Residue-Specific 13C‘ CSA Tensor Principal Components for Ubiquitin: Correlation between Tensor Components and Hydrogen Bonding

Scaled recoupling of chemical shift anisotropies at high magnetic fields under MAS with interspersed C-elements

The power of chemical shift anisotropy (CSA) measurements for probing structure and dynamics of molecules has been long recognized. NMR pulse sequences that allow measurement of CSA values in an indirect dimension of a protein correlation spectrum have been employed for aliphatic groups, but for practical reasons, carbonyl functional groups have been little studied, despite the fact that carbonyls are expected to give particularly varied and informative CSA values. Specifically, the wide spectral widths of carbonyl tensors make their measurements difficult with typically attainable spectrometer settings. We present here an extended family of experiments that enable the recovery of static CSA lineshapes in an indirect dimension of magic angle spinning (MAS) solid-state NMR experiments, except for various real valued scaling factors. The experiment is suitable for uniformly labeled material, at moderate MAS rates (10 kHz-30 kHz) and at higher magnetic fields (ν_0H > 600 MHz). Specifically, the experiments are based on pulse sequence elements from a previous commonly used pulse sequence for CSA measurement, recoupling of chemical shift anisotropy (ROCSA), while modification of scaling factors is achieved by interspersing different blocks of C-elements of the same Cn_n ¹ cycle. Using experimental conditions similar to the parent ROCSA sequence, a CSA scaling factor between 0 and 0.272 can be obtained, thus allowing a useful practical range of possibilities in experimental conditions for measurement of larger CSA values. Using these blocks, it is also possible to make a constant-time CSA recoupling sequence. The effectiveness of this approach, fROCSA, is shown on model compounds 1-¹³C-Gly, U-¹³C,¹⁵N-l-His, and microcrystalline U-¹³C,¹⁵N-Ubiquitin.

Phase-sensitive γ-encoded recoupling of heteronuclear dipolar interactions and 1H chemical shift anisotropy

γ-encoded recoupling sequences are known to produce strong amplitude modulations that lead to sharp doublets when Fourier transformed. These doublets depend very little on the recoupled tensor asymmetry and thus enable for the straightforward determination of dynamic order parameters. It can, however, be difficult to measure small anisotropies, or small order parameters, using such sequences; the resonances from the doublet may overlap with each other, or with the zero-frequency glitch. This limitation has prevented the widespread use of ¹H chemical shift anisotropy (CSA) for the measurement of dynamics, particularly for CH protons which typically have CSAs of only a few ppm when immobile. Here, we introduce a simple modification to the traditional ¹H CSA and proton-detected local field pulse sequences that enables the acquisition of a hypercomplex dataset and the removal of the uncorrelated magnetization that results in the zero-frequency glitch. These new sequences then yield a frequency shift in the indirect dimension, rather than a splitting, which is easily identifiable even in cases of weak interactions.

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.

The use of residual dipolar coupling in studying proteins by NMR

The development of residual dipolar coupling (RDC) in protein NMR spectroscopy, over a decade ago, has become a useful and almost routine tool for accurate protein solution structure determination. RDCs provide orientation information of magnetic dipole-dipole interaction vectors within a common reference frame. Its measurement requires a nonisotropic orientation, through a direct or indirect magnetic field alignment, of the protein in solution. There has been recent progress in the developments of alignment methods to allow the measurement of RDC and of methods to analyze the resulting data. In this chapter we briefly go through the mathematical expressions for the RDC and common descriptions of the alignment tensor, which may be represented using either Saupe order or the principal order matrix. Then we review the latest developments in alignment media. In particular we looked at the lipid-compatible media that allow the measurement of RDCs for membrane proteins. Other methods including conservative surface residue mutation have been invented to obtain up to five orthogonal alignment tensors that provide a potential for de novo structure and dynamics study using RDCs exclusively. We then discuss approximations assumed in RDC interpretations and different views on dynamics uncovered from the RDC method. In addition to routine usage of RDCs in refining a single structure, novel applications such as ensemble refinement against RDCs have been implemented to represent protein structure and dynamics in solution. The RDC application also extends to the study of protein-substrate interaction as well as to solving quaternary structure of oligomer in equilibrium with a monomer, opening an avenue for RDCs in high-order protein structure determination.

The impact of hydrogen bonding on amide 1H chemical shift anisotropy studied by cross-correlated relaxation and liquid crystal NMR spectroscopy

Site-specific ¹H chemical shift anisotropy (CSA) tensors have been derived for the well-ordered backbone amide moieties in the B3 domain of protein G (GB3). Experimental input data include residual chemical shift anisotropy (RCSA), measured in six mutants that align differently relative to the static magnetic field when dissolved in a liquid crystalline Pf1 suspension, and cross-correlated relaxation rates between the ¹H^N CSA tensor and either the ¹H−¹⁵N, the ¹H−¹³C′, or the ¹H−¹³C^α dipolar interactions. Analyses with the assumption that the ¹H^N CSA tensor is symmetric with respect to the peptide plane (three-parameter fit) or without this premise (five-parameter fit) yield very similar results, confirming the robustness of the experimental input data, and that, to a good approximation, one of the principal components orients orthogonal to the peptide plane. ¹H^N CSA tensors are found to deviate strongly from axial symmetry, with the most shielded tensor component roughly parallel to the N−H vector, and the least shielded component orthogonal to the peptide plane. DFT calculations on pairs of N-methyl acetamide and acetamide in H-bonded geometries taken from the GB3 X-ray structure correlate with experimental data and indicate that H-bonding effects dominate variations in the ¹H^N CSA. Using experimentally derived ¹H^N CSA tensors, the optimal relaxation interference effect needed for narrowest ¹H^N TROSY line widths is found at ∼1200 MHz.

Site-specific backbone amide (15)N chemical shift anisotropy tensors in a small protein from liquid crystal and cross-correlated relaxation measurements

Site-specific (15)N chemical shift anisotropy (CSA) tensors have been derived for the well-ordered backbone amide (15)N nuclei in the B3 domain of protein G (GB3) from residual chemical shift anisotropy (RCSA) measured in six different mutants that retain the native structure but align differently relative to the static magnetic field when dissolved in a liquid crystalline Pf1 suspension. This information is complemented by measurement of cross-correlated relaxation rates between the (15)N CSA tensor and either the (15)N-(1)H or (15)N-(13)C' dipolar interaction. In agreement with recent solid state NMR measurements, the (15)N CSA tensors exhibit only a moderate degree of variation from averaged values, but have larger magnitudes in alpha-helical (-173 +/- 7 ppm) than in beta-sheet (-162 +/- 6 ppm) residues, a finding also confirmed by quantum computations. The orientations of the least shielded tensor component cluster tightly around an in-peptide-plane vector that makes an angle of 19.6 +/- 2.5 degrees with the N-H bond, with the asymmetry of the (15)N CSA tensor being slightly smaller in alpha-helix (eta = 0.23 +/- 0.17) than in beta-sheet (eta = 0.31 +/- 0.11). The residue-specific (15)N CSA values are validated by improved agreement between computed and experimental (15)N R(1rho) relaxation rates measured for (15)N-{(2)H} sites in GB3, which are dominated by the CSA mechanism. Use of residue-specific (15)N CSA values also results in more uniform generalized order parameters, S(2), and predicts considerable residue-by-residue variations in the magnetic field strengths where TROSY line narrowing is most effective.

Multidimensional solid state NMR of anisotropic interactions in peptides and proteins

Accurate determinations of chemical shift anisotropy (CSA) tensors are valuable for NMR of biological systems. In this review we describe recent developments in CSA measurement techniques and applications, particularly in the context of peptides and proteins. These techniques include goniometeric measurements of single crystals, slow magic-angle spinning studies of powder samples, and CSA recoupling under moderate to fast MAS. Experimental CSA data can be analyzed by comparison with ab initio calculations for structure determination and refinement. This approach has particularly high potential for aliphatic (13)C analysis, especially Calpha tensors which are directly related to structure. Carbonyl and (15)N CSA tensors demonstrate a more complex dependence upon hydrogen bonding and electrostatics, in addition to conformational dependence. The improved understanding of these tensors and the ability to measure them quantitatively provide additional opportunities for structure determination, as well as insights into dynamics.

Assignment of congested NMR spectra: carbonyl backbone enrichment via the Entner-Doudoroff pathway

In NMR spectra of complex proteins, sparse isotope enrichment can be important, in that the removal of many (13)C-(13)C homonuclear J-couplings can narrow the lines and thereby facilitate the process of spectral assignment and structure elucidation. We present a simple scheme for selective yet extensive isotopic enrichment applicable for production of proteins in organisms utilizing the Entner-Doudoroff (ED) metabolic pathway. An enrichment scheme so derived is demonstrated in the context of a magic-angle spinning solid-state NMR (MAS SSNMR) study of Pf1 bacteriophage, the host of which is Pseudomonas aeruginosa, strain K (PAK), an organism that uses the ED pathway for glucose catabolism. The intact and infectious Pf1 phage in this study was produced by infected PAK cells grown on a minimal medium containing 1-(13)C d-glucose ((13)C in position 1) as the sole carbon source, as well as (15)NH(4)Cl as the only nitrogen source. The 37MDa Pf1 phage consists of about 93% major coat protein, 1% minor coat proteins, and 6% single-stranded, circular DNA. As a consequence of this composition and the enrichment scheme, the resonances in the MAS SSNMR spectra of the Pf1 sample were almost exclusively due to carbonyl carbons in the major coat protein. Moreover, 3D heteronuclear NCOCX correlation experiments also show that the amino acids leucine, serine, glycine, and tyrosine were not isotopically enriched in their carbonyl positions (although most other amino acids were), which is as expected based upon considerations of the ED metabolic pathway. 3D NCOCX NMR data and 2D (15)N-(15)N data provided strong verification of many previous assignments of (15)N amide and (13)C carbonyl shifts in this highly congested spectrum; both the semi-selective enrichment patterns and the narrowed linewidths allowed for greater certainty in the assignments as compared with use of uniformly enriched samples alone.

Vibrational averaging of chemical shift anisotropies in model peptides

The effects of chemical shift anisotropy (CSA) are evident in line-shapes or side-band analysis in solid-state NMR, in the observed line positions in partially oriented samples, and in relaxation effects in liquid-state studies. In all of these cases, the effective shielding tensor is influenced by fast vibrational averaging in addition to larger-amplitude internal motions and to overall libration or rotation. Here we compute the contributions of vibrational averaging (including zero-point motions) to the CSA relaxation strengths for the nitrogen and carbonyl carbon in two simple peptide models, and for snapshots taken from a path-integral simulation of a small protein. Because the (15)N shielding tensor is determined by all the atoms of the peptide group, it is less influenced by vibrational motion than (for example) the N-H dipolar interaction, which is more sensitive to the motion of the light hydrogen atom. Computed order parameters for CSA averaging are hence much closer to unity than are N-H dipolar order parameters. This leads to a reduction by about 9% in the magnitude of the amide nitrogen CSA that is needed to fit liquid-state relaxation data. Similar considerations apply to the carbonyl carbon shielding tensor, but in this case the differences between dipolar and CSA averaging are smaller. These considerations will be important for making comparisons between CSA tensors extracted from various NMR experiments, and for comparisons to quantum chemical calculations carried out on static conformers.