C Chemical Shift and C–N Dipolar Coupling Tensors Determined by C Rotary Resonance Solid-State NMR

This work explores the utility of simple rotary resonance experiments for the determination of the magnitude and orientation of ¹³C chemical shift tensors relative to one or more ¹³C–¹⁴N internuclear axes from ¹³C magic-angle-spinning NMR experiments. The experiment relies on simultaneous recoupling of the anisotropic ¹³C chemical shift and ¹³C–¹⁴N dipole–dipole coupling interactions using 2D rotary resonance NMR with RF irradiation on the ¹³C spins only. The method is demonstrated by experiments and numerical simulations for the ¹³C^α spins in powder samples of -alanine and glycine with ¹³C in natural abundance. To investigate the potential of the experiment for determination of relative/absolute tensor orientations and backbone dihedral angles in peptides, the influence from long-range dipolar coupling to sequential ¹⁴N spins in a peptide chain (¹⁴N_i–¹³C^α_i–¹⁴N_i+1 and ¹⁴N_i+1–¹³C′_i–¹⁴N_i three-spin systems) as well as residual quadrupolar–dipolar coupling cross-terms is analyzed numerically.     

Asymmetric MRI magnet design using a hybrid numerical method

Two-dimensional 1H/13C polarization inversion spin exchange at the magic angle experiments were applied to single crystal samples of amino acids to demonstrate their potential utility on oriented samples of peptides and proteins. High resolution is achieved and structural information obtained on backbone and side chain sites from these spectra. A triple-resonance experiment that correlates the 1H-13Calpha dipolar coupling frequency with the chemical shift frequencies of the alpha-carbon, as well as the directly bonded amide 15N site, is also demonstrated. In this experiment the large 1H-13Calpha heteronuclear dipolar interaction provides an independent frequency dimension that significantly improves the resolution among overlapping 13C resonances of oriented polypeptides, while simultaneously providing measurements of the 13Calpha chemical shift, 1H-13C dipolar coupling, and 15N chemical shift frequencies and angular restraints for backbone structure determination.     

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.     

Recoupled Polarization-Transfer Methods for Solid-State H–C Heteronuclear Correlation in the Limit of Fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for ¹H–¹³C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR π-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized ¹H–¹³C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with ¹³C in natural abundance, as well as simulations, confirm the very weak effect of ¹H–¹H homonuclear couplings on the spectra recorded with spinning frequencies of 25–30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH_n groups is discussed, and ¹³C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Three-Dimensional C Shift/H–N Coupling/N Shift Solid-State NMR Correlation Spectroscopy

Triple-resonance experiments capable of correlating directly bonded and proximate carbon and nitrogen backbone sites of uniformly ¹³C- and ¹⁵N-labeled peptides in stationary oriented samples are described. The pulse sequences integrate cross-polarization from ¹H to ¹³C and from ¹³C to ¹⁵N with flip-flop (phase and frequency switched) Lee–Goldburg irradiation for both ¹³C homonuclear decoupling and ¹H–¹⁵N spin exchange at the magic angle. Because heteronuclear decoupling is applied throughout, the three-dimensional pulse sequence yields ¹³C shift/¹H–¹⁵N coupling/¹⁵N shift correlation spectra with single-line resonances in all three frequency dimensions. Not only do the three-dimensional spectra correlate ¹³C and ¹⁵N resonances, they are well resolved due to the three independent frequency dimensions, and they can provide up to four orientationally dependent frequencies as input for structure determination. These experiments have the potential to make sequential backbone resonance assignments in uniformly ¹³C- and ¹⁵N-labeled proteins.     

N Chemical Shift Tensor Magnitude and Orientation in the Molecular Frame of Uracil Determined via MAS NMR

The potential of heteronuclear MAS NMR spectroscopy for the characterization of ¹⁵N chemical shift (CS) tensors in multiply labeled systems has been illustrated, in one of the first studies of this type, by a measurement of the chemical shift tensor magnitude and orientation in the molecular frame for the two ¹⁵N sites of uracil. Employing polycrystalline samples of ¹⁵N₂ and 2-¹³C,¹⁵N₂-labeled uracil, we have measured, via ¹⁵N–¹³C REDOR and ¹⁵N–¹H dipolar-shift experiments, the polar and azimuthal angles (θ, ψ) of orientation of the ¹⁵N–¹³C and ¹⁵N–¹H dipolar vectors in the ¹⁵N CS tensor frame. The (θ_NC, ψ_NC) angles are determined to be (92 ± 10°, 100 ± 5°) and (132 ± 3°, 88 ± 10°) for the N1 and N3 sites, respectively. Similarly, (θ_NH, ψ_NH) are found to be (15 ± 5°, −80 ± 10°) and (15 ± 5°, 90 ± 10°) for the N1 and N3 sites, respectively. These results obtained based only on MAS NMR measurements have been compared with the data reported in the literature.     

Structural analysis of uniformly C-labelled solids from selective angle measurements at rotational resonance

We demonstrate that individual H–C–C–H torsional angles in uniformly labelled organic solids can be estimated by selective excitation of ¹³C double-quantum coherences under magic-angle spinning at rotational resonance. By adapting a straightforward one-dimensional experiment described earlier [T. Karlsson, M. Eden, H. Luhman, M.H. Levitt, J. Magn. Reson. 145 (2000) 95–107], a double-quantum filtered spectrum selective for Cα and Cβ of uniformly labelled l-[¹³C,¹⁵N]valine is obtained with 25% efficiency. The evolution of Cα–Cβ double-quantum coherence under the influence of the dipolar fields of bonded protons is monitored to provide a value of the Hα–Cα–Cβ–Hβ torsional angle that is consistent with the crystal structure. In addition, double-quantum filtration selective for C6 and C1′ of uniformly labelled [¹³C,¹⁵N]uridine is achieved with 12% efficiency for a ¹³C–¹³C distance of 2.5 Å, yielding a reliable estimate of the C6–H and C1′–H projection angle defining the relative orientations of the nucleoside pyrimidine and ribose rings. This procedure will be useful, in favourable cases, for structural analysis of fully labelled small molecules such as receptor ligands that are not readily synthesised with labels placed selectively at structurally diagnostic sites.     

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.     

Measurement of Cross Correlation between Dipolar Coupling and Chemical Shift Anisotropy in the Spin Relaxation ofC,N-Labeled Proteins

We present a simple method for extracting interference effects between chemical shift anisotropy (CSA) and dipolar coupling from spin relaxation measurements in macromolecules, and we apply this method to extracting cross-correlation rates involving interference of amide¹⁵N CSA and¹⁵N–¹H dipolar coupling and interference of carbonyl¹³C′ CSA and¹⁵N–¹³C′ dipolar coupling, in a small protein. A theoretical basis for the interpretation of these rates is presented. While it proves difficult to quantitatively separate the structural and dynamic contributions to these cross-correlation rates in the presence of anisotropic overall tumbling and a nonaxially symmetric chemical shift tensor, some useful qualitative correlations of data with protein structure can be seen when simplifying assumptions are made.     

CHHC and H–H magnetization exchange: Analysis by experimental solid-state NMR and 11-spin density-matrix simulations

A protocol is presented for correcting the effect of non-specific cross-polarization in CHHC solid-state MAS NMR experiments, thus allowing the recovery of the ¹H–¹H magnetization exchange functions from the mixing-time dependent buildup of experimental CHHC peak intensity. The presented protocol also incorporates a scaling procedure to take into account the effect of multiplicity of a CH₂ or CH₃ moiety. Experimental CHHC buildup curves are presented for l-tyrosine·HCl samples where either all or only one in 10 molecules are U–¹³C labeled. Good agreement between experiment and 11-spin SPINEVOLUTION simulation (including only isotropic ¹H chemical shifts) is demonstrated for the initial buildup (t_mix < 100 μs) of CHHC peak intensity corresponding to an intramolecular close (2.5 Å) H–H proximity. Differences in the initial CHHC buildup are observed between the one in 10 dilute and 100% samples for cases where there is a close intermolecular H–H proximity in addition to a close intramolecular H–H proximity. For the dilute sample, CHHC cross-peak intensities tended to significantly lower values for long mixing times (500 μs) as compared to the 100% sample. This difference is explained as being due to the dependence of the limiting total magnetization on the ratio N_obs/N_tot between the number of protons that are directly attached to a ¹³C nucleus and hence contribute significantly to the observed ¹³C CHHC NMR signal, and the total number of ¹H spins into the system. ¹H–¹H magnetization exchange curves extracted from CHHC spectra for the 100% l-tyrosine·HCl sample exhibit a clear sensitivity to the root sum squared dipolar coupling, with fast buildup being observed for the shortest intramolecular distances (2.5 Å) and slower, yet observable buildup for the longer intermolecular distances (up to 5 Å).     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation betweenC–H Dipolar Interaction andC Chemical Shift Anisotropy: Application to aC-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Cation Binding Induced Changes inN CSA in a Membrane-Bound Polypeptide

Cation binding to the monovalent cation selective channel, gramicidin A, is shown to induce changes in the dipolar and chemical shift observables from uniformly aligned samples. While these changes could be the result of structural or dynamic changes, they are shown to be primarily induced by through-bond polarizability effects when cations are solvated by the carbonyl oxygens of the peptide backbone. Upon cation binding partial charges are changed throughout the peptide plane, inducing large changes in the¹³C₁chemical shifts, smaller changes in the¹⁵N chemical shifts, and even smaller effects for the¹⁵N–¹³C₁and¹⁵N–²H dipolar interactions. These conclusions are substantiated by characterizing the¹⁵N chemical shift tensors in the presence and absence of cations in fast-frozen lipid bilayer preparations of gramicidin A.     

The roles of homonuclear line narrowing and the1H amide chemical shift tensor in structure determination of proteins by solid-state NMR spectroscopy

The seminal contributions of Ulrich Haeberlen to homonuclear line narrowing and the determination of¹H chemical shift tensors are crucial for protein structure determination by solid-state nuclear magnetic resonance spectroscopy. The¹H chemical shift is particularly important in spectra obtained on oriented samples of membrane proteins as a mechanism for providing dispersion among resonances that are not resolved with the¹H-¹⁵N dipolar coupling and¹⁵N chemical shift frequencies. This is demonstrated with three-dimensional experiments on uniformly¹⁵N-labeled samples of Magainin antibiotic peptide and the protein Vpu from HIV-1 in oriented lipid bilayers. These experiments enable resonances in two-dimensional¹H-¹⁵N dipolar coupling/¹⁵N chemical shift planes separated by¹H chemical shift frequencies to be resolved and analyzed. These three-dimensional spectra are compared to one-dimensional spectra of full-length Vpu, the cytoplasmic domain of Vpu, and Magainin, as well as to two-dimensional spectra of fd coat protein and Colicin El polypeptide. The¹H amide chemical shift tensor provides valuable structural information, and this is demonstrated with its contributions to orientational restrictions to one of the in-plane helical residues of Magainin.     

Triple resonance experiments for aligned sample solid-state NMR of (13)C and (15)N labeled proteins

Initial steps in the development of a suite of triple-resonance (1)H/(13)C/(15)N solid-state NMR experiments applicable to aligned samples of (13)C and (15)N labeled proteins are described. The experiments take advantage of the opportunities for (13)C detection without the need for homonuclear (13)C/(13)C decoupling presented by samples with two different patterns of isotopic labeling. In one type of sample, the proteins are approximately 20% randomly labeled with (13)C in all backbone and side chain carbon sites and approximately 100% uniformly (15)N labeled in all nitrogen sites; in the second type of sample, the peptides and proteins are (13)C labeled at only the alpha-carbon and (15)N labeled at the amide nitrogen of a few residues. The requirement for homonuclear (13)C/(13)C decoupling while detecting (13)C signals is avoided in the first case because of the low probability of any two (13)C nuclei being bonded to each other; in the second case, the labeled (13)C(alpha) sites are separated by at least three bonds in the polypeptide chain. The experiments enable the measurement of the (13)C chemical shift and (1)H-(13)C and (15)N-(13)C heteronuclear dipolar coupling frequencies associated with the (13)C(alpha) and (13)C' backbone sites, which provide orientation constraints complementary to those derived from the (15)N labeled amide backbone sites. (13)C/(13)C spin-exchange experiments identify proximate carbon sites. The ability to measure (13)C-(15)N dipolar coupling frequencies and correlate (13)C and (15)N resonances provides a mechanism for making backbone resonance assignments. Three-dimensional combinations of these experiments ensure that the resolution, assignment, and measurement of orientationally dependent frequencies can be extended to larger proteins. Moreover, measurements of the (13)C chemical shift and (1)H-(13)C heteronuclear dipolar coupling frequencies for nearly all side chain sites enable the complete three-dimensional structures of proteins to be determined with this approach.     

Sample Optimization and Identification of Signal Patterns of Amino Acid Side Chains in 2D RFDR Spectra of the α-Spectrin SH3 Domain

Future structural investigations of proteins by solid-state CPMAS NMR will rely on uniformly labeled protein samples showing spectra with an excellent resolution. NMR samples of the solid α-spectrin SH3 domain were generated in four different ways, and their ¹³C CPMAS spectra were compared. The spectrum of a [u-¹³C, ¹⁵N]-labeled sample generated by precipitation shows very narrow ¹³C signals and resolved scalar carbon–carbon couplings. Linewidths of 16–19 Hz were found for the three alanine C^β signals of a selectively labeled [70% 3-¹³C]alanine-enriched SH3 sample. The signal pattern of the isoleucine, of all prolines, valines, alanines, and serines, and of three of the four threonines were identified in 2D ¹³C–¹³C RFDR spectra of the [u-¹³C,¹⁵N]-labeled SH3 sample. A comparison of the ¹³C chemical shifts of the found signal patterns with the ¹³C assignment obtained in solution shows an intriguing match.     

Carbon-13 and Fluorine-19 NMR Spectroscopy of the Supramolecular Solid p-tert-Butylcalix[4]arene ·α,α,α-trifluorotoluene

The supramolecular 1 : 1 host–guest inclusion compound, p-tert-butylcalix[4]arene ·α,α,α-trifluorotoluene, 1, is characterized by ¹⁹F and ¹³C solid-state NMR spectroscopy. Whereas the ¹³C NMR spectra are easily interpreted in the context of earlier work on similar host–guest compounds, the ¹⁹F NMR spectra of solid 1 are, initially, more difficult to understand. The ¹⁹F{¹H} NMR spectrum obtained under cross-polarization and magic-angle spinning conditions shows a single isotropic resonance with a significant spinning sideband manifold. The static ¹⁹F{¹H} CP NMR spectrum consists of a powder pattern dominated by the contributions of the anisotropic chemical shift and the homonuclear dipolar interactions. The ¹⁹F MREV-8 experiment, which minimizes the ¹⁹F–¹⁹F dipolar contribution, helps to identify the chemical shift contribution as an axial lineshape. The full static ¹⁹F{¹H} CP NMR spectrum is analysed using subspectral analysis and subsequently simulated as a function of the ¹⁹F–¹⁹F internuclear distance (D_FF = 2.25 ± 0.01 Å) of the rapidly rotating CF₃ group without including contributions from additional libration motions and the anisotropy in the scalar tensor. The shielding span is found to be 56 ppm. The width of the centerband in the ¹⁹F{¹H} sample-spinning CP NMR spectrum is very sensitive to the angle between the rotor and the magnetic field. Compound 1 is thus an attractive standard for setting the magic angle for NMR probes containing a fluorine channel with a proton-decoupling facility.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

Measurement of one and two bond N–C couplings in large proteins by TROSY-based J-modulation experiments

Residual dipolar couplings (RDCs) between NC′ and NC^α atoms in polypeptide backbones of proteins contain information on the orientation of bond vectors that is complementary to that contained in NH RDCs. The ¹J_NC^α and ²J_NC^α scalar couplings between these atoms also display a Karplus relation with the backbone torsion angles and report on secondary structure. However, these N–C couplings tend to be small and they are frequently unresolvable in frequency domain spectra having the broad lines characteristic of large proteins. Here a TROSY-based J-modulated approach for the measurement of small ¹⁵N–¹³C couplings in large proteins is described. The cross-correlation interference effects inherent in TROSY methods improve resolution and signal to noise ratios for large proteins, and the use of J-modulation to encode couplings eliminates the need to remove frequency distortions from overlapping peaks during data analysis. The utility of the method is demonstrated by measurement of ¹J_NC′, ¹J_NC^α, and ²J_NC^α scalar couplings and ¹D_NC′ and ¹D_NC^α residual dipolar couplings for the myristoylated yeast ARF1·GTPγs protein bound to small lipid bicelles, a system with an effective molecule weight of 70 kDa.     

Using multiple quantum coherence to increase the N resolution in a three-dimensional TROSY HNCO experiment for accurate PRE and RDC measurements

We present a new version of the 3D TROSY HNCO pulse scheme, referred to as HR-TROSY HNCO, with comparable resolution in the ¹⁵N dimension to a 2D ¹H–¹⁵N HSQC experiment. In the conventional 3D TROSY HNCO, the constant time period (1/2J_NC  32 ms) severely limits the maximum resolution in the ¹⁵N dimension. In the HR-TROSY HNCO experiment presented here, both constant time periods (32 ms each) for coherence forward and backward transfer between ¹⁵N and ¹³C′ are utilized to double the ¹⁵N evolution time. This leads to a dramatic enhancement in peak separation along the ¹⁵N dimension, making the HR-TROSY HNCO an ideal pulse scheme for accurate paramagnetic relaxation enhancement and residual dipolar coupling measurements.     

Fluorine-19 Solid-State NMR Magic-Angle-Turning Experiments Using Multiple-Pulse Homonuclear Decoupling

For compounds giving “crowded” 1-dimensional magic-angle-spinning spectra, information about the local atomic environment in the form of the chemical shift anisotropy (CSA) is sacrificed for high resolution of the less informative isotropic chemical shift. Magic-angle-turning (MAT) NMR pulse sequences preserve the CSA information by correlating it to the isotropic chemical shift in a 2-dimensional experiment. For low natural abundance nuclei such as ¹³C and ¹⁵N and under ¹H heteronuclear dipolar decoupling conditions, the dominant NMR interaction is the chemical shift. For abundant nuclei such as ¹H, ¹⁹F, and ³¹P, the homonuclear dipolar interaction becomes a significant contribution to the observed linewidth in both F₁ and F₂ dimensions. We incorporate MREV8 homonuclear multiple-pulse decoupling sequences into the MAT experiment to give a multiple-pulse MAT (MP-MAT) experiment in which the homonuclear dipolar interaction is suppressed while maintaining the chemical shift information. Extensive use of computer simulation using GAMMA has guided the pulse sequence development. In particular, we show how the MREV8 pulses can be incorporated into a quadrature-detected sequence such as MAT. The MP-MAT technique is demonstrated for a model two-site system containing a mixture of silver trifluoroacetate and calcium difluoride. The resolution in the isotropic evolution dimension is improved by faster sample spinning, shorter MREV8 cycle times in the evolution dimension, and modifications of the MAT component of the pulse sequence.