A solid-state 55Mn NMR spectroscopy and DFT investigation of manganese pentacarbonyl compounds

Central transition (55)Mn NMR spectra of several solid manganese pentacarbonyls acquired at magnetic field strengths of 11.75, 17.63, and 21.1 T are presented. The variety of distinct powder sample lineshapes obtained demonstrates the sensitivity of solid-state (55)Mn NMR to the local bonding environment, including the presence of crystallographically unique Mn sites, and facilitates the extraction of the Mn chemical shift anisotropies, CSAs, and the nuclear quadrupolar parameters. The compounds investigated include molecules with approximate C(4v) symmetry, LMn(CO)(5)(L = Cl, Br, I, HgMn(CO)(5), CH(3)) and several molecules of lower symmetry (L = PhCH(2), Ph(3-n)Cl(n)Sn (n= 1, 2, 3)). For these compounds, the Mn CSA values range from <100 ppm for Cl(3)SnMn(CO)(5) to 1260 ppm for ClMn(CO)(5). At 21.1 T the (55)Mn NMR lineshapes are appreciably influenced by the Mn CSA despite the presence of significant (55)Mn quadrupolar coupling constants that range from 8.0 MHz for Cl(3)SnMn(CO)(5) to 35.0 MHz for CH(3)Mn(CO)(5). The breadth of the solid-state (55)Mn NMR spectra of the pentacarbonyl halides is dominated by the CSA at all three applied magnetic fields. DFT calculations of the Mn magnetic shielding tensors reproduce the experimental trends and the magnitude of the CSA is qualitatively rationalized using a molecular orbital, MO, interpretation based on Ramsey's theory of magnetic shielding. In addition to the energy differences between symmetry-appropriate occupied and virtual MOs, the d-character of the Mn MOs is important for determining the paramagnetic shielding contribution to the principal components of the magnetic shielding tensor.     

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.     

Experimental and theoretical studies of 45Sc NMR interactions in solids

Solid-state 45Sc NMR spectroscopy, ab initio calculations, and X-ray crystallography are applied to examine the relationships between 45Sc NMR interactions and molecular structure and symmetry. Solid-state 45Sc (I = 7/2) magic-angle spinning (MAS) and static NMR spectra of powdered samples of Sc(acac)3, Sc(TMHD)3, Sc(NO3)3.5H2O, Sc(OAc)3, ScCl3.6H2O, ScCl3.3THF, and ScCp3 have been acquired. These systems provide a variety of scandium coordination environments yielding an array of distinct 45Sc chemical shielding (CS) and electric field gradient (EFG) tensor parameters. Acquisition of spectra at two distinct magnetic fields allows for the first observations of scandium chemical shielding anisotropy (CSA). 45Sc quadrupolar coupling constants (CQ) range from 3.9 to 13.1 MHz and correlate directly with the symmetry of the scandium coordination environment. Single-crystal X-ray structures were determined for Sc(TMHD)3, ScCl3.6H2O, and Sc(NO3)3.5H2O to establish the hitherto unknown scandium coordination environments. A comprehensive series of ab initio calculations of EFG and CS tensor parameters are in excellent agreement with the observed parameters. Theoretically determined orientations of the NMR interaction tensors allow for correlations between NMR tensor characteristics and scandium environments. Solid-state 45Sc, 13C, and 19F NMR experiments are also applied to characterize the structures of the microcrystalline Lewis acid catalyst Sc(OTf)3 (for which the crystal structure is unknown) and a noncrystalline, microencapsulated, polystyrene-supported form of the compound.     

Ortho effect in fluorobenzenes: cross-correlated relaxation and quantum chemical studies

An early solid-state NMR study of the shielding tensors in substituted fluorobenzenes had indicated the presence of the 'ortho effect'. This was confirmed recently in the liquid state from a study of cross-correlated relaxation, which gives a handle on the shielding tensor. We report here a combined experimental and computational study on substituted fluorobenzenes where the ortho substituent is varied systematically. Experimental measurements of the longitudinal relaxation of 19F indicate the cross-correlation between the chemical shift anisotropy (CSA) of fluorine and its dipolar interaction with the ortho proton, and provide a measure of the CSA orientation parameter. This parameter is obtained also from quantum chemical calculations of the 19F CSA tensor. We establish a correlation between the CSA orientation parameter and linear free energy parameters by resorting to a multi-parameter regression analysis. Excellent correlation is obtained for most of these substituents only when a parameter for the ortho effect is included.     

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.     

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.     

Continuous symmetry measures: A note in proof of the folding/unfolding method

The measurement of the degree of symmetry proved to be a useful tool in the prediction of quantitative structural–physical correlations. These measurements have been based, in the most general form, on the folding/unfolding algorithm, for which we provide here a new and simpler proof. We generalize this proof to the case of objects composed of more than one (full) orbit. An important practical issue we consider is the division of the graph into symmetry orbits and the mapping of the symmetry group elements onto the points of the graph. The logical constraints imposed by the edges of the graph are reviewed and used for the successful resolution of the coupling between different orbits.     

An experimental and theoretical investigation of the chemical shielding tensors of (13)C(alpha) of alanine, valine, and leucine residues in solid peptides and in proteins in solution

We have carried out a solid-state magic-angle sample-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopic investigation of the (13)C(alpha) chemical shielding tensors of alanine, valine, and leucine residues in a series of crystalline peptides of known structure. For alanine and leucine, which are not branched at the beta-carbon, the experimental chemical shift anisotropy (CSA) spans (Omega) are large, about 30 ppm, independent of whether the residues adopt helical or sheet geometries, and are in generally good accord with Omega values calculated by using ab initio Hartree-Fock quantum chemical methods. The experimental Omegas for valine C(alpha) in two peptides (in sheet geometries) are also large and in good agreement with theoretical predictions. In contrast, the "CSAs" (Deltasigma) obtained from solution NMR data for alanine, valine, and leucine residues in proteins show major differences, with helical residues having Deltasigma values of approximately 6 ppm while sheet residues have Deltasigma approximately 27 ppm. The origins of these differences are shown to be due to the different definitions of the CSA. When defined in terms of the solution NMR CSA, the solid-state results also show small helical but large sheet CSA values. These results are of interest since they lead to the idea that only the beta-branched amino acids threonine, valine, and isoleucine can have small (static) tensor spans, Omega (in helical geometries), and that the small helical "CSAs" seen in solution NMR are overwhelmingly dominated by changes in tensor orientation, from sheet to helix. These results have important implications for solid-state NMR structural studies which utilize the CSA span, Omega, to differentiate between helical and sheet residues. Specifically, there will be only a small degree of spectral editing possible in solid proteins since the spans, Omega, for the dominant nonbranched amino acids are quite similar. Editing on the basis of Omega will, however, be very effective for many Thr, Val, and Ileu residues, which frequently have small ( approximately 15-20 ppm) helical CSA (Omega) spans.     

Carbon-13 NMR shielding in the twenty common amino acids: comparisons with experimental results in proteins

We have used ab initio quantum chemical techniques to compute the (13)C(alpha) and (13)C(beta) shielding surfaces for the 14 amino acids not previously investigated (R. H. Havlin et al., J. Am. Chem. Soc. 1997, 119, 11951-11958) in their most popular conformations. The spans (Omega = sigma(33) - sigma(11)) of all the tensors reported here are large ( approximately 34 ppm) and there are only very minor differences between helical and sheet residues. This is in contrast to the previous report in which Val, Ile and Thr were reported to have large ( approximately 12 ppm) differences in Omega between helical and sheet geometries. Apparently, only the beta-branched (beta-disubstituted) amino acids have such large CSA span (Omega) differences; however, there are uniformly large differences in the solution-NMR-determined CSA (Deltasigma = sigma(orth) - sigma(par)) between helices and sheets in all amino acids considered. This effect is overwhelmingly due to a change in shielding tensor orientation. With the aid of such shielding tensor orientation information, we computed Deltasigma values for all of the amino acids in calmodulin/M13 and ubiquitin. For ubiquitin, we find only a 2.7 ppm rmsd between theory and experiment for Deltasigma over an approximately 45 ppm range, a 0.96 slope, and an R(2) = 0.94 value when using an average solution NMR structure. We also report C(beta) shielding tensor results for these same amino acids, which reflect the small isotropic chemical shift differences seen experimentally, together with similar C(beta) shielding tensor magnitudes and orientations. In addition, we describe the results of calculations of C(alpha), C(beta), C(gamma)1, C(gamma)2, and C(delta) shifts in the two isoleucine residues in bovine pancreatic trypsin inhibitor and the four isoleucines in a cytochrome c and demonstrate that the side chain chemical shifts are strongly influenced by chi(2) torsion angle effects. There is very good agreement between theory and experiment using either X-ray or average solution NMR structures. Overall, these results show that both C(alpha) backbone chemical shift anisotropy results as well as backbone and side chain (13)C isotropic shifts can now be predicted with good accuracy by using quantum chemical methods, which should facilitate solution structure determination/refinement using such shielding tensor surface information.     

Development of modulated rf sequences for decoupling and recoupling of nuclear-spin interactions in sample-spinning solid-state NMR: application to chemical-shift anisotropy determination

An approach to design modulated rf sequences under sample spinning which decouple/recouple a specific nuclear-spin interaction in solid-state NMR is presented. The Euler angles of the spin rotation caused by a general rf field are forced to fulfill the symmetry principle theory for selecting an interaction of interest. Then, modulated rf sequences are directly obtained from the Euler angles with a large degree of freedom. rf sequences with high performance can be selected from them by numerically optimizing rf sequence parameters. As an example of this approach, an amplitude- and phase-modulated rf sequence to recouple chemical-shift anisotropy (CSA) is developed, which is robust with respect to rf inhomogeneity. Two-dimensional (2D) experiments with this rf sequence under on and off magic-angle spinning (MAS) provide one-dimensional and 2D powder patterns, respectively. The latter enables us to determine the CSA principal values more accurately even for overlapped signals in MAS spectra. The effectiveness of this modulated rf sequence is experimentally demonstrated on [(15)N]-N-acetyl-D,L-alanine for determination of the (15)N and (13)CO CSA principal values.     

Calculations of the contribution of ring currents to the chemical shielding anisotropy

Ring currents can exert a large effect upon the chemical shielding of NMR resonances. The analytical expression developed by Waugh and Fessenden (Waugh, J. S.; Fessenden, R. W. J. Am. Chem. Soc. 1957, 79, 846) and Johnson and Bovey (Johnson, C. E.; Bovey, F. A. J. Chem. Phys. 1957, 29, 1012) only quantifies the contribution of ring currents to the isotropic component of the shielding tensor. In the work described here an additional analytical expression is developed so that the contribution of ring currents to the full shielding tensor can be calculated, allowing an estimate of the influence of ring currents upon the chemical shielding anisotropy (CSA, Deltasigma). To test that this pair of analytical expressions can provide a reasonable estimate of the contribution of ring currents to the full shielding tensor a series of density functional calculations (DFT) were carried out. A shielding tensor in a model compound was calculated in two distinct ways. For the first series, DFT shielding calculations of the model compound were carried out in the presence of a benzene ring. For the second series a ring current contribution to the shielding tensor was calculated via the new expressions, and this was added to the result of a DFT shielding calculation which used in place of benzene the nonaromatic analogue 1,3 cyclohexadiene. The two series of results proved to be in excellent agreement. The pair of analytical expressions are used to calculate ring current contributions to the CSA (Deltasigma) of 1H(N) backbone amide resonances in a structure of the second type 2 module from the protein fibronectin. Significant CSA variations are predicted in particular for the 1H(N) of G42 which is most likely involved in a N-H...tpi aromatic hydrogen bond.     

Using the 19F NMR chemical shift anisotropy tensor to differentiate between the zigzag and chiral forms of fluorinated single-walled carbon nanotubes

The structural characterization of different kinds of zigzag and chiral single-walled carbon nanotubes (SWNTs) has been investigated theoretically using (19)F NMR spectroscopy. The chemical shift anisotropy (CSA) tensor is computed at different levels of theory for the (19)F nuclei in different forms of functionalized fluorinated carbon nanotubes (CNT). A set of fluorine CSA parameters comprising the span, skew, and isotropic chemical shift is computed for each form of the fluoronanotubes and multidimensional CSA parameter correlation maps are constructed. We show that these correlations are able to clearly distinguish between the chiral and zigzag forms of fluorinated carbon nanotubes (F-SWNTs). Implications for solid-state and liquid-state NMR experiments are discussed.     

Secondary structures of peptides and proteins via NMR chemical-shielding anisotropy (CSA) parameters

Complete nuclear magnetic resonance (NMR) chemical-shielding tensors, sigma, have been computed at different levels of density-functional theory (DFT), within the gauge-including atomic orbital (GIAO) formalism, for the atoms of the peptide model For-L-Ala-NH2 as a function of the backbone dihedral angles phi and psi by employing a dense grid of 10 degrees. A complete set of rigorously orthogonal symmetric tensor invariants, {sigma iso, rho, tau}, is introduced, where sigma iso is the usual isotropic chemical shielding, while the newly introduced rho and tau parameters describe the magnitude and the orientation/shape of the chemical-shielding anisotropy (CSA), respectively. The set {sigma iso, rho, tau} is unaffected by unitary transformations of the symmetric part of the shielding tensor. The mathematically and physically motivated {rho, tau} anisotropy pair is easily connected to more traditional shielding anisotropy measures, like span (Omega) and skew (kappa). The effectiveness of the different partitions of the CSA information in predicting conformations of peptides and proteins has been tested throughout the Ramachandran space by generating theoretical NMR anisotropy surfaces for our For-L-Ala-NH2 model. The CSA surfaces, including Omega(phi, psi), kappa(phi, psi), rho(phi, psi), and tau(phi, psi) are highly structured. Individually, none of these surfaces is able to distinguish unequivocally between the alpha-helix and beta-strand secondary structural types of proteins. However, two- and three-dimensional correlated plots, including Omega versus kappa, rho versus tau, and sigma iso versus rho versus tau, especially for 13Calpha, have considerable promise in distinguishing among all four of the major secondary structural elements.     

Characterization of divalent metal metavanadates by 51V magic-angle spinning NMR spectroscopy of the central and satellite transitions

51V quadrupole coupling and chemical shielding tensors have been determined from 51V magic-angle spinning (MAS) NMR spectra at a magnetic field of 14.1 T for nine divalent metal metavanadates: Mg(VO3)2, Ca(VO3)2, Ca(VO3)(2).4H2O, alpha-Sr(VO3)2, Zn(VO3)2, alpha- and beta-Cd(VO3)2. The manifold of spinning sidebands (ssbs) from the central and satellite transitions, observed in the 15V MAS NMR spectra, have been analyzed using least-squares fitting and numerical error analysis. This has led to a precise determination of the eight NMR parameters characterizing the magnitudes and relative orientations of the quadrupole coupling and chemical shielding tensors. The optimized data show strong similarities between the NMR parameters for the isostructural groups of divalent metal metavanadates. This demonstrates that different types of metavanadates can easily be distinguished by their anisotropic NMR parameters. The brannerite type of divalent metal metavanadates exhibits very strong 51V quadrupole couplings (i.e., CQ = 6.46-7.50 MHz), which reflect the highly distorted octahedral environments for the V5+ ion in these phases. Linear correlations between the principal tensor elements for the 51V quadrupole coupling tensors and electric field gradient tensor elements, estimated from point-monopole calculations, are reported for the divalent metal metavanadates. These correlations are used in the assignment of the NMR parameters for the different crystallographic 51V sites of Ca(VO3)(2).4H2O, Pb(VO3)2, and Ba(VO3)2. For alpha-Sr(VO3)2, with an unknown crystal structure, the 51V NMR data strongly suggest that this metavanadate is isostructural with Ba(VO3)2, for which the crystal structure has been reported. Finally, the chemical shielding parameters for orthovanadates and mono- and divalent metal metavanadates are compared.     

Limited variations in 15N CSA magnitudes and orientations in ubiquitin are revealed by joint analysis of longitudinal and transverse NMR relaxation

The site-specific magnitudes and orientations of the chemical shift tensors have been estimated for 70 backbone (15)N-nuclei in human ubiquitin from the field dependence of dynamic independent ratios between relaxation rates, both longitudinal and transverse, measured at 9.4, 11.7, 14.1, and 18.8 T. The results were jointly analyzed with previously published relaxation data [Fushman; Tjandra; Cowburn. J.Am. Chem. Soc. 1998, 120, 10947-10952] [Kover; Batta. J. Mag. Reson. 2001, 150, 137-146]. The effective magnitudes of the anisotropies distribute around 169 ppm with a variability of 5 ppm. The orientation factors, reflecting the orientation of the CSA relative to the NH bond, distribute around -0.80 with a variability of 0.04, which corresponds to an angle between the symmetry axis of an assumed axially symmetric shielding tensor and the NH bond of 21.4 degrees, and a variability of 2.3 degrees. Correlations with the isotropic (15)N-chemical shifts are observed. Variations in the shielding anisotropies add uncertainty to the obtained order parameters proportional to the square of the magnetic field, when data are analyzed using an assumed invariant CSA tensor for all sites. Around 3% additional uncertainty in the order parameters for 800 MHz data is expected. The optimal TROSY field for amide nitrogen TROSY is estimated, with only marginal variations due to site-to-site variations. Variations in the shielding tensors add uncertainty to the exchange terms calculated from cross-correlation rates. An approach for estimating the exchange terms is suggested, where the uncertainty due to CSA-variations is minimized.     

Symmetry‐Enthalpy Correlations in Diels–Alder Reactions

Woodward–Hoffmann (WH) rules provide strict symmetry selection rules: when they are obeyed, a reaction proceeds; when they are not obeyed, there is no reaction. However, the voluminous experimental literature provides ample evidence that strict compliance to symmetry requirements is not an obstacle for a concerted reaction to proceed, and therefore the idea has developed that it is enough to have a certain degree of the required symmetry to have reactivity. Here we provide quantitative evidence of that link, and show that as one deviates from the desired symmetry, the enthalpy of activation increases, that is, we show that concerted reactions slow down the further they are from the ideal symmetry. Specifically, we study the deviation from mirror symmetry (evaluated with the continuous symmetry measure (CSM)) of the [4+2] carbon skeleton of the transition state of a series of twelve Diels–Alder reactions in seven different solvents (and in the gas phase), in which the dienes are butadiene, cyclopentadiene, cyclohexadiene, and cycloheptadiene; the dienophiles are the 1‐, 1,1‐, and 1,1,2‐cyanoethylene derivatives; the solvents were chosen to sample a range of dielectric constants from heptane to ethanol. These components provide twenty‐four symmetry–enthalpy DFT‐calculated correlation lines (out of which only one case is a relatively mild exception) that show the general trend of increase in enthalpy as symmetry decreases. The various combinations between the dienophiles, cyanoethylenes, and solvents provide all kinds of sources for symmetry deviations; it is therefore remarkable that although the enthalpy of activation is dictated by various parameters, symmetry emerges as a primary parameter. In our analysis we also bisected this overall picture into solvent effects and geometry variation effects to evaluate under which conditions the electronic effects are more dominant than symmetry effects.     

Anisotropic NMR interaction tensors in the decamethylaluminocenium cation

Solid-state NMR experiments, analytical and numerical simulations of solid NMR powder patterns, ab initio self-consistent field and hybrid density functional theory calculations, and single-crystal X-ray diffraction are used to characterize the molecular structure and anisotropic NMR interaction tensors in the bis(pentamethylcyclopentadienyl)aluminum cation, [Cp(2)Al](+). This highly symmetric main group metallocene has a structure analogous to that of ferrocene and the cobaltocenium cation. The single-crystal X-ray diffraction structure is reported for [Cp(2)Al][AlCl(4)]. Solid-state (27)Al[(1)H] magic-angle spinning and static NMR experiments are used to study the aluminum chemical shielding and electric field gradient tensors, revealing axial symmetry in both cases with a large chemical shielding span of Omega = 83(3) ppm and a small nuclear quadrupole coupling constant, C(Q)((27)Al) = 0.86(10) MHz. Carbon-13 CPMAS NMR experiments in combination with ab initio calculations and simulations of the effects of chemical exchange on (13)C static powder patterns reveal dynamic rotation of rings and suggest a low internal rotational barrier for this process. Theoretical computations of interaction tensors using the Gaussian 98 and Amsterdam Density Functional software packages are in good agreement with experiment and lend insight into the molecular origin of these NMR interactions. Orientations of the NMR tensors determined from theory, the large chemical shielding span, and the very small value of C(Q)((27)Al) can all be rationalized in terms of the high molecular symmetry.     

Residue-specific 13C' CSA tensor principal components for ubiquitin: correlation between tensor components and hydrogen bonding

The residue-specific 13C' CSA tensor principal components, sigma(11), sigma(22), sigma(33), and the tensor orientation defined by the rotation angles beta and gamma have been determined by solution NMR for uniformly labeled ubiquitin partially aligned in four different media. Spurious chemical shift deviations due to solvent effects were corrected with an offset calculated by linear regression of the residual dipolar couplings and chemical shifts at increasing alignment strengths. Analysis of this effect revealed no obvious correlation to solvent exposure. Data obtained in solution from a protein offer a better sampling of 13C' CSA for different amino acid types in a complex heterogeneous environment, thereby allowing for the evaluation of structural variables that would be challenging to achieve by other methods. The 13C' CSA principal components cluster about the average values previously determined, and experimental correlations observed between sigma(11), sigma(22) tensorial components and C'O...H(N) hydrogen bonding are discussed. The inverse association of sigma(11) and sigma(22) exemplify the calculated and solid-state NMR observed effect on the tensor components by hydrogen bonding. We also show that 13C' CSA tensors are sensitive to hydrogen-bond length but not hydrogen-bond angle. This differentiation was previously unavailable. Similarly, hydrogen bonding to the conjugated NH of the same peptide plane has no detectable effect. Importantly, the observed weak correlations signify the presence of confounding influences such as nearest-neighbor effects, side-chain conformation, electrostatics, and other long-range factors to the 13C' CSA tensor. These analyses hold future potential for exploration provided that more accurate data from a larger number of proteins and alignments become available.     

Chemical shift tensors of protonated base carbons in helical RNA and DNA from NMR relaxation and liquid crystal measurements

Knowledge of (13)C chemical shift anisotropy (CSA) tensors in nucleotide bases is important for interpretation of NMR relaxation data in terms of local dynamic properties of nucleic acids and for analysis of residual chemical shift anisotropy (RCSA) resulting from weak alignment. CSA tensors for protonated nucleic acid base carbons have been derived from measurements on a uniformly (13)C-enriched helical A-form RNA segment and a helical B-form DNA dodecamer at natural (13)C abundance. The magnitudes of the derived CSA principal values are tightly restricted by the magnetic field dependencies of the (13)C transverse relaxation rates, whereas the tensor orientation and asymmetry follow from quantitative measurements of interference between (13)C-{(1)H} dipolar and (13)C CSA relaxation mechanisms. Changes in the chemical shift between the isotropic and aligned states, Deltadelta, complement these measurements and permit cross-validation. The CSA tensors are determined from the experimental Deltadelta values and relaxation rates, under the assumption that the CSA tensor of any specific carbon in a given type of base is independent of the base position in either the RNA or DNA helix. However, the experimental data indicate that for pyrimidine C(6) carbons in A-form RNA the CSA magnitude is considerably larger than in B-form DNA. This result is supported by quantum chemical calculations and is attributed in part to the close proximity between intranucleotide C(6)H and O(5)' atoms in RNA. The magnitudes of the measured CSA tensors, on average, agree better with previous solid-state NMR results obtained on powdered nucleosides than with prior results from quantum chemical calculations on isolated bases, which depend rather strongly on the level of theory at which the calculations are carried out. In contrast, previously computed orientations of the chemical shift tensors agree well with the present experimental results and exhibit less dependence on the level of theory at which the computations are performed.     

Symmetry-enthalpy correlations in diels-alder reactions

Woodward-Hoffmann (WH) rules provide strict symmetry selection rules: when they are obeyed, a reaction proceeds; when they are not obeyed, there is no reaction. However, the voluminous experimental literature provides ample evidence that strict compliance to symmetry requirements is not an obstacle for a concerted reaction to proceed, and therefore the idea has developed that it is enough to have a certain degree of the required symmetry to have reactivity. Here we provide quantitative evidence of that link, and show that as one deviates from the desired symmetry, the enthalpy of activation increases, that is, we show that concerted reactions slow down the further they are from the ideal symmetry. Specifically, we study the deviation from mirror symmetry (evaluated with the continuous symmetry measure (CSM)) of the [4+2] carbon skeleton of the transition state of a series of twelve Diels-Alder reactions in seven different solvents (and in the gas phase), in which the dienes are butadiene, cyclopentadiene, cyclohexadiene, and cycloheptadiene; the dienophiles are the 1-, 1,1-, and 1,1,2-cyanoethylene derivatives; the solvents were chosen to sample a range of dielectric constants from heptane to ethanol. These components provide twenty-four symmetry-enthalpy DFT-calculated correlation lines (out of which only one case is a relatively mild exception) that show the general trend of increase in enthalpy as symmetry decreases. The various combinations between the dienophiles, cyanoethylenes, and solvents provide all kinds of sources for symmetry deviations; it is therefore remarkable that although the enthalpy of activation is dictated by various parameters, symmetry emerges as a primary parameter. In our analysis we also bisected this overall picture into solvent effects and geometry variation effects to evaluate under which conditions the electronic effects are more dominant than symmetry effects.