Effective Hamiltonians by optimal control: solid-state NMR double-quantum planar and isotropic dipolar recoupling

We report the use of optimal control algorithms for tailoring the effective Hamiltonians in nuclear magnetic resonance (NMR) spectroscopy through sophisticated radio-frequency (rf) pulse irradiation. Specifically, we address dipolar recoupling in solid-state NMR of powder samples for which case pulse sequences offering evolution under planar double-quantum and isotropic mixing dipolar coupling Hamiltonians are designed. The pulse sequences are constructed numerically to cope with a range of experimental conditions such as inhomogeneous rf fields, spread of chemical shifts, the intrinsic orientation dependencies of powder samples, and sample spinning. While the vast majority of previous dipolar recoupling sequences are operating through planar double-or zero-quantum effective Hamiltonians, we present here not only improved variants of such experiments but also for the first time homonuclear isotropic mixing sequences which transfers all I(x), I(y), and I(z) polarizations from one spin to the same operators on another spin simultaneously and with equal efficiency. This property may be exploited to increase the signal-to-noise ratio of two-dimensional experiments by a factor of square root 2 compared to conventional solid-state methods otherwise showing the same efficiency. The sequences are tested numerically and experimentally for a powder of (13)C(alpha),(13)C(beta)-L-alanine and demonstrate substantial sensitivity gains over previous dipolar recoupling experiments.     

Improving solid-state NMR dipolar recoupling by optimal control

We present the first solid-state NMR experiments developed using optimal control theory. Taking heteronuclear dipolar recoupling in magic-angle-spinning NMR as an example, it proves possible to significantly improve the efficiency of the experiments while introducing robustness toward instrumental imperfections such as radio frequency inhomogeneity. The improvements are demonstrated by numerical simulations as well as practical experiments on a 13Calpha,15N-labeled powder of glycine. The experiments demonstrate a gain of 53% in the efficiency for 15N to 13Calpha coherence transfer relative to the typically double-cross-polarization experiments.     

A study of homonuclear dipolar recoupling pulse sequences in solid-state nuclear magnetic resonance

Dipolar recoupling pulse sequences are of great importance in magic angle spinning solid-state NMR. Recoupling sequences are used for excitation of double-quantum coherence, which, in turn, is employed in experiments to estimate internuclear distances and molecular torsion angles. Much effort is spent on the design of recoupling sequences that are able to produce double-quantum coherence with high efficiency in demanding spin systems, i.e., spin systems with small dipole-dipole couplings and large chemical-shift anisotropies (CSAs). The sequence should perform robustly under a variety of experimental conditions. This paper presents experiments and computer calculations that extend the theory of double-quantum coherence preparation from the strong coupling/small CSA limit to the weak coupling limit. The performance of several popular dipole-dipole recoupling sequences-DRAWS, POST-C7, SPC-5, R1, and R2-are compared. It is found that the optimum performance for several of these sequences, in the weak coupling/large CSA limit, varies dramatically, with respect to the sample spinning speed, the magnitude and orientation of the CSAs, and the magnitude of dipole-dipole couplings. It is found that the efficiency of double-quantum coherence preparation by gamma-encoded sequences departs from the predictions of first-order theory. The discussion is supported by density-matrix calculations.     

Triple oscillating field technique for accurate distance measurements by solid-state NMR

We present a new concept for homonuclear dipolar recoupling in magic-angle-spinning (MAS) solid-state NMR experiments which avoids the problem of dipolar truncation. This is accomplished through the introduction of a new NMR pulse sequence design principle: the triple oscillating field technique. We demonstrate this technique as an efficient means to accomplish broadband dipolar recoupling of homonuclear spins, while decoupling heteronuclear dipolar couplings and anisotropic chemicals shifts and retaining influence from isotropic chemical shifts. In this manner, it is possible to synthesize Ising interaction (2IzSz) Hamiltonians in homonuclear spin networks and thereby avoid dipolar truncation--a serious problem essentially all previous homonuclear dipolar recoupling experiments suffer from. Combination of this recoupling concept with rotor assisted dipolar refocusing enables easy readout of internuclear distances through comparison with analytical Fresnel curves. This forms the basis for a new class of solid-state NMR experiments with potential for structure analysis of uniformly 13C labeled proteins through accurate measurement of 13C-13C internuclear distances. The concept is demonstrated experimentally by measurement of C alpha-C', C beta-C', and C gamma-C' internuclear distances in powder samples of the amino acids L-alanine and L-threonine.     

Indirect detection of nitrogen-14 in solid-state NMR spectroscopy.

NMR spectra of (14)N (spin I=1) are obtained by indirect detection in powders spinning at the magic angle. The method relies on the transfer of coherence from a neighboring "spy" nucleus with S=1/2, such as (13)C or (1)H, to single- or double-quantum transitions of (14)N nuclei. The transfer of coherence can occur through a combination of scalar and residual dipolar splittings (RDS); the latter are also known as second-order quadrupole-dipole cross terms. The two-dimensional NMR spectra reveal powder patterns determined by second- and third-order quadrupolar couplings. These spectra depend on the quadrupolar coupling constant C(Q) (typically a few megahertz), on the asymmetry parameter eta(Q) of the (14)N nucleus, and on the orientation of the internuclear vector r(IS) between the I ((14)N) and S (spy) nuclei with respect to the quadrupolar tensor. These parameters, which can be subject to motional averaging, can reveal valuable information about the structure and dynamics of nitrogen-containing solids. Application of this technique to various amino acids, either enriched in (13)C or with natural carbon isotope abundance, with spectra recorded at various magnetic fields, illustrates the scope of the method.     

Determination of peptide backbone torsion angles using double-quantum dipolar recoupling solid-state NMR spectroscopy

Several approaches for utilizing dipolar recoupling solid-state NMR (ssNMR) techniques to determine local structure at high resolution in peptides and proteins have been developed. However, many of these techniques measure only one torsion angle or are accurate for only certain classes of secondary structure. Additionally, the efficiency with which these dipolar recoupling experiments suppress the deleterious effects of chemical shift anisotropy (CSA) at high magnetic field strengths varies. Dipolar recoupling with a windowless sequence (DRAWS) has proven to be an effective pulse sequence for exciting double-quantum (DQ) coherences between adjacent carbonyl carbons along the peptide backbone. By allowing this DQ coherence to evolve, it is possible to measure the relative orientations of the CSA tensors and subsequently use this information to determine the Ramachandran torsion angles phi and psi. Here, we explore the accuracies of the assumptions made in interpreting DQ-DRAWS data and demonstrate their fidelity in measuring torsion angles corresponding to a variety of secondary structures irrespective of hydrogen-bonding patterns. It is shown how a simple choice of isotopic labels and experimental conditions allows accurate measurement of backbone secondary structures without any prior knowledge. This approach is considerably more sensitive for determining structure in helices and has comparable accuracy for beta-sheet and extended conformations relative to other methods. We also illustrate the ability of DQ-DRAWS to distinguish between structures in heterogeneous samples.     

On the orientational dependence of resolution in 1H solid-state NMR, and its role in MAS, CRAMPS and delayed-acquisition experiments

Numerical simulations and experiments are used to show that the spin dynamics of the dipolar-coupled networks in solids is often strongly dependent on crystallite orientation. In particular, different rates of dephasing of the magnetisation mean that NMR signals obtained at longer dephasing times are dominated by orientations in which the local dipolar coupling strength is relatively weak. This often leads to a distinct improvement in spectral resolution as the dephasing time is increased. The effects are particularly noticeable under magic-angle spinning (MAS), but are also observed when homonuclear decoupling is used to reduce the rate of dipolar dephasing. Numerical simulation is seen to be a powerful and easily used tool for understanding the behaviour of solid-state NMR experiments involving dipolar-coupled networks. The implications for solid-state NMR spectra of abundant spins acquired under MAS and homonuclear decoupling are discussed, as well as insights provided into the performance of 'delayed-acquisition' and 'constant-time' experiments.     

An experimental study of decoupling sequences for multiple-quantum and high-resolution MAS experiments in solid-state NMR

Recently, a sequence for heteronuclear dipolar decoupling in solid-state NMR, namely SWf-TPPM, was introduced by us. Under magic-angle spinning (MAS), the decoupling efficiency of the sequence was unaffected over a range of values for various experimental parameters such as the pulse length, pulse phase, and 1H resonance offset. We here demonstrate its use in multiple-quantum (MQ) and high-resolution (HR) MAS experiments. This sequence further improves the MQMAS spectra compared to the earlier reported decoupling sequences with improved immunity to any missets of the pulse length, pulse phase and decoupler offset. In contrast, for HRMAS, the simple CW scheme is as efficient as any of the decoupling schemes that were studied.     

Frequency-selective homonuclear dipolar recoupling in solid state NMR

We introduce a new approach to frequency-selective homonuclear dipolar recoupling in solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS). This approach, to which we give the acronym SEASHORE, employs alternating periods of double-quantum recoupling and chemical shift evolution to produce phase modulations of the recoupled dipole-dipole interactions that average out undesired couplings, leaving only dipole-dipole couplings between nuclear spins with a selected pair of NMR frequencies. In principle, SEASHORE is applicable to systems with arbitrary coupling strengths and arbitrary sets of NMR frequencies. Arbitrary MAS frequencies are also possible, subject only to restrictions imposed by the pulse sequence chosen for double-quantum recoupling. We demonstrate the efficacy of SEASHORE in experimental (13)C NMR measurements of frequency-selective polarization transfer in uniformly (15)N, (13)C-labeled L-valine powder and frequency-selective intermolecular polarization transfer in amyloid fibrils formed by a synthetic decapeptide containing uniformly (15)N, (13)C-labeled residues.     

Relaxation-allowed transfer of coherence in NMR between spins which are not scalar coupled

In nuclear magnetic resonance spectroscopy in an isotropic phase it is shown that coherence can be transferred with a single rf pulse between two spins which possess no mutual scalar coupling. Such anomalous coherence transfer processes are associated with multiexponential transverse relaxation that can arise, amongst other mechanisms, from cross-correlation between two time-dependent dipolar interactions.     

Solid-state NMR and quantum chemical investigations of 13Calpha shielding tensor magnitudes and orientations in peptides: determining phi and psi torsion angles

We report the experimental determination of the (13)C(alpha) chemical shift tensors of Ala, Leu, Val, Phe, and Met in a number of polycrystalline peptides with known X-ray or de novo solid-state NMR structures. The 700 Hz dipolar coupling between (13)C(alpha) and its directly bonded (14)N permits extraction of both the magnitude and the orientation of the shielding tensor with respect to the C(alpha)-N bond vector. The chemical shift anisotropy (CSA) is recoupled under magic-angle spinning using the SUPER technique (Liu et al., J. Magn. Reson. 2002, 155, 15-28) to yield quasi-static chemical shift powder patterns. The tensor orientation is extracted from the (13)C-(14)N dipolar modulation of the powder line shapes. The magnitudes and orientations of the experimental (13)C(alpha) chemical shift tensors are found to be in good accord with those predicted from quantum chemical calculations. Using these principal values and orientations, supplemented with previously measured tensor orientations from (13)C-(15)N and (13)C-(1)H dipolar experiments, we are able to predict the (phi, psi, chi(1)) angles of Ala and Val within 5.8 degrees of the crystallographic values. This opens up a route to accurate determination of torsion angles in proteins based on shielding tensor magnitude and orientation information using labeled compounds, as well as the structure elucidation of noncrystalline organic compounds using natural abundance (13)C NMR techniques.     

Efficient CH-group selection and identification in 13C solid-state NMR by dipolar DEPT and 1H chemical-shift filtering

A new spectral-editing technique for solid-state nuclear magnetic resonance (NMR), based principally on the different dipolar-dephasing properties of CH and CH(2) multiple-quantum (MQ) coherence, yields pure C-H spectra with overall efficiencies of up to 14%. The selection is based on dephasing of methylene heteronuclear MQ coherence by the second proton and can be considered essentially as a solid-state, slow-magic-angle-spinning version of the distortionless enhancement by polarization transfer (DEPT) experiment. A short dipolar transfer and inverse gated decoupling suppress quaternary-carbon resonances, and T(1)-filtering reduces methyl signals. Applications to amorphous polymers with long, flexible sidegroups demonstrate excellent suppression of the signals of partially mobile methylene groups, consistent with simulations and superior to existing methods. CH selection in various model compounds and a humic acid confirms the robust nature and good sensitivity of the technique. Distinction of NCH and CCH groups, which have overlapping (13)C chemical-shift ranges, is achieved by combining dipolar DEPT with (1)H isotropic-chemical-shift filtering. In the humic acid, this permits unequivocal assignment of the methine resonance near 53 ppm to NCH groups.     

Nitrogen-14 NMR spectroscopy using residual dipolar splittings in solids

It is shown that nuclear magnetic resonance (NMR) spectra of nitrogen-14 (spin I = 1) can be obtained by indirect detection in powders spinning at the magic angle (MAS). The method relies on the transfer of coherence from a neighboring nucleus with S = 1/2, such as carbon-13, to single- or double-quantum transitions of nitrogen-14 nuclei. The transfer of coherence occurs through second-order quadrupole-dipole cross terms, also known as residual dipolar splittings. The two-dimensional NMR spectra reveal powder patterns determined by the second-order quadrupolar interactions of nitrogen-14. Analysis of the spectra yields the quadrupolar coupling constant, CQ, and asymmetry parameter, etaQ, of nitrogen-14. These parameters can be related to the structure of nitrogen-containing solids.     

Broadband rotational resonance in solid state NMR spectroscopy

A new technique for restoring nuclear magnetic dipole-dipole couplings under magic-angle spinning (MAS) in solid state nuclear magnetic resonance (NMR) spectroscopy is described and demonstrated. In this technique, called broadband rotational resonance (BroBaRR), the coupling between a pair of nuclear spins with NMR frequency difference close (but not necessarily equal) to the MAS frequency is restored by the application of a train of weak radio-frequency pulses at a carrier frequency close to the average of the two NMR frequencies. Phase or amplitude modulation of the pulse train at half the MAS frequency splits the carrier into sidebands close to the two NMR frequencies. The pulse train then removes offsets from the exact rotational resonance condition, leading to dipolar recoupling over a bandwidth controlled by the amplitude of the pulse train. (13)C NMR experiments on uniformly (15)N,(13)C-labeled L-valineHClH(2)O powder validate the theoretical analysis. BroBaRR will be useful in studies of molecular structures by solid state NMR, for example in the detection of long-range couplings between carbons in uniformly labeled organic and biological materials.     

High-resolution 2D NMR spectroscopy of bicelles to measure the membrane interaction of ligands

Magnetically aligned bicelles are increasingly being used as model membranes in solution- and solid-state NMR studies of the structure, dynamics, topology, and interaction of membrane-associated peptides and proteins. These studies commonly utilize the PISEMA pulse sequence to measure dipolar coupling and chemical shift, the two key parameters used in subsequent structural analysis. In the present study, we demonstrate that the PISEMA and other rotating-frame pulse sequences are not suitable for the measurement of long-range heteronuclear dipolar couplings, and that they provide inaccurate values when multiple protons are coupled to a 13C nucleus. Furthermore, we demonstrate that a laboratory-frame separated-local-field experiment is capable of overcoming these difficulties in magnetically aligned bicelles. An extension of this approach to accurately measure 13C-31P and 1H-31P couplings from phospholipids, which are useful to understand the interaction of molecules with the membrane, is also described. In these 2D experiments, natural abundance 13C was observed from bicelles containing DMPC and DHPC lipid molecules. As a first application, these solid-state NMR approaches were utilized to probe the membrane interaction of an antidepressant molecule, desipramine, and its location in the membrane.     

Structure determination of a membrane protein in proteoliposomes

An NMR method for determining the three-dimensional structures of membrane proteins in proteoliposomes is demonstrated by determining the structure of MerFt, the 60-residue helix-loop-helix integral membrane core of the 81-residue mercury transporter MerF. The method merges elements of oriented sample (OS) solid-state NMR and magic angle spinning (MAS) solid-state NMR techniques to measure orientation restraints relative to a single external axis (the bilayer normal) from individual residues in a uniformly (13)C/(15)N labeled protein in unoriented liquid crystalline phospholipid bilayers. The method relies on the fast (>10(5) Hz) rotational diffusion of membrane proteins in bilayers to average the static chemical shift anisotropy and heteronuclear dipole-dipole coupling powder patterns to axially symmetric powder patterns with reduced frequency spans. The frequency associated with the parallel edge of such motionally averaged powder patterns is exactly the same as that measured from the single line resonance in the spectrum of a stationary sample that is macroscopically aligned parallel to the direction of the applied magnetic field. All data are collected on unoriented samples undergoing MAS. Averaging of the homonuclear (13)C/(13)C dipolar couplings, by MAS of the sample, enables the use of uniformly (13)C/(15)N labeled proteins, which provides enhanced sensitivity through direct (13)C detection as well as the use of multidimensional MAS solid-state NMR methods for resolving and assigning resonances. The unique feature of this method is the measurement of orientation restraints that enable the protein structure and orientation to be determined in unoriented proteoliposomes.     

Theory of stochastic dipolar recoupling in solid-state nuclear magnetic resonance

Dipolar recoupling techniques in solid-state nuclear magnetic resonance (NMR) consist of radio frequency (rf) pulse sequences applied in synchrony with magic-angle spinning (MAS) that create nonzero average magnetic dipole-dipole couplings under MAS. Stochastic dipolar recoupling (SDR) is a variant in which randomly chosen rf carrier frequency offsets are introduced to cause random phase modulations of individual pairwise couplings in the dipolar spin Hamiltonian. Several aspects of SDR are investigated through analytical theory and numerical simulations: (1) An analytical expression for the evolution of nuclear spin polarization under SDR in a two-spin system is derived and verified through simulations, which show a continuous evolution from coherent, oscillatory polarization exchange to incoherent, exponential approach to equilibrium as the range of random carrier offsets (controlled by a parameter f(max)) increases; (2) in a many-spin system, polarization transfers under SDR are shown to be described accurately by a rate matrix in the limit of large f(max), with pairwise transfer rates that are proportional to the inverse sixth power of pairwise internuclear distances; (3) quantum mechanical interferences among noncommuting pairwise dipole-dipole couplings, which are a complicating factor in solid-state NMR studies of molecular structures by traditional dipolar recoupling methods, are shown to be absent from SDR data in the limit of large f(max), provided that coupled nuclei have distinct NMR chemical shifts.     

Investigation of dipolar-mediated water-protein interactions in microcrystalline Crh by solid-state NMR spectroscopy

Water-protein interactions play a major role in protein folding, structure, and function, and solid-state NMR has recently been shown to be a powerful tool for the site-resolved observation of these interactions in solid proteins. In this article we report investigations on possible water-protein dipolar transfer mechanisms in the microcrystalline deuterated protein Crh by a set of solid-state NMR techniques. Double-quantum (DQ) filtered and edited heteronuclear correlation experiments are used to follow direct dipolar water-protein magnetization transfers. Experimental data reveal no evidence for "solid-like" water molecules, indicating that residence times of solvent molecules are shorter than required for DQ creation, typically a few hundred microseconds. An alternative magnetization pathway, intermolecular cross-relaxation via heteronuclear nuclear Overhauser effects (NOEs), is probed by saturation transfer experiments. The significant additional enhancements observed when irradiating at the water frequency can possibly be attributed to direct heteronuclear water-protein NOEs; however, a contribution from relayed magnetization transfer via chemical exchange or proton-proton dipolar mechanisms cannot be excluded.     

A 2D solid-state NMR experiment to resolve overlapping aromatic resonances of thiophene-based nematogens

In this study, we demonstrate the feasibility of resolving overlapping 13C chemical shift spectral lines of aromatic rings in a thiophene-based nematogen in the mesophase using a 2D PITANSEMA solid-state NMR method. This technique provided the information about chemical shift values as well as dipolar couplings that are used for determining the orientational order parameter. Large C-H dipolar coupling values measured for thiophene in contrast to phenyl rings suggest that the heterocyclic ring is not part of the molecular axis. Using the order parameter, we determined the orientation of C-H vectors of the thiophene ring. We believe that the 2D solid-state NMR can be extended to other types of liquid crystalline materials such as the banana-based mesogens for determining the orientational order and bent angle.     

SESAME-HSQC for simultaneous measurement of NH and CH scalar and residual dipolar couplings

We present a novel pulse sequence, SESAME-HSQC, for the simultaneous measurement of several NH and CH scalar and residual dipolar couplings in double labeled proteins. The proposed Spin-statE Selective All Multiplicity Edited (SESAME)-HSQC combines gradient selected and sensitivity enhanced (15)N- and constant-time (13)C-HSQC experiments with the recently introduced spin-state selective method (Nolis et al., J. Magn. Reson. 180 (2006) 39-50) for measuring couplings simultaneously at amide and aliphatic regions. Excellent resolution and high sensitivity is warranted by removing all coupling interactions during the indirectly detected t(1) period, and by employing pulsed field gradients for coherence selection and utilizing coherence order selective spin-state selection. The scalar and residual dipolar couplings can be readily measured from a two-dimensional (15)N/(13)C-HSQC spectrum without additional spectral crowding. SESAME-HSQC can be used for epitope mapping by observing chemical shift changes in both amide and aliphatic regions. Simultaneously, potential conversion in protein conformation can be probed by analyzing changes in residual dipolar couplings induced by ligand binding. The pulse sequence is experimentally verified with a sample of (15)N/(13)C enriched human ubiquitin. The internuclear vector directions determined from the residual dipolar couplings are found to be in excellent correlation with those predicted from ubiquitin's refined solution structure.