneously determines the 3D structures formed by the ground-state (GS) and ES subensembles, their relative abundance, and kinetic rates of interconversion. The approach is demonstrated on HIV-1 TAR, whose six-nucleotide apical loop was previously shown to form a sparsely populated (∼13%) short-lived (lifetime ∼ 45 μs) ES. In the GS, the apical loop forms a broad distribution of open conformations interconverting on the pico-to-nanosecond time scale. Most residues are unpaired and preorganized to bind the Tat-superelongation protein complex. The apical loop zips up in the ES, forming a narrow distribution of closed conformations, which sequester critical residues required for protein recognition. Our work introduces an approach for determining the 3D ensemble models formed by sparsely populated RNA conformational states, provides a rare atomic view of an RNA ES, and kinetically resolves the atomic 3D structures of RNA conformational substates, interchanging on time scales spanning 6 orders of magnitude, from picoseconds to microseconds.

Automated Fragmentation Quantum Mechanical Calculation of 15N and 13C Chemical Shifts in a Membrane Protein

In this work, we developed an accurate and cost-effective automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method to calculate the chemical shifts of 15N and 13C of membrane proteins. The convergence of the AF-QM/MM method was tested using Krokinobacter eikastus rhodopsin 2 as a test case. When the distance threshold of the QM region is equal to or larger than 4.0 Å, the results of the AF-QM/MM calculations are close to convergence. In addition, the effects of selected density functionals, basis sets, and local chemical environment of target atoms on the chemical shift calculations were systematically investigated. Our results demonstrate that the predicted chemical shifts are more accurate when important environmental factors including cross-protomer interactions, lipid molecules, and solvent molecules are taken into consideration, especially for the 15N chemical shift prediction. Furthermore, with the presence of sodium ions in the environment, the chemical shift of residues, retinal, and retinal Schiff base are affected, which is consistent with the results of the solid-state nuclear magnetic resonance (NMR) experiment. Upon comparing the performance of various density functionals (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB95, and OPBE), the results show that mPW1PW91 is a suitable functional for the 15N and 13C chemical shift prediction of the membrane proteins. Meanwhile, we find that the improved accuracy of the 13Cβ chemical shift calculations can be achieved by the employment of the triple-ζ basis set. However, the employment of the triple-ζ basis set does not improve the accuracy of the 15N and 13Cα chemical shift calculations nor does the addition of a diffuse function improve the overall prediction accuracy of the chemical shifts. Our study also underscores that the AF-QM/MM method has significant advantages in predicting the chemical shifts of key ligands and nonstandard residues in membrane proteins than most widely used empirical models; therefore, it could be an accurate computational tool for chemical shift calculations on various types of biological systems.

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.

Predicted and Experimental NMR Chemical Shifts at Variable Temperatures: The Effect of Protein Conformational Dynamics

NMR chemical shifts provide a sensitive probe of protein structure and dynamics. Prediction of shifts, and therefore interpretation of shifts, particularly for the frequently measured amidic 15 N sites, remains a tall challenge. We demonstrate that protein 15 N chemical shift prediction from QM/MM predictions can be improved if conformational variation is included via MD sampling, focusing on the antibiotic target, E. coli Dihydrofolate reductase (DHFR). Variations of up to 25 ppm in predicted 15 N chemical shifts are observed over the trajectory. For solution shifts the average of fluctuations on the low picosecond timescale results in a superior prediction to a single optimal conformation. For low temperature solid state measurements, the histogram of predicted shifts for locally minimized snapshots with specific solvent arrangements sampled from the trajectory explains the heterogeneous linewidths; in other words, the conformations and associated solvent are 'frozen out' at low temperatures and result in inhomogeneously broadened NMR peaks. We identified conformational degrees of freedom that contribute to chemical shift variation. Backbone torsion angles show high amplitude fluctuations during the trajectory on the low picosecond timescale. For a number of residues, including I60, ψ varies by up to 60º within a conformational basin during the MD simulations, despite the fact that I60 (and other sites studied) are in a secondary structure element and remain well folded during the trajectory. Fluctuations in ψ appear to be compensated by other degrees of freedom in the protein, including φ of the succeeding residue, resulting in "rocking" of the amide plane with changes in hydrogen bonding interactions. Good agreement for both room temperature and low temperature NMR spectra provides strong support for the specific approach to conformational averaging of computed chemical shifts.

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.

Probing Watson-Crick and Hoogsteen base pairing in duplex DNA using dynamic nuclear polarization solid-state NMR spectroscopy

The majority of base pairs in double-stranded DNA exist in the canonical Watson-Crick geometry. However, they can also adopt alternate Hoogsteen conformations in various complexes of DNA with proteins and small molecules, which are key for biological function and mechanism. While detection of Hoogsteen base pairs in large DNA complexes and assemblies poses considerable challenges for traditional structural biology techniques, we show here that multidimensional dynamic nuclear polarization-enhanced solid-state NMR can serve as a unique spectroscopic tool for observing and distinguishing Watson-Crick and Hoogsteen base pairs in a broad range of DNA systems based on characteristic NMR chemical shifts and internuclear dipolar couplings. We illustrate this approach using a model 12-mer DNA duplex, free and in complex with the antibiotic echinomycin, which features two central adenine-thymine base pairs with Watson-Crick and Hoogsteen geometry, respectively, and subsequently extend it to the ∼200 kDa Widom 601 DNA nucleosome core particle.

Imaging active site chemistry and protonation states: NMR crystallography of the tryptophan synthase α-aminoacrylate intermediate

NMR-assisted crystallography-the integrated application of solid-state NMR, X-ray crystallography, and first-principles computational chemistry-holds significant promise for mechanistic enzymology: by providing atomic-resolution characterization of stable intermediates in enzyme active sites, including hydrogen atom locations and tautomeric equilibria, NMR crystallography offers insight into both structure and chemical dynamics. Here, this integrated approach is used to characterize the tryptophan synthase α-aminoacrylate intermediate, a defining species for pyridoxal-5'-phosphate-dependent enzymes that catalyze β-elimination and replacement reactions. For this intermediate, NMR-assisted crystallography is able to identify the protonation states of the ionizable sites on the cofactor, substrate, and catalytic side chains as well as the location and orientation of crystallographic waters within the active site. Most notable is the water molecule immediately adjacent to the substrate β-carbon, which serves as a hydrogen bond donor to the ε-amino group of the acid-base catalytic residue βLys87. From this analysis, a detailed three-dimensional picture of structure and reactivity emerges, highlighting the fate of the L-serine hydroxyl leaving group and the reaction pathway back to the preceding transition state. Reaction of the α-aminoacrylate intermediate with benzimidazole, an isostere of the natural substrate indole, shows benzimidazole bound in the active site and poised for, but unable to initiate, the subsequent bond formation step. When modeled into the benzimidazole position, indole is positioned with C3 in contact with the α-aminoacrylate Cβ and aligned for nucleophilic attack. Here, the chemically detailed, three-dimensional structure from NMR-assisted crystallography is key to understanding why benzimidazole does not react, while indole does.

Dynamic Coupling of Tyrosine 185 with the Bacteriorhodopsin Photocycle, as Revealed by Chemical Shifts, Assisted AF-QM/MM Calculations and Molecular Dynamic Simulations

Aromatic residues are highly conserved in microbial photoreceptors and play crucial roles in the dynamic regulation of receptor functions. However, little is known about the dynamic mechanism of the functional role of those highly conserved aromatic residues during the receptor photocycle. Tyrosine 185 (Y185) is one of the highly conserved aromatic residues within the retinal binding pocket of bacteriorhodopsin (bR). In this study, we explored the molecular mechanism of its dynamic coupling with the bR photocycle by automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) calculations and molecular dynamic (MD) simulations based on chemical shifts obtained by 2D solid-state NMR correlation experiments. We observed that Y185 plays a significant role in regulating the retinal cis–trans thermal equilibrium, stabilizing the pentagonal H-bond network, participating in the orientation switch of Schiff Base (SB) nitrogen, and opening the F42 gate by interacting with the retinal and several key residues along the proton translocation channel. Our findings provide a detailed molecular mechanism of the dynamic couplings of Y185 and the bR photocycle from a structural perspective. The method used in this paper may be applied to the study of other microbial photoreceptors.

Rapid assessment of Watson-Crick to Hoogsteen exchange in unlabeled DNA duplexes using high-power SELOPE imino 1H CEST

In duplex DNA, Watson-Crick A-T and G-C base pairs (bp's) exist in dynamic equilibrium with an alternative Hoogsteen conformation, which is low in abundance and short-lived. Measuring how the Hoogsteen dynamics varies across different DNA sequences, structural contexts and physiological conditions is key for identifying potential Hoogsteen hot spots and for understanding the potential roles of Hoogsteen base pairs in DNA recognition and repair. However, such studies are hampered by the need to prepare 13 C or 15 N isotopically enriched DNA samples for NMR relaxation dispersion (RD) experiments. Here, using SELective Optimized Proton Experiments (SELOPE) 1 H CEST experiments employing high-power radiofrequency fields (B 1  >  250 Hz) targeting imino protons, we demonstrate accurate and robust characterization of Watson-Crick to Hoogsteen exchange, without the need for isotopic enrichment of the DNA. For 13 residues in three DNA duplexes under different temperature and pH conditions, the exchange parameters deduced from high-power imino 1 H CEST were in very good agreement with counterparts measured using off-resonance 13 C /  15 N spin relaxation in the rotating frame (R 1 ρ ). It is shown that 1 H-1 H NOE effects which typically introduce artifacts in 1 H-based measurements of chemical exchange can be effectively suppressed by selective excitation, provided that the relaxation delay is short (≤  100 ms). The 1 H CEST experiment can be performed with ∼  10× higher throughput and ∼  100× lower cost relative to 13 C /  15 N R 1 ρ and enabled Hoogsteen chemical exchange measurements undetectable by R 1 ρ . The results reveal an increased propensity to form Hoogsteen bp's near terminal ends and a diminished propensity within A-tract motifs. The 1 H CEST experiment provides a basis for rapidly screening Hoogsteen breathing in duplex DNA, enabling identification of unusual motifs for more in-depth characterization.

Probabilistic Modeling of RNA Ensembles Using NMR Chemical Shifts

NMR-derived chemical shifts are structural fingerprints that are sensitive to the underlying conformational distributions of molecules. Thus, chemical shift data are now routinely used to infer the dynamical or conformational ensembles of peptides and proteins. However, for RNAs, techniques for inferring their conformational ensembles from chemical shift data have received less attention. Here, we used chemical shift data and the Bayesian/maximum entropy (BME) approach to model the secondary structure ensembles of several single-stranded RNAs. Inspection of the resulting ensembles indicates that the secondary structure of the highest weighted (most probable) conformer in the ensemble typically resembled the known NMR structure. Furthermore, using apo chemical shifts measured for the HIV-1 TAR RNA, we found that our framework reproduces the expected structure yet predicts the existence of a previously unobserved base pair, which we speculate may be sampled transiently. We expect that the chemical shift-based BME (CS-BME) framework we describe here should find utility as a general strategy for modeling RNA ensembles using chemical shift data.

A quantitative model predicts how m6A reshapes the kinetic landscape of nucleic acid hybridization and conformational transitions

N6-methyladenosine (m6A) is a post-transcriptional modification that controls gene expression by recruiting proteins to RNA sites. The modification also slows biochemical processes through mechanisms that are not understood. Using temperature-dependent (20°C-65°C) NMR relaxation dispersion, we show that m6A pairs with uridine with the methylamino group in the anti conformation to form a Watson-Crick base pair that transiently exchanges on the millisecond timescale with a singly hydrogen-bonded low-populated (1%) mismatch-like conformation in which the methylamino group is syn. This ability to rapidly interchange between Watson-Crick or mismatch-like forms, combined with different syn:anti isomer preferences when paired (~1:100) versus unpaired (~10:1), explains how m6A robustly slows duplex annealing without affecting melting at elevated temperatures via two pathways in which isomerization occurs before or after duplex annealing. Our model quantitatively predicts how m6A reshapes the kinetic landscape of nucleic acid hybridization and conformational transitions, and provides an explanation for why the modification robustly slows diverse cellular processes.

Developments in solution-state NMR yield broader and deeper views of the dynamic ensembles of nucleic acids

Nucleic acids do not fold into a single conformation, and dynamic ensembles are needed to describe their propensities to cycle between different conformations when performing cellular functions. We review recent advances in solution-state nuclear magnetic resonance (NMR) methods and their integration with computational techniques that are improving the ability to probe the dynamic ensembles of DNA and RNA. These include computational approaches for predicting chemical shifts from structure and generating conformational libraries from sequence, measurements of exact nuclear Overhauser effects, development of new probes to study chemical exchange using relaxation dispersion, faster and more sensitive real-time NMR techniques, and new NMR approaches to tackle large nucleic acid assemblies. We discuss how these advances are leading to new mechanistic insights into gene expression and regulation.

Automated fragmentation quantum mechanical calculation of 13C and 1H chemical shifts in molecular crystals

In this work, the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach was applied to calculate the ¹³C and ¹H nuclear magnetic resonance (NMR) chemical shifts in molecular crystals. Two benchmark sets of molecular crystals were selected to calculate the NMR chemical shifts. Systematic investigation was conducted to examine the convergence of AF-QM/MM calculations and the impact of various density functionals with different basis sets on the NMR chemical shift prediction. The result demonstrates that the calculated NMR chemical shifts are close to convergence when the distance threshold for the QM region is larger than 3.5 Å. For ¹³C chemical shift calculations, the mPW1PW91 functional is the best density functional among the functionals chosen in this study (namely, B3LYP, B3PW91, M06-2X, M06-L, mPW1PW91, OB98, and OPBE), while the OB98 functional is more suitable for the ¹H NMR chemical shift prediction of molecular crystals. Moreover, with the B3LYP functional, at least a triple-ζ basis set should be utilized to accurately reproduce the experimental ¹³C and ¹H chemical shifts. The employment of diffuse basis functions will further improve the accuracy for ¹³C chemical shift calculations, but not for the ¹H chemical shift prediction. We further proposed a fragmentation scheme of dividing the central molecule into smaller fragments. By comparing with the results of the fragmentation scheme using the entire central molecule as the core region, the AF-QM/MM calculations with the fragmented central molecule can not only achieve accurate results but also reduce the computational cost. Therefore, the AF-QM/MM approach is capable of predicting the ¹³C and ¹H NMR chemical shifts for molecular crystals accurately and effectively, and could be utilized for dealing with more complex periodic systems such as macromolecular polymers and biomacromolecules. The AF-QM/MM program for molecular crystals is available at https://github.com/shiman1995/NMR.

Structural and Molecular Dynamics of Mycobacterium tuberculosis Malic Enzyme, a Potential Anti-TB Drug Target

Tuberculosis (TB) is the most lethal bacterial infectious disease worldwide. It is notoriously difficult to treat, requiring a cocktail of antibiotics administered over many months. The dense, waxy outer membrane of the TB-causing agent, Mycobacterium tuberculosis (Mtb), acts as a formidable barrier against uptake of antibiotics. Subsequently, enzymes involved in maintaining the integrity of the Mtb cell wall are promising drug targets. Recently, we demonstrated that Mtb lacking malic enzyme (MEZ) has altered cell wall lipid composition and attenuated uptake by macrophages. These results suggest that MEZ contributes to lipid biosynthesis by providing reductants in the form of NAD(P)H. Here, we present the X-ray crystal structure of MEZ to 3.6 Å. We use biochemical assays to demonstrate MEZ is dimeric in solution and to evaluate the effects of pH and allosteric regulators on its kinetics and thermal stability. To assess the interactions between MEZ and its substrate malate and cofactors, Mn²⁺ and NAD(P)⁺, we ran a series of molecular dynamics (MD) simulations. First, the MD analysis corroborates our empirical observations that MEZ is unusually flexible, which persists even with the addition of substrate and cofactors. Second, the MD simulations reveal that dimeric MEZ subunits alternate between open and closed states, and that MEZ can stably bind its NAD(P)⁺ cofactor in multiple conformations, including an inactive, compact NAD⁺ form. Together the structure of MEZ and insights from its dynamics can be harnessed to inform the design of MEZ inhibitors that target Mtb and not human malic enzyme homologues.

Hybrid methods for combined experimental and computational determination of protein structure

Knowledge of protein structure is paramount to the understanding of biological function, developing new therapeutics, and making detailed mechanistic hypotheses. Therefore, methods to accurately elucidate three-dimensional structures of proteins are in high demand. While there are a few experimental techniques that can routinely provide high-resolution structures, such as x-ray crystallography, nuclear magnetic resonance (NMR), and cryo-EM, which have been developed to determine the structures of proteins, these techniques each have shortcomings and thus cannot be used in all cases. However, additionally, a large number of experimental techniques that provide some structural information, but not enough to assign atomic positions with high certainty have been developed. These methods offer sparse experimental data, which can also be noisy and inaccurate in some instances. In cases where it is not possible to determine the structure of a protein experimentally, computational structure prediction methods can be used as an alternative. Although computational methods can be performed without any experimental data in a large number of studies, inclusion of sparse experimental data into these prediction methods has yielded significant improvement. In this Perspective, we cover many of the successes of integrative modeling, computational modeling with experimental data, specifically for protein folding, protein-protein docking, and molecular dynamics simulations. We describe methods that incorporate sparse data from cryo-EM, NMR, mass spectrometry, electron paramagnetic resonance, small-angle x-ray scattering, Förster resonance energy transfer, and genetic sequence covariation. Finally, we highlight some of the major challenges in the field as well as possible future directions.

Accurate and cost-effective NMR chemical shift predictions for proteins using a molecules-in-molecules fragmentation-based method

We have developed an efficient protocol using our two-layer Molecules-in-Molecules (MIM2) fragmentation-based quantum chemical method for the prediction of NMR chemical shifts of large biomolecules. To investigate the performance of our fragmentation approach and demonstrate its applicability, MIM-NMR calculations are first calibrated on a test set of six proteins. The MIM2-NMR method yields a mean absolute deviation (MAD) from unfragmented full molecule calculations of 0.01 ppm for 1H and 0.06 ppm for 13C chemical shifts. Thus, the errors from fragmentation are only about 3% of our target accuracy of ∼0.3 ppm for 1H and 2-3 ppm for 13C chemical shifts. To compare with experimental chemical shifts, a standard protocol is first derived using two smaller proteins 2LHY (176 atoms) and 2LI1 (146 atoms) for obtaining an appropriate protein structure for NMR chemical shift calculations. The effect of the solvent environment on the calculated NMR chemical shifts is incorporated through implicit, explicit, or explicit-implicit solvation models. The expensive first solvation shell calculations are replaced by a micro-solvation model in which only the immediate interaction between the protein and the explicit solvation environment is considered. A single explicit water molecule for each amine and amide proton is found to be sufficient to yield accurate results for 1H chemical shifts. The 1H and 13C NMR chemical shifts calculated using our protocol give excellent agreement with experiments for two larger proteins, 2MC5 (the helical part with 265 atoms) and 3UMK (33 residue slice with 547 atoms). Overall, our target accuracy of ∼0.3 ppm for 1H and ∼2-3 ppm for 13C has been achieved for the larger proteins. The proposed MIM-NMR method is accurate and computationally cost-effective and should be applicable to study a wide range of large proteins.

Characterization of DNA G-quadruplex Topologies with NMR Chemical Shifts

G-quadruplexes are nucleic acid motifs formed by stacking of guanosine-tetrad pseudoplanes. They perform varied biological roles, and their distinctive structural features enable diverse applications. High-resolution structural characterization of G-quadruplexes is often time-consuming and expensive, calling for effective methods. Herein, we develop NMR chemical shifts and machine learning-based methodology that allows direct, rapid, and reliable analysis of canonical three-plane DNA G-quadruplexes sans isotopic enrichment. We show, for the first time, that each unique topology enforces a specific distribution of glycosidic torsion angles. Newly acquired carbon chemical shifts are exquisite probes for the dihedral angle distribution and provide immediate and unambiguous backbone topology assignment. The support vector machine learning methodology aids resonance assignment by providing plane indices for tetrad-forming guanosines. We further demonstrate the robustness by successful application of the methodology to a sequence that folds in two dissimilar topologies under different ionic conditions, providing its first atomic-level characterization.

Using quantum chemistry to estimate chemical shifts in biomolecules

An automated fragmentation quantum mechanics/molecular mechanics approach (AFNMR) has shown promising results in chemical shift calculations for biomolecules. Sample results for ubiquitin, and an RNA hairpin and helix are presented, and used to recent directions in quantum calculations. Trends in chemical shift are stable with regards to change in density functional or basis sets, and the use of the small "pcSseg-0" basis, which was optimized for chemical shift prediction [1], opens the way to more extensive conformational averaging, which can often be necessary, even for fairly well-defined structures.

Chemical shifts-based similarity restraints improve accuracy of RNA structures determined via NMR

Determination of structure of RNA via NMR is complicated in large part by the lack of a precise parameterization linking the observed chemical shifts to the underlying geometric parameters. In contrast to proteins, where numerous high-resolution crystal structures serve as coordinate templates for this mapping, such models are rarely available for smaller oligonucleotides accessible via NMR, or they exhibit crystal packing and counter-ion binding artifacts that prevent their use for the chemical shifts analysis. On the other hand, NMR-determined structures of RNA often are not solved at the density of restraints required to precisely define the variable degrees of freedom. In this study we sidestep the problems of direct parameterization of the RNA chemical shifts/structure relationship and examine the effects of imposing local fragmental coordinate similarity restraints based on similarities of the experimental secondary ribose ¹³C/¹H chemical shifts instead. The effect of such chemical shift similarity (CSS) restraints on the structural accuracy is assessed via residual dipolar coupling (RDC)-based cross-validation. Improvements in the coordinate accuracy are observed for all of the six RNA constructs considered here as test cases, which argues for routine inclusion of these terms during NMR-based oligonucleotide structure determination. Such accuracy improvements are expected to facilitate derivation of the chemical shift/structure relationships for RNA.

Rapid and accurate determination of atomistic RNA dynamic ensemble models using NMR and structure prediction

Biomolecules form dynamic ensembles of many inter-converting conformations which are key for understanding how they fold and function. However, determining ensembles is challenging because the information required to specify atomic structures for thousands of conformations far exceeds that of experimental measurements. We addressed this data gap and dramatically simplified and accelerated RNA ensemble determination by using structure prediction tools that leverage the growing database of RNA structures to generate a conformation library. Refinement of this library with NMR residual dipolar couplings provided an atomistic ensemble model for HIV-1 TAR, and the model accuracy was independently supported by comparisons to quantum-mechanical calculations of NMR chemical shifts, comparison to a crystal structure of a substate, and through designed ensemble redistribution via atomic mutagenesis. Applications to TAR bulge variants and more complex tertiary RNAs support the generality of this approach and the potential to make the determination of atomic-resolution RNA ensembles routine.

Determining dynamic ensembles of biomolecules is still challenging. Here the authors present an approach for rapid RNA ensemble determination that combines RNA structure prediction tools and NMR residual dipolar coupling data and use it to determine atomistic ensemble models for a variety of RNAs.

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.

Accurate Backbone 13 C and 15 N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate 13 C and 15 N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for 15 N atoms. Here we compare experimentally determined backbone 13 Cα and 15 NH chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed 15 NH chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.

Nuclear Magnetic Resonance of Single-Stranded RNAs and DNAs of CAAU and UCAAUC as Benchmarks for Molecular Dynamics Simulations

RNA and DNA are rapidly emerging as targets for therapeutics and as potential frameworks for nanotechnology. Accurate methods for predicting and designing structures and dynamics of nucleic acids would accelerate progress in these and other applications. Suitable approximations for modeling nucleic acids are being developed but require validation against disparate experimental observations. Here, nuclear magnetic resonance spectra for RNA and DNA single strands, CAAU and UCAAUC, are used as benchmarks to test molecular dynamics simulations with AMBER force fields OL3 and ROC-RNA for RNA and BSC1 for DNA. A detailed scheme for making comparisons is also presented. The results reflect recent progress in approximations and reveal remaining challenges.

Characterizing micro-to-millisecond chemical exchange in nucleic acids using off-resonance R1ρ relaxation dispersion

This review describes off-resonance R1ρ relaxation dispersion NMR methods for characterizing microsecond-to-millisecond chemical exchange in uniformly 13C/15N labeled nucleic acids in solution. The review opens with a historical account of key developments that formed the basis for modern R1ρ techniques used to study chemical exchange in biomolecules. A vector model is then used to describe the R1ρ relaxation dispersion experiment, and how the exchange contribution to relaxation varies with the amplitude and frequency offset of an applied spin-locking field, as well as the population, exchange rate, and differences in chemical shifts of two exchanging species. Mathematical treatment of chemical exchange based on the Bloch-McConnell equations is then presented and used to examine relaxation dispersion profiles for more complex exchange scenarios including three-state exchange. Pulse sequences that employ selective Hartmann-Hahn cross-polarization transfers to excite individual 13C or 15N spins are then described for measuring off-resonance R1ρ(13C) and R1ρ(15N) in uniformly 13C/15N labeled DNA and RNA samples prepared using commercially available 13C/15N labeled nucleotide triphosphates. Approaches for analyzing R1ρ data measured at a single static magnetic field to extract a full set of exchange parameters are then presented that rely on numerical integration of the Bloch-McConnell equations or the use of algebraic expressions. Methods for determining structures of nucleic acid excited states are then reviewed that rely on mutations and chemical modifications to bias conformational equilibria, as well as structure-based approaches to calculate chemical shifts. Applications of the methodology to the study of DNA and RNA conformational dynamics are reviewed and the biological significance of the exchange processes is briefly discussed.

Characterizing Watson-Crick versus Hoogsteen Base Pairing in a DNA-Protein Complex Using Nuclear Magnetic Resonance and Site-Specifically 13C- and 15N-Labeled DNA

A( syn)-T and G( syn)-C⁺ Hoogsteen base pairs in protein-bound DNA duplexes can be difficult to resolve by X-ray crystallography due to ambiguous electron density and by nuclear magnetic resonance (NMR) spectroscopy due to poor chemical shift dispersion and size limitations with solution-state NMR spectroscopy. Here we describe an NMR strategy for characterizing Hoogsteen base pairs in protein-DNA complexes, which relies on site-specifically incorporating ¹³C- and ¹⁵N-labeled nucleotides into DNA duplexes for unambiguous resonance assignment and to improve spectral resolution. The approach was used to resolve the conformation of an A-T base pair in a crystal structure of an ∼43 kDa complex between a 34 bp duplex DNA and the integration host factor (IHF) protein. In the crystal structure (Protein Data Bank entry 1IHF ), this base pair adopts an unusual Hoogsteen conformation with a distorted sugar backbone that is accommodated by a nearby nick used to aid in crystallization. The NMR chemical shifts and interproton nuclear Overhauser effects indicate that this base pair predominantly adopts a Watson-Crick conformation in the intact DNA-IHF complex under solution conditions. Consistent with these NMR findings, substitution of 7-deazaadenine at this base pair resulted in only a small (∼2-fold) decrease in the IHF-DNA binding affinity. The NMR strategy provides a new approach for resolving crystallographic ambiguity and more generally for studying the structure and dynamics of protein-DNA complexes in solution.

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.

Determination of accurate backbone chemical shift tensors in microcrystalline proteins by integrating MAS NMR and QM/MM

Chemical shifts are highly sensitive probes of local conformation and overall structure. Both isotropic shifts and chemical shift tensors are readily accessible from NMR experiments but their quantum mechanical calculations remain challenging. In this work, we report and compare accurately measured and calculated 15NH and 13Cα chemical shift tensors in proteins, using the microcrystalline agglutinin from Oscillatoria agardhii (OAA). Experimental 13Cα and 15NH chemical tensors were obtained by solid-state NMR spectroscopy, employing tailored recoupling sequences, and for their quantum mechanics/molecular mechanics (QM/MM) calculations different sets of functionals were evaluated. We show that 13Cα chemical shift tensors are primarily determined by backbone dihedral angles and dynamics, while 15NH tensors mainly depend on local electrostatic contributions from solvation and hydrogen bonding. In addition, the influence of including crystallographic waters, the molecular mechanics geometry optimization protocol, and the level of theory on the accuracy of the calculated chemical shift tensors is discussed. Specifically, the power of QM/MM calculations in accurately predicting the unusually upfield shifted 1HN G26 and G93 resonances is highlighted. Our integrated approach is expected to benefit structure refinement of proteins and protein assemblies.

Atomic structures of excited state A-T Hoogsteen base pairs in duplex DNA by combining NMR relaxation dispersion, mutagenesis, and chemical shift calculations

NMR relaxation dispersion studies indicate that in canonical duplex DNA, Watson-Crick base pairs (bps) exist in dynamic equilibrium with short-lived low abundance excited state Hoogsteen bps. N1-methylated adenine (m¹A) and guanine (m¹G) are naturally occurring forms of damage that stabilize Hoogsteen bps in duplex DNA. NMR dynamic ensembles of DNA duplexes with m¹A-T Hoogsteen bps reveal significant changes in sugar pucker and backbone angles in and around the Hoogsteen bp, as well as kinking of the duplex towards the major groove. Whether these structural changes also occur upon forming excited state Hoogsteen bps in unmodified duplexes remains to be established because prior relaxation dispersion probes provided limited information regarding the sugar-backbone conformation. Here, we demonstrate measurements of C3' and C4' spin relaxation in the rotating frame (R1ρ) in uniformly ¹³C/¹⁵N labeled DNA as sensitive probes of the sugar-backbone conformation in DNA excited states. The chemical shifts, combined with structure-based predictions using an automated fragmentation quantum mechanics/molecular mechanics method, show that the dynamic ensemble of DNA duplexes containing m¹A-T Hoogsteen bps accurately model the excited state Hoogsteen conformation in two different sequence contexts. Formation of excited state A-T Hoogsteen bps is accompanied by changes in sugar-backbone conformation that allow the flipped syn adenine to form hydrogen-bonds with its partner thymine and this in turn results in overall kinking of the DNA toward the major groove. Results support the assignment of Hoogsteen bps as the excited state observed in canonical duplex DNA, provide an atomic view of DNA dynamics linked to formation of Hoogsteen bps, and lay the groundwork for a potentially general strategy for solving structures of nucleic acid excited states.

Chemical Shifts of the Carbohydrate Binding Domain of Galectin-3 from Magic Angle Spinning NMR and Hybrid Quantum Mechanics/Molecular Mechanics Calculations

Magic angle spinning NMR spectroscopy is uniquely suited to probe the structure and dynamics of insoluble proteins and protein assemblies at atomic resolution, with NMR chemical shifts containing rich information about biomolecular structure. Access to this information, however, is problematic, since accurate quantum mechanical calculation of chemical shifts in proteins remains challenging, particularly for ¹⁵N^H. Here we report on isotropic chemical shift predictions for the carbohydrate recognition domain of microcrystalline galectin-3, obtained from using hybrid quantum mechanics/molecular mechanics (QM/MM) calculations, implemented using an automated fragmentation approach, and using very high resolution (0.86 Å lactose-bound and 1.25 Å apo form) X-ray crystal structures. The resolution of the X-ray crystal structure used as an input into the AF-NMR program did not affect the accuracy of the chemical shift calculations to any significant extent. Excellent agreement between experimental and computed shifts is obtained for ¹³C^α, while larger scatter is observed for ¹⁵N^H chemical shifts, which are influenced to a greater extent by electrostatic interactions, hydrogen bonding, and solvation.

Slow Dynamics of Tryptophan-Water Networks in Proteins

Water has a profound effect on the dynamics of biomolecules and governs many biological processes, leading to the concept that function is slaved to solvent dynamics within and surrounding the biomolecule. Protein conformational changes on μs-ms time scales are frequently associated with protein function, but little is known about the behavior of protein-bound water on these time scales. Here we have used NMR relaxation dispersion measurements to probe the tryptophan indoles in the enzyme dihydrofolate reductase (DHFR). We find that during structural changes on the μs-ms time scale, large chemical shift changes are often observed for the NH proton on the indole ring, while relatively smaller chemical shift changes are observed for the ring nitrogen atom. Comparison with experimental chemical shifts and density functional theory-based chemical shift predictions show that during the structural change the tryptophan indole NHs remain bound to water, but the geometry of the protein-bound water networks changes. These results establish that relaxation dispersion measurements can indirectly probe water dynamics and indicate that water can influence, or be influenced by, protein conformational changes on the μs-ms time scale. Our data show that structurally conserved bound water molecules can play a critical role in transmitting information between functionally important regions of the protein and provide evidence that internal protein motions can be coupled through the mediation of hydrogen-bonded water bound in the protein structure.

Insights into Watson-Crick/Hoogsteen breathing dynamics and damage repair from the solution structure and dynamic ensemble of DNA duplexes containing m1A

In the canonical DNA double helix, Watson-Crick (WC) base pairs (bps) exist in dynamic equilibrium with sparsely populated (∼0.02-0.4%) and short-lived (lifetimes ∼0.2-2.5 ms) Hoogsteen (HG) bps. To gain insights into transient HG bps, we used solution-state nuclear magnetic resonance spectroscopy, including measurements of residual dipolar couplings and molecular dynamics simulations, to examine how a single HG bp trapped using the N1-methylated adenine (m1A) lesion affects the structural and dynamic properties of two duplexes. The solution structure and dynamic ensembles of the duplexes reveals that in both cases, m1A forms a m1A•T HG bp, which is accompanied by local and global structural and dynamic perturbations in the double helix. These include a bias toward the BI backbone conformation; sugar repuckering, major-groove directed kinking (∼9°); and local melting of neighboring WC bps. These results provide atomic insights into WC/HG breathing dynamics in unmodified DNA duplexes as well as identify structural and dynamic signatures that could play roles in m1A recognition and repair.

Computing the Diamagnetic Susceptibility and Diamagnetic Anisotropy of Membrane Proteins from Structural Subunits

The behavior of large, complex molecules in the presence of magnetic fields is experimentally challenging to measure and computationally intensive to predict. This work proposes a novel, mixed-methods approach for efficiently computing the principal magnetic susceptibilities and diamagnetic anisotropy of membrane proteins. The hierarchical primary (amino acid), secondary (α helical and β sheet), and tertiary (α helix and β barrel) structure of transmembrane proteins enables analysis of a complex molecule using discrete subunits of varying size and resolution. The proposed method converts the magnetic susceptibility tensor for all protein subunits to a unit coordinate system and sums them to build the magnetic susceptibility tensor for the membrane protein. Using this approach, we calculate the diamagnetic anisotropy for all transmembrane proteins of known structure and investigate the effect of different subunit resolutions on the resulting predictions of diamagnetic anisotropy. We demonstrate that amino acid residues with aromatic side groups exhibit higher diamagnetic anisotropies. On average, high percentages of aromatic amino acid subunits, a β barrel tertiary structure, and a small volume are correlated with high volumetric diamagnetic anisotropy. Finally, we demonstrate that accounting for the spatial position of the residues with respect to one another is critical to accurately computing the magnetic properties of the complex protein molecule.

Toward Closing the Gap: Quantum Mechanical Calculations and Experimentally Measured Chemical Shifts of a Microcrystalline Lectin

NMR chemical shifts are exquisitely sensitive probes for conformation and dynamics in molecules and supramolecular assemblies. Although isotropic chemical shifts are easily measured with high accuracy and precision in conventional NMR experiments, they remain challenging to calculate quantum mechanically, particularly in inherently dynamic biological systems. Using a model benchmark protein, the 133-residue agglutinin from Oscillatoria agardhii (OAA), which has been extensively characterized by us previously, we have explored the integration of X-ray crystallography, solution NMR, MAS NMR, and quantum mechanics/molecular mechanics (QM/MM) calculations for analysis of 13Cα and 15NH isotropic chemical shifts. The influence of local interactions, quaternary contacts, and dynamics on the accuracy of calculated chemical shifts is analyzed. Our approach is broadly applicable and expected to be beneficial in chemical shift analysis and chemical-shift-based structure refinement for proteins and protein assemblies.

Automated Fragmentation Polarizable Embedding Density Functional Theory (PE-DFT) Calculations of Nuclear Magnetic Resonance (NMR) Shielding Constants of Proteins with Application to Chemical Shift Predictions

Full-protein nuclear magnetic resonance (NMR) shielding constants based on ab initio calculations are desirable, because they can assist in elucidating protein structures from NMR experiments. In this work, we present NMR shielding constants computed using a new automated fragmentation (J. Phys. Chem. B 2009, 113, 10380-10388) approach in the framework of polarizable embedding density functional theory. We extend our previous work to give both basis set recommendations and comment on how large the quantum mechanical region should be to successfully compute ¹³C NMR shielding constants that are comparable with experiment. The introduction of a probabilistic linear regression model allows us to substantially reduce the number of snapshots that are needed to make comparisons with experiment. This approach is further improved by augmenting snapshot selection with chemical shift predictions by which we can obtain a representative subset of snapshots that gives the smallest predicted error, compared to experiment. Finally, we use this subset of snapshots to calculate the NMR shielding constants at the PE-KT3/pcSseg-2 level of theory for all atoms in the protein GB3.

HIV-1 Capsid Function Is Regulated by Dynamics: Quantitative Atomic-Resolution Insights by Integrating Magic-Angle-Spinning NMR, QM/MM, and MD

HIV-1 CA capsid protein possesses intrinsic conformational flexibility, which is essential for its assembly into conical capsids and interactions with host factors. CA is dynamic in the assembled capsid, and residues in functionally important regions of the protein undergo motions spanning many decades of time scales. Chemical shift anisotropy (CSA) tensors, recorded in magic-angle-spinning NMR experiments, provide direct residue-specific probes of motions on nano- to microsecond time scales. We combined NMR, MD, and density-functional-theory calculations, to gain quantitative understanding of internal backbone dynamics in CA assemblies, and we found that the dynamically averaged 15N CSA tensors calculated by this joined protocol are in remarkable agreement with experiment. Thus, quantitative atomic-level understanding of the relationships between CSA tensors, local backbone structure, and motions in CA assemblies is achieved, demonstrating the power of integrating NMR experimental data and theory for characterizing atomic-resolution dynamics in biological systems.

ProCS15: a DFT-based chemical shift predictor for backbone and Cβ atoms in proteins

We present ProCS15: a program that computes the isotropic chemical shielding values of backbone and Cβ atoms given a protein structure in less than a second. ProCS15 is based on around 2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding. The ProCS15-predicted chemical shielding values are compared to experimentally measured chemical shifts for Ubiquitin and the third IgG-binding domain of Protein G through linear regression and yield RMSD values of up to 2.2, 0.7, and 4.8 ppm for carbon, hydrogen, and nitrogen atoms. These RMSD values are very similar to corresponding RMSD values computed using OPBE/6-31G(d,p) for the entire structure for each proteins. These maximum RMSD values can be reduced by using NMR-derived structural ensembles of Ubiquitin. For example, for the largest ensemble the largest RMSD values are 1.7, 0.5, and 3.5 ppm for carbon, hydrogen, and nitrogen. The corresponding RMSD values predicted by several empirical chemical shift predictors range between 0.7–1.1, 0.2–0.4, and 1.8–2.8 ppm for carbon, hydrogen, and nitrogen atoms, respectively.