Insights into the spin dynamics of a large anisotropy spin subjected to long-pulse irradiation under a modified REDOR experiment

Simplified Preservation of Equivalent Pathways Spectroscopy

Inspired by the recently proposed transverse mixing optimal control pulses (TROP) approach for improving signal in multidimensional magic-angle spinning (MAS) NMR experiments, we present simplified preservation of equivalent pathways spectroscopy (SPEPS). It transfers both transverse components of magnetization that occur during indirect evolutions, theoretically enabling a √2 improvement in sensitivity for each such dimension. We compare SPEPS transfer with TROP and cross-polarization (CP) using membrane protein and fibril samples at MAS of 55 and 100 kHz. In three-dimensional (3D) (H)CANH spectra, SPEPS outperformed TROP and CP by factors of on average 1.16 and 1.69, respectively, for the membrane protein, but only a marginal improvement of 1.09 was observed for the fibril. These differences are discussed, making note of the longer transfer time used for CP, 14 ms, as compared with 2.9 and 3.6 ms for SPEPS and TROP, respectively. Using SPEPS for two transfers in the 3D (H)CANCO experiment resulted in an even larger benefit in signal intensity, with an average improvement of 1.82 as compared with CP. This results in multifold time savings, in particular considering the weaker peaks that are observed to benefit the most from SPEPS.

Heteronuclear and homonuclear radio-frequency-driven recoupling

The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

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.

Transferred-Rotational-Echo Double Resonance

Internuclear distance determination is the foundation for NMR-based structure calculation. However, high-precision distance measurement is a laborious process requiring lengthy data acquisitions due to the large set of multidimensional spectra needed at different mixing times. This prevents application to large or challenging molecular systems. Here, we present a new approach, transferred-rotational-echo double resonance (TREDOR), a heteronuclear transfer method in which we simultaneously detect both starting and transferred signals in a single spectrum. This co-acquisition is used to compensate for coherence decay, resulting in accurate and precise distance determination by a single parameter fit using a single spectrum recorded at an ideal mixing time. We showcase TREDOR with the microcrystalline SH3 protein using 3D spectra to resolve resonances. By combining the measured N-C and H-C distances, we calculate the structure of SH3, which converges to the correct fold, with a root-mean-square deviation of 2.1 Å compared to a reference X-ray structure. The TREDOR data used in the structure calculation were acquired in only 4 days on a 600 MHz instrument. This is achieved due to the more than 2-fold time saving afforded by co-acquisition of additional information and demonstrates TREDOR as a fast and straightforward method for determining structures via magic-angle spinning NMR.

A modification of γ-encoded RN symmetry pulses for increasing the scaling factor and more accurate measurements of the strong heteronuclear dipolar couplings

Symmetry based γ-encoded RN_n^ν elements are broadly used in magic-angle spinning solid-state NMR experiments to achieve selective recoupling of the heteronuclear dipolar interactions. The recoupled dipolar couplings in such experiments are scaled by a factor, K_sc, which theoretically depends on the chosen symmetry numbers N, n, and ν. However, the maximum theoretical value of K_sc for γ-encoded RN_n^ν pulses is limited to ~0.25, resulting in long RN_n^ν experiment times. Also, the dependence of K_sc on the experimental parameters can result in systematic errors in the experimental determination of the dipolar couplings, especially at low and moderate MAS rates. In this manuscript, we investigate the use of MODifiEd RN_n^ν symmetry (MODERN_n^ν(ϕ_M)) pulses that increase the dipolar scaling factor by at least 1.45 fold compared to γ-encoded RN_n^ν. The second advantage of MODERN_n^ν(ϕ_M) pulses with respect to traditional RN_n^ν pulses is the reduced influence of experimental parameters on K_sc, which allows for more accurate measurement of short-range distances. The robustness of MODERN_n^ν(ϕ_M) is compared with γ-encoded R14₂³ symmetry pulses. The enhanced performance is demonstrated on two uniformly-¹³C-enriched samples, N-acetyl valine and the microcrystalline protein GB1, at a 31.111 kHz MAS rate.

Exact distance measurements for structure and dynamics in solid proteins by fast-magic-angle-spinning NMR

Fast-magic-angle-spinning solid-state NMR is a developing technique for determination of protein structure and dynamics. Proton-proton correlations usually lead to rough distance restraints, a serious hurdle towards high-resolution structures. Analogous to the "eNOE" concept in solution, an integrative approach for more accurate restraints enables improved structural accuracy with minimal analytical effort.

Observation of proximities between spin-1/2 and quadrupolar nuclei in solids: Improved robustness to chemical shielding using adiabatic symmetry-based recoupling

We introduce a novel heteronuclear dipolar recoupling based on the R2₁^-1 symmetry, which uses the tanh/tan (tt) shaped pulse as a basic inversion element and is denoted R2₁^-1(tt). Using first-order average Hamiltonian theory, we show that this sequence is non-γ-encoded and that it reintroduces the |m| = 1 spatial component of the Chemical Shift Anisotropy (CSA) of the irradiated isotope and its heteronuclear dipolar interactions. Using numerical simulations and one-dimensional (1D) ²⁷Al-{³¹P} through-space D-HMQC (Dipolar Heteronuclear Multiple-Quantum Correlation) experiments on VPI-5, we compare the performances of this recoupling to those of other non-γ-encoded |m| = 1 heteronuclear recoupling schemes: REDOR (Rotational-Echo DOuble Resonance), SFAM (Simultaneous Frequency and Amplitude Modulation) and R4₂^-1(tt). Such comparison indicates that the R2₁^-1(tt) scheme is more robust to CSA, offset and radiofrequency field inhomogeneities than the other schemes. We take advantage of the high robustness of R2₁^-1(tt) to CSA and offset to demonstrate the possibility to correlate the signals of ²⁰⁷Pb isotope with those of neighboring half-integer spin quadrupolar nuclei. Such approach is demonstrated experimentally by acquiring ¹¹B-{²⁰⁷Pb} D-HMQC 2D spectra of Pb₄O(BO₃)₂ crystalline powder.

Pushing the limit of NMR-based distance measurements - retrieving dipolar couplings to spins with extensively large quadrupolar frequencies

Dipolar recoupling under magic-angle spinning allows to measure accurate inter-nuclear distances provided that the two interacting spins can be efficiently and uniformly excited. Alexander (Lex) Vega has shown that adiabatic transfers of populations in quadrupolar spins during the application of constant-wave (cw) radio-frequency pulses lead to efficient and quantifiable dipolar recoupling curves. Accurate distance determination within and beyond the adiabatic regime using cw pulses is limited by the size of the quadrupolar coupling constant. Here we show that using the approach of long-pulse phase modulation, dipolar recoupling and accurate distances can be obtained for nuclei having extensively large quadrupolar frequencies of 5-10 MHz. We demonstrate such results by obtaining a ³¹P-^79/81Br distance in a compound for which bromine-79 (spin-3/2) has a quadrupolar coupling constant of 11.3 MHz, and a ¹³C-²⁰⁹Bi distance where the bismuth (spin-9/2) has a quadrupolar coupling constant of 256 MHz, equaling a quadrupolar frequency of 10.7 MHz. For Bromine, we demonstrate that an analytical curve based on the assumption of complete spin saturation fits the data. In the case of bismuth acetate, a C-Bi₃ spin system must be used in order to match the correct saturation recoupling curve, and results are in agreement with the crystallographic structure.

Analysis of large-anisotropy-spin recoupling pulses for distance measurement under magic-angle spinning NMR shows the superiority and robustness of a phase modulated saturation pulse

The distance between a spin one-half and an attached spin possessing a large anisotropy can be obtained using different dipolar recoupling sequences that are based on the rotational-echo double resonance technique under magic-angle spinning solid-state NMR. The general difference between these sequences with respect to the coupled spin is the set of pulses applied in order to drive this spin out of equilibrium, thereby recoupling the dipolar interaction. Since complete inversion is practically not possible due to the coupled-spin anisotropy, using one or another pulse depends on the experimental and spin conditions: the spinning speed, the strength of the radio frequency field, the size of the anisotropic interaction (quadrupolar or chemical shiftanisotropy couplings), the offset, and the accuracy of setting the magic angle. Here we present a detailed description of the behavior of the anisotropic spin magnetization, including the macroscopic level transition probabilities, the degree of inversion, and the microscopic and macroscopic magnetizations during the applications of these pulses under different experimental conditions. As simulations show, a complete randomization of spin populations under a wide range of experimental conditions occurs under a specific phase modulation of the recoupling pulse while for all other cases dependence on experimental conditions is large and the achievable bandwidth is limited. A result of this detailed analysis is that the extension of the phase modulated pulse extends even further its robustness. The saturation capability is demonstrated experimentally for the quadrupolar spin of boron-11 in 4-methoxyphenylboronic acid.

Exploiting 13C/14N solid-state NMR distance measurements to assign dihedral angles and locate neighboring molecules

The RESPDOR NMR method rapidly provides multiple ¹³C/¹⁴N distance measurements in natural abundance solids.

Saturation capability of short phase modulated pulses facilitates the measurement of longitudinal relaxation times of quadrupolar nuclei

The ability of various pulse types, which are commonly applied for distance measurements, to saturate or invert quadrupolar spin polarization has been compared by observing their effect on magnetization recovery curves under magic-angle spinning. A selective central transition inversion pulse yields a bi-exponential recovery for a diamagnetic sample with a spin-3/2, consistent with the existence of two processes: the fluctuations of the electric field gradients with identical single (W₁) and double (W₂) quantum quadrupolar-driven relaxation rates, and spin exchange between the central transition of one spin and satellite transitions of a dipolar-coupled similar spin. Using a phase modulated pulse, developed for distance measurements in quadrupolar spins (Nimerovsky et al., JMR 244, 2014, 107-113) and suggested for achieving the complete saturation of all quadrupolar spin energy levels, a mono-exponential relaxation model fits the data, compatible with elimination of the spin exchange processes. Other pulses such as an adiabatic pulse lasting one-third of a rotor period, and a two-rotor-period long continuous-wave pulse, both used for distance measurements under special experimental conditions, yield good fits to bi-exponential functions with varying coefficients and time constants due to variations in initial conditions. Those values are a measure of the extent of saturation obtained from these pulses. An empirical fit of the recovery curves to a stretched exponential function can provide general recovery times. A stretching parameter very close to unity, as obtained for a phase modulated pulse but not for other cases, suggests that in this case recovery times and longitudinal relaxation times are similar. The results are experimentally demonstrated for compounds containing ¹¹B (spin-3/2) and ⁵¹V (spin-7/2). We propose that accurate spin lattice relaxation rates can be measured by a short phase modulated pulse (<1-2ms), similarly to the "true T₁" measured by saturation with an asynchronous pulse train (Yesinowski, JMR 252, 2015, 135-144).

Reprint of: Localization of Cl-35 Nuclei in Biological Solids using Rotational-Echo Double-Resonance Experiments

Chloride ions play important roles in many chemical and biological processes. This paper investigates the possibility of localizing ³⁵Cl nuclei using solid-state NMR. It demonstrates that distances shorter than 3.8Å, between ¹³C atoms and ³⁵Cl atoms in 10% uniformly labeled ¹³C L-tyrosine·HCl and natural abundance Glycine·HCl can be measured using rotational-echo (adiabatic passage) double-resonance (RE(AP)DOR). Furthermore the effect of quadrupolar interaction on the REDOR/REAPDOR experiment is quantified. The dephasing curve is plotted in a three dimensional chart as a function of the dephasing time and of the strength of quadrupolar interaction felt by each orientation. During spinning each orientation feels a quadrupolar interaction that varies in time, and therefore at each moment in time we reorder the crystallite orientations as a function of their contribution to the dephasing curve. In this way the effect of quadrupolar interaction on the dipolar dephasing curve can be fitted with a polynomial function. The numerical investigation performed allows us to generate REDOR/REAPDOR curves which are then used to simulate the experimental data.

Localization of Cl-35 nuclei in biological solids using rotational-echo double-resonance experiments

Chloride ions play important roles in many chemical and biological processes. This paper investigates the possibility of localizing ³⁵Cl nuclei using solid-state NMR. It demonstrates that distances shorter than 3.8Å, between ¹³C atoms and ³⁵Cl atoms in 10% uniformly labeled ¹³C L-tyrosine·HCl and natural abundance Glycine·HCl can be measured using rotational-echo (adiabatic passage) double-resonance (RE(AP)DOR). Furthermore the effect of quadrupolar interaction on the REDOR/REAPDOR experiment is quantified. The dephasing curve is plotted in a three dimensional chart as a function of the dephasing time and of the strength of quadrupolar interaction felt by each orientation. During spinning each orientation feels a quadrupolar interaction that varies in time, and therefore at each moment in time we reorder the crystallite orientations as a function of their contribution to the dephasing curve. In this way the effect of quadrupolar interaction on the dipolar dephasing curve can be fitted with a polynomial function. The numerical investigation performed allows us to generate REDOR/REAPDOR curves which are then used to simulate the experimental data.

Solid-state NMR indirect detection of nuclei experiencing large anisotropic interactions using spinning sideband-selective pulses

Under Magic-Angle Spinning (MAS), a long radio-frequency (rf) pulse applied on resonance achieves the selective excitation of the center-band of a wide NMR spectrum. We show herein that these rf pulses can be applied on the indirect channel of Hetero-nuclear Multiple-Quantum Correlation (HMQC) sequences, which facilitate the indirect detection via spin-1/2 isotopes of nuclei exhibiting wide spectra. Numerical simulations show that this indirect excitation method is applicable to spin-1/2 nuclei experiencing a large chemical shift anisotropy, as well as to spin-1 isotopes subject to a large quadrupole interaction, such as (14)N. The performances of the long pulses are analyzed by the numerical simulations of scalar-mediated HMQC (J-HMQC) experiments indirectly detecting spin-1/2 or spin-1 nuclei, as well as by dipolar-mediated HMQC (D-HMQC) experiments achieving indirect detection of (14)N nuclei via (1)H in crystalline γ-glycine and N-acetyl-valine samples at a MAS frequency of 60kHz. We show on these solids that for the acquisition of D-HMQC spectra between (1)H and (14)N nuclei, the efficiency of selective moderate excitation with long-pulses at the (14)N Larmor frequency, ν0((14)N), is comparable to those with strong excitation pulses at ν0((14)N) or 2ν0((14)N) frequencies, given the rf field delivered by common solid-state NMR probes. Furthermore, the D-HMQC experiments also demonstrate that the use of long pulses does not produce significant spectral distortions along the (14)N dimension. In summary, the use of center-band selective weak pulses is advantageous for HMQC experiments achieving the indirect detection of wide spectra since it (i) requires a moderate rf field, (ii) can be easily optimized, (iii) displays a high robustness to CSAs, offsets, rf-field inhomogeneities, and fluctuations in MAS frequency, and (iv) is little dependent on the quadrupolar coupling constant.

An optimal double-magic flip angle for performing the distance measurement REDOR experiment on a spin S=1

Distance measurements between a half-spin and a quadrupolar S=1 spin having a small quadrupolar coupling constant can be performed using the rotational echo double resonance (REDOR) experiment. We derived an analytical expression for the probability of transitions between energy levels resulting from the application of an arbitrary pulse flip angle to the quadrupolar spin and consequently minimized the probability that populations of individual levels do not undergo a spin transition during the pulse. As a result we discovered that if the flip angle of the quadrupolar spin pulse is 109.47°, the maximal recoupling values are the largest possible and the signal reaches a maximum value of 8/9, larger than in the use of either a 90° pulse or a 180° pulse. In addition, the slope of the initial decay is higher than that of the 90° pulse. The recoupling signal can be modeled by an exact analytical formula in the ideal case and simulations show that the advantage of the 109.47° pulse is preserved when the quadrupolar coupling constant CQ has a finite value typical of (2)H and (6)Li spins (up to CQ~200kHz). Experimental results on two spin pairs, (2)H-(13)C and (6)Li-(13)C, demonstrate the validity and accuracy of this method.

Two heteronuclear dipolar results at the price of one: quantifying Na/P contacts in phosphosilicate glasses and biomimetic hydroxy-apatite

The analysis of S{I} recoupling experiments applied to amorphous solids yields a heteronuclear second moment M(2)(S-I) that represents the effective through-space dipolar interaction between the detected S spins and the neighboring I-spin species. We show that both M(2)(S-I) and M(2)(I-S) values are readily accessible from a sole S{I} or I{S} experiment, which may involve either S or I detection, and is naturally selected as the most favorable option under the given experimental conditions. For the common case where I has half-integer spin, an I{S} REDOR implementation is preferred to the S{I} REAPDOR counterpart. We verify the procedure by (23)Na{(31)P} REDOR and (31)P{(23)Na} REAPDOR NMR applied to Na(2)O-CaO-SiO(2)-P(2)O(5) glasses and biomimetic hydroxyapatite, where the M(2)(P-Na) values directly determined by REAPDOR agree very well with those derived from the corresponding M(2)(Na-P) results measured by REDOR. Moreover, we show that dipolar second moments are readily extracted from the REAPDOR NMR protocol by a straightforward numerical fitting of the initial dephasing data, in direct analogy with the well-established procedure to determine M(2)(S-I) values from REDOR NMR experiments applied to amorphous materials; this avoids the problems with time-consuming numerically exact simulations whose accuracy is limited for describing the dynamics of a priori unknown multi-spin systems in disordered structures.

Phase-modulated LA-REDOR: a robust, accurate and efficient solid-state NMR technique for distance measurements between a spin-1/2 and a quadrupole spin

Distances between a spin-1/2 and a spin>1/2 can be efficiently measured by a variety of magic-angle spinning solid state NMR methods such as Rotational Echo Adiabatic Passage Double Resonance (REAPDOR), Low-Alpha/Low-Amplitude REDOR (LA-REDOR) and Rotational-Echo Saturation-Pulse Double-Resonance (R/S-RESPDOR). In this manuscript we show that the incorporation of a phase modulation into a long quadrupolar recoupling pulse, lasting 10 rotor periods that are sandwiched between rotor-synchronized pairs of dipolar recoupling π pulses, extends significantly the range of the values of the quadrupole moments that can be accessed by the experiment. We show by a combination of simulations and experiments that the new method, phase-modulated LA-REDOR, is very weakly dependent on the actual value of the radio-frequency field, and is highly robust with respect to off-resonance irradiation. The experimental results can be fitted by numerical simulations or using a universal formula corresponding to an equal-transition-probability model. Phase-modulated LA-REDOR (13)C{(11)B} and (15)N{(51)V} dipolar recoupling experiments confirm the accuracy and applicability of this new method.

Broadband excitation in solid-state NMR using interleaved DANTE pulse trains with N pulses per rotor period

We analyze the direct excitation of wide one-dimensional spectra of nuclei with spin I=1/2 or 1 in rotating solids submitted to pulse trains in the manner of Delays Alternating with Nutations for Tailored Excitation (DANTE), either with one short rotor-synchronized pulse of duration τp in each of K rotor periods (D1(K)) or with N interleaved equally spaced pulses τp in each rotor period, globally also extending over K rotor periods (D(N)(K)). The excitation profile of D(N)(K) scheme is a comb of rf-spikelets with Nν(R)=N/T(R) spacing from the carrier frequency, and a width of each spikelet inversely proportional to the length, KT(R), of D(N)(K) scheme. Since the individual pulse lengths, τp, are typically of a few hundreds of ns, D(N)(K) scheme can readily excite spinning sidebands families covering several MHz, provided the rf carrier frequency is close enough to the resonance frequency of one the spinning sidebands. If the difference of isotropic chemical shifts between distinct chemical sites is less than about 1.35/(KT(R)), D(N)(K) scheme can excite the spinning sidebands families of several sites. For nuclei with I=1/2, if the homogeneous and inhomogeneous decays of coherences during the DANTE sequence are neglected, the K pulses of a D1(K) train have a linearly cumulative effect, so that the total nutation angle is θ(tot)=K2πν1τp, where ν1 is the rf-field amplitude. This allows obtaining nearly ideal 90° pulses for excitation or 180° rotations for inversion and refocusing across wide MAS spectra comprising many spinning sidebands. If one uses interleaved DANTE trains D(N)(K) with N>1, only spinning sidebands separated by intervals of Nν(R) with respect to the carrier frequency are observed as if the effective spinning speed was Nν(R). The other sidebands have vanishing intensities because of the cancellation of the N contributions with opposite signs. However, the intensities of the remaining sidebands obey the same rules as in spectra obtained with νR. With increasing N, the intensities of the non-vanishing sidebands increase, but the total intensity integrated over all sidebands decreases. Furthermore, the NK pulses in a D(N)(K) train do not have a simple cumulative effect and the optimal cumulated flip angle for optimal excitation, θ(tot)(opt)=NK2πν1τp, exceeds 90°. Such D(N)(K) pulse trains allow achieving efficient broadband excitation, but they are not recommended for broadband inversion or refocusing as they cannot provide proper 180° rotations. Since D(N)(K) pulse trains with N>1 are shorter than basic D1(K) sequences, they are useful for broadband excitation in samples with rapid homogeneous or inhomogeneous decay. For nuclei with I=1 (e.g., for (14)N), the response to basic D1(K) pulse train is moreover affected by inhomogeneous decay due to 2nd-order quadrupole interactions, since these are not of rank 2 and therefore cannot be eliminated by spinning about the magic angle. For large quadrupole interactions, the signal decay produced by second-order quadrupole interaction can be minimized by (i) reducing the length of D(N)(K) pulse trains using N>1, (ii) fast spinning, (iii) large rf-field, and (iv) using high magnetic fields to reduce the 2nd-order quadrupole interaction.