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

Single-crystal NMR spectroscopy

Single-crystal (SC) NMR spectroscopy is a solid-state NMR method that has been used since the early days of NMR to study the magnitude and orientation of tensorial nuclear spin interactions in solids. This review first presents the field of SC NMR instrumentation, then provides a survey of software for analysis of SC NMR data, and finally it highlights selected applications of SC NMR in various fields of research. The aim of the last part is not to provide a complete review of all SC NMR literature but to provide examples that demonstrate interesting applications of SC NMR.

Determination of relative orientation between (1)H CSA tensors from a 3D solid-state NMR experiment mediated through (1)H/(1)H RFDR mixing under ultrafast MAS

To obtain piercing insights into inter and intramolecular H-bonding, and π-electron interactions measurement of (1)H chemical shift anisotropy (CSA) tensors is gradually becoming an obvious choice. While the magnitude of CSA tensors provides unique information about the local electronic environment surrounding the nucleus, the relative orientation between these tensors can offer further insights into the spatial arrangement of interacting nuclei in their respective three-dimensional (3D) space. In this regard, we present a 3D anisotropic/anisotropic/isotropic proton chemical shift (CSA/CSA/CS) correlation experiment mediated through (1)H/(1)H radio frequency-driven recoupling (RFDR) which enhances spin diffusion through recoupled (1)H-(1)H dipolar couplings under ultrafast magic angle spinning (MAS) frequency (70kHz). Relative orientation between two interacting 1H CSA tensors is obtained by fitting two-interacting (1)H CSA tensors by fitting two-dimensional (2D) (1)H/(1)H CSA/CSA spectral slices through extensive numerical simulations. To recouple (1)H CSAs in the indirect frequency dimensions of a 3D experiment we have employed γ-encoded radio frequency (RF) pulse sequence based on R-symmetry (R188(7)) with a series of phase-alternated 2700(°)-90180(°) composite-180° pulses on citric acid sample. Due to robustness of applied (1)H CSA recoupling sequence towards the presence of RF field inhomogeneity, we have successfully achieved an excellent (1)H/(1)H CSA/CSA cross-correlation efficiency between H-bonded sites of citric acid.

Single-crystal NMR approach for determining chemical shift tensors from powder samples via magnetically oriented microcrystal arrays

The single-crystal rotation technique was applied to magnetically oriented microcrystal arrays (MOMAs) of cellobiose (monoclinic) to determine the principal values and principal axes of the chemical shift tensors of C1 and C1' carbons. Rotations were performed about the magnetic χ1, χ2, and χ3 axes of MOMA, and the measurements were taken at six different orientations with respect to the applied magnetic field. Under these rotations, crowded peaks were reduced and the peaks for the C1 and C1' carbons were identified by comparing with simulation results. Six components of the chemical shift tensor expressed with respect to the magnetic χ1χ2χ3-frame were determined. The tensors thus obtained were transformed into those relative to the molecular frame.

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.

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.

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.

Polarization transfer from remote protons in 13C CP/MAS

An experimental procedure for CP/MAS polarization transfer from remote 1H nuclear spins is introduced, which is applicable to protonated carbons in organic solids. It is based on preparing a state of non-uniform polarization, where directly bonded 13C-1H nuclei are de-polarized prior to recording the CP buildup curve. This curve is then expected to quantify the polarization transfer from remote protons only. The ability of the cross-polarization/polarization-inversion (CPPI) sequence to generate an initial state suitable for remote 1H CP/MAS scheme is analyzed both theoretically and experimentally. Confining to aliphatic groups, it was found that complete de-polarization of bonded proton is possible in the case of CH, whereas for CH2 and CH3 moieties only a partial de-polarization can be achieved. The theoretical predictions have been verified in practice for the particular case of L-alanine. The significance of the results from fundamental, as well as practical point of view, is also discussed. In particular, it is shown that: (i) the coherent description of polarization transfer under CP/MAS, including 1H polarization redistribution, is valid over time-scales longer than commonly assumed in many treatments of cross-polarization, and (ii) the remote protons polarization transfer curve can be used in combination with the conventional CP/MAS curve to get additional structural and dynamical information in organic systems.

Determinations of 15N Chemical Shift Anisotropy Magnitudes in a Uniformly 15N,13C-Labeled Microcrystalline Protein by Three-Dimensional Magic-Angle Spinning Nuclear Magnetic Resonance Spectroscopy

Amide 15N chemical shift anisotropy (CSA) tensors provide quantitative insight into protein structure and dynamics. Experimental determinations of 15N CSA tensors in biologically relevant molecules have typically been performed by NMR relaxation studies in solution, goniometric analysis of single-crystal spectra, or slow magic-angle spinning (MAS) NMR experiments of microcrystalline samples. Here we present measurements of 15N CSA tensor magnitudes in a protein of known structure by three-dimensional MAS solid-state NMR. Isotropic 15N, 13C alpha, and 13C' chemical shifts in two dimensions resolve site-specific backbone amide recoupled CSA line shapes in the third dimension. Application of the experiments to the 56-residue beta1 immunoglobulin binding domain of protein G (GB1) enabled 91 independent determinations of 15N tensors at 51 of the 55 backbone amide sites, for which 15N-13C alpha and/or 15N-13C' cross-peaks were resolved in the two-dimensional experiment. For 37 15N signals, both intra- and interresidue correlations were resolved, enabling direct comparison of two experimental data sets to enhance measurement precision. Systematic variations between beta-sheet and alpha-helix residues are observed; the average value for the anisotropy parameter, delta (delta = delta(zz) - delta(iso)), for alpha-helical residues is 6 ppm greater than that for the beta-sheet residues. The results show a variation in delta of 15N amide backbone sites between -77 and -115 ppm, with an average value of -103.5 ppm. Some sites (e.g., G41) display smaller anisotropy due to backbone dynamics. In contrast, we observe an unusually large 15N tensor for K50, a residue that has an atypical, positive value for the backbone phi torsion angle. To our knowledge, this is the most complete experimental analysis of 15N CSA magnitude to date in a solid protein. The availability of previous high-resolution crystal and solution NMR structures, as well as detailed solid-state NMR studies, will enhance the value of these measurements as a benchmark for the development of ab initio calculations of amide 15N shielding tensor magnitudes.

Determination of the orientation and dynamics of ergosterol in model membranes using uniform 13C labeling and dynamically averaged 13C chemical shift anisotropies as experimental restraints

A new strategy was established to determine the average orientation and dynamics of ergosterol in dimyristoylphosphatidylcholine model membranes. It is based on the analysis of chemical shift anisotropies (CSAs) averaged by the molecular dynamics. Static (13)C CSA tensors were computed by quantum chemistry, using the gauge-including atomic-orbital approach within Hartree-Fock theory. Uniformly (13)C-labeled ergosterol was purified from Pichia pastoris cells grown on labeled methanol. After reconstitution into dimyristoylphosphatidylcholine lipids, the complete (1)H and (13)C assignment of ergosterol's resonances was performed using a combination of magic-angle spinning two-dimensional experiments. Dynamically averaged CSAs were determined by standard side-band intensity analysis for isolated (13)C resonances (C(3) and ethylenic carbons) and by off-magic-angle spinning experiments for other carbons. A set of 18 constraints was thus obtained, from which the sterol's molecular order parameter and average orientation could be precisely defined. The validity of using computed CSAs in this strategy was verified on cholesterol model systems. This new method allowed us to quantify ergosterol's dynamics at three molar ratios: 16 mol % (Ld phase), 30 mol % (Lo phase), and 23 mol % (mixed phases). Contrary to cholesterol, ergosterol's molecular diffusion axis makes an important angle (14 degrees) with the inertial axis of the rigid four-ring system.

The alignment, structure and dynamics of membrane-associated polypeptides by solid-state NMR spectroscopy

Solid-state NMR spectroscopy is being developed at a fast pace for the structural investigation of immobilized and non-crystalline biomolecules. These include proteins and peptides associated with phospholipid bilayers. In contrast to solution NMR spectroscopy, where complete or almost complete averaging leads to isotropic values, the anisotropic character of nuclear interactions is apparent in solid-state NMR spectra. In static samples the orientation dependence of chemical shift, dipolar or quadrupolar interactions, therefore, provides angular constraints when the polypeptides have been reconstituted into oriented membranes. Furthermore, solid-state NMR spectroscopy of aligned samples offers distinct advantages in allowing access to dynamic processes such as topological equilibria or rotational diffusion in membrane environments. Alternatively, magic angle sample spinning (MAS) results in highly resolved NMR spectra, provided that the sample is sufficiently homogenous. MAS spinning solid-state NMR spectra allow to measure distances and dihedral angles with high accuracy. The technique has recently been developed to selectively establish through-space and through-bond correlations between nuclei, similar to the approaches well-established in solution-NMR spectroscopy.

How Does an Amide-N Chemical Shift Tensor Vary in Peptides?

This study addresses a void in the existing literature on the amide-(15)N chemical shift anisotropy (CSA) tensor of peptides: a systematic investigation of how the tensor varies in different peptides. Amide-(15)N CSA tensors for several dipeptides are obtained using quantum chemical calculations, as well as for a series of model Ala-X and X-Ala sequences in both α-helical and β-sheet conformations (where X is one of the naturally occurring amino acids). The calculated values show a significant variation in both isolated and extended peptide structures. Hydrogen bonding at both the carbonyl group and the N-H bond of the peptide plane is shown to affect the principal values of the tensor. Calculations on model peptides indicate that the amide-(15)N CSA tensor is dependent on atoms located within a distance of five bonds. Consequently, the tensor of a given peptide residue is unaffected by residues other than those adjacent to it, which implies that the amide-(15)N CSA tensor should be considered in the context of tripeptide sequences. This further suggests that the amide-(15)N CSA tensor of the second residue of a given tripeptide sequence may be extrapolated to the same sequence in any other polypeptide or protein, given the same backbone conformation and intermolecular environment. These conclusions will facilitate future NMR structural studies of proteins.

15N Chemical Shielding in Glycyl Tripeptides: Measurement by Solid-State NMR and Correlation with X-ray Structure

15N chemical shielding parameters are reported for central glycyl residues in crystallographically characterized tripeptides with alpha-helix, beta-strand, polyglycine II (3(1)-helix), and extended structures. Accurate values of the shielding components (2-5 ppm) are determined from MAS and stationary spectra of peptides containing [2-(13)C,(15)N]Gly. Two dipolar couplings, (1)H-(15)N and (13)C(alpha)-(15)N, are used to examine (15)N shielding tensor orientations in the molecular frame and the results indicate that the delta(11), delta(33) plane of the shielding tensor is not coincident with the peptide plane. The observed isotropic shifts, which vary over a range of 13 ppm, depend on hydrogen bonding (direct and indirect) and local conformation. Tensor spans, delta(span) = delta(11) - delta(33), and their deviations from axial symmetry, delta(dev) = delta(22) - delta(33), vary over a larger range and are grouped according to 2 degrees structure. Augmented by previously reported (13)C(alpha) shielding parameters, a prediction scheme for the 2 degrees structure of glycyl residues in proteins based on shielding parameters is proposed.