2D(13)C-(13)C MAS NMR correlation spectroscopy with mixing by true (1)H spin diffusion reveals long-range intermolecular distance restraints in ultra high magnetic field

An improved 2D (13)C-(13)C CP(3) MAS NMR correlation experiment with mixing by true (1)H spin diffusion is presented. With CP(3), correlations can be detected over a much longer range than with direct (1)H-(13)C or (13)C-(13)C dipolar recoupling. The experiment employs a (1)H spin diffusion mixing period tau(m) sandwiched between two cross-polarization periods. An optimized CP(3) sequence for measuring polarization transfer on a length scale between 0.3 and 1.0 nm using short mixing times of 0.1 ms < tau(m) < 1 ms is presented. For such a short tau(m), cross talk from residual transverse magnetization of the donating nuclear species after a CP can be suppressed by extended phase cycling. The utility of the experiment for genuine structure determination is demonstrated using a self-aggregated Chl a/H(2)O sample. The number of intramolecular cross-peaks increases for longer mixing times and this obscures the intermolecular transfer events. Hence, the experiment will be useful for short mixing times only. For a short tau(m) = 0.1 ms, intermolecular correlations are detected between the ends of phytyl tails and ring carbons of neighboring Chl a molecules in the aggregate. In this way the model for the structure, with stacks of Chl a that are arranged back to back with interdigitating phytyl chains stretched between two bilayers, is validated.     

Improved narrowband dipolar recoupling for homonuclear distance measurements in rotating solids

Recovery of the magnetic dipolar interaction between nuclei bearing the same gyromagnetic ratio in rotating solids can be promoted by synchronous rf irradiation. Determination of the dipolar interaction strength can serve as a tool for structural elucidation in polycrystalline powders. Spinning frequency dependent narrow-band (nb) RFDR and SEDRA experiments are utilized as simple techniques for the determination of dipolar interactions between the nuclei in coupled homonuclear spin pairs. The magnetization exchange and coherence dephasing due to a fixed number of rotor-synchronously applied pi-pulses is monitored at spinning frequencies in the vicinity of the rotational resonance (R(2)) conditions. The powder nbRFDR and nbSEDRA decay curves of spin magnetizations and coherences, respectively, as a function of the spinning frequency can be measured and analyzed using simple rate equations providing a quantitative measure of the dipolar coupling. The effects of the phenomenological relaxation parameters in these rate equations are discussed and an improved methodology is suggested for analyzing nbRFDR data for small dipolar couplings. The distance between the labeled nuclei in the 1,3-(13)C(2)-hydroxybutyric acid molecule is rederived using existing nbRFDR results and the new simulation procedure. A nbSEDRA experiment has been performed successfully on a powder sample of singly labeled 1-(13)C-L-leucine measuring the dipolar interaction between the labeled carboxyl carbon and the natural abundant beta-carbon. Both narrowband techniques are employed for the determination of the nuclear distances between the side-chain carbons of leucine and its carbonyl carbon in a tripeptide Leu-Gly-Phe that is singly (13)C-labeled at the leucine carbonyl carbon position.     

Dipolar and J encoded DQ MAS spectra under rotational resonance

A two-dimensional (2D) double-quantum (DQ) experiment under rotational resonance (R(2)) conditions is introduced for evaluating dipolar couplings in rotating solids. The contributions from the R(2)-recoupled dipolar interaction and the J coupling can be conveniently separated in the resulting 2D R(2)-DQ spectrum, so that the unknown dipolar coupling can readily be extracted, provided that the values of the involved J coupling constants are known. Since the measured parameters are integral intensity ratios between suitably chosen absorption peaks in the 2D spectrum, the proposed method is characterized by a reduced sensitivity to relaxation parameters. The effect of rotor-modulated terms, including chemical shift anisotropy, is efficiently averaged out by synchronizing the excitation/reconversion time with the rotor period. All of these features are demonstrated theoretically by the example of two model systems, namely, isolated spin-pairs and a three-spin system. The results of the theoretical models are applied to both (13)C and (1)H nuclei to extract dipolar couplings in uniformly (13)C labeled L-alanine and a crosslinked natural rubber.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

An Efficient NMR Experiment for Analyzing Sugar-Puckering in Unlabeled DNA: Application to the 26-kDa Dead Ringer–DNA Complex

We present a new NMR experiment for estimating the type and degree of sugar-puckering in high-molecular-weight unlabeled DNA molecules. The experiment consists of a NOESY sequence preceded by a constant-time scalar coupling period. Two subexperiments are compared, each differing in the amount of time the (3)J(H3'H2') and (3)J(H3'H2") couplings are active on the H3' magnetization. The resultant data are easy to analyze, since a comparison of the signal intensities of any resolved NOE cross peak originating from H3' atoms of the duplex can be used to estimate the sum of the (3)J(H3'H2') and (3)J(H3'H2") couplings and thus the puckering type of the deoxyribose ring. Isotope filters to eliminate signals of the (13)C-labeled component in the F1-dimension are implemented, facilitating analyses of high-molecular-weight protein-DNA complexes containing (13)C-labeled protein and unlabeled DNA. The utility of the experiment is demonstrated on the 26-kDa Dead Ringer protein-DNA complex and reveals that the DNA uniformly adopts the S-type configuration when bound to protein.     

Double-quantum dipolar recoupling at high magic-angle spinning rates

A full investigation of the possible homonuclear double-quantum recoupling sequences, based on the RN family of sequences with N < or = 20, is given. Several new RN sequences, R16(6)(5), R18(8)(5), and R18(10)(5), were applied at high magic-angle spinning rates and compared with theory. The R18(10)(5) technique can be used to recouple dipolar couplings at spinning rates up to 39 kHz, and the application of the sequence in an INADEQUATE experiment is shown for a spinning rate of 30 kHz.     

Variation of molecular alignment as a means of resolving orientational ambiguities in protein structures from dipolar couplings

Residual dipolar couplings for pairs of proximate magnetic nuclei in macromolecules can easily be measured using high-resolution NMR methods when the molecules are dissolved in dilute liquid crystalline media. The resulting couplings can in principle be used to constrain the relative orientation of molecular fragments in macromolecular systems to build a complete structure. However, determination of relative fragment orientations based on a single set of residual dipolar couplings is inherently hindered by the multi-valued nature of the angular dependence of the dipolar interaction. Even with unlimited dipolar data, this gives rise to a fourfold degeneracy in fragment orientations. In this Communication, we demonstrate a procedure based on an order tensor analysis that completely removes this degeneracy by combining residual dipolar coupling measurements from two alignment media. Application is demonstrated on (15)N-(1)H residual dipolar coupling data acquired on the protein zinc rubredoxin from Clostridium pasteurianum dissolved in two different bicelle media.     

A subspace time-domain algorithm for automated NMR spectral normalization

Recently, two methods have been proposed for quantitatively comparing NMR spectra of control and treated samples, in order to examine the possible occurring variations in cell metabolism and/or structure in response to numerous physical, chemical, and biological agents. These methods are the maximum superposition normalization algorithm (MaSNAl) and the minimum rank normalization algorithm (MiRaNAl). In this paper a new subspace-based time-domain normalization algorithm, denoted by SuTdNAl (subspace time-domain normalization algorithm), is presented. By the determination of the intersection of the column spaces of two Hankel matrices, the common signal poles and further on the components having proportionally varying amplitudes are detected. The method has the advantage that it is computationally less intensive than the MaSNAl and the MiRaNAl. Furthermore, no approximate estimate of the normalization factor is required. The algorithm was tested by Monte Carlo simulations on a set of simulation signals. It was shown that the SuTdNAl has a statistical performance similar to that of the MiRaNAl, which itself is an improvement over the MaSNAl. Furthermore, two samples of known contents are compared with the MiRaNAl, the SuTdNAl, and an older method using a standard. Finally, the SuTdNAl is tested on a realistic simulation example derived from an in vitro measurement on cells.     

Obtaining molecular and structural information from 13C-14N systems with 13C FIREMAT experiments

The effect of dipolar coupling to 14N on 13C FIREMAT (five pi replicated magic angle turning) experiments is investigated. A method is developed for fitting the 13C FIREMAT FID employing the full theory to extract the 13C-14N dipolar and 13C chemical shift tensor information. The analysis requires prior knowledge of the electric field gradient (EFG) tensor at the 14N nucleus. In order to validate the method the analysis is done for the amino acids alpha-glycine, gamma-glycine, l-alanine, l-asparagine, and l-histidine on FIREMAT FIDs recorded at 13C frequencies of 50 and 100 MHz. The dipolar and chemical shift data obtained with this analysis are in very good agreement with the previous single-crystal 13C NMR results and neutron diffraction data on alpha-glycine, l-alanine, and l-asparagine. The values for gamma-glycine and l-histidine obtained with this new method are reported for the first time. The uncertainties in the EFG tensor on the resultant 13C chemical shift and dipolar tensor values are assessed.     

Measurement of one-bond heteronuclear dipolar coupling contributions for amine and diastereotopic methylene protons

One-bond heteronuclear and two-bond homonuclear residual dipolar couplings measured at methylene or amine sites can be utilized as long-range constraints in structure determination of molecules as well as to facilitate characterization of local conformation by stereospecific assignment of diastereotopic protons. We present two J-modulated HMQC type experiments to measure the one-bond heteronuclear dipolar coupling contributions of geminal protons individually. In addition two-bond homonuclear residual dipolar couplings between the diastereotopic protons are also obtained.     

Imaging the long-range dipolar field in structured liquid state samples

We describe imaging experiments in which the pattern of the dipolar field generated by spatially modulated nuclear magnetization is directly visualized in simply structured phantoms. Two types of experiment have been carried out at 11.7 T using (1)H NMR signals. In the first, the field from a single spin species is imaged via its own NMR signal. In the second, the NMR signal from one spin species is used to image the field generated by a second species. The field patterns measured in these experiments correspond well with those calculated using simple theoretical expressions for the dipolar field. The results also directly demonstrate the spatial sensitivity of the signal generated using dipolar field effects, indicating that the range of the field depends upon the inverse of the spatial frequency with which the magnetization is modulated.     

Separating Structure and Dynamics in CSA/DD Cross-Correlated Relaxation: A Case Study on Trehalose and Ubiquitin

We present two new sensitivity enhanced gradient NMR experiments for measuring interference effects between chemical shift anisotropy (CSA) and dipolar coupling interactions in a scalar coupled two-spin system in both the laboratory and rotating frames. We apply these methods for quantitative measurement of longitudinal and transverse cross-correlation rates involving interference of ¹³C CSA and ¹³C–¹H dipolar coupling in a disaccharide, α,α- -trehalose, at natural abundance of ¹³C as well as interference of amide ¹⁵N CSA and ¹⁵N–¹H dipolar coupling in uniformly ¹⁵N-labeled ubiquitin. We demonstrate that the standard heteronuclear T₁, T₂, and steady-state NOE autocorrelation experiments augmented by cross-correlation measurements provide sufficient experimental data to quantitatively separate the structural and dynamic contributions to these relaxation rates when the simplifying assumptions of isotropic overall tumbling and an axially symmetric chemical shift tensor are valid.     

Sensitivity enhancement in structural measurements by solid state NMR through pulsed spin locking

Free induction decay (FID) signals in solid state NMR measurements performed with magic angle spinning can often be extended in time by factors on the order of 10 by a simple pulsed spin locking technique. The sensitivity of a structural measurement in which the structural information is contained in the dependence of the integrated FID amplitude on a preceding evolution period can therefore be enhanced substantially by pulsed spin locking in the signal detection period. We demonstrate sensitivity enhancements in a variety of solid state NMR techniques that are applicable to selectively isotopically labeled samples, including 13C-15N rotational echo double resonance (REDOR), 13C-13C dipolar recoupling measurements using the constant-time finite-pulse radio-frequency-driven recoupling (fpRFDR-CT) and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) techniques, and torsion angle measurements using the double quantum chemical shift anisotropy (DQCSA) technique. Further, we demonstrate that the structural information in the solid state NMR data is not distorted by pulsed spin locking in the detection period.     

Protein Backbone N Relaxation Rates as a Tool for the Diagnosis of Structure Quality

In the work reported herein we define a structure validation factor that depends on protein backbone ¹⁵N relaxation rates. This is an alternative method to the previously defined quality factors derived from anisotropic chemical shifts or residual dipolar couplings. We have used the structure dependence of ¹⁵N relaxation rates of anisotropically tumbling proteins to calculate this structure diagnosis factor and have used it to demonstrate the improvement of protein structures refined with residual dipolar couplings.     

Analysis of protein/ligand interactions with NMR diffusion measurements: the importance of eliminating the protein background

Pulsed-field gradient nuclear magnetic resonance (PFG-NMR) is a well-established method for the determination of translational diffusion coefficients. Recently, this method has found applicability in the combinatorial arena with the introduction of affinity NMR for characterizing protein/ligand interactions. Although affinity NMR has been reported to be an effective method for the identification of active compounds in a complex mixture, there are limitations of this method. We have developed a simple mathematical model to predict optimum concentration ratios of the ligand and protein in order to observe maximum changes in the ligand diffusion coefficient upon protein binding. The ligand/protein systems of L-tryptophan and ibuprofen binding to human serum albumin were chosen to demonstrate the usefulness of this model. However, even when the conditions of the mathematical model are satisfied, the spectral background arising from the protein in proton-detected experiments can be problematic. To this end, we have employed spectral subtraction of the protein spectrum to yield ligand diffusion coefficients that are in agreement with those predicted by simulation.     

Magnetization transfer via residual dipolar couplings: application to proton-proton correlations in partially aligned proteins

A novel three-dimensional NMR experiment is reported that allows the observation of correlations between amide and other protons via residual dipolar couplings in partially oriented proteins. The experiment is designed to permit quantitative measurement of the magnitude of proton-proton residual dipolar couplings in larger molecules and at higher degree of alignments. The observed couplings contain data valuable for protein resonance assignment, local protein structure refinement, and determination of low-resolution protein folds.     

Magnetization Transfer via Residual Dipolar Couplings: Application to Proton–Proton Correlations in Partially Aligned Proteins

A novel three-dimensional NMR experiment is reported that allows the observation of correlations between amide and other protons via residual dipolar couplings in partially oriented proteins. The experiment is designed to permit quantitative measurement of the magnitude of proton–proton residual dipolar couplings in larger molecules and at higher degree of alignments. The observed couplings contain data valuable for protein resonance assignment, local protein structure refinement, and determination of low-resolution protein folds.     

PELDOR at S- and X-band frequencies and the separation of exchange coupling from dipolar coupling

A pulsed electron double resonance (PELDOR) setup working at S-band frequencies is introduced and its performance compared with an X-band setup. Furthermore, to verify experimentally that it is possible to disentangle the dipolar coupling nu(Dip) from the exchange coupling J by PELDOR we synthesized and investigated four bisnitroxide radicals. They exhibit in pairs the same distances r(AB) between the nitroxide moieties but only one of each pair possesses a non-zero J. The experimental values for r(AB) match the ones from molecular modeling very well for the molecules without exchange coupling. For one bisnitroxide it was possible to separate nu(Dip) from J and to ascertain the magnitude and sign of J to +11 MHz (antiferromagnetic spin-spin coupling).     

Sequential HNCACB and CBCANH protein NMR pulse sequences

The pulse sequences HNCACB and CBCANH correlating side chain C(beta) resonances with amide resonances in the protein backbone do not distinguish between inter- and intraresidue correlations. The new pulse sequences sequential HNCACB and sequential CBCANH make this distinction by suppressing coherence transfer between 13C(alpha) and 15N via the one-bond J(NC(alpha)) coupling so that only the sequential correlations are observed in the spectrum. The experimental results of applying sequential HNCACB in a clean-TROSY-adapted implementation to the protein Chymotrypsin Inhibitor 2 at 800 MHz are presented.     

A Residual-Based Compact Scheme for the Compressible Navier–Stokes Equations

A simple and efficient time-dependent method is presented for solving the steady compressible Euler and Navier–Stokes equations with third-order accuracy. Owing to its residual-based structure, the numerical scheme is compact without requiring any linear algebra, and it uses a simple numerical dissipation built on the residual. The method contains no tuning parameter. Accuracy and efficiency are demonstrated for 2-D inviscid and viscous model problems. Navier–Stokes calculations are presented for a shock/boundary layer interaction, a separated laminar flow, and a transonic turbulent flow over an airfoil.