Symmetry-based 29Si dipolar recoupling magic angle spinning NMR spectroscopy: a new method for investigating three-dimensional structures of zeolite frameworks

A new 29Si solid-state MAS NMR experiment is described for investigating the framework structures of pure silica zeolites. The symmetry-based homonuclear dipolar recoupling sequence SR26411 has been incorporated into a two-dimensional NMR experiment to probe the Si-O-Si bonding connectivities and long-range Si-Si distances in zeolite frameworks. This dipolar recoupling sequence is shown to have a number of advantages over the J-coupling-based INADEQUATE experiment. For the clathrasil Sigma-2, it is demonstrated that there is excellent agreement between experimental double-quantum build-up curves obtained from a series of two-dimensional double-quantum correlation spectra and simulated curves which consider all Si-Si distances out to 8 A. This result suggests that this experiment could be used to solve zeolite frameworks with unknown structures.     

Measuring distances between half-integer quadrupolar nuclei and detecting relative orientations of quadrupolar and dipolar tensors by double-quantum homonuclear dipolar recoupling nuclear magnetic resonance experiments

We studied the possibility of using double-quantum homonuclear dipolar recoupling magic angle spinning nuclear magnetic resonance experiments for structural analysis of systems of half-integer quadrupolar nuclei. We investigated symmetry-based recoupling schemes R2(2) (1) and R2(2) (1)R2(2) (-1) and showed that the obtained double-quantum filtered signals depend substantially on magnitudes and relative orientations of dipolar and quadrupolar tensors. Experimental results measured on aluminophosphate molecular sieve AlPO(4)-14, containing dipolar-coupled spin-52 aluminum nuclei, were compared to results of time-consuming numerical simulations. The comparison for short mixing times allowed us to roughly measure internuclear Al-Al distances, if constraints about relative tensor orientations were available. Inspection of relative orientations of dipolar and quadrupolar tensors, using known distances between nuclei, required experimental and simulated data for long mixing times and yielded less accurate results. Two experimental protocols were employed for measuring double-quantum filtered curves, the symmetric protocol, in which excitation and reconversion periods are incremented simultaneously, and the asymmetric protocol, in which only the length of the excitation period is incremented and the length of the reconversion period is kept constant. The former experimental protocol was more convenient for the detection of internuclear distances, and the latter one was more appropriate for the inspection of relative orientations of interaction tensors.     

Double-quantum homonuclear correlation magic angle sample spinning nuclear magnetic resonance spectroscopy of dipolar-coupled quadrupolar nuclei

A double-quantum homonuclear correlation nuclear magnetic resonance experiment for dipolar-coupled half-integer quadrupolar nuclei in solids is presented. The experiment is based on rotary resonance dipolar recoupling and uses bracketed spin-lock pulses to excite double-quantum coherence and later to convert it to the zero-quantum one. A central-transition-selective pi pulse at the beginning of the t1 evolution period differentiates coherence transfer pathways of double-quantum coherences arising from coupled spins and from a single spin, so that the latter can be efficiently filtered out by phase cycling. The experiment was tested on an aluminophosphate molecular sieve AlPO4-14, a material with a variety of aluminum quadrupolar coupling constants, isotropic chemical shifts and homonuclear distances. In a two-dimensional spectrum aluminum dipolar couplings with internuclear distances between 2.9 and 5.5 A were resolved. Although the experiment requires an application of weak radio-frequency fields, frequency offsets did not affect its performance crucially.     

Description of depolarization effects in double-quantum solid state nuclear magnetic resonance experiments using multipole-multimode Floquet theory

Using an analytical model based on multipole-multimode Floquet theory (MMFT), we describe the polarization loss (or depolarization) observed in double-quantum (DQ) dipolar recoupling magic angle spinning (MAS) experiments. Specifically, the factors responsible for depolarization are analyzed in terms of higher order corrections to the spin Hamiltonian in addition to the usual phenomenological decay rate constant. From the MMFT model and the effective Hamiltonians, we elucidate the rationale behind the inclusion of a phenomenological damping term in DQ recoupling experiments. As a test of this theoretical approach, the recoupling efficiency of one class of (13)C-(13)C and (13)C-(15)N resonance width dipolar recoupling experiments are investigated at different magnetic field strengths and compared with the more exact numerical simulations. In contrast to existing analytical treatments, the role of higher order corrections is clearly explained in the context of the MMFT approach leading to a better understanding of the underlying spin physics. Furthermore, the analytical model presented herein provides a general framework for describing coherent and incoherent effects in homonuclear and heteronuclear DQ MAS recoupling experiments.     

The structure of poly(carbonsuboxide) on the atomic scale: a solid-state NMR study

In this contribution we present a study of the structure of amorphous poly(carbonsuboxide) (C3O2)x by 13C solid-state NMR spectroscopy supported by infrared spectroscopy and chemical analysis. Poly(carbonsuboxide) was obtained by polymerization of carbonsuboxide C3O2, which in turn was synthesized from malonic acid bis(trimethylsilylester). Two different 13C labeling schemes were applied to probe inter- and intramonomeric bonds in the polymer by dipolar solid-state NMR methods and also to allow quantitative 13C MAS NMR spectra. Four types of carbon environments can be distinguished in the NMR spectra. Double-quantum and triple-quantum 2D correlation experiments were used to assign the observed peaks using the through-space and through-bond dipolar coupling. In order to obtain distance constraints for the intermonomeric bonds, double-quantum constant-time experiments were performed. In these experiments an additional filter step was applied to suppress contributions from not directly bonded 13C,13C spin pairs. The 13C NMR intensities, chemical shifts, connectivities and distances gave constraints for both the polymerization mechanism and the short-range order of the polymer. The experimental results were complemented by bond lengths predicted by density functional theory methods for several previously suggested models. Based on the presented evidence we can unambiguously exclude models based on gamma-pyronic units and support models based on alpha-pyronic units. The possibility of planar ladder- and bracelet-like alpha-pyronic structures is discussed.     

Selective double-quantum nmr in solids

A simple method for selective double-quantum NMR in solids is described. The spin system is first prepared in a state having only dipolar, or quadrupolar, order. Selective excitation and detection of double-quantum coherence is then achieved by the 90°_x,y-t-45°_y pulse sequence.     

Symmetry-based constant-time homonuclear dipolar recoupling in solid state NMR

Constant-time dipolar recoupling pulse sequences are advantageous in structural studies by solid state nuclear magnetic resonance (NMR) with magic-angle spinning (MAS) because they yield experimental data that are relatively insensitive to radio-frequency pulse imperfections and nuclear spin relaxation processes. A new approach to the construction of constant-time homonuclear dipolar recoupling sequences is described, based on symmetry properties of the recoupled dipole-dipole interaction Hamiltonian under cyclic displacements in time with respect to the MAS sample rotation period. A specific symmetry-based pulse sequence called PITHIRDS-CT is introduced and demonstrated experimentally. (13)C NMR data for singly-(13)C-labeled amino acid powders and amyloid fibrils indicate the effectiveness of PITHIRDS-CT in measurements of intermolecular distances in solids. (15)N-detected and (13)C-detected measurements of intramolecular (15)N-(15)N distances in peptides with alpha-helical and beta-sheet structures indicate the utility of PITHIRDS-CT in studies of molecular conformations, especially measurements of backbone psi torsion angles in peptides containing uniformly (15)N- and (13)C-labeled amino acids.     

NMR polarization echoes in a nematic liquid crystal

We have modified the polarization echo (PE) sequence through the incorporation of Lee-Goldburg cross polarization steps to quench the 1H-1H dipolar dynamics. In this way, the 13C becomes an ideal local probe to inject and detect polarization in the proton system. This improvement made possible the observation of the local polarization P(00)(t) and polarization echoes in the interphenyl proton of the liquid crystal N-(4-methoxybenzylidene)-4-butylaniline. The decay of P(00)(t) was well fitted to an exponential law with a characteristic time tau(C) approximately 310 micros. The hierarchy of the intramolecular dipolar couplings determines a dynamical bottleneck that justifies the use of the Fermi Golden Rule to obtain a spectral density consistent with the structural parameters. The time evolution of P(00)(t) was reversed by the PE sequence generating echoes at the time expected by the scaling of the dipolar Hamiltonian. This indicates that the reversible 1H-1H dipolar interaction is the main contribution to the local polarization decrease and that the exponential decay for P(00)(t) does not imply irreversibility. The attenuation of the echoes follows a Gaussian law with a characteristic time tau(phi) approximately 527 micros. The shape and magnitude of the characteristic time of the PE decay suggest that it is dominated by the unperturbed homonuclear dipolar Hamiltonian. This means that tau(phi) is an intrinsic property of the dipolar coupled network and not of other degrees of freedom. In this case, one cannot unambiguously identify the mechanism that produces the decoherence of the dipolar order. This is because even weak interactions are able to break the fragile multiple coherences originated on the dipolar evolution, hindering its reversal. Other schemes to investigate these underlying mechanisms are proposed.     

Dipolar double-quantum filtered rotational-echo double resonance

The homonuclear dipolar coupling of a directly bonded (13)C-(13)C pair has been used to create a dipolar double-quantum filter (D-DQF) to remove the natural-abundance (13)C background in (13)C[(2)H] rotational-echo double-resonance (REDOR) experiments. The most efficient version of this experiment has the D-DQF excitation and reconversion preceding the REDOR evolution period. Calculated and observed (13)C[(2)H]D-DQF-REDOR dephasings were in agreement for a test sample of mixed recrystallized labeled alanines.     

Heteronuclear dipolar decoupling effects on multiple-quantum and satellite-transition magic-angle spinning NMR spectra

We here report on the influence of heteronuclear dipolar decoupling on the (27)Al 3QMAS, 5QMAS, and the double-quantum filter-satellite-transition magic-angle spinning (DQF-STMAS) spectra of a strongly dipolar-coupled system, gibbsite. The requirements for heteronuclear dipolar decoupling increase with the order of coherence evolving in the indirect dimension of a two-dimensional (2D) experiment. The isotropic line width of the high-resolution 2D spectra, in samples like gibbsite, is composed of four parts: the distribution of isotropic shifts (delta(ISO), delta(QIS)), the homogeneous broadening related to the proton-proton flip-flop terms, the (27)Al-(27)Al homonulcear dipolar couplings, and the (1)H-(27)Al heteronuclear dipolar couplings. It is shown that, even in the case of gibbsite, where a strong proton-proton bath exists, the main resolution limiting factor in these experiments resides in the (1)H-(27)Al dipolar interaction.     

Dipolar recoupling in NOESY-type 1H-1H NMR experiments under HRMAS conditions

[structure: see text]. The concept of dipolar recoupling is introduced to 1H-1H NOESY experiments performed under HRMAS conditions. Dipole-dipole couplings are selectively recoupled during the mixing period, while MAS ensures high resolution in the spectral dimensions. Incoherent dipolar exchange is replaced by amplified coherent processes, such that time scales for polarization transfer are shortened, and dipolar double-quantum techniques become applicable. In this way, dipole-dipole couplings, as well as J-couplings, can be individually measured.     

An investigation of the hydrogen-bonding structure in bilirubin by 1H double-quantum magic-angle spinning solid-state NMR spectroscopy.

The complex hydrogen-bonding arrangement in the biologically important molecule bilirubin IXalpha is probed by using 1H double-quantum (DQ) magic-angle spinning (MAS) NMR spectroscopy. Employing fast MAS (30 kHz) and a high magnetic field (16.4 T), three low-field resonances corresponding to the different hydrogen-bonding protons are resolved in a 1H MAS NMR spectrum of bilirubin. These resonances are assigned on the basis of the proton-proton proximities identified from a two-dimensional rotor-synchronized 1H DQ MAS NMR spectrum. An analysis of 1H DQ MAS spinning-sideband patterns for the NH protons in bilirubin allows the quantitative determination of proton-proton distances and the geometry. The validity of this procedure is proven by simulated spectra for a model three-spin system, which show that the shortest distance can be determined to a very high degree of accuracy. The distance between the lactam and pyrrole NH protons in bilirubin is determined to be 0.186 +/- 0.002 nm (corresponding to a dominant dipolar coupling constant of 18.5 +/- 0.5 kHz). The analysis also yields a distance between the lactam NH and carboxylic acid OH protons of 0.230 +/- 0.008 nm (corresponding to a perturbing dipolar coupling constant of 9.9 +/- 1.0 kHz) and an H-H-H angle of 122 +/- 4 degrees. Finally, a comparison of 1H DQ MAS spinning-sideband patterns for bilirubin and its dimethyl ester reveals a significantly longer distance between the two NH protons in the latter case.     

A Bis‐Manganese(II)–DOTA Complex for Pulsed Dipolar Spectroscopy

High‐spin gadolinium(III) and manganese(II) complexes have emerged as alternatives to standard nitroxide radical spin labels for measuring nanometric distances by using pulsed electron–electron double resonance (PELDOR or DEER) at high fields/frequencies. For certain complexes, particularly those with relatively small zero‐field splitting (ZFS) and short distances between the two metal centers, the pseudosecular term of the dipolar coupling Hamiltonian is non‐negligible. However, in general, the contribution from this term during conventional data analysis is masked by the flexibility of the molecule of interest and/or the long tethers connecting them to the spin labels. The efficient synthesis of a model system consisting of two [Mn(dota)]^2? (MnDOTA; DOTA^4?=1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetraacetate) directly connected to the ends of a central rodlike oligo(phenylene–ethynylene) (OPE) spacer is reported. The rigidity of the OPE is confirmed by Q‐band PELDOR measurements on a bis‐nitroxide analogue. The Mn^II?Mn^II distance distribution profile determined by W‐band PELDOR is in reasonable agreement with one simulated by using a simple rotamer analysis. The small degree of flexibility arising from the linking MnDOTA arm appears to outweigh the contribution from the pseudosecular term at this interspin distance. This study illustrates the potential of MnDOTA‐based spin labels for measuring fairly short nanometer distances, and also presents an interesting candidate for in‐depth studies of pulsed dipolar spectroscopy methods on Mn^II?Mn^II systems.     

Observing 13C-13C connectivities at high magnetic fields and very high spinning frequencies

We report the application of a dipolar recoupling sequence for the observation of (13)C-(13)C connectivities in biomolecules at high magnetic fields (B(0)≥ 21.1 T) and ultra-high magic angle spinning frequencies (ν(R) = 60 kHz). The efficiency and the robustness of this double-quantum technique are demonstrated on the YajG protein (19.6 kDa).     

Theory and applications of supercycled symmetry-based recoupling sequences in solid-state nuclear magnetic resonance

We present the theoretical principles of supercycled symmetry-based recoupling sequences in solid-state magic-angle-spinning NMR. We discuss the construction procedure of the SR26 pulse sequence, which is a particularly robust sequence for double-quantum homonuclear dipole-dipole recoupling. The supercycle removes destructive higher-order average Hamiltonian terms and renders the sequence robust over long time intervals. We demonstrate applications of the SR26 sequence to double-quantum spectroscopy, homonuclear spin counting, and determination of the relative orientations of chemical shift anisotropy tensors.     

Heteronuclear proton assisted recoupling

We describe a theoretical framework for understanding the heteronuclear version of the third spin assisted recoupling polarization transfer mechanism and demonstrate its potential for detecting long-distance intramolecular and intermolecular (15)N-(13)C contacts in biomolecular systems. The pulse sequence, proton assisted insensitive nuclei cross polarization (PAIN-CP) relies on a cross term between (1)H-(15)N and (1)H-(13)C dipolar couplings to mediate zero- and∕or double-quantum (15)N-(13)C recoupling. In particular, using average Hamiltonian theory we derive effective Hamiltonians for PAIN-CP and show that the transfer is mediated by trilinear terms of the form N(±)C(?)H(z) (ZQ) or N(±)C(±)H(z) (DQ) depending on the rf field strengths employed. We use analytical and numerical simulations to explain the structure of the PAIN-CP optimization maps and to delineate the appropriate matching conditions. We also detail the dependence of the PAIN-CP polarization transfer with respect to local molecular geometry and explain the observed reduction in dipolar truncation. In addition, we demonstrate the utility of PAIN-CP in structural studies with (15)N-(13)C spectra of two uniformly (13)C,(15)N labeled model microcrystalline proteins-GB1, a 56 amino acid peptide, and Crh, a 85 amino acid domain swapped dimer (MW=2×10.4 kDa). The spectra acquired at high magic angle spinning frequencies (ω(r)∕2π>20 kHz) and magnetic fields (ω(0H)∕2π=700-900 MHz) using moderate rf fields, yield multiple long-distance intramonomer and intermonomer (15)N-(13)C contacts. We use these distance restraints, in combination with the available x-ray structure as a homology model, to perform a calculation of the monomer subunit of the Crh protein.     

Measurement of long-range cross-correlation rates using a combination of single- and multiple-quantum NMR spectroscopy in one experiment

A method is described to determine long-range cross-correlations between the modulations of an anisotropic chemical shift (e.g., of a C' carbonyl carbon in a protein) and the fluctuations of a weak long-range dipolar interaction (e.g., in cross-correlation between the same C' carbonyl and the H(N) proton of the neighboring amide group). Such long-range correlations are difficult to measure because the corresponding long-range scalar couplings are so small that Redfield's secular approximation is often violated. The method, which combines features of single- and double-quantum NMR spectroscopy, allows one to cancel the effects of dominant short-range dipolar interactions (e.g., between the CSA of the amide nitrogen N and the dipolar coupling to its attached proton H(N)) and is designed so that the secular approximation is rescued even if the scalar coupling between the long-range dipolar coupling partners is very small. The cross-correlation rates thus determined in ubiquitin cover a wide range because of local motions and variations of the CSA tensors.     

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.     

Probing proton-proton proximities in the solid state: high-resolution two-dimensional 1H-1H double-quantum CRAMPS NMR spectroscopy

A new 1H DQ (double-quantum) CRAMPS (combined rotation and multiple-pulse sequence) solid-state nuclear magnetic resonance experiment incorporating DUMBO homonuclear 1H dipolar decoupling is presented. The major resolution enhancement enables DQ peaks corresponding to all 22 close (<3.5 A) proton-proton proximities in the dipeptide beta-AspAla to be observed. In particular, the DQ CRAMPS spectrum provides access to the alkyl region of the spectrum and yields a clear assignment of the two CH and two diastereotopic CH2 proton resonances.     

Measurement of large distances in biomolecules using double-quantum filtered refocused electron spin-echoes

It is shown how the new technique of double-quantum filtered refocused electron spin-echoes is a significant improvement over double-quantum coherence ESR, since it increases the experimental acquisition time. This enables the measurement of longer distances in bilabeled biomolecules. The method is demonstrated on a long double-stranded A-type RNA, spin labeled at both ends. The measured distance of 72 A is in excellent agreement with molecular modeling.