Effects of Dynamics and Environment on 15N Chemical Shielding Anisotropy in Proteins. A Combination of Density Functional Theory, Molecular Dynamics Simulation, and NMR Relaxation

One touch is all it takes: the supramolecular interaction between ubiquitin and lanthanide complexes revisited by paramagnetic NMR and molecular dynamics

The supramolecular interaction between lanthanide complexes and proteins is at the heart of numerous chemical and biological studies. Some of these complexes have demonstrated remarkable interaction properties with proteins or peptides in solution and in the crystalline state. Here we have used the paramagnetism of lanthanide ions to characterize the affinity of two lanthanide complexes for ubiquitin. As the interaction process is dynamic, the acquired NMR data only reflect the time average of the different steps. We have used molecular dynamics (MD) simulations to get a deeper insight into the detailed interaction scenario at the microsecond scale. This NMR/MD approach enabled us to establish that the tris-dipicolinate complex interacts specifically with arginines and lysines, while the crystallophore explores the protein surface through weak interactions with carboxylates. These observations shed new light on the dynamic interaction properties of these complexes, which will ultimately enable us to propose a crystallization mechanism.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C' CSA-13C'-13Cα DD CCR rate [Formula: see text] and present a novel 3D version of the transverse [Formula: see text] CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

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.

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.

13C Direct Detected NMR for Challenging Systems

Thanks to recent improvements in NMR spectrometer hardware and pulse sequence design, modern 13C NMR has become a useful tool for biomolecular applications. The complete assignment of a protein can be accomplished by using 13C detected multinuclear experiments and it can provide unique information relevant for the study of a variety of different biomolecules including paramagnetic proteins and intrinsically disordered proteins. A wide range of NMR observables can be measured, concurring to the structural and dynamic characterization of a protein in isolation, as part of a larger complex, or even inside a living cell. We present the different properties of 13C with respect to 1H, which provide the rationale for the experiments developed and their application, the technical aspects that need to be faced, and the many experimental variants designed to address different cases. Application areas where these experiments successfully complement proton NMR are also described.

Solid-State NMR Dipolar and Chemical Shift Anisotropy Recoupling Techniques for Structural and Dynamical Studies in Biological Systems

With the development of NMR methodology and technology during the past decades, solid-state NMR (ssNMR) has become a particularly important tool for investigating structure and dynamics at atomic scale in biological systems, where the recoupling techniques play pivotal roles in modern high-resolution MAS NMR. In this review, following a brief introduction on the basic theory of recoupling in ssNMR, we highlight the recent advances in dipolar and chemical shift anisotropy recoupling methods, as well as their applications in structural determination and dynamical characterization at multiple time scales (i.e., fast-, intermediate-, and slow-motion). The performances of these prevalent recoupling techniques are compared and discussed in multiple aspects, together with the representative applications in biomolecules. Given the recent emerging advances in NMR technology, new challenges for recoupling methodology development and potential opportunities for biological systems are also discussed.

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.

Ab Initio Simulation of pH-Sensitive Biomarkers in Magnetic Resonance Imaging

An ab initio simulation scheme is introduced as a theoretical prescreening approach to facilitate and enhance the research for pH-sensitive biomarkers. The proton ¹H and carbon ¹³C nuclear magnetic resonance (NMR) chemical shifts of the recently published marker for extracellular pH, [1,5-¹³C₂]zymonic acid (ZA), and the as yet unpublished ( Z)-4-methyl-2-oxopent-3-enedioic acid (OMPD) were calculated with ab initio methods as a function of the pH. The influence of the aqueous solvent was taken into account either by an implicit solvent model or by explicit water molecules, where the latter improved the accuracy of the calculated chemical shifts considerably. The theoretically predicted chemical shifts allowed for a reliable NMR peak assignment. The p K_a value of the first deprotonation of ZA and OMPD was simulated successfully whereas the parametrization of the implicit solvent model does not allow for an accurate description of the second p K_a. The theoretical models reproduce the pH-induced chemical shift changes and the first p K_a with sufficient accuracy to establish the ab initio prescreening approach as a valuable support to guide the experimental search for pH-sensitive biomarkers.

Dynamics and Rigidity of an Intact Filamentous Bacteriophage Virus Probed by Magic Angle Spinning NMR

The capsid dynamics of filamentous bacteriophages is related to their function, stability, and interactions with the genome, and can be assessed by measuring the chemical shift anisotropy (CSA) of ¹⁵ N amides, which are sensitive to large amplitude motions. In this study, CSA recoupling experiments under magic-angle spinning NMR were used to probe the dynamics of the y21m capsid mutant of fd bacteriophage. Based on fitting the generated CSA lineshapes, residues located in the N-terminus undergo increased motional amplitudes suggesting its global motion, whereas other backbone residues are rigid, and imply a tight hydrophobic packing of the phage.

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.

The influence of Mg2+ coordination on 13C and 15N chemical shifts in CKI1RD protein domain from experiment and molecular dynamics/density functional theory calculations

Sequence dependence of (13) C and (15) N chemical shifts in the receiver domain of CKI1 protein from Arabidopsis thaliana, CKI1RD , and its complexed form, CKI1RD •Mg(2+), was studied by means of MD/DFT calculations. MD simulations of a 20-ns production run length were performed. Nine explicitly hydrated structures of increasing complexity were explored, up to a 40-amino-acid structure. The size of the model necessary depended on the type of nucleus, the type of amino acid and its sequence neighbors, other spatially close amino acids, and the orientation of amino acid NH groups and their surface/interior position. Using models covering a 10 and a 15 Å environment of Mg(2+), a semi-quantitative agreement has been obtained between experiment and theory for the V67-I73 sequence. The influence of Mg(2+) binding was described better by the 15 Å as compared to the 10 Å model. Thirteen chemical shifts were analyzed in terms of the effect of Mg(2+) insertion and geometry preparation. The effect of geometry was significant and opposite in sign to the effect of Mg(2+) binding. The strongest individual effects were found for (15) N of D70, S74, and V68, where the electrostatics dominated; for (13) Cβ of D69 and (15) N of K76, where the influences were equal, and for (13) Cα of F72 and (13) Cβ of K76, where the geometry adjustment dominated. A partial correlation between dominant geometry influence and torsion angle shifts upon the coordination has been observed.

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.

The structure of the SOLE element of oskar mRNA

mRNA localization by active transport is a regulated process that requires association of mRNPs with protein motors for transport along either the microtubule or the actin cytoskeleton. oskar mRNA localization at the posterior pole of the Drosophila oocyte requires a specific mRNA sequence, termed the SOLE, which comprises nucleotides of both exon 1 and exon 2 and is assembled upon splicing. The SOLE folds into a stem-loop structure. Both SOLE RNA and the exon junction complex (EJC) are required for oskar mRNA transport along the microtubules by kinesin. The SOLE RNA likely constitutes a recognition element for a yet unknown protein, which either belongs to the EJC or functions as a bridge between the EJC and the mRNA. Here, we determine the solution structure of the SOLE RNA by Nuclear Magnetic Resonance spectroscopy. We show that the SOLE forms a continuous helical structure, including a few noncanonical base pairs, capped by a pentanucleotide loop. The helix displays a widened major groove, which could accommodate a protein partner. In addition, the apical helical segment undergoes complex dynamics, with potential functional significance.

Cytochrome-P450-cytochrome-b5 interaction in a membrane environment changes 15N chemical shift anisotropy tensors

It has been well realized that the dependence of chemical shift anisotropy (CSA) tensors on the amino acid sequence, secondary structure, dynamics, and electrostatic interactions can be utilized in the structural and dynamic studies of proteins by NMR spectroscopy. In addition, CSA tensors could also be utilized to measure the structural interactions between proteins in a protein-protein complex. To this end, we report the experimentally measured backbone amide-(15)N CSA tensors for a membrane-bound 16.7 kDa full-length rabbit cytochrome-b5 (cytb5), in complexation with a 55.8 kDa microsomal rabbit cytochrome P450 2B4 (cytP4502B4). The (15)N-CSAs, determined using the (15)N CSA/(15)N-(1)H dipolar coupling transverse cross-correlated rates, for free cytb5 are compared with those for the cytb5 bound to cytP4502B4. An overall increase in backbone amide-(15)N transverse cross-correlated rates for the cytb5 residues in the cytb5-cytP450 complex is observed as compared to the free cytb5 residues. Due to fast spin-spin relaxation (T2) and subsequent broadening of the signals in the complex, we could measure amide-(15)N CSAs only for 48 residues of cytb5 as compared to 84 residues of free cytb5. We observed a change in (15)N CSA for most residues of cytb5 in the complex, as compared to free cytb5, suggesting a dynamic interaction between the oppositely charged surfaces of anionic cytb5 and cationic cytP450. The mean values of (15)N CSA determined for residues in helical, sheet, and turn regions of cytb5 in the complex are -184.5, -146.8, and -146.2 ppm, respectively, with an overall average value of -165.5 ppm (excluding the values from residues in more flexible termini). The measured CSA value for residues in helical conformation is slightly larger as compared to previously reported values. This may be attributed to the paramagnetic effect from Fe(III) of the heme in cytb5, which is similar to our previously reported values for the free cytb5.

An extrapolation method for the efficient calculation of molecular response properties within Born-Oppenheimer molecular dynamics

The calculation of molecular response properties in dynamic molecular systems is a major challenge that requires sampling over many steps of, e.g., Born-Oppenheimer molecular dynamics (BO-MD) simulations. We present an extrapolation scheme to accelerate such calculations for multiple steps within BO-MD trajectories or equivalently within other sampling methods of conformational space. The extrapolation scheme is related to the one introduced by Pulay and Fogarasi [Chem. Phys. Lett., 2004, 386, 272] for self-consistent field (SCF) energy calculations. We extend the extrapolation to the quantities within our density matrix-based Laplace-transformed coupled perturbed SCF (DL-CPSCF) method that allows for linear-scaling calculations of response properties for large molecular systems. Here, we focus on the example of calculating NMR chemical shifts for which the number of required DL-CPSCF iterations reduces by roughly 40-70%.

Quantum chemical calculations of amide-15N chemical shift anisotropy tensors for a membrane-bound cytochrome-b5

There is considerable interest in determining amide-(15)N chemical shift anisotropy (CSA) tensors from biomolecules and understanding their variation for structural and dynamics studies using solution and solid-state NMR spectroscopy and also by quantum chemical calculations. Due to the difficulties associated with the measurement of CSA tensors from membrane proteins, NMR-based structural studies heavily relied on the CSA tensors determined from model systems, typically single crystals of model peptides. In the present study, the principal components of backbone amide-(15)N CSA tensors have been determined using density functional theory for a 16.7 kDa membrane-bound paramagnetic heme containing protein, cytochrome-b(5) (cytb(5)). All the calculations were performed by taking residues within 5 Å distance from the backbone amide-(15)N nucleus of interest. The calculated amide-(15)N CSA spans agree less well with our solution NMR data determined for an effective internuclear distance r(N-H) = 1.023 Å and a constant angle β = 18° that the least shielded component (δ(11)) makes with the N-H bond. The variation of amide-(15)N CSA span obtained using quantum chemical calculations is found to be smaller than that obtained from solution NMR measurements, whereas the trends of the variations are found to be in close agreement. We believe that the results reported in this study will be useful in studying the structure and dynamics of membrane proteins and heme-containing proteins, and also membrane-bound protein-protein complexes such as cytochromes-b5-P450.

Determination of 15N chemical shift anisotropy from a membrane-bound protein by NMR spectroscopy

Chemical shift anisotropy (CSA) tensors are essential in the structural and dynamic studies of proteins using NMR spectroscopy. Results from relaxation studies in biomolecular solution and solid-state NMR experiments on aligned samples are routinely interpreted using well-characterized CSA tensors determined from model compounds. Since CSA tensors, particularly the (15)N CSA, highly depend on a number of parameters including secondary structure, electrostatic interaction, and the amino acid sequence, there is a need for accurately determined CSA tensors from proteins. In this study, we report the backbone amide-(15)N CSA tensors for a 16.7-kDa membrane-bound and paramagnetic-heme containing protein, rabbit Cytochrome b(5) (cytb(5)), determined using the (15)N CSA/(15)N-(1)H dipolar transverse cross-correlation rates. The mean values of (15)N CSA determined for residues in helical, sheet, and turn regions are -187.9, -166.0, and -161.1 ppm, respectively, with an overall average value of -171.7 ppm. While the average CSA value determined from this study is in good agreement with previous solution NMR experiments on small globular proteins, the CSA value determined for residues in helical conformation is slightly larger, which may be attributed to the paramagnetic effect from Fe(III) of the heme unit in cytb(5). However, like in previous solution NMR studies, the CSA values reported in this study are larger than the values measured from solid-state NMR experiments. We believe that the CSA parameters reported in this study will be useful in determining the structure, dynamics, and orientation of proteins, including membrane proteins, using NMR spectroscopy.

Calculation of chemical shift anisotropy in proteins

Individual peptide groups in proteins must exhibit some variation in the chemical shift anisotropy (CSA) of their constituent atoms, but not much is known about the extent or origins of this dispersion. Direct spectroscopic measurement of CSA remains technically challenging, and theoretical methods can help to overcome these limitations by estimating shielding tensors for arbitrary structures. Here we use an automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach to compute (15)N, (13)C' and (1)H chemical shift tensors for human ubiquitin and the GB1 and GB3 fragments of staphylococcal protein G. The average and range of variation of the anisotropies is in good agreement with experimental estimates from solid-state NMR, and the variation among residues is somewhat smaller than that estimated from solution-state measurements. Hydrogen-bond effects account for much of the variation, both between helix and sheet regions, and within elements of secondary structure, but other effects (including variations in torsion angles) may play a role as well.

Protein NMR chemical shift calculations based on the automated fragmentation QM/MM approach

An automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach has been developed to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field (SCF) calculations of the NMR chemical shieldings for the mini-protein Trp cage. The root-mean-square errors (RMSEs) for 1H, 13C, and 15N NMR chemical shieldings are equal to or less than 0.09, 0.32, and 0.78 ppm, respectively, for all Hartree-Fock (HF) and density functional theory (DFT) calculations reported in this work. The environmental electrostatic potential is necessary to accurately reproduce the NMR chemical shieldings using the AF-QM/MM approach. The point-charge models provided by AMBER, AM1/CM2, PM3/CM1, and PM3/CM2 all effectively model the electrostatic field. The latter three point-charge models are generated via semiempirical linear-scaling SCF calculations of the entire protein system. The correlations between experimental 1H NMR chemical shifts and theoretical predictions are >0.95 for AF-QM/MM calculations using B3LYP with the 6-31G**, 6-311G**, and 6-311++G** basis sets. Our study, not unexpectedly, finds that conformational changes within a protein structure play an important role in the accurate prediction of experimental NMR chemical shifts from theory.

Utilizing the charge field effect on amide (15)N chemical shifts for protein structure validation

Of all the nuclei in proteins, the nuclear magnetic resonance (NMR) chemical shifts of nitrogen are the theoretically least well understood. In this study, quantum chemical methods are used in combination with polarizable-continuum models in order to show that consideration of the effective electric field, including charge screening due to solvation, improves considerably the consistencies of statistical relationships between experimental and computed amide (15)N shifts between various sets of charged and uncharged oligopeptides and small organic molecules. A single conversion scheme between shielding parameters from first principles using density functional theory (DFT) and experimental shifts is derived that holds for all classes of compounds examined here. This relationship is then used to test the accuracy of such (15)N chemical shift predictions in the cyclic decapeptide antibiotic gramicidin S (GS). GS has previously been studied in great detail, both by NMR and X-ray crystallography. It adopts a well-defined backbone conformation, and hence, only a few discrete side chain conformational states need to be considered. Moreover, a charge-relay effect of the two cationic ornithine side chains to the protein backbone has been described earlier by NMR spectroscopy. Here, DFT-derived backbone amide nitrogen chemical shifts were calculated for multiple conformations of GS. Overall, the structural dynamics of GS is revisited in view of chemical shift behavior along with energetic considerations. Together, the study demonstrates proof of concept that (15)N chemical shift information is particularly useful in the analysis and validation of protein conformational states in a charged environment.

Density functional theory investigation of hydrogen bonding effects on the oxygen, nitrogen and hydrogen electric field gradient and chemical shielding tensors of anhydrous chitosan crystalline structure

A systematic computational investigation was carried out to characterize the 17O, 14N and 2H electric field gradient, EFG, as well as 17O, 15N, 13C and 1H chemical shielding tensors in the anhydrous chitosan crystalline structure. To include the hydrogen-bonding effects in the calculations, the most probable interacting molecules with the target molecule in the crystalline phase were considered through a hexameric cluster. The computations were performed with the B3LYP method and 6-311++G(d,p) and 6-31++G(d,p) standard basis sets using the Gaussian 98 suite of programs. Calculated EFG and chemical shielding tensors were used to evaluate the 17O, 14N and 2H nuclear quadrupole resonance, NQR, and 17O, 15N, 13C and 1H nuclear magnetic resonance, NMR, parameters in the hexameric cluster, which are in good agreement with the available experimental data. The difference between the calculated NQR and NMR parameters of the monomer and hexamer cluster shows how much hydrogen bonding interactions affect the EFG and chemical shielding tensors of each nucleus. These results indicate that both O(3)-H(33)...O(5-3) and N-H(22)...O(6-4) hydrogen bonding have a major influence on NQR and NMR parameters. Also, the quantum chemical calculations indicate that the intra- and intermolecular hydrogen bonding interactions play an essential role in determining the relative orientation of EFG and chemical shielding principal components in the molecular frame axes.

Determination of the residue-specific 15N CSA tensor principal components using multiple alignment media

The individual components of the backbone (15)N CSA tensor, sigma(11), sigma(22), sigma(33), and the orientation of sigma(11) relative to the NH bond described by the angle beta have been determined for uniformly labeled (15)N, (13)C ubiquitin from partial alignment in phospholipid bicelles, Pf1 phage, and poly(ethylene glycol) by measuring the residue-specific residual dipolar couplings and chemical shift deviations. No strong correlation between any of the CSA tensor components is observed with any single structural feature. However, the experimentally determined tensor components agree with the previously determined average CSA principal components [Cornilescu and Bax (2000) J. Am. Chem. Soc. 122, 10143-10154]. Significant deviations from the averages coincide with residues in beta-strand or extended regions, while alpha-helical residue tensor components cluster close to the average values.

Single-Crystal Studies of Peptide Prolyl and Glycyl 15N Shielding Tensors

15N shielding tensors were determined for the central peptide groups in GGV, AGG, and APG by single-crystal NMR. We find that the angle between the downfield component (delta11) and the N-H or the N-C(delta) (pro) bonds is in the range of 20-23 degrees and in accord with previous solid-state NMR measurements. However, AGG, unlike APG or GGV, has a distorted peptide plane, and delta11 lies approximately in the plane of N, C(alpha), and H rather than in the peptide plane defined by heavy atoms. Accurate orientations of delta22 and delta33 were determined, and the usual assumption that delta22 is along the peptide normal was found only in APG which has a highly nonaxial tensor. More generally, delta22 and delta33 are rotated about the delta11 axis (36 degrees in GGV). These results are compared with DFT calculations to gain a structural understanding of the effects of intermolecular interactions on shielding tensor principal components and orientations. Trimeric clusters containing H-bonded neighbors predict the orientations of the principal components within 2-3 degrees, but calculated principal components are less quantitative. Possible reasons for this disagreement are explored.

Estimates of methyl 13C and 1H CSA values (Deltasigma) in proteins from cross-correlated spin relaxation

Simple pulse schemes are presented for the measurement of methyl (13)C and (1)H CSA values from (1)H-(13)C dipole/(13)C CSA and (1)H-(13)C dipole/(1)H CSA cross-correlated relaxation. The methodology is applied to protein L and malate synthase G. Average (13)C CSA values are considerably smaller for Ile than Leu/Val (17 vs 25 ppm) and are in good agreement with previous solid state NMR studies of powders of amino acids and dipeptides and in reasonable agreement with quantum-chemical DFT calculations of methyl carbon CSA values in peptide fragments. Small averaged (1)H CSA values on the order of 1 ppm are measured, consistent with a solid state NMR determination of the methyl group (1)H CSA in dimethylmalonic acid.

Measurement of 15N chemical shift anisotropy in a protein dissolved in a dilute liquid crystalline medium with the application of magic angle sample spinning

The chemical shifts of nuclei that have chemical shielding anisotropy, such as the 15N amide in a protein, show significant changes in their chemical shifts when the sample is altered from an isotropic state to an aligned state. Such orientation-dependent chemical shift changes provide information on the magnitudes and orientation of the chemical shielding tensors relative to the molecule's alignment frame. Because of the extremely high sensitivity of the chemical shifts to the sample conditions, the changes in chemical shifts induced by adding aligned bicelles do not arise only from the protein alignment but should also include the accumulated effects of environmental changes including protein-bicelle interactions. With the aim of determining accurate 15N chemical shielding tensor values for solution proteins, here we have used magic angle sample spinning (MAS) to observe discriminately the orientation-dependent changes in the 15N chemical shift. The application of MAS to an aligned bicelle solution removes the torque that aligns the bicelles against the magnetic field. Thus, the application of MAS to a protein in a bicelle solution eliminates only the molecular alignment effect, while keeping all other sample conditions the same. The observed chemical shift differences between experiments with and without MAS therefore provide accurate values of the orientation-dependent 15N chemical shifts. From the values for ubiquitin in a 7.5% (w/v) bicelle medium, we determined the 15N chemical shielding anisotropy (CSA) tensor. For this evaluation, we considered uncertainties in measuring the 1H-15N dipolar couplings and the 15N chemical shifts and also structural noise present in the reference X-ray structure, assuming a random distribution of each NH bond vector in a cone with 5 degrees deviation from the original orientation. Taking into account these types of noise, we determined the average 15N CSA tensor for the residues in ubiquitin as Delta sigma=-162.0+/-4.3 ppm, eta=0.18+/-0.02, and beta=18.6+/-0.5 degrees, assuming a 1H-15N bond length of 1.02 A. These tensor values are consistent with those obtained from solid-state NMR experiments.

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.

Determination of the chemical shielding tensor orientation from two or one of the three conventional rotations of a single crystal

Chemical shift anisotropy (CSA) is an immensely useful interaction to study the structure, dynamics, and function of a wide variety of chemical and biological molecules. Traditionally the only unambiguous way to determine both the principal values and the orientation of the principal axes of the CSA tensor has been to follow the chemical shift frequency changes as a crystal of known structure is rotated relative to the direction of the external magnetic field. This classic method employs rotations about three mutually orthogonal axes of a single crystal. It is shown here that just two, or one, of the above rotations suffice to determine the CSA tensor orientation by borrowing, the easy to obtain, principal values of CSA from an independent source. Methods for using two rotation patterns or even a single rotation pattern are described and illustrated with known chemical shielding tensors.

Determination of carbon-13 chemical shielding tensor in the liquid state by combining NMR relaxation experiments and quantum chemical calculations

Based on multifield NMR relaxation measurements and quantum chemistry calculations, a strategy aiming at the determination of the chemical shielding tensor (CST) in the liquid state is described. Brownian motions in the liquid state restrict the direct observation of CST to a third of its trace (isotropic shift), and even if CST can be probed indirectly through some spin relaxation rates (specific longitudinal relaxation rates, dipolar chemical shift anisotropy (CSA) cross-correlation rates), an insufficient number of experimental parameters prevents its complete determination. This lack of information can be compensated by using quantum chemical calculations so as to obtain the molecular CST orientation even if a relatively modest level of computation is used. As relaxation parameters involve a dynamic part, a prerequisite is the determination of the molecular anisotropic reorientation which can be obtained independently from dipolar cross-relaxation rates. A polycyclic molecule exhibiting a well-characterized anisotropic reorientation serves as an example for such a study, and some (but not all) carbon-13 chemical shielding tensors can be accurately determined. A comparison with solid-state NMR data and numerous chemical quantum calculations are presented.

Nmr probes of molecular dynamics: overview and comparison with other techniques

NMR spin relaxation spectroscopy is a powerful approach for characterizing intramolecular and overall rotational motions in proteins. This review describes experimental methods for measuring laboratory frame spin relaxation rate constants by high-resolution solution-state NMR spectroscopy, together with theoretical approaches for interpreting spin relaxation data in order to quantify protein conformational dynamics on picosecond-nanosecond time scales. Recent applications of these techniques to proteins are surveyed, and investigations of the contribution of conformational chain entropy to protein function are highlighted. Insights into the dynamical properties of proteins obtained from NMR spin relaxation spectroscopy are compared with results derived from other experimental and theoretical techniques.

Separating structure and dynamics in CSA/DD cross-correlated relaxation: a case study on trehalose and ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of (13)C CSA and (13)C-(1)H dipolar coupling in a disaccharide, alpha,alpha-D-trehalose, at natural abundance of (13)C as well as interference of amide (15)N CSA and (15)N-(1)H dipolar coupling in uniformly (15)N-labeled ubiquitin. We demonstrate that the standard heteronuclear T(1), T(2), and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.

(13)C chemical shift and (13)C-(14)N dipolar coupling tensors determined by (13)C rotary resonance solid-state NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of (13)C chemical shift tensors relative to one or more (13)C--(14)N internuclear axes from (13)C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic (13)C chemical shift and (13)C--(14)N dipole--dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the (13)C spins only. The method is demonstrated by experiments and numerical simulations for the (13)C(alpha) spins in powder samples of L-alanine and glycine with (13)C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential (14)N spins in a peptide chain ((14)N(i)--(13)C(alpha)(i)--(14)N(i+1) and (14)N(i+1)--(13)C'(i)--(14)N(i) three-spin systems) as well as residual quadrupolar-dipolar coupling cross-terms is analyzed numerically.

A Bayesian statistical method for the detection and quantification of rotational diffusion anisotropy from NMR relaxation data

It has recently become more widely appreciated that the presence of rotational diffusional anisotropy in proteins and other macromolecules can have a significant affect on the interpretation of NMR relaxation data in terms of molecular motion. In this paper, we show how commonly used NMR relaxation data (R(1), R(2), and NOE) obtained at two spectrometer frequencies can be analyzed using a Bayesian statistical approach to reliably detect and quantify the degree of rotational diffusion anisotropy. Our approach differs from previous methods in that it does not make assumptions concerning the internal motions experienced by the residues which are used to quantify the diffusion anisotropy, but rather averages the results over all internal motions consistent with the data. We demonstrate our method using synthetic data corresponding to isotropic, axially symmetric anisotropic, and fully asymmetric anisotropic rotational diffusion, as well as experimental NMR data. We compare the Bayesian statistical approach with a widely used method for extracting tumbling parameters using both synthetic and experimental data. While it can be difficult to separate the effects of chemical exchange from rotational anisotropy using this "standard" method, these effects are readily separated using Bayesian statistics. In addition, we find that the Bayesian statistical approach requires considerably less CPU time than an equivalent standard analysis.