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 ¹⁵N 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.     

Influence of the O-phosphorylation of serine, threonine and tyrosine in proteins on the amidic 15N chemical shielding anisotropy tensors

Density functional theory was employed to study the influence of O-phosphorylation of serine, threonine, and tyrosine on the amidic ¹⁵N chemical shielding anisotropy (CSA) tensor in the context of the complex chemical environments of protein structures. Our results indicate that the amidic ¹⁵N CSA tensor has sensitive responses to the introduction of the phosphate group and the phosphorylation-promoted rearrangement of solvent molecules and hydrogen bonding networks in the vicinity of the phosphorylated site. Yet, the calculated ¹⁵N CSA tensors in phosphorylated model peptides were in range of values experimentally observed for non-phosphorylated proteins. The extent of the phosphorylation induced changes suggests that the amidic ¹⁵N CSA tensor in phosphorylated proteins could be reasonably well approximated with averaged CSA tensor values experimentally determined for non-phosphorylated amino acids in practical NMR applications, where chemical surrounding of the phosphorylated site is not known a priori in majority of cases. Our calculations provide estimates of relative errors to be associated with the averaged CSA tensor values in interpretations of NMR data from phosphorylated proteins.     

Density functional calculations of backbone 15N shielding tensors in beta-sheet and turn residues of protein G

We performed density functional calculations of backbone ¹⁵N shielding tensors in the regions of beta-sheet and turns of protein G. The calculations were carried out for all twenty-four beta-sheet residues and eight beta-turn residues in the protein GB3 and the results were compared with the available experimental data from solid-state and solution NMR measurements. Together with the alpha-helix data, our calculations cover 39 out of the 55 residues (or 71%) in GB3. The applicability of several computational models developed previously (Cai et al. in J Biomol NMR 45:245–253, 2009) to compute ¹⁵N shielding tensors of alpha-helical residues is assessed. We show that the proposed quantum chemical computational model is capable of predicting isotropic ¹⁵N chemical shifts for an entire protein that are in good correlation with experimental data. However, the individual components of the predicted ¹⁵N shielding tensor agree with experiment less well: the computed values show much larger spread than the experimental data, and there is a profound difference in the behavior of the tensor components for alpha-helix/turns and beta-sheet residues. We discuss possible reasons for this.     

The protein amide <Superscript>1</Superscript>H<Superscript>N</Superscript> chemical shift temperature coefficient reflects thermal expansion of the N–H···O=C hydrogen bond

The protein amide ¹H^N chemical shift temperature coefficient can be determined with high accuracy by recording spectra at different temperatures, but the physical mechanism responsible for this temperature dependence is not well understood. In this work, we find that this coefficient strongly correlates with the temperature coefficient of the through-hydrogen-bond coupling, ^3hJ_NC′, based on NMR measurements of protein GB3. Parallel tempering molecular dynamics simulation suggests that the hydrogen bond distance variation at different temperatures/replicas is largely responsible for the ¹H^N chemical shift temperature dependence, from which an empirical equation is proposed to predict the hydrogen bond thermal expansion coefficient, revealing responses of individual hydrogen bonds to temperature changes. Different expansion patterns have been observed for various networks formed by β strands.     

Using P MAS NMR to monitor a gel phase thermal disorder transition in sphingomyelin/cholesterol bilayers

The impact of low cholesterol concentrations on an egg sphingomyelin bilayer is investigated using ³¹P magic angle spinning (MAS) NMR spectroscopy. The magnitude of the isotropic ³¹P MAS NMR line width is used to monitor the main gel to liquid crystalline phase transition, along with a unique gel phase pretransition. In addition, the ³¹P chemical shift anisotropy (CSA) and spin-spin relaxation times (T₂), along with the effects of spinning speed, proton decoupling and magnetic field strength, are reported. The variation of this unique gel phase thermal pretransition with the inclusion of 5 through 21 mol% cholesterol is presented and discussed.     

Analysis of the amide <Superscript>15</Superscript>N chemical shift tensor of the C<Subscript>α</Subscript> tetrasubstituted constituent of membrane-active peptaibols,the α-aminoisobutyric acid residue,compared to those of di- and tri-substituted proteinogenic amino acid residues

In protein NMR spectroscopy the chemical shift provides important information for the assignment of residues and a first structural evaluation of dihedral angles. Furthermore, angular restraints are obtained from oriented samples by solution and solid-state NMR spectroscopic approaches. Whereas the anisotropy of chemical shifts, quadrupolar couplings and dipolar interactions have been used to determine the structure, dynamics and topology of oriented membrane polypeptides using solid-state NMR spectroscopy similar concepts have been introduced to solution NMR through the measurements of residual dipolar couplings. The analysis of ¹⁵N chemical shift spectra depends on the accuracy of the chemical shift tensors. When investigating alamethicin and other peptaibols, i.e. polypeptides rich in α-aminoisobutyric acid (Aib), the ¹⁵N chemical shift tensor of this C_α-tetrasubstituted amino acid exhibits pronounced differences when compared to glycine, alanine and other proteinogenic residues. Here we present an experimental investigation on the ¹⁵N amide Aib tensor of N-acetyl-Aib-OH and for the Aib residues within peptaibols. Furthermore, a statistical analysis of the tensors published for di- (glycine) and tri-substituted residues has been performed, where for the first time the published data sets are compiled using a common reference. The size of the isotropic chemical shift and main tensor elements follows the order di- < tri- < tetra-substituted amino acids. A ¹⁵N chemical shift-¹H-¹⁵N dipolar coupling correlation NMR spectrum of alamethicin is used to evaluate the consequences of variations in the main tensor elements for the structural analysis of this membrane peptide.     

Band-selective 13C Homonuclear 3D Spectroscopy for Solid Proteins at High Field with Rotor-synchronized Soft Pulses

We demonstrate improved 3D ¹³C–¹³C–¹³C chemical shift correlation experiments for solid proteins, utilizing band-selective coherence transfer, scalar decoupling and homonuclear zero-quantum polarization transfer. Judicious use of selective pulses and a z-filter period suppress artifacts with a two-step phase cycle, allowing higher digital resolution in a fixed measurement time. The novel correlation of C^ali–C^ali–CX (C^ali for aliphatic carbons, CX for any carbon) reduces measurement time by an order of magnitude without sacrificing digital resolution. The experiment retains intensity from side-chain carbon resonances whose chemical shift dispersion is critical to minimize spectral degeneracy for large proteins with a predominance of secondary structure, such as β-sheet rich fibrillar proteins and α-helical membrane proteins. We demonstrate the experiment for the β1 immunoglobulin binding domain of protein G (GB1) and fibrils of the A30P mutant of α-synuclein, which is implicated in Parkinson’s disease. Selective pulses of duration comparable the rotor period give optimal performance, but must be synchronized with the spinning in non-trivial ways to minimize chemical shift anisotropy recoupling effects. Soft pulses with a small bandwidth-duration product are best for exciting the ~70 ppm bandwidth required for aliphatic-only dimensions.     

The effect of noncollinearity of 15N-1H dipolar and 15N CSA tensors and rotational anisotropy on 15N relaxation, CSA/dipolar cross correlation, and TROSY

Current approaches to 15N relaxation in proteins assume that the 15N-1H dipolar and 15N CSA tensors are collinear. We show theoretically that, when there is significant anisotropy of molecular rotation, different orientations of the two tensors, experimentally observed in proteins, nucleic acids, and small peptides, will result in differences in site- specific correlation functions and spectral densities. The standard treatments of the rates of longitudinal and transverse relaxation of amide 15N nuclei, of the 15N CSA/15N-1H dipolar cross correlation, and of the TROSY experiment are extended to account for the effect of noncollinearity of the 15N-1H dipolar and 15N CSA (chemical shift anisotropy) tensors. This effect, proportional to the degree of anisotropy of the overall motion, (D/D–1), is sensitive to the relative orientation of the two tensors and to the orientation of the peptide plane with respect to the diffusion coordinate frame. The effect is negligible at small degrees of anisotropy, but is predicted to become significant for D/D1.5, and at high magnetic fields. The effect of noncollinearity of 15N CSA and 15N-1H dipolar interaction is sensitive to both gross (hydrodynamic) properties and atomic-level details of protein structure. Incorporation of this effect into relaxation data analysis is likely to improve both precision and accuracy of the derived characteristics of protein dynamics, especially at high magnetic fields and for molecules with a high degree of anisotropy of the overall motion. The effect will also make TROSY efficiency dependent on local orientation in moderately anisotropic systems.     

Quantitative estimation of magnitude and orientation of the CSA tensor from field dependence of longitudinal NMR relaxation rates

A method is presented that makes it possible to estimate both the orientation and the magnitude of the chemical shift anisotropy (CSA) tensor in molecules with a pair of spin 1/2 nuclei, typically ¹³C-¹H or ¹⁵ N-¹H. The method relies on the fact that the longitudinal cross-correlation rate as well as a linear combination of the autorelaxation rates of longitudinal heterospin magnetization, longitudinal two-spin order and longitudinal proton magnetization are proportional to the spectral density at the Larmor frequency of the heterospin. Therefore the ratio between the cross-correlation rate and the above linear combination is independent of the dynamics. From the field dependence of the ratio both the magnitude and the orientation of the CSA tensor can be estimated. The method is applicable to molecules in all motional regimes and is not limited to molecules in extreme narrowing or slow tumbling, nor is it sensitive to chemical exchange broadening. It is tested on the 22 amino acid residue peptide motilin, selectively ¹³ C labeled in the ortho positions in the ring of the single tyrosine residue. In the approximation of an axially symmetric ¹³C CSA tensor, the symmetry axis of the CSA tensor makes an angle of 23° ± 1° to the ¹³ C-¹H bond vector, and has a magnitude of 156 ± 5 ppm. This is in close agreement with solid-state NMR data on tyrosine powder [Frydman et al. (1992) Isr. J. Chem., 32, 161–164].     

Can PISEMA experiments be used to extract structural parameters for mobile β-barrels?

The effect of mobility on ¹⁵N chemical shift/¹⁵N–¹H dipolar coupling (PISEMA) solid state NMR experiments applied to macroscopically oriented β-barrels is assessed using molecular dynamics simulation data of the NalP autotransporter domain embedded in a DMPC bilayer. In agreement with previous findings for α-helices, the fast librational motion of the peptide planes is found to have a considerable effect on the calculated PISEMA spectra. In addition, the dependence of the chemical shift anisotropy (CSA) and dipolar coupling parameters on the calculated spectra is evaluated specifically for the β-barrel case. It is found that the precise choice of the value of the CSA parameters σ₁₁,σ₂₂ and σ₃₃ has only a minor effect, whereas the choice of the CSA parameter θ shifts the position of the peaks by up to 20 ppm and changes the overall shape of the spectrum significantly. As was found for α-helices, the choice of the NH bond distance has a large effect on the dipolar coupling constant used for the calculations. Overall, it is found that the alternating β-strands in the barrel occupy distinct regions of the PISEMA spectra, forming patterns which may prove useful in peak assignment.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s10858-005-5094-5     

Structural origins of pH‐dependent chemical shifts in the B1 domain of protein G

We report chemical shifts for H^N, N, and C′ nuclei in the His‐tagged B1 domain of protein G (GB1) over a range of pH values from pH 2.0 to 9.0, which fit well to standard pH‐dependent equations. We also report a 1.2 Å resolution crystal structure of GB1 at pH 3.0. Comparison of this crystal structure with published crystal structures at higher pHs provides details of the structural changes in GB1 associated with protonation of the carboxylate groups, in particular a conformational change in the C‐terminus of the protein at low pH. An additional change described recently is not seen in the crystal structure because of crystal contacts. We show that the pH‐dependent changes in chemical shifts can be almost entirely understood based on structural changes, thereby providing insight into the relationship between structure and chemical shift. In particular, we describe through‐bond effects extending up to five bonds, affecting N and C′ but not H^N; through‐space effects of carboxylates, which fit well to a simple electric field model; and effects due to conformational change, which have a similar magnitude to many of the direct effects. Finally, we discuss cooperative effects, demonstrating a lack of cooperative unfolding in the helix, and the existence of a β‐sheet “iceberg” extending over three of the four strands. This study therefore extends the application of chemical shifts to understanding protein structure. Proteins 2010; © 2010 Wiley‐Liss, Inc.     

31P NMR relaxation measurements of the phosphate backbone of a double stranded hexadeoxynucleotide in solution: determination of the chemical shift anisotropy

The five phosphates of the deoxynucleotide d(CpGpTpApCpG)₂ have been assigned by two-dimensional heteronuclear NMR spectroscopy. The chemical shift anisotropy and correlation time of each phosphate group has been determined from measurements of the spin-lattice, spin-spin relaxation rate constants and the ³¹P-{¹H} nuclear Overhauser enhancement (NOE) at three magnetic field strengths (4.7 T, 9.4 T, and 11.75 T) and two temperatures (288 K and 298 K). As expected, the relaxation data require two mechanisms to account for the observed rate constants, i.e. dipole-dipole and chemical shift anisotropy. At 9.4 T and 11.75 T, the latter mechanism dominates the relaxation, leading to insignificant NOE intensities. The correlation time, chemical shift anisotropy and effective P-H distance were obtained from least-squares fitting to the data. Comparison of the fitted value for the correlation time with that obtained from ¹H measurements shows that the molecule behaves essentially as rigid rotor on the nanosecond timescale. Large amplitude motions observed in long segments of DNA are due to bending motions that do not contribute significantly to relaxation in short oligonucleotides.Abbreviations CSA chemical shift anisotropy - NOE nuclear Overhauser enhancement Offprint requests to: A. N. Lane     

Pressure effect on the dynamics of an isolated α-helix studied by 15N-1H NMR relaxation

Dynamics and structure of (1–36)bacteriorhodopsin solubilized in chloroform/methanol mixture (1:1) were investigated by ¹H-¹⁵N NMR spectroscopy under a hydrostatic pressure of 2000 bar. It was shown that the peptide retains its spatial structure at high pressure. ¹⁵N transverse and longitudinal relaxation times, ¹⁵N{¹H} nuclear Overhauser effects, chemical shifts and the translation diffusion rate of the peptide at 2000 bar were compared with the respective data at ambient pressure [Orekhov et al. (1999) J. Biomol. NMR, 14, 345–356]. The model free analysis of the relaxation data for the helical 9–31 fragment revealed that the high pressure decreases the overall rotation and translation diffusion, as well as apparent order parameters of fast picosecond internal motions (S² _f) but has no effect on internal nanosecond motions (S² _s and _s) of the peptide. The decrease of translation and overall rotation diffusion was attributed to the increase in solvent viscosity and the decrease of apparent order parameters S² _f to a compression of hydrogen bonds. It is suggested that this compression causes an elongation of H-N bonds and a decrease of absolute values of chemical shift anisotropy (CSA). In particular, the observed decrease of S² _f at 2000 bar can be explained by 0.001 nm increase of N-H bond lengths and 10 ppm decrease of ¹⁵N CSA values.     

Correlated motions of C′–N and C<Subscript>α</Subscript>–C<Subscript>β</Subscript> pairs in protonated and per-deuterated GB3

We investigated correlated µs-ms time scale motions of neighboring ¹³C′–¹⁵N and ¹³C_α–¹³C_β nuclei in both protonated and perdeuterated samples of GB3. The techniques employed, NMR relaxation due to cross-correlated chemical shift modulations, specifically target concerted changes in the isotropic chemical shifts of the two nuclei associated with spatial fluctuations. Field-dependence of the relaxation rates permits identification of the parameters defining the chemical exchange rate constant under the assumption of a two-site exchange. The time scale of motions falls into the intermediate to fast regime (with respect to the chemical shift time scale, 100–400 s^?1 range) for the ¹³C′–¹⁵N pairs and into the slow to intermediate regime for the ¹³C_α–¹³C_β pairs (about 150 s^?1). Comparison of the results obtained for protonated and deuterated GB3 suggests that deuteration has a tendency to reduce these slow scale correlated motions, especially for the ¹³C_α–¹³C_β pairs.     

Refinement of protein structure against non-redundant carbonyl <Superscript>13</Superscript>C NMR relaxation

Carbonyl ¹³C′ relaxation is dominated by the contribution from the ¹³C′ chemical shift anisotropy (CSA). The relaxation rates provide useful and non-redundant structural information in addition to dynamic parameters. It is straightforward to acquire, and offers complimentary structural information to the ¹⁵N relaxation data. Furthermore, the non-axial nature of the ¹³C′ CSA tensor results in a T₁/T₂ value that depends on an additional angular variable even when the diffusion tensor of the protein molecule is axially symmetric. This dependence on an extra degree of freedom provides new geometrical information that is not available from the NH dipolar relaxation. A protocol that incorporates such structural restraints into NMR structure calculation was developed within the program Xplor-NIH. Its application was illustrated with the yeast Fis1 NMR structure. Refinement against the ¹³C′ T₁/T₂ improved the overall quality of the structure, as evaluated by cross-validation against the residual dipolar coupling as well as the ¹⁵N relaxation data. In addition, possible variations of the CSA tensor were addressed. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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

The individual components of the backbone ¹⁵N CSA tensor, σ₁₁, σ₂₂, σ₃₃, and the orientation of σ₁₁ relative to the NH bond described by the angle β have been determined for uniformly labeled ¹⁵N, ¹³C 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 β-strand or extended regions, while α-helical residue tensor components cluster close to the average values.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Magnetic field induced residual dipolar couplings of imino groups in nucleic acids from measurements at a single magnetic field

For base-paired nucleic acids, variations in ¹ J _NH and the imino ¹H chemical shift are both dominated by hydrogen bond length. In the absence of molecular alignment, the ¹ J _NH coupling for the imino proton then can be approximated by ¹ J _NH = (1.21Hz/ppm)δ_H − 103.5 ± 0.6 Hz, where δ_H represents the chemical shift of the imino proton in ppm. This relation permits imino residual dipolar couplings (RDCs) resulting from magnetic susceptibility anisotropy (MSA) to be extracted from measurement of (¹ J _NH + RDC) splittings at a single magnetic field strength. Magnetic field-induced RDCs were measured for tRNA^Val and the alignment tensor determined from magnetic-field alignment of tRNA^Val agrees well with the tensor calculated by summation of the MSA tensors of the individual nucleobases. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Jinfa Ying, Alexander Grishaev and Michael P. Latham contributed equally to this work.     

Theoretical study of the NMR chemical shift of Xe in supercritical condition

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the ¹²⁹Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the ¹²⁹Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe _n clusters (n =?2 ? 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe _n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of ¹²⁹Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.     

Solid state NMR of proteins at high MAS frequencies: symmetry-based mixing and simultaneous acquisition of chemical shift correlation spectra

We have carried out chemical shift correlation experiments with symmetry-based mixing sequences at high MAS frequencies and examined different strategies to simultaneously acquire 3D correlation spectra that are commonly required in the structural studies of proteins. The potential of numerically optimised symmetry-based mixing sequences and the simultaneous recording of chemical shift correlation spectra such as: 3D NCAC and 3D NHH with dual receivers, 3D NC??C and 3D C??NCA with sequential ¹³C acquisitions, 3D NHH and 3D NC??H with sequential ¹H acquisitions and 3D CANH and 3D C??NH with broadband ¹³C?C¹⁵N mixing are demonstrated using microcrystalline samples of the ??1 immunoglobulin binding domain of protein G (GB1) and the chicken ??-spectrin SH3 domain.     

The Nature and Origin of Chemical Shift for Intracellular Water Nuclei in Artemia Cysts

We investigated the possible existence of chemical shift of water nuclei in Artemia cysts using high resolution nuclear magnetic resonance (NMR) methods. The results conducted at 60, 200, and 500 MHz revealed an unusually large chemical shift for intracellular water protons. After correcting for bulk susceptibility effects, a residual downfield chemical shift of 0.11 ppm was observed in fully hydrated cysts. Similar results have been observed for the deuterium and ¹⁷O nuclei.

We have ruled out unusual intracellular pH, diamagnetic susceptibility of intracellular water, or interaction of water molecules with lipids, glycerol, and/or trehalose as possible origins of the residual chemical shift. We conclude that the residual chemical shift observed for water nuclei (¹H, ²H, and ¹⁷O) is due to significant water-macromolecular interactions.