Residual dipolar couplings by off-magic-angle spinning in solid-state nuclear magnetic resonance spectroscopy

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.

Proton Detected Solid-State NMR of Membrane Proteins at 28 Tesla (1.2 GHz) and 100 kHz Magic-Angle Spinning

The available magnetic field strength for high resolution NMR in persistent superconducting magnets has recently improved from 23.5 to 28 Tesla, increasing the proton resonance frequency from 1 to 1.2 GHz. For magic-angle spinning (MAS) NMR, this is expected to improve resolution, provided the sample preparation results in homogeneous broadening. We compare two-dimensional (2D) proton detected MAS NMR spectra of four membrane proteins at 950 and 1200 MHz. We find a consistent improvement in resolution that scales superlinearly with the increase in magnetic field for three of the four examples. In 3D and 4D spectra, which are now routinely acquired, this improvement indicates the ability to resolve at least 2 and 2.5 times as many signals, respectively.

Weak Intermolecular CH···N Hydrogen Bonding: Determination of 13CH-15N Hydrogen-Bond Mediated J Couplings by Solid-State NMR Spectroscopy and First-Principles Calculations

Weak hydrogen bonds are increasingly hypothesized to play key roles in a wide range of chemistry from catalysis to gelation to polymer structure. Here, ¹⁵N/¹³C spin-echo magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) experiments are applied to "view" intermolecular CH···N hydrogen bonding in two selectively labeled organic compounds, 4-[¹⁵N] cyano-4'-[¹³C₂] ethynylbiphenyl (1) and [¹⁵N₃,¹³C₆]-2,4,6-triethynyl-1,3,5-triazine (2). The synthesis of 2-¹⁵N₃,¹³C₆ is reported here for the first time via a multistep procedure, where the key element is the reaction of [¹⁵N₃]-2,4,6-trichloro-1,3,5-triazine (5) with [¹³C₂]-[(trimethylsilyl)ethynyl]zinc chloride (8) to afford its immediate precursor [¹⁵N₃,¹³C₆]-2,4,6-tris[(trimethylsilyl)ethynyl]-1,3,5-triazine (9). Experimentally determined hydrogen-bond-mediated ^2hJ_CN couplings (4.7 ± 0.4 Hz (1) and 4.1 ± 0.3 Hz (2)) are compared with density functional theory (DFT) gauge-including projector augmented wave (GIPAW) calculations, whereby species-independent coupling values ^2hK_CN (29.0 × 10¹⁹ kg m^-2 s^-2 A^-2 (1) and 27.9 × 10¹⁹ kg m^-2 s^-2 A^-2 (2)) quantitatively demonstrate the J couplings for these "weak" CH···N hydrogen bonds to be of a similar magnitude to those for conventionally observed NH···O hydrogen-bonding interactions in uracil (^2hK_NO: 28.1 and 36.8 × 10¹⁹ kg m^-2 s^-2 A^-2). Moreover, the GIPAW calculations show a clear correlation between increasing ^2hJ_CN (and ^3hJ_CN) coupling and reducing C(H)···N and H···N hydrogen-bonding distances, with the Fermi contact term accounting for at least 98% of the isotropic ^2hJ_CN coupling.

Determination of methyl order parameters using solid state NMR under off magic angle spinning

Quantification of dipolar couplings in biological solids is important for the understanding of dynamic processes. Under Magic Angle Spinning (MAS), order parameters are normally obtained by recoupling of anisotropic interactions involving the application of radio frequency pulses. We have recently shown that amide backbone order parameters can be estimated accurately in a spin-echo experiment in case the rotor spinning angle is slightly mis-calibrated. In this work, we apply this method to determine methyl order parameters in a deuterated sample of the SH3 domain of chicken α-spectrin in which the methyl containing side chains valine and leucine are selectively protonated.

Accurate Determination of 1 H-15 N Dipolar Couplings Using Inaccurate Settings of the Magic Angle in Solid-State NMR Spectroscopy

Magic-angle spinning (MAS) is an essential ingredient in a wide variety of solid-state NMR experiments. The standard procedures to adjust the rotor angle are not highly accurate, resulting in a slight misadjustment of the rotor from the magic angle ( θ R L = tan - 1 2 ) on the order of a few millidegrees. This small missetting has no significant impact on the overall spectral resolution, but is sufficient to reintroduce anisotropic interactions. Shown here is that site-specific ¹ H-¹⁵ N dipolar couplings can be accurately measured in a heavily deuterated protein. This method can be applied at arbitrarily high MAS frequencies, since neither rotor synchronization nor particularly high radiofrequency field strengths are required. The off-MAS method allows the quantification of order parameters for very dynamic residues, which often escape an analysis using existing methods.

Setting the magic angle for fast magic-angle spinning probes

Fast magic-angle spinning, coupled with ¹H detection is a powerful method to improve spectral resolution and signal to noise in solid-state NMR spectra. Commercial probes now provide spinning frequencies in excess of 100 kHz. Then, one has sufficient resolution in the ¹H dimension to directly detect protons, which have a gyromagnetic ratio approximately four times larger than ¹³C spins. However, the gains in sensitivity can quickly be lost if the rotation angle is not set precisely. The most common method of magic-angle calibration is to optimize the number of rotary echoes, or sideband intensity, observed on a sample of KBr. However, this typically uses relatively low spinning frequencies, where the spinning of fast-MAS probes is often unstable, and detection on the ¹³C channel, for which fast-MAS probes are typically not optimized. Therefore, we compare the KBr-based optimization of the magic angle with two alternative approaches: optimization of the splitting observed in ¹³C-labeled glycine-ethylester on the carbonyl due to the Cα-C' J-coupling, or optimization of the H-N J-coupling spin echo in the protein sample itself. The latter method has the particular advantage that no separate sample is necessary for the magic-angle optimization.

Deuterium off-magic-angle spinning NMR spectroscopy for pure-quadrupole spectra of paramagnetic solids

We examined a simple two-dimensional ²H nuclear magnetic resonance spectroscopy for paramagnetic solids utilizing off-magic-angle spinning (OMAS). By adding a rotor-synchronized 180° pulse to rotational echo (RE) measurement, the effect of the shift interaction was removed from the indirect dimension. The obtained pure-quadrupole spectrum could be simulated by calculating a quasi-one-dimensional NMR signal without considering the shift interaction. The sensitivity of the proposed method was compared with that of previous static NMR methods.

Restoring Resolution in Biological Solid-State NMR under Conditions of Off-Magic-Angle Spinning

Spin-state-selective excitation (S3E) experiments allow the selection of individual transitions in a coupled two spin system. We show that in the solid state, the dipole-dipole interaction (DD) between (15)N and (1)H in a (1)H-(15)N bond and the chemical shift anisotropy (CSA) of (15)N in an amide moiety mutually cancel each other for a particular multiplet component at high field, when the sample is spun off the magic angle (Arctan [√2] = 54.74°). The accuracy of the adjustment of the spinning angle is crucial in conventional experiments. We demonstrate that for S3E experiments, the requirement to spin the sample exactly at the magic angle is not mandatory. Applications of solid state NMR in narrow bore magnets will be facilitated where the adjustment of the magic angle is often difficult. The method opens new perspectives for the development of schemes to determine distances and to quantify dynamics in the solid state.

Solid-state Hadamard NMR spectroscopy: simultaneous measurements of multiple selective homonuclear scalar couplings

Unambiguous measurement of homonuclear scalar couplings (J) in multi-spin scalar network systems is not straightforward. Further, the direct measurement of J-couplings is obscured in solid-state samples due to the dipolar and chemical shift anisotropy (CSA)-dominated line broadening, even under the magic angle spinning (MAS). We present a new multiple frequency selective spin-echo method based on Hadamard matrix encoding, for simultaneous measurement of multiple homonuclear scalar couplings (J) in the solid-state. In contrast to the Hadamard encoded selective excitation schemes known for the solution-state, herein the selectivity is achieved during refocusing period. The Hadamard encoded refocusing scheme concurrently allows to create the spin-spin commutation property between number of spin-pairs of choice in uniformly labelled molecules, which, therefore avoids (1) the repetition of the double selective refocusing experiments for each spin-pair and (2) the synthesis of expensive selective labelled molecules. The experimental scheme is exemplified for determining (1)JCC and (3)JCC values in (13)C6l-Histidine.HCl molecule, which are found to be in excellent agreement with those measured in conventional double frequency selective refocusing mode as well as in the solution-state. This method can be simply extended to 2D/3D pulse schemes and be applied to small bio-molecular solids.

Probing crystal packing of uniformly (13)C-enriched powder samples using homonuclear dipolar coupling measurements

The relationship between the crystal packing of powder samples and long-range (13)C-(13)C homonuclear dipolar couplings is presented and illustrated for the case of uniformly (13)C-enriched L-alanine and L-histidine·HCl·H2O. Dipolar coupling measurement is based on the partial reintroduction of dipolar interactions by spinning the sample slightly off-magic-angle, while the coupling of interest for a given spin pair is isolated with a frequency-selective pulse. A cost function is used to correlate the so-derived dipolar couplings to trial crystal structures of the samples under study. This procedure allowed for the investigation of the l-alanine space group and L-histidine·HCl·H2O space group and unit-cell parameters.

Selective inversion of 1H resonances in solid-state nuclear magnetic resonance: Use of double-DANTE pulse sequence

We here present a method based on DANTE pulses and homonuclear dipolar decoupling scheme to invert selectively any desired resonance in a proton spin system under magic-angle spinning. Experimental results are reported on a sample of L-histidine·HCl·H2O at magic-angle spinning frequencies of 15 and 60kHz. The results are also substantiated numerically.

Selective measurements of long-range homonuclear J-couplings in solid-state NMR

We demonstrate here that the principle of frequency-selective spin-echoes can be extended to the measurements of long-range homonuclear scalar J-couplings in the solid-state. Singly or doubly frequency-selective pulses were used to generate either a J-modulated experiment (S) or a reference experiment (S0). The combination of these two distinct experiments provides experimental data that, in favorable cases, are insensitive to incoherent relaxation effects, and which can be used to estimate long-range homonuclear J-couplings in multiple spin-systems. The concept is illustrated in the case of a uniformly (13)C and (15)N labeled sample of L-histidine, where the absolute value of homonuclear J-couplings between two spins separated by one, two or three covalent bonds are measured. Moreover, we show that a (2)J((15)N-C-(15)N) coupling as small as 0.9 Hz can be precisely measured with the method presented here.

A general protocol for determining the structures of molecularly ordered but noncrystalline silicate frameworks

A general protocol is demonstrated for determining the structures of molecularly ordered but noncrystalline solids, which combines constraints provided by X-ray diffraction (XRD), one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, and first-principles quantum chemical calculations. The approach is used to determine the structure(s) of a surfactant-directed layered silicate with short-range order in two dimensions but without long-range periodicity in three-dimensions (3D). The absence of long-range 3D molecular order and corresponding indexable XRD reflections precludes determination of a space group for this layered silicate. Nevertheless, by combining structural constraints obtained from solid-state (29)Si NMR analyses, including the types and relative populations of distinct (29)Si sites, their respective (29)Si-O-(29)Si connectivities and separation distances, with unit cell parameters (though not space group symmetry) provided by XRD, a comprehensive search of candidate framework structures leads to the identification of a small number of candidate structures that are each compatible with all of the experimental data. Subsequent refinement of the candidate structures using density functional theory calculations allows their evaluation and identification of "best" framework representations, based on their respective lattice energies and quantitative comparisons between experimental and calculated (29)Si isotropic chemical shifts and (2)J((29)Si-O-(29)Si) scalar couplings. The comprehensive analysis identifies three closely related and topologically equivalent framework configurations that are in close agreement with all experimental and theoretical structural constraints. The subtle differences among such similar structural models embody the complexity of the actual framework(s), which likely contain coexisting or subtle distributions of structural order that are intrinsic to the material.

Modulation of cross polarization in motionally averaged solids by Variable Angle Spinning NMR

In systems where the dipolar couplings are partially averaged by molecular motion, cross-polarization is modulated by sample spinning. The cross-polariation efficiency in Variable Angle Spinning (VAS) and Switched Angle Spinning (SAS) experiments on mobile samples is therefore strongly dependent on the spinning angle. We describe simulations and experimental measurements of these effects over a range of spinning angles from 0° to 90°.

New perspectives in the PAW/GIPAW approach: J(P-O-Si) coupling constants, antisymmetric parts of shift tensors and NQR predictions

In 2001, Pickard and Mauri implemented the gauge including projected augmented wave (GIPAW) protocol for first-principles calculations of NMR parameters using periodic boundary conditions (chemical shift anisotropy and electric field gradient tensors). In this paper, three potentially interesting perspectives in connection with PAW/GIPAW in solid-state NMR and pure nuclear quadrupole resonance (NQR) are presented: (i) the calculation of J coupling tensors in inorganic solids; (ii) the calculation of the antisymmetric part of chemical shift tensors and (iii) the prediction of (14)N and (35)Cl pure NQR resonances including dynamics. We believe that these topics should open new insights in the combination of GIPAW, NMR/NQR crystallography, temperature effects and dynamics. Points (i), (ii) and (iii) will be illustrated by selected examples: (i) chemical shift tensors and heteronuclear (2)J(P-O-Si) coupling constants in the case of silicophosphates and calcium phosphates [Si(5)O(PO(4))(6), SiP(2)O(7) polymorphs and α-Ca(PO(3))(2)]; (ii) antisymmetric chemical shift tensors in cyclopropene derivatives, C(3)X(4) (X = H, Cl, F) and (iii) (14)N and (35)Cl NQR predictions in the case of RDX (C(3)H(6)N(6)O(6)), β-HMX (C(4)H(8)N(8)O(8)), α-NTO (C(2)H(2)N(4)O(3)) and AlOPCl(6). RDX, β-HMX and α-NTO are explosive compounds.

Determination of J coupling constants between spin-1/2 and quadrupolar nuclei in inorganic solids from spin echo and refocused INEPT experiments: a case study on AlPO₄ berlinite

A systematic study utilizing rotor-synchronized homonuclear ((31)P, (27)Al) and heteronuclear ({(31)P}(27)Al and {(27)Al}(31)P) spin echo, and {(27)Al}(31)P refocused INEPT experiments (employing soft pulses for selective excitation of the central transition for the quadrupolar (27)Al (I=5/2)) have been performed on AlPO(4) berlinite at 30 kHz MAS to better understand the J modulation behavior involving half-integer quadrupolar nuclei in solid materials with framework structure. Analyses of the J modulation on either the (27)Al or (31)P coherence in both the {(31)P}(27)Al and {(27)Al}(31)P spin echo experiments, and both periods of the refocused INEPT experiment yield consistent results for the (2)J(AlP) (Al-O-P) coupling constant (ca. 25 Hz). It is noted that the coupling of each (27)Al to four (31)P spins during the first ((27)Al) evolution period of the refocused INEPT, and the populations of (31)P coupled to different numbers (0-4) of (27)Al in the ± 1/2 Zeeman states during (31)P coherence evolution, which have been neglected in previous studies, must be taken into account for proper treatment. Analysis of J modulation on the spin ((27)Al) coupled to spin-1/2 nuclei in general gives more accurate results. Weak long-range homonuclear (4)J(PP) (P-O-Al-O-P) coupling was also observed from the (31)P spin echo and INADEQUATE experiments.

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.

A Hall effect angle detector for solid-state NMR

We describe a new method for independent monitoring of the angle between the spinning axis and the magnetic field in solid-state NMR. A Hall effect magnetic flux sensor is fixed to the spinning housing, so that a change in the stator orientation leads to a change in the angle between the Hall plane and the static magnetic field. This leads to a change in the Hall voltage generated by the sensor when an electric current is passed through it. The Hall voltage may be measured externally by a precision voltmeter, allowing the spinning angle to be measured non-mechanically and independent of the NMR experiment. If the Hall sensor is mounted so that the magnetic field is approximately parallel to the Hall plane, the Hall voltage becomes highly sensitive to the stator orientation. The current angular accuracy is around 10 millidegrees. The precautions needed to achieve higher angular accuracy are described.

Low-load rotor-synchronised Hahn-echo pulse train (RS-HEPT) 1H decoupling in solid-state NMR: factors affecting MAS spin-echo dephasing times

Transverse dephasing times T(2)' in spin-echo MAS NMR using rotor-synchronised Hahn-echo pulse-train (RS-HEPT) low-load (1)H decoupling are evaluated. Experiments were performed at 300 and 600 MHz for (13)CH-labelled L-alanine and (15)NH(delta)-labelled L-histidine.HCl.H(2)O, together with SPINEVOLUTION simulations for a ten-spin system representing the crystal structure environment of the (13)CH carbon in L-alanine. For 30 kHz MAS and nu(1)((1)H) = 100 kHz at 300 MHz, a RS-HEPT T(2)' value of 17 +/- 1 ms was obtained for (13)CH-labelled L-alanine which is approximately 50% of the XiX T(2)' value of 33 +/- 2 ms. Optimum RS-HEPT decoupling performance is observed for a relative phase of alternate RS-HEPT pi-pulses, Deltaphi = phi'- phi, between 40 and 60 degrees . For experiments at 600 MHz and 30 kHz MAS with (13)CH-labelled L-alanine, the best RS-HEPT (nu(1)((1)H) = 100 kHz) T(2)' value was 3 times longer than that observed for low-power continuously applied sequences with nu(1)((1)H) < or =40 kHz, i.e. corresponding to the same average power dissipated in the probe. A marked improvement in RS-HEPT (1)H decoupling is observed for increasing MAS frequency: at 55.6 kHz MAS, a best RS-HEPT T(2)' value of 34 +/- 5 ms was recorded for (13)CH-labelled L-alanine. Much improved RS-HEPT broadband performance was also observed at 55.6 kHz MAS as compared to 30 kHz MAS.