Chemical Shielding Anisotropy Tensors Research Articles

Accurate 13-C and 15-N molecular crystal chemical shielding tensors from fragment-based electronic structure theory

Standard nuclear magnetic resonance (NMR) spectroscopy experiments measure isotropic chemical shifts, but measuring the chemical shielding anisotropy (CSA) tensor can provide additional insights into solid state chemical structures. Interpreting the principal components of these tensors is facilitated by first-principles chemical shielding tensor predictions. Here, the ability to predict molecular crystal CSA tensor components for 13C and 15N nuclei with fragment-based electronic structure techniques is explored. Similar to what has been found previously for isotropic chemical shifts, the benchmarking demonstrates that fragment-based techniques can accurately reproduce CSA tensor components. The use of hybrid density functionals like PBE0 or B3LYP provide higher accuracy than generalized gradient approximation functionals like PBE. Unlike for planewave density functional techniques, hybrid density functionals can be employed routinely with modest computational cost in fragment approaches. Finally, good consistency between the regression parameters used to map either isotropic shieldings or CSA tensor components is demonstrated, providing further evidence for the quality of the models and highlighting that models trained for isotropic shifts can also be applied to CSA tensor components.

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 (15)N chemical shielding anisotropy (CSA) tensor in the context of the complex chemical environments of protein structures. Our results indicate that the amidic (15)N 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 (15)N 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 (15)N 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.

Parameterization of Peptide 13C Carbonyl Chemical Shielding Anisotropy in Molecular Dynamics Simulations

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.

51V magic angle spinning NMR spectroscopy of Keggin anions [PVnW12-nO40](3+n)-: effect of countercation and vanadium substitution on fine structure constants.

Vanadium environments in Keggin oxopolytungstates were characterized by (51)V solid-state MAS NMR spectroscopy. (C(4)H(9))(4)N(+)-, K(+)-, Cs(+)-, as well as mixed Na(+)/Cs(+)- salts of the mono-, di-, and trivanadium substituted oxotungstates, [VW(11)O(40)](4-), [V(2)W(10)O(40)](5-), and [V(3)W(9)O(40)](6-), have been prepared as microcrystalline and crystalline solids. Solid-state NMR spectra report on the local environment of the vanadium site in these Keggin ions via their anisotropic quadrupolar and chemical-shielding interactions. These (51)V fine structure constants in the solid state are determined by the number of vanadium atoms present in the oxoanion core. Surprisingly, the quadrupolar anisotropy tensors do not depend to any significant extent on the nature of the countercations. On the other hand, the chemical-shielding anisotropy tensors, as well as the isotropic chemical shifts, display large variations as a function of the cationic environment. This information can be used as a probe of the local cationic environment in the vanadium-substituted Keggin solids.

Peptide models XXXII. Computed chemical shift analysis of penetratin fragments

Connections between the three-dimensional structure and the computational chemical shifts were investigated for the third helix of the Antennapedia homeodomain (called penetratin). Since the whole peptide cannot be studied at an acceptable ab initio level of theory, this molecule was disintegrated into fragments (mono-, tri- and octapeptides of the N- and C-terminus). Chemical shielding anisotropy tensors have been determined using the GIAO-RHF formalism employing four different basis sets: 3-21G(d), 6-31+G(d), 6-311++G(d,p) and 6-311+G(2d,p) for the one-residue-long fragments of penetratin. For three-residue-long fragments, as well as for the N- and C-terminal octapeptide part of penetratin, the 6-31+G(d) basis set was used. In examining the computed chemical shifts, we have concluded that they depend significantly on the backbone conformation of the amino acid residues, as expected. Correlation of the chemical shift values of small split-valence basis set (3-21G(d)) and those of the highest TZ2P-type basis set (6-311+G(2d,p)) is quite good for C α, C′ and H α and moderately significant for C β, N and NH nuclei. Thus, a small split-valence basis set may also be successfully used for the chemical shielding calculations of longer peptides. We have also noticed that the differences between the chemical shifts of all 16 amino acid residues remain almost the same at each basis set as function of the size of the theory set for Cα, Hα, N and C′ nuclei. The conformation or constitution of the residue influences this only to a small degree. The chemical shifts of the mono- and tripeptides were compared to the N- and C-terminal octapeptides, which represent longer and more ‘realistic’ systems. We have concluded that the mono- and tripeptide fragments can be used reliably to ‘predict’ the chemical shielding values of the octapeptides only for Cα, Hα and Cβ nuclei because their N, NH and C′ chemical shifts do not appear to model the longer system well. We have noticed that N and NH data of the tripeptides are significantly closer to the values of the N- and C-terminal octapeptide than the chemical shieldings of monopeptides. In contrast, the Cα, Hα, C′ and Cβ chemical shifts of the octapeptides do not have an unambiguous preference for values similar to the tripeptides or monopeptides. All experimental 1H chemical shift values of penetratin [J. Pept. Sci. 8 (2002) 151] were compared with their computed counterparts (N-, C- and (C−1)-terminal octapeptide). Since penetratin was composed of 13C and 15N at natural abundance levels, the latter types of shielding data are not available for comparison. By examining experimental and theoretical Hα chemical shift data, we have concluded that the correspondence of these values is moderate. The chemical shielding values of penetratin were also compared with values in known databases, and we achieved better results. However, the databases could be used only for the four common backbone conformers (α L, β L, γ L, ε L). In contrast, the chemical shift can be calculated for all backbone conformers. Furthermore, we believe that improvements to the computational method will allow the calculated chemical shielding values to approach experimental values.

Measurement of [formula omitted] 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 15 N 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 15 N 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 15 N 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 15 N chemical shifts. From the values for ubiquitin in a 7.5% (w/v) bicelle medium, we determined the 15 N chemical shielding anisotropy (CSA) tensor. For this evaluation, we considered uncertainties in measuring the 1 H– 15 N dipolar couplings and the 15 N 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° deviation from the original orientation. Taking into account these types of noise, we determined the average 15 N CSA tensor for the residues in ubiquitin as Δ σ=−162.0±4.3 ppm, η=0.18±0.02, and β=18.6±0.5°, assuming a 1 H– 15 N bond length of 1.02 Å. These tensor values are consistent with those obtained from solid-state NMR experiments.

A Theoretical Case Study of Type I and Type II β‐Turns

NMR chemical shielding anisotropy tensors have been computed by employing a medium size basis set and the GIAO-DFT(B3LYP) formalism of electronic structure theory for all of the atoms of type I and type II beta-turn models. The models contain all possible combinations of the amino acid residues Gly, Ala, Val, and Ser, with all possible side-chain orientations where applicable in a dipeptide. The several hundred structures investigated contain either constrained or optimized phi, psi, and chi dihedral angles. A statistical analysis of the resulting large database was performed and multidimensional (2D and 3D) chemical-shift/chemical-shift plots were generated. The (1)H(alpha-13)C(alpha), (13)C(alpha-1)H(alpha-13)C(beta), and (13)C(alpha-1)H(alpha-13)C' 2D and 3D plots have the notable feature that the conformers clearly cluster in distinct regions. This allows straightforward identification of the backbone and side-chain conformations of the residues forming beta-turns. Chemical shift calculations on larger For-(L-Ala)(n)-NH(2) (n=4, 6, 8) models, containing a single type I or type II beta-turn, prove that the simple models employed are adequate. A limited number of chemical shift calculations performed at the highly correlated CCSD(T) level prove the adequacy of the computational method chosen. For all nuclei, statistically averaged theoretical and experimental shifts taken from the BioMagnetic Resonance Bank (BMRB) exhibit good correlation. These results confirm and extend our previous findings that chemical shift information from selected multiple-pulse NMR experiments could be employed directly to extract folding information for polypeptides and proteins.

Toward direct determination of conformations of protein building units from multidimensional NMR experiments III

Chemical shielding anisotropy tensors have been determined, within the GIAO-RHF formalism using a smaller (6-31+G(d)) and two medium-size basis sets (6-311++G(d,p) and TZ2P), for all elements of the conformational library (altogether 27 structures) of the hydrophobic model peptide For{L-Phe{NH2. The individual chemical shifts and their conformational averages have been compared to their experimental counterparts taken from the BioMagnetic Resonance Bank (BMRB). At the highest level of theory applied, for all nuclei but the amide proton, deviations between statistically averaged theoretical and experimental chemical shifts are as low as a few percent. One-dimensional (1D) chemical shift { structure plots do not allow unambiguous identication of backbone conformations. On the other hand, on chemical shift { chemical shift plots of selected nuclei, e.g., 1 H N with 15 No r 15 Nw ith 13 C, regions corresponding to major conformational motifs have been found, providing basis for the identication of peptide conformers solely from NMR shift data. The 2D 1 H{ 13 C as well as the 3D 1 H{ 13 C{ 13 C chemical shift { chemical shift plots appear to be of special importance for direct determination of conformations of protein building units from multidimensional NMR experiments. 48 pairs of 1 H{ 13 C data for phenylalanine residues have been extracted from 18 selected proteins and compared to relevant ab initio results, supporting the calculated results. Thus, the appealing idea of establishing backbone folding information of peptides and proteins from chemical shift information alone, obtained from selected multiple-pulse NMR experiments (e.g., 2D-HSQC, 2D-HMQC, and 3D-HNCA), has received further support.

Ab Initio Calculations of 31P NMR Chemical Shielding Anisotropy Tensors in Phosphates: Variations Due to Ring Formation

Ring formation in phosphate systems is expected to influence both the magnitude and orientation of the phosphorus (31P) nuclear magnetic resonance (NMR) chemical shielding anisotropy (CSA) tensor. Ab initio calculations of the 31P CSA tensor in both cyclic and acyclic phosphate clusters were performed as a function of the number of phosphate tetrahedral in the system. The calculation of the 31P CSA tensors employed the GAUSSIAN 98 implementation of the gauge-including atomic orbital (GIAO) method at the Hartree-Fock (HF) level. It is shown that both the 31P CSA tensor anisotropy, and the isotropic chemical shielding can be used for the identification of cyclic phosphates. The differences between the 31P CSA tensor in acyclic and cyclic phosphate systems become less pronounced with increasing number of phosphate groups within the ring. The orientation of the principal components for the 31P CSA tensor shows some variation due to cyclization, most notably with the smaller, highly strained ring systems.

Toward direct determination of conformations of protein building units from multidimensional NMR experiments I. A theoretical case study of For-Gly-NH2 and For-L-Ala-NH2

NMR chemical shielding anisotropy tensors have been computed, employing several basis sets and the GIAO-RHF and GIAO-MP2 formalisms of electronic structure theory, for all the atoms of the five and nine typical backbone conformers of For-Gly-NH2 and For-L-Ala-NH2, respectively. Multidimensional chemical shift plots, as a function of the respective backbone fold, have been generated for both peptide models. On the 2D 1HNH-15NNH and 15NNH-13Cα plots the most notable feature is that at all levels of theory studied the backbone conformers cluster in different regions. Computed chemical shifts, as well as their averages, have been compared to relevant experimental values taken from the BioMagnetic Resonance Bank (BMRB). At the highest levels of theory, for all nuclei but the amide protons, deviations between statistically averaged theoretical and experimental shifts are as low as 1–3%. These results indicate that chemical shift information from selected multiple-pulse NMR experiments (e.g., 2D-HSQC and 3D-HNCA) could directly be employed to extract folding information for polypeptides and proteins. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 882–900, 2000

A15N-1H dipolar CSA solid-state NMR study of polymorphous polyglycine (-CO-CD2-15NH-)n

The solid-state1H MAS (magic-angle spinning),2H static,15N CP (cross polarization)-MAS and15N-1H dipolar CSA (chemical shielding anisotropy) NMR (nuclear magnetic resonance) spectra of two different modifications of Cα-deuteratedl5N-polyglycine, namely PG I and PG II (-CO-CD2-l5NH-)n are measured. The data from these spectra are compared to previous NMR, infrared, Raman and inelastic neutron scattering work. The deuteration of Cα eliminates the largest intramolecular1H-1H dipolar coupling. The effect of the remaining (N)H-(N)H interaction (∼5 kHz) is not negligible compared to the15N-1H coupling (about 10 kHz). Its effect on the dipolar CSA spectra, described as a two-spin system, is analyzed analytically and numerically and it is shown that those parts of the powder spectrum, which correspond to orientations with a strong dipolar15N-1H interaction, can be described as an effective two-spin system, permitting the measurement of the strength of the15N-1H dipolar interaction and the orientation of the dipolar vector with respect to the15N CSA frame. While in the PG II system the15N CSA tensor is collinear with the amide plane, in the PG I system the CSA tensor is tilted ca. 16° with respect to the (δ11δ22) CSA plane.

Crystal Structure Studies by Single-Crystal NMR Spectroscopy. 71Ga and 69Ga Single-Crystal NMR of β-Ga2O3 Twins

71Ga and 69Ga single-crystal NMR spectra of a β-Ga2O3 twin have been analyzed in terms of the 71Ga/69Ga quadrupole coupling and chemical shielding anisotropy (CSA) interactions. Analyses of the magnitudes and orientations of the interaction tensors for the two distinct crystallographic gallium sites in the two twin crystals resulted in accurate values for the parameters describing the quadrupole coupling and CSA tensors. Moreover, it has been possible to determine the actual twin-law of our sample crystal. Along with a recent 71Ga single-crystal NMR investigation of YGG, this work shows that gallium CSA generally has to be taken into account in addition to the dominant quadrupole coupling interaction.

Orientation of the Chemical Shielding Anisotropy Tensor of the Carbonate Carbon in Diphenyl Carbonate and Its Consequences for NMR Studies on Polycarbonate

The orientation of the chemical shielding anisotropy tensor of the carbonate carbon in diphenyl carbonate was determined by using solid state NMR spectroscopy. The same tensor orientation was obtained from quantum mechanical calculation based on density functional theory. The most shielded direction of the tensor is along the CO double bond. The least shielded direction is for the carbonate plane perpendicular to the CO double bond. Chemical shielding calculations in diphenyl carbonate fragments with different conformations show that the tensor orientation measured in crystalline diphenyl carbonate also applies to the carbonate groups of bisphenol A polycarbonate. However, this orientation is not identical to that assumed so far in the work on bisphenol A polycarbonate. The consequences of this incorrect assumption in previous studies are examined.