Heteronuclear decoupling interference during symmetry-based homonuclear recoupling in solid-state NMR

Selective correlations between aliphatic 13C nuclei in protein solid-state NMR

Solid-state nuclear magnetic resonance (NMR) is a potent tool for studying the structures and dynamics of insoluble proteins. It starts with signal assignment through multi-dimensional correlation experiments, where the aliphatic 13Cα-13Cβ correlation is indispensable for identifying specific residues. However, developing efficient methods for achieving this correlation is a challenge in solid-state NMR. We present a simple band-selective zero-quantum (ZQ) recoupling method, named POST-C4161 (PC4), which enhances 13Cα-13Cβ correlations under moderate magic-angle spinning (MAS) conditions. PC4 requires minimal 13C radio-frequency (RF) field and proton decoupling, exhibits high stability against RF variations, and achieves superior efficiency. Comparative tests on various samples, including the formyl-Met-Leu-Phe (fMLF) tripeptide, microcrystalline β1 immunoglobulin binding domain of protein G (GB1), and membrane protein of mechanosensitive channel of large conductance from Methanosarcina acetivorans (MaMscL), demonstrate that PC4 selectively enhances 13Cα-13Cβ correlations by up to 50 % while suppressing unwanted correlations, as compared to the popular dipolar-assisted rotational resonance (DARR). It has addressed the long-standing need for selective 13C-13C correlation methods. We anticipate that this simple but efficient PC4 method will have immediate applications in structural biology by solid-state NMR.

Solid-State NMR: Methods for Biological Solids

In the last two decades, solid-state nuclear magnetic resonance (ssNMR) spectroscopy has transformed from a spectroscopic technique investigating small molecules and industrial polymers to a potent tool decrypting structure and underlying dynamics of complex biological systems, such as membrane proteins, fibrils, and assemblies, in near-physiological environments and temperatures. This transformation can be ascribed to improvements in hardware design, sample preparation, pulsed methods, isotope labeling strategies, resolution, and sensitivity. The fundamental engagement between nuclear spins and radio-frequency pulses in the presence of a strong static magnetic field is identical between solution and ssNMR, but the experimental procedures vastly differ because of the absence of molecular tumbling in solids. This review discusses routinely employed state-of-the-art static and MAS pulsed NMR methods relevant for biological samples with rotational correlation times exceeding 100's of nanoseconds. Recent developments in signal filtering approaches, proton methodologies, and multiple acquisition techniques to boost sensitivity and speed up data acquisition at fast MAS are also discussed. Several examples of protein structures (globular, membrane, fibrils, and assemblies) solved with ssNMR spectroscopy have been considered. We also discuss integrated approaches to structurally characterize challenging biological systems and some newly emanating subdisciplines in ssNMR spectroscopy.

Optimization of band-selective homonuclear dipolar recoupling in solid-state NMR by a numerical phase search

Spin polarization transfers among aliphatic ¹³C nuclei, especially ¹³Cα-¹³Cβ transfers, permit correlations of their nuclear magnetic resonance (NMR) frequencies that are essential for signal assignments in multidimensional solid-state NMR of proteins. We derive and demonstrate a new radio-frequency (RF) excitation sequence for homonuclear dipolar recoupling that enhances spin polarization transfers among aliphatic ¹³C nuclei at moderate magic-angle spinning (MAS) frequencies. The phase-optimized recoupling sequence with five π pulses per MAS rotation period (denoted as PR5) is derived initially from systematic numerical simulations in which only the RF phases are varied. Subsequent theoretical analysis by average Hamiltonian theory explains the favorable properties of numerically optimized phase schemes. The high efficiency of spin polarization transfers in simulations is preserved in experiments, in part because the RF field amplitude in PR5 is only 2.5 times the MAS frequency so that relatively low ¹H decoupling powers are required. Experiments on a microcrystalline sample of the β1 immunoglobulin binding domain of protein G demonstrate an average enhancement factor of 1.6 for ¹³Cα → ¹³Cβ polarization transfers, compared to the standard ¹³C-¹³C spin-diffusion method, implying a two-fold time saving in relevant 2D and 3D experiments.

Selective high-resolution DNP-enhanced NMR of biomolecular binding sites

Locating binding sites in biomolecular assemblies and solving their structures are of the utmost importance to unravel functional aspects of the system and provide experimental data that can be used for structure-based drug design. This often still remains a challenge, both in terms of selectivity and sensitivity for X-ray crystallography, cryo-electron microscopy and NMR. In this work, we introduce a novel method called Selective Dynamic Nuclear Polarization (Sel-DNP) that allows selective highlighting and identification of residues present in the binding site. This powerful site-directed approach relies on the use of localized paramagnetic relaxation enhancement induced by a ligand-functionalized paramagnetic construct combined with difference spectroscopy to recover high-resolution and high-sensitivity information from binding sites. The identification of residues involved in the binding is performed using spectral fingerprints obtained from a set of high-resolution multidimensional spectra with varying selectivities. The methodology is demonstrated on the galactophilic lectin LecA, for which we report well-resolved DNP-enhanced spectra with linewidths between 0.5 and 1 ppm, which enable the de novo assignment of the binding interface residues, without using previous knowledge of the binding site location. Since this approach produces clean and resolved difference spectra containing a limited number of residues, resonance assignment can be performed without any limitation with respect to the size of the biomolecular system and only requires the production of one protein sample (e.g. 13C,15N-labeled protein).

A robust heteronuclear dipolar recoupling method comparable to TEDOR for proteins in magic-angle spinning solid-state NMR

In this letter, we propose a robust heteronuclear dipolar recoupling method for proteins in magic-angle spinning (MAS) solid-state NMR. This method is as simple, robust and efficient as the well-known TEDOR in the aspect of magnetization transfer between ¹⁵N and ¹³C. Deriving from our recent band-selective dual back-to-back pulses (DBP) (Zhang et al., 2016), this method uses new phase-cycling schemes to realize broadband DBP (Bro-DBP). For broadband ¹⁵N-¹³C magnetization transfer (simultaneous ¹⁵N→¹³C' and ¹⁵N→¹³Cα), Bro-DBP has almost the same ¹⁵N→¹³Cα efficiency while offers 30-40% enhancement on ¹⁵N→¹³C' transfer, compared to TEDOR. Besides, Bro-DBP can also be used as a carbonyl (¹³C')-selected method, whose ¹⁵N→¹³C' efficiency is up to 1.7 times that of TEDOR and is also higher than that of band-selective DBP. The performance of Bro-DBP is demonstrated on the N-formyl-[U-¹³C,¹⁵N]-Met-Leu-Phe-OH (fMLF) peptide and the U-¹³C, ¹⁵N labeled β1 immunoglobulin binding domain of protein G (GB1) microcrystalline protein. Since Bro-DBP is as robust, simple and efficient as TEDOR, we believe it is very useful for protein studies in MAS solid-state NMR.

Efficient dipolar double quantum filtering under magic angle spinning without a (1)H decoupling field

We present a systematic study of dipolar double quantum (DQ) filtering in (13)C-labeled organic solids over a range of magic-angle spinning rates, using the SPC-n recoupling sequence element with a range of n symmetry values from 3 to 11. We find that efficient recoupling can be achieved for values n⩾7, provided that the (13)C nutation frequency is on the order of 100kHz or greater. The decoupling-field dependence was investigated and explicit heteronuclear decoupling interference conditions identified. The major determinant of DQ filtering efficiency is the decoupling interference between (13)C and (1)H fields. For (13)C nutation frequencies greater than 75kHz, optimal performance is observed without an applied (1)H field. At spinning rates exceeding 20kHz, symmetry conditions as low as n=3 were found to perform adequately.

Determining carbon-carbon connectivities in natural abundance organic powders using dipolar couplings

We present a solid-state NMR methodology capable of investigating the carbon skeleton of natural abundance organic powders. The methodology is based on the (13)C-(13)C dipolar coupling interaction and allows carbon-carbon connectivities to be unambiguously established for a wide range of organic solids. This methodology is particularly suitable for disordered solids, such as natural or synthetic macromolecules, which cannot be studied using conventional diffraction or NMR techniques.

Low-power broadband homonuclear dipolar recoupling in MAS NMR by two-fold symmetry pulse schemes for magnetization transfers and double-quantum excitation

We provide an experimental, numerical, and high-order average Hamiltonian evaluation of an open-ended series of homonuclear dipolar recoupling sequences, SR [Formula: see text] with p=1,2,3,…. While operating at a very low radio-frequency (rf) power, corresponding to a nutation frequency of 1/2 of the magic-angle spinning (MAS) rate (ωnut=ωr/2), these recursively generated double-quantum (2Q) dipolar recoupling schemes offer a progressively improved compensation to resonance offsets and rf inhomogeneity for increasing pulse-sequence order p. The excellent recoupling robustness to these experimental obstacles, as well as to CSA, is demonstrated for 2Q filtering (2QF) experiments and for driving magnetization transfers in 2D NMR correlation spectroscopy, where the sequences may provide either double or zero quantum dipolar Hamiltonians during mixing. Experimental and numerical demonstrations, which mostly target conditions of "ultra-fast" MAS (≳50kHz) and high magnetic fields, are provided for recoupling of (13)C across a wide range of isotropic and anisotropic chemical shifts, as well as dipolar coupling constants, encompassing [2,3-(13)C2]alanine, [1,3-(13)C2]alanine, diammonium [1,4-(13)C2]fumarate, and [U-(13)C]tyrosine. When compared at equal power levels, a superior performance is observed for the SR [Formula: see text] sequences with p⩾3 relative to existing and well-established 2Q recoupling techniques. At ultra-fast MAS, proton decoupling is redundant during the homonuclear dipolar recoupling of dilute spins in organic solids, which renders the family of SR [Formula: see text] schemes the first efficient 2Q recoupling option for general applications, such as 2Q-1Q correlation NMR and high-order multiple-quantum excitation, under truly low-power rf conditions.

Spin-locking and cross-polarization under magic-angle spinning of uniformly labeled solids

Spin-locking and cross-polarization under magic-angle spinning are investigated for uniformly (13)C and (15)N labeled solids. In particular, the interferences from chemical shift anisotropy, and (1)H heteronuclear and (13)C homonuclear dipolar couplings are identified. The physical origin of these interferences provides guidelines for selecting the best (13)C and (15)N polarization transfer rf fields. Optimal settings for both the zero- and double-quantum cross-polarization transfer mechanisms are recommended.

Influence of proton coupling on symmetry-based homonuclear (19)F dipolar recoupling experiments

We study the efficiency of two symmetry based homonuclear (19)F double-quantum recoupling sequences for moderate (R142(6)) and ultra-fast (R144(5)) MAS under the influence of strong (1)H-(1)H and (1)H-(19)F dipolar interactions and (1)H continuous wave decoupling. Simulations based on various spin systems derived from the organic solid 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene (F-BTA), used as a model system, reveal that the strong-decoupling limit is not accessible even for moderate spinning speeds. Additionally, for the no-decoupling limit improved DQ efficiencies are predicted for both moderate and ultra-fast MAS. Strong perturbations of build-up curves can be avoided by additional stabilisation through supercycling. Additional (1)H cw decoupling during (19)F recoupling rapidly reduces the maximum DQ efficiency when deviating from the no-decoupling limit. These effects were confirmed by experimental data on F-BTA. For moderate spinning the influence of (1)H-(1)H and (1)H-(19)F couplings is markedly stronger compared to ultra-fast MAS. For the latter case those influences reduce to a constant scaling if only short excitation times up to the first minimum are taken into account. Based on this analysis the experimental build-up curves of 1,3,5-tris(2-fluoro-2-methylpropionylamino)benzene can be refined with homonuclear (19)F spin systems which allow to probe even subtle structural differences for the fluorine atoms of F-BTA.

Improved decoupling during symmetry-based C9-TOBSY sequences

We show that heteronuclear decoupling during symmetry-based C9 TOBSY sequences can be improved by using phase-alternating pulse sequences (XiX) instead of cw irradiation. The use of XiX sequences makes the optimization of the decoupling rf-field amplitude simpler and lowers the decoupling rf-field requirements to attain a comparable performance. A Floquet analysis of the first-order resonance conditions was used to determine the correct timing of the XiX sequence to avoid interference between the C sequence and the decoupling. The decoupling performance is analyzed analytically using Floquet theory and verified using numerical simulations as well as experimental results.

Genetic algorithms and solid state NMR pulse sequences

The use of genetic algorithms for the optimisation of magic angle spinning NMR pulse sequences is discussed. The discussion uses as an example the optimisation of the C7(2)(1) dipolar recoupling pulse sequence, aiming to achieve improved efficiency for spin systems characterised by large chemical shielding anisotropies and/or small dipolar coupling interactions. The optimised pulse sequence is found to be robust over a wide range of parameters, requires only minimal a priori knowledge of the spin system for experimental implementations with buildup rates being solely determined by the magnitude of the dipolar coupling interaction, but is found to be less broadbanded than the original C7(2)(1) pulse sequence. The optimised pulse sequence breaks the synchronicity between r.f. pulses and sample spinning.

A large geometric distortion in the first photointermediate of rhodopsin, determined by double-quantum solid-state NMR

Double-quantum magic-angle-spinning NMR experiments were performed on 11,12-(13)C(2)-retinylidene-rhodopsin under illumination at low temperature, in order to characterize torsional angle changes at the C11-C12 photoisomerization site. The sample was illuminated in the NMR rotor at low temperature (~120 K) in order to trap the primary photointermediate, bathorhodopsin. The NMR data are consistent with a strong torsional twist of the HCCH moiety at the isomerization site. Although the HCCH torsional twist was determined to be at least 40°, it was not possible to quantify it more closely. The presence of a strong twist is in agreement with previous Raman observations. The energetic implications of this geometric distortion are discussed.

Characteristics of zero-quantum correlation spectroscopy in MAS NMR experiments

Zero-quantum coherence generation and reconversion in magic-angle spinning solid-state NMR is analyzed. Two methods are discussed based on implementations using symmetry-based pulse sequences that utilize either isotropic J couplings or dipolar couplings. In either case, the decoupling of abundant proton spins plays a crucial role for the efficiency of the zero-quantum generation. We present optimized sequences for measuring zero-quantum single-quantum correlation spectra in solids, achieving an efficiency of 50% in ubiquitin. The advantages and disadvantages of zero-quantum single-quantum over single-quantum single-quantum correlation spectroscopy are explored, and similarities and differences with double-quantum single-quantum correlation spectroscopy are discussed. Finally, possible application of zero-quantum single-quantum experiments to polypeptides, where it can lead to better spectral resolution is investigated using ubiquitin, where we find high efficiency and high selectivity, but also increased line widths in the MQ dimension.

Double-quantum NMR spectroscopy of 31P species submitted to very large CSAs

We introduce an original pulse sequence, BR2(2)(1)(taupitau), which is a block super-cycled R2(2)(1) sequence employing as basic element a pi pulse sandwiched by 'window' intervals. This homonuclear dipolar recoupling method allows the efficient excitation of double-quantum coherences between spin-1/2 nuclei submitted to very large chemical shift anisotropy. We demonstrate that this technique can be employed in double-quantum<-->single-quantum (31)P homonuclear correlation experiment at high magnetic field (B(0)>or=14 T) and high MAS frequencies (nu(R)>or=30 kHz). The performances of BR2(2)(1)(taupitau) are compared to those of the double-quantum recoupling methods, such as BABA and bracketed fp-RFDR, which were already employed at fast MAS rates. The BR2(2)(1)(taupitau) sequence displays a higher robustness to CSA and offset than the other existing techniques.

NMR line shapes from AB spin systems in solids — The role of antisymmetric spin–spin coupling

NMR parameters such as indirect nuclear spin–spin coupling (J), nuclear magnetic shielding (σ), direct dipolar coupling (D), and electric field gradient (V) are properly described by second-rank tensors. Each may be decomposed into isotropic, symmetric, and antisymmetric components; the number of these three components which may be nonzero is a distinguishing attribute of each interaction tensor. The rank-1 antisymmetric portion of J (Janti) holds the distinction of remaining the only nonzero part of these fundamental NMR interaction tensors which has never been observed experimentally. Accordingly, effects from Janti are usually ignored, but it is important to consider when this is valid. An experimental strategy for observing Janti in powdered samples of tightly coupled homonuclear spin pairs, based on ideas originally presented by Andrew and Farnell ( Mol. Phys. 1968, 15, 157 ), is described. The theory of Andrew and Farnell is extended to powder samples, and methods for analyzing NMR spectra from powdered samples are presented. It is found that, in certain rare cases, Janti has the potential to affect the NMR line shapes from AB spin systems, but that even in these systems, the most intense features of the spectra are not affected and may be analyzed independently of Janti. Furthermore, Janti will only have an observable effect on the NMR spectra when its magnitude is comparable with that of Jiso and with the difference in chemical shifts (in Hz) between the two sites. Finally, the first experimental attempts to measure Janti are reported, and experimental proof that no elements of Janti(119Sn,119Sn) in hexa(p-tolyl)ditin are larger than 2900 Hz is given. The benefits of modern double-quantum filtering NMR pulse sequences in isolating effects from Janti are also illustrated.

Structure and dynamics of membrane proteins by magic angle spinning solid-state NMR

Membrane proteins remain difficult to study by traditional methods. Magic angle spinning solid-state NMR (MAS SSNMR) methods present an important approach for studying membrane proteins of moderate size. Emerging MAS SSNMR methods are based on extensive assignments of the nuclei as a basis for structure determination and characterization of function. These methods have already been used to characterize fibrils and globular proteins and are being increasingly used to study membrane proteins embedded in lipids. This review highlights recent applications to intrinsic membrane proteins and summarizes recent technical advances that will enable these methods to be utilized for more complex membrane protein systems in the near future.

Light penetration and photoisomerization in rhodopsin studied by numerical simulations and double-quantum solid-state NMR spectroscopy

The penetration of light into optically thick samples containing the G-protein-coupled receptor rhodopsin is studied by numerical finite-element simulations and double-quantum solid-state NMR experiments. Illumination with white light leads to the generation of the active bathorhodopsin photostate in the outer layer of the sample but generates a large amount of the side product, isorhodopsin, in the sample interior. The overall yield of bathorhodopsin is improved by using monochromatic 420 nm illumination and by mixing the sample with transparent glass beads. The implications of these findings on the interpretation of previously published rhodopsin NMR data are discussed.

Dipolar truncation in magic-angle spinning NMR recoupling experiments

Quantitative solid-state NMR distance measurements in strongly coupled spin systems are often complicated due to the simultaneous presence of multiple noncommuting spin interactions. In the case of zeroth-order homonuclear dipolar recoupling experiments, the recoupled dipolar interaction between distant spins is attenuated by the presence of stronger couplings to nearby spins, an effect known as dipolar truncation. In this article, we quantitatively investigate the effect of dipolar truncation on the polarization-transfer efficiency of various homonuclear recoupling experiments with analytical theory, numerical simulations, and experiments. In particular, using selectively (13)C-labeled tripeptides, we compare the extent of dipolar truncation in model three-spin systems encountered in protein samples produced with uniform and alternating labeling. Our observations indicate that while the extent of dipolar truncation decreases in the absence of directly bonded nuclei, two-bond dipolar couplings can generate significant dipolar truncation of small, long-range couplings. Therefore, while alternating labeling alleviates the effects of dipolar truncation, and thus facilitates the application of recoupling experiments to large spin systems, it does not represent a complete solution to this outstanding problem.

Towards an interpretation of 13C chemical shifts in bathorhodopsin, a functional intermediate of a G-protein coupled receptor

Photoisomerization of the membrane-bound light receptor protein rhodopsin leads to an energy-rich photostate called bathorhodopsin, which may be trapped at temperatures of 120 K or lower. We recently studied bathorhodopsin by low-temperature solid-state NMR, using in situ illumination of the sample in a purpose-built NMR probe. In this way we acquired (13)C chemical shifts along the retinylidene chain of the chromophore. Here we compare these results with the chemical shifts of the dark state chromophore in rhodopsin, as well as with the chemical shifts of retinylidene model compounds in solution. An earlier solid-state NMR study of bathorhodopsin found only small changes in the (13)C chemical shifts upon isomerization, suggesting only minor perturbations of the electronic structure in the isomerized retinylidene chain. This is at variance with our recent measurements which show much larger perturbations of the (13)C chemical shifts. Here we present a tentative interpretation of our NMR results involving an increased charge delocalization inside the polyene chain of the bathorhodopsin chromophore. Our results suggest that the bathochromic shift of bathorhodopsin is due to modified electrostatic interactions between the chromophore and the binding pocket, whereas both electrostatic interactions and torsional strain are involved in the energy storage mechanism of bathorhodopsin.

Design of high-power, broadband 180 degrees pulses and mixing sequences for fast MAS solid state chemical shift correlation NMR spectroscopy

An approach for the design of high-power, broadband 180 degrees pulses and mixing sequences for generating dipolar and scalar coupling mediated (13)C-(13)C chemical shift correlation spectra of isotopically labelled biological systems at fast magic-angle spinning frequencies without (1)H decoupling during mixing is presented. Considering RF field strengths in the range of 100-120 kHz, as typically available in MAS probes employed at high spinning speeds, and limited B (1) field inhomogeneities, the Fourier coefficients defining the phase modulation profile of the RF pulses were optimised numerically to obtain broadband inversion and refocussing pulses and mixing sequences. Experimental measurements were carried out to assess the performance characteristics of the mixing sequences reported here.

Proton assisted recoupling and protein structure determination

We introduce a homonuclear version of third spin assisted recoupling, a second-order mechanism that can be used for polarization transfer between (13)C or (15)N spins in magic angle spinning (MAS) NMR experiments, particularly at high spinning frequencies employed in contemporary high field MAS experiments. The resulting sequence, which we refer to as proton assisted recoupling (PAR), relies on a cross-term between (1)H-(13)C (or (1)H-(15)N) couplings to mediate zero quantum (13)C-(13)C (or (15)N-(15)N recoupling). In particular, using average Hamiltonian theory we derive an effective Hamiltonian for PAR and show that the transfer is mediated by trilinear terms of the form C(1) (+/-)C(2) (-/+)H(Z) for (13)C-(13)C recoupling experiments (or N(1) (+/-)N(2) (-/+)H(Z) for (15)N-(15)N). We use analytical and numerical simulations to explain the structure of the PAR optimization maps and to delineate the PAR matching conditions. We also detail the PAR polarization transfer dependence with respect to the local molecular geometry and explain the observed reduction in dipolar truncation. Finally, we demonstrate the utility of PAR in structural studies of proteins with (13)C-(13)C spectra of uniformly (13)C, (15)N labeled microcrystalline Crh, a 85 amino acid model protein that forms a domain swapped dimer (MW=2 x 10.4 kDa). The spectra, which were acquired at high MAS frequencies (omega(r)2pi>20 kHz) and magnetic fields (750-900 MHz (1)H frequencies) using moderate rf fields, exhibit numerous cross peaks corresponding to long (up to 6-7 A) (13)C-(13)C distances which are particularly useful in protein structure determination. Using results from PAR spectra we calculate the structure of the Crh protein.

Radio frequency-driven recoupling at high magic-angle spinning frequencies: homonuclear recoupling sans heteronuclear decoupling

We describe solid-state NMR homonuclear recoupling experiments at high magic-angle spinning (MAS) frequencies using the radio frequency-driven recoupling (RFDR) scheme. The effect of heteronuclear decoupling interference during RFDR recoupling at high spinning frequencies is investigated experimentally and via numerical simulations, resulting in the identification of optimal decoupling conditions. The effects of MAS frequency, RF field amplitude, bandwidth, and chemical shift offsets are examined. Most significantly, it is shown that broadband homonuclear correlation spectra can be efficiently obtained using RFDR without decoupling during the mixing period in fully protonated samples, thus considerably reducing the rf power requirements for acquisition of (13)C-(13)C correlation spectra. The utility of RFDR sans decoupling is demonstrated with broadband correlation spectra of a peptide and a model protein at high MAS frequencies and high magnetic field.

ICMRBS founder's medal 2006: biological solid-state NMR, methods and applications

Solid-state NMR (ssNMR) provides increasing possibilities to study structure and dynamics of biomolecular systems. Our group has been interested in developing ssNMR-based approaches that are applicable to biomolecules of increasing molecular size and complexity without the need of specific isotope-labelling. Methodological aspects ranging from spectral assignments to the indirect detection of proton-proton contacts in multi-dimensional ssNMR are discussed and applied to (membrane) protein complexes.

Analytical theory of gamma-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being gamma-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for gamma-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a (13)C(2)-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.

Broadband homonuclear chemical shift correlation at high MAS frequencies: a study of tanh/tan adiabatic RF pulse schemes without 1H decoupling during mixing

At high magic angle spinning (MAS) frequencies the potential of tanh/tan adiabatic RF pulse schemes for 13C chemical shift correlation without 1H decoupling during mixing has been evaluated. It is shown via numerical simulations that a continuous train of adiabatic 13C inversion pulses applied at high RF field strengths leads to efficient broadband heteronuclear decoupling. It is demonstrated that this can be exploited effectively for generating through-bond and through-space, including double-quantum, correlation spectra of biological systems at high magnetic fields and spinning speeds with no 1H decoupling applied during the mixing period. Experiments carried out on a polycrystalline sample of histidine clearly suggest that an improved signal to noise ratio can be realised by eliminating 1H decoupling during mixing.

Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a gamma-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for (13)C and (31)P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [(13)C(3)]alanine.

Broadband homonuclear correlation spectroscopy at high magnetic fields and MAS frequencies

We present a new homonuclear recoupling sequence, CMAR, that allows observation of 2D 13C-13C correlation spectra at high magnetic fields and MAS frequencies (10-30 kHz). The main advantages of the sequence are that it provides efficient, broadband dipolar recoupling and concurrently decouples the 1H spins from the 13C's. Thus, no additional 1H decoupling is required during the mixing period, thereby significantly reducing the radio frequency power requirements for the experiment. Thus, CMAR significantly extends the range of applicability of the usual homonuclear recoupling techniques and should be of major interest for structure determinations of biomolecules at high magnetic fields.

Accurate Measurements of 13C−13C J-Couplings in the Rhodopsin Chromophore by Double-Quantum Solid-State NMR Spectroscopy

A new double-quantum solid-state NMR pulse sequence is presented and used to measure one-bond 13C-13C J-couplings in a set of 13C2-labeled rhodopsin isotopomers. The measured J-couplings reveal a perturbation of the electronic structure at the terminus of the conjugated chain but show no evidence for protein-induced electronic perturbation near the C11-C12 isomerization site. This work establishes NMR methodology for measuring accurate 1JCC values in noncrystalline macromolecules and shows that the measured J-couplings may reveal local electronic perturbations of mechanistic significance.