Coherence selection in double CP MAS NMR spectroscopy

Applications of double cross-polarization (CP) magic-angle spinning (MAS) NMR spectroscopy, via (1)H/(15)N and then (15)N/(13)C coherence transfers, for (13)C coherence selection are demonstrated on a (15)N/(13)C-labeled N-acetyl-glucosamine (GlcNAc) compound. The (15)N/(13)C coherence transfer is very sensitive to the settings of the experimental parameters. To resolve explicitly these parameter dependences, we have systematically monitored the (13)C{(15)N/(1)H} signal as a function of the rf field strength and the MAS frequency. The data reveal that the zero-quantum coherence transfer, with which the (13)C effective rf field is larger than that of the (15)N by the spinning frequency, would give better signal sensitivity. We demonstrate in one- and two-dimensional double CP experiments that spectral editing can be achieved by tailoring the experimental parameters, such as the rf field strengths and/or the MAS frequency.     

The Effect of RF Inhomogeneity on Heteronuclear Dipolar Recoupling in Solid State NMR: Practical Performance of SFAM and REDOR

Practical heteronuclear dipolar recoupling performances under magic angle spinning for SFAM and REDOR have been investigated under well-defined rf inhomogeneity environments with variation of resonance offsets for the irradiated nucleus. The heteronuclear dipolar recoupling efficiencies were quantitatively determined based on the experimentally obtained rf homogeneity. As a result, SFAM retains higher recoupling efficiency (>95%) at an 85% effective nutation frequency, and its recoupling efficiency is gradually reduced at lower effective nutation frequencies. On the other hand, although REDOR retains higher recoupling (>95%) efficiency at high (>92%) effective nutation frequency with an XY-8 compensation pulse sequence, the recoupling efficiency is dramatically decreased when the effective nutation frequency is below 90%. Over all, SFAM has significant advantages for insensitivity to carrier frequency offset and rf inhomogeneity.     

Recoupling of heteronuclear dipolar interactions with rotational-echo double-resonance at high magic-angle spinning frequencies

Heteronuclear dipolar recoupling with rotational-echo double-resonance (REDOR) is investigated in the rapid magic-angle spinning regime, where radiofrequency irradiation occupies a significant fraction of the rotor period (10-60%). We demonstrate, in two model (13)C-(15)N spin systems, [1-(13)C, (15)N] and [2-(13)C, (15)N]glycine, that REDOR DeltaS/S(0) curves acquired at high MAS rates and relatively low recoupling fields are nearly identical to the DeltaS/S(0) curve expected for REDOR with ideal delta-function pulses. The only noticeable effect of the finite pi pulse length on the recoupling is a minor scaling of the dipolar oscillation frequency. Experimental results are explained using both numerical calculations and average Hamiltonian theory, which is used to derive analytical expressions for evolution under REDOR recoupling sequences with different pi pulse phasing schemes. For xy-4 and extensions thereof, finite pulses scale only the dipolar oscillation frequency by a well-defined factor. For other phasing schemes (e.g., xx-4 and xx-4) both the frequency and amplitude of the oscillation are expected to change.     

Rotary resonance echo double resonance for measuring heteronuclear dipolar coupling under MAS

A rotary resonance echo double resonance (R-REDOR) experiment is described for measuring heteronuclear dipolar coupling under magic-angle spinning. Rotary resonance reintroduces both dipolar coupling and chemical shift anisotropy with an rf field matching the spinning frequency. The resonance effect from chemical shift anisotropy can be refocused with a rotary resonance echo. The R-REDOR experiment thus measures the dephasing of the rotary resonance echo from the heteronuclear dipolar coupling to determine the dipolar coupling constant. The rotary resonance experiment is suitable for measuring dipolar coupling with quadrupolar nuclei because it applies the recoupling rf only to the observed spin-1/2. The rotary resonance scheme has the advantages of a long T2' and susceptible to spinning frequency fluctuation.     

Heteronuclear dipolar recoupling in liquid crystals and solids by PISEMA-type pulse sequences

A pulse sequence is described for the recoupling of heteronuclear dipolar interactions under MAS. The method is similar to the PISEMA experiment, but employs a well-defined amplitude modulation of one of the two radio-frequency fields. The technique is used for measurements of 1H-13C dipolar couplings in unoriented solid and liquid-crystalline samples.     

C–H dipolar recoupling under very fast magic-angle spinning using virtual pulses

A new solid-state NMR pulse sequence for recoupling ¹³C–¹H dipolar interactions under magic-angle spinning is proposed, which works under a spinning speed of a few to several tens kilohertz. The sequence is composed of two different frequency switched Lee–Goldburg sequences, and the modulation of the spin part of the ¹³C–¹H dipolar interaction is introduced by a virtual pulse sequence consisting of unitary operators connecting the rotating frame and the tilted rotating frame. When the cycle time of the spinning is equal to or twice the cycle time of the sequence, the ¹³C–¹H dipolar interactions can be recoupled. The sequence is insensitive to experimental imperfections such as rf inhomogeneity or frequency offset, and the resulting lineshape can be represented by a simple analytical equation based on the zeroth-order average Hamiltonian. Experimental results for [2-¹³C] -valine·HCl are reported.     

Band-selective recoupling of homonuclear double-quantum dipolar interaction with a generalized composite 0 degrees pulse: application to 13C aliphatic region-selective magnetization transfer in solids

Recoupling of homonuclear double quantum (DQ)-dipolar interactions is a useful technique for the structural analysis of molecules in solids. We have designed a series of elemental 0 degrees pulses for the recoupling sequences with the rf phase rotation about the z-axis, known as CN. The proposed 0 degrees pulses whose total flip angle >/=360 degrees provide spin rotation vectors in the xy-plane. Thus, the residual spin rotation can be canceled by rf phase rotation about the z-axis. An analysis by the coherent averaging theory showed that effective bandwidths of the recoupling sequences are limited not by the reduction in the dipolar scaling factor but by the increase in the residual spin rotation due to offset. A CN sequence with these elemental pulses provides an effective bandwidth of DQ-dipolar recoupling from ca. 0.5nu(R) to 4nu(R) for numerical simulations. Here, nu(R) is the sample spinning frequency. The 0 degrees pulses were applied to band-selective recoupling for the magnetization transfer in uniformly 13C-labeled molecules. Narrow-band recoupling enhances the magnetization transfer between spins within the effective range by decoupling the dipolar interactions between spins one of which is outside the range. The narrow band operation reduces rf field strength, which improves the CH decoupling. Increases in signal intensities by the use of the proposed 0 degrees pulses are experimentally shown for 13C-labeled amino acids.     

One- and two-dimensional 13C-1H/15N- 1H dipolar correlation experiments under fast magic-angle spinning for determining the peptide dihedral angle phi

A recently proposed 13C-1H recoupling sequence operative under fast magic-angle spinning (MAS) [K. Takegoshi, T. Terao, Solid State Nucl. Magn. Reson. 13 (1999) 203-212.] is applied to observe 13C-1H and 15N-1H dipolar powder patterns in the IH-15N- 3C- H system of a peptide bond. Both patterns are correlated by 15N-to-13C cross polarization to observe one- or two-dimensional (1D or 2D) correlation spectra, which can be simulated by using a simple analytical expression to determine the H-N-C-H dihedral angle. The 1D and 2D experiments were applied to N-acetyl[1,2-13C,15N] DL-valine, and the peptide q angle was determined with high precision by the 2D experiment to be +/- 155.0 degrees +/- 1.2 degrees. The positive one is in good agreement with the X-ray value of 154 degrees +/- 5 degrees. The 1D experiment provided the value of phi = +/- 156.0 degrees +/- 0.8 degrees.     

Sensitivity enhanced recoupling experiments in solid-state NMR by gamma preparation

In this paper, we introduce a class of dipolar recoupling experiments under magic angle spinning (MAS), which use gamma dependent antiphase polarization during the t1 evolution period. We show that this helps us to design dipolar recoupling experiments that transfer both components of the transverse magnetization of spin S to a coupled spin I in the mixing step of a 2D NMR experiment. We show that it is possible to design such transfer schemes and make them insensitive to the orientation dependency of the couplings in powders. This helps us to develop sensitivity enhanced 2D NMR experiments of powder samples under MAS.     

Relaxation-induced dipolar exchange with recoupling-An MAS NMR method for determining heteronuclear distances without irradiating the second spin

A new magic-angle spinning NMR method for distance determination between unlike spins, where one of the two spins in question is not irradiated at all, is introduced. Relaxation-induced dipolar exchange with recoupling (RIDER) experiments can be performed with conventional double-resonance equipment and utilize the familiar π-pulse trains to recouple the heteronuclear dipolar interaction under magic-angle spinning conditions. Longitudinal relaxation of the passive spin during a delay between two recoupling periods results in a dephasing of the heteronuclear coherence and consequently a dephasing of the magnetization detected after the second recoupling period. The information about the dipolar coupling is obtained by recording normalized dephasing curves in a fashion similar to the REDOR experiment. At intermediate mixing times, the dephasing curves also depend on the relaxation properties of the passive spin, i.e., on single- and double-quantum longitudinal relaxation times for the case of I = 1 nuclei, and these relaxation times can be estimated with this new method. To a good approximation, the experiment does not depend on possible quadrupolar interactions of the passive spin, which makes RIDER an attractive method when distances to quadrupolar nuclei are to be determined. The new method is demonstrated experimentally with ¹⁴N and ²H as heteronuclei and observation of ¹³C in natural abundance.     

A 2D MAS solid-state NMR method to recover the amplified heteronuclear dipolar and chemical shift anisotropic interactions

A two-dimensional solid-state NMR method for the measurement of chemical shift anisotropy tensors of X nuclei (15N or 13C) from multiple sites of a polypeptide powder sample is presented. This method employs rotor-synchronized pi pulses to amplify the magnitude of the inhomogeneous X-CSA and 1H-X dipolar coupling interactions. A combination of on-resonance and magic angle rf irradiation of protons is used to vary the ratio of the magnitudes of the 1H-X dipolar and X-CSA interactions which are recovered under MAS, in addition to suppressing the 1H-1H dipolar interactions. The increased number of spinning sidebands in the recovered anisotropic interactions is useful to determine the CSA tensors accurately. The performance of this method is examined for powder samples of N-acetyl-(15)N-L-valine (NAV), N-acetyl-15N-L-valyl-15N-L-leucine (NAVL), and alpha-13C-L-leucine. The sources of experimental errors in the measurement of CSA tensors and the application of the pulse sequences under high-field fast MAS operations are discussed.     

Comparison of several hetero-nuclear dipolar recoupling NMR methods to be used in MAS HMQC/HSQC

We compare several hetero-nuclear dipolar recoupling sequences available for HMQC or HSQC experiments applied to spin-1/2 and quadrupolar nuclei. These sequences, which are applied to a single channel, are based either on the rotary resonance recoupling (R3) irradiation, or on two continuous rotor-synchronized modulations (SFAM1 and SFAM2), or on four symmetry-based sequences (R2(1)1,SR4(1)2,R12(3)5,R20(5)9), or on the REDOR scheme. We analyze systems exhibiting purely hetero-nuclear dipolar interactions as well as systems where homo-nuclear dipolar interactions need to be canceled. A special attention is given to the behavior of these sequences at very fast MAS. It is shown that R3 methods behave poorly due to the narrowness of their rf-matching curves, and that the best methods are SR4(1)2 and SFAM (SFAM1 or SFAM2 if homo-nuclear interactions are not negligible). REDOR can also recouple efficiently hetero-nuclear dipolar interactions, provided the sequence is sent on the non-observed channel and homo-nuclear dipolar interactions are negligible. We anticipate that at ultra-fast spinning speed, SFAM1 and SFAM2 will be the most efficient methods.     

BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies

We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.     

Recoupled polarization-transfer methods for solid-state (1)H--(13)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 (1)H--(13)C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR pi-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 (1)H--(13)C 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 (13)C in natural abundance, as well as simulations, confirm the very weak effect of (1)H--(1)H 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 (13)C spectral editing of rigid organic solids is shown to be practicable with these techniques.     

Frequency-selective heteronuclear dephasing and selective carbonyl labeling to deconvolute crowded spectra of membrane proteins by magic angle spinning NMR

We present a new method that combines carbonyl-selective labeling with frequency-selective heteronuclear recoupling to resolve the spectral overlap of magic angle spinning (MAS) NMR spectra of membrane proteins in fluid lipid membranes with broad lines and high redundancy in the primary sequence. We implemented this approach in both heteronuclear (15)N-(13)C(α) and homonuclear (13)C-(13)C dipolar assisted rotational resonance (DARR) correlation experiments. We demonstrate its efficacy for the membrane protein phospholamban reconstituted in fluid PC/PE/PA lipid bilayers. The main advantage of this method is to discriminate overlapped (13)C(α) resonances by strategically labeling the preceding residue. This method is highly complementary to (13)C(i-1)(')-(15)N(i)-(13)C(i)(α) and (13)C(i-1)(α)-(15)N(i-1)-(13)C(i)(') experiments to distinguish inter-residue spin systems at a minimal cost to signal-to-noise.     

Amplitude-modulated decoupling in rotating solids: a bimodal Floquet approach

This paper centers on a theoretical study of amplitude-modulated heteronuclear decoupling in solid-state NMR under magic-angle spinning (MAS). A spin system with a single isolated rare spin coupled to a large number of abundant spins is used in the analysis. The phase-alternating decoupling scheme (XiX decoupling) is analyzed using bimodal Floquet theory and the operator-based perturbation method developed by van Vleck. An effective Hamiltonian correct to second order is calculated for the spin system under XiX decoupling. The results of these calculations indicate that under XiX decoupling the main contribution to the residual line width comes from a cross-term between the heteronuclear and the homonuclear dipolar couplings. This is in contrast to continuous-wave decoupling, where the residual line width is dominated by the cross-term between the heteronuclear dipolar coupling and the chemical-shielding tensor of the irradiated spin. For high-power decoupling the method results in very good decoupling provided that certain unfavorable recoupling conditions, imposed by specific ratios of the amplitude modulation frequency and the MAS frequency, are avoided. For low-power decoupling, the method leads to acceptable decoupling when the pulse length corresponds to an integer multiple of a 2pi rotation and the rf-field amplitude is less than a quarter of the MAS frequency. The performance of the XiX scheme is analyzed over a range of values of the rf power, and numerical results that agree well with the most recent experimental observations are presented.     

Resolution enhancement using a new multiple-pulse decoupling sequence for quadrupolar nuclei

A new decoupling composite pulse sequence is proposed to remove the broadening on spin S=1/2 magic-angle spinning (MAS) spectra arising from the scalar coupling with a quadrupolar nucleus I. It is illustrated on the (31)P spectrum of an aluminophosphate, AlPO(4)-14, which is broadened by the presence of (27)Al/(31)P scalar couplings. The multiple-pulse (MP) sequence has the advantage over the continuous wave (CW) irradiation to efficiently annul the scalar dephasing without reintroducing the dipolar interaction. The MP decoupling sequence is first described in a rotor-synchronised version (RS-MP) where one parameter only needs to be adjusted. It clearly avoids the dipolar recoupling in order to achieve a better resolution than using the CW sequence. In a second improved version, the MP sequence is experimentally studied in the vicinity of the perfect rotor-synchronised conditions. The linewidth at half maximum (FWHM) of 65 Hz using (27)Al CW decoupling decreases to 48 Hz with RS-MP decoupling and to 30 Hz with rotor-asynchronised MP (RA-MP) decoupling. The main phenomena are explained using both experimental results and numerical simulations.     

Multidimensional dipolar exchange-assisted recoupling measurements in solid-state NMR

Aseries of uni- and multidimensional variants of the dipolar exchange-assisted recoupling (DEAR) NMR experiment is described and applied to determinations of (13)C-(14)N dipolar local field spectra in amino acids and dipeptides. The DEAR protocol recouples nearby nuclei by relying on differences in their relative rates of longitudinal relaxation, and has the potential to give quantitative geometric results without requiring radiofrequency pulsing on both members of a coupled spin pair. One- and two-dimensional variants of this recoupling strategy on generic I-S pairs are discussed, and measurements of (13)C-(14)N distances and 2D local field experiments sensitive to the relative orientation of CN vectors with respect to the (13)C shielding tensor are presented. Since these measurements did not involve pulsing on the broad nitrogen resonance, their results were independent of the quadrupolar parameters of this nucleus. High-resolution 3D NMR versions of the 2D experiments were also implemented in order to separate their resulting local field patterns according to the isotropic shifts of inequivalent (13)C sites. These high-resolution 3D acquisitions involved collecting a series of 2D DEAR NMR data sets on rotating samples as a function of spinning angle, and then subjecting the resulting data to a processing akin to that involved in variable-angle correlation NMR. Once successfully tested on l-alanine this experiment was applied to the analysis of a series of dipeptides, allowing us to extract separate local field (13)C-(14)N spectra from this type of multisite systems.     

NMR determination of the torsion angle psi in alpha-helical peptides and proteins: the HCCN dipolar correlation experiment

Several existing methods permit measurement of the torsion angles phi, psi and chi in peptides and proteins with solid-state MAS NMR experiments. Currently, however, there is not an approach that is applicable to measurement of psi in the angular range -20 degree to -70 degree, commonly found in alpha-helical structures. Accordingly, we have developed a HCCN dipolar correlation MAS experiment that is sensitive and accurate in this regime. An initial REDOR driven (13)C'--(15)N dipolar evolution period is followed by the C' to C(alpha) polarization transfer and by Lee--Goldburg cross polarization recoupling of the (13)C(alpha)(1)H dipolar interaction. The difference between the effective (13)C(1)H and (13)C(15)N dipolar interaction strengths is balanced out by incrementing the (13)C--(15)N dipolar evolution period in steps that are a factor of R(R approximately omega(CH)/omega(CN)) larger than the (13)C--(1)H steps. The resulting dephasing curves are sensitive to variations in psi in the angular region associated with alpha-helical secondary structure. To demonstrate the validity of the technique, we apply it to N-formyl-[U-(13)C,(15)N] Met-Leu-Phe-OH (MLF). The value of psi extracted is consistent with the previous NMR measurements and close to that reported in diffraction studies for the methyl ester of MLF, N-formyl-[U-(13)C,(15)N]Met-Leu-Phe-OMe.     

Correlating fast and slow chemical shift spinning sideband patterns in solid-state NMR

An experiment is presented that enables the measurement of small chemical shift anisotropy tensors under fast magic-angle spinning (MAS). The two-dimensional spectra obtained give a fast MAS sideband pattern in the directly observed dimension with the spinning sideband intensities equivalent to the chemical shift anisotropy scaled by a factor of N, or equivalently the sample spinning frequency scaled by 1/N, in the indirectly observed dimension. The scaling factor may be arbitrarily varied by changing the number and timings of the rotor synchronized pi-pulses used. Desirable features of the experiment include a fixed length pulse sequence and efficient sampling of the indirectly observed dimension. In addition, neither quadrature detection in the indirect dimension nor storage periods are required, consequently no signal intensity is discarded by the pulse sequence. The experiment is demonstrated using (31)P NMR of sodium phosphate and (13)C NMR of fumaric acid monoethyl ester for which a scaling factor of N=10.2 was employed.