Efficient Dipolar Double Quantum Filtering Under Magic Angle Spinning without a ¹H Decoupling Field

Abstract

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

Graphical Abstract

INTRODUCTION

Pulse sequences that excite double-quantum (DQ) coherence give the experimenter access to a wealth of structural information and techniques for simplifying the interpretation of NMR spectra of biomolecules. In addition to the ubiquitous application of suppressing natural abundance background signals, DQ coherence can be used to measure vector (torsion) angles in peptide backbones [1,2,3,4,5] and polymers [6], study dynamics [2], and simplify chemical shift assignment [7].

Homonuclear recoupling sequences that rely on zero-quantum mixing—such as dipolar-assisted rotational resonance (DARR) [8], RFDR [9] or CORD-RFDR [10]—provide robust methods for gaining information about spatial proximity but lack selectivity of individual spin pairs and are prone to multi-spin sequential polarization transfers that complicate interpretation. Adiabatic mixing schemes that rely on DQ excitation with low power carbon fields do not permit the isolation of that DQ coherence [11,12]. Mixing schemes traditionally used for the excitation and isolation of homonuclear DQ coherence—such as C7 [13], POST-C7 [14], CMR7 [15], and SPC-5 [16]—have broad bandwidth but require ¹H decoupling fields during mixing that are at least three times the ¹³C field strength [17, 18]. The high power ¹H decoupling is necessary to avoid the broad heteronuclear interference described in relation to C and R symmetry sequences [19]. This requirement significantly limits the usage of C symmetry sequences not only for the measurement of dipolar couplings, but chemical shift tensors, through the use of sequences like ROCSA [34], which are valuable for developing extremely high resolution protein structures [35].

At higher MAS rates low-power ¹H decoupling both during chemical shift evolution and detection are common, and investigations have made clear that at high MAS rates low-power ¹H decoupling during recoupling was feasible [18]. While high MAS solves many problems for both resolution and sensitivity for ideal samples, many important systems such as amyloids exhibit inhomogeneous broadening that negates the advantages of long transverse relaxation rates (T₂) at high MAS rates requiring the use of larger capacity rotors to maintain sufficient sensitivity. Additionally, at present all commercially available dynamic nuclear polarization instruments require the use of rotors with maximum MAS frequency of 25 kHz [36]. These experimental limitations motivate the investigation of low-power ¹H decoupling at moderate to high MAS rates. While low power proton decoupling during dipolar recoupling has been reported previously [14, 19, 20, 21, 31, 32, 33], double quantum filtering (DQF) has not been fully explored in the context of difficult proteins with limited relaxation times and inhomogeneous broadening. Here we present an exploration of the low power decoupling regime for the SPC-n family of recoupling sequences that generalizes the SPC-5 recoupling sequence to arbitrary symmetry conditions [16]. We confirm the feasibility of DQ spectroscopy with SPC-n double-quantum filters in the absence of decoupling from 13 to 40 kHz MAS rates. We show experimental results for U-¹³C,¹⁵N-N-acetylvaline and U-¹³C,¹⁵N-α-synuclein that demonstrate DQ excitation over the full chemical shift range with high efficiency. These conditions are thus well suited for the study of temperature-sensitive systems and for incorporation into pulse sequences that make use of proton detection and other fast MAS techniques.

MATERIALS AND METHODS

Materials

Uniformly ¹³C-¹⁵N-labeled wild-type α-synuclein was prepared following the method of [22] and fibrils were prepared for solid-state NMR (SSNMR) as described in [23] and packed into a 1.6 mm FastMAS rotor.

Solid-state NMR spectroscopy

All experiments were conducted on a 17.6 T (750 MHz) Varian VNMRS spectrometer (Agilent Technologies, Santa Clara, CA) equipped with a FastMAS probe tuned to ¹H-¹³C double resonance. The ¹H and ¹³C π/2 pulse widths for N-acetyl-L-valine (NAV) were 1.80 and 1.80 μs, respectively, and were 1.75 and 1.70 μs for α-synuclein. MAS frequencies were controlled with a Varian MAS controller to within ±5 Hz at 13.333 kHz MAS and ±15 Hz at 40 kHz. All experiments were carried out with the variable temperature gas at 0 °C, which corresponded to actual sample temperatures of 5±3 °C at 13.333 kHz MAS, 15±5 °C at 40 kHz MAS and intermediate values at moderate spinning rates.

All data were collected using the pulse sequence shown in Fig. 1. In this work the mixing sequence was tested in the context of a standard ¹³C-¹³C, 2D experiment with an initial ¹H 90° pulse followed by tangent-ramped ¹H-¹³C cross polarization before the indirect evolution period. The carbon magnetization is then placed along the z-axis during a short z-filter, the SPC-n recoupling is performed on the ¹³C channel with or without constant wave ¹H decoupling, a second z-filter is performed, the magnetization is placed back in the transverse plane, and is detected with ¹H SPINAL decoupling. The SPC-n sequence consists of a repeated POST-C element with phases determined by the symmetry condition as in Ref. [16]. The SPC-n element is the repeated with its phase shifted by 90° in alternate scans, with a subsequent 180° phase shift of the receiver, to filter for DQ coherence.

Fig. 1.

Pulse sequence utilized for the evaluation of DQ excitation with ¹³C-¹³C SPC-n homonuclear mixing. The hatching on the second half of the SPC-n period indicates that the phase cycle is shifted by 90 degrees every other scan (with a 180 degree phase shift of the receiver), according to ref [16].

One-dimensional spectra were collected with the indirect evolution time (t₁) set to zero. High power SPINAL ¹H decoupling with an RF field of 100 kHz was used during the t₁ and detection periods. The ¹H-¹³C cross polarization was performed with a tangent ramp on ¹³C with ¹H and ¹³C nutation frequencies matched to modified Hartmann-Hahn conditions optimized at each spinning rate. The SPC pulse width was set to an initial condition defined by the theoretical value (according to the MAS frequency and desired symmetry condition) and then optimized over a range of ±5% in order to maximize DQ filtered (DQF) signal intensity with a total excitation and reconversion time of about 1 ms. All NMR data were processed with nmrglue [24] using standard methods including zero-filling, Fourier transformation, and phase correction. Integration and plotting of data were performed with scripts written in Python utilizing matplotlib [25].

RESULTS AND DISCUSSION

Double quantum filtering efficiency over a range of MAS frequencies

At low (<10 kHz) MAS rates, dipolar (as opposed to scalar) recoupling is the preferred approach to generating DQ coherence in organic solids, typically using POST-C7 for MAS rates from ~5 to ~7 kHz [14], SPC-5 for ~7 to ~10 kHz [16], and SPC-5₃ for ~9 to ~12 kHz [26]. These conditions result in ¹³C nutation frequencies ranging from ~30 to ~50 kHz. In this regime, optimal DQ filtering (DQF) efficiency is observed with the ¹H decoupling nutation frequency several times greater than for ¹³C: often >100 kHz and limited by the coil breakdown voltage. Although this condition avoids heteronuclear decoupling interference [19], it severely limits application of DQ sequences for higher magnetic field and/or MAS rates.

We explored solutions to this problem by comparing several values of symmetry number for SPC-n recoupling at 13 kHz MAS rate, with the ¹H field turned off during the ¹³C-¹³C recoupling period (Fig. 2). Using α-synuclein fibrils we observe DQF efficiencies up to 28% using the n = 9 condition with a ¹³C nutation frequency of 120 kHz, and similar results for n = 10 (133 kHz ¹³C nutation frequency). A slight reduction (to ~20–22%) in efficiency is observed for n = 8 (107 kHz ¹³C nutation frequency) and n = 11 (147 kHz ¹³C nutation frequency), and then performance degrades considerably for lower n values (5, 6, and 7, with ¹³C nutation frequencies of 67, 80, and 93 kHz, respectively). Optimal results are observed when the ¹³C nutation frequency is in the range of ~100 to ~150 kHz.

Fig. 2.

DQF efficiency as a function of mixing time for α-synuclein at a range of symmetry conditions and a constant MAS rate of 13.333 kHz. The ¹H decoupling field is off.

These trends are also observed also at higher MAS rates in Fig. 3, where the DQF efficiency of the SPC-n recoupling sequence in the absence of ¹H decoupling is shown for spinning rates of 13.333, 16.667, 24.000, and 40.000 kHz and symmetry conditions n = 3 and 5 ≤ n ≤ 11.

Fig. 3.

DQ efficiency as a function of mixing time for α-synuclein MAS rates ranging from 16.667 to 40.000 kHz.

As described in the formalism of Edén and Levitt [36], SPC-n is a $C{N}_2^1$ symmetry sequence with an additional supercycle applied to suppress terms in the Hamiltonian with μ = ±1. According to the selection rule specified in equation 1,

$$mn-\mu \nu \ne Nd\mathit{for}d\in \mathbb{Z}$$

for n ≥ 5 SPC-n recouples the (m, μ) = (−1, −2) and (1, 2) terms. However, for n = 4, the additional terms (m, μ) = (−2, 0) and (2, 0) are recoupled leading to ¹³C CSA and heteronuclear dipolar recoupling, leading to poor DQF performance. For n = 3, the additional terms (m,μ) = (−2, −1) and (2, 1) are allowed by the selection rule but suppressed by the supercycle. We observed maxima in DQF at approximately 1 ms with lower symmetry conditions tending towards maxima at longer mixing times for all symmetry conditions which is consistent with the scaling factors for the POST-CN element given in [14] as:

$${\kappa }_n=\frac{3{in}^3(1-exp\left\{\frac{4i\pi }{n}\right\})}{8\sqrt{2}\pi (4n^2-1)}$$

Values of this scaling factor for the symmetry conditions are tabulated in Table 1.

Table 1.

Dipolar scaling factors for the symmetry conditions examined. Values calculated using equation 2.

SPC Symmetry	Dipolar Scaling factor
n = 3	0.113
n = 4	0.171
n = 5	0.203
n = 6	0.221
n = 7	0.232
n = 8	0.240
n = 9	0.245
n = 10	0.248
n = 11	0.251

Fig. 4 shows that the maximum DQF efficiency for a given symmetry condition plateaus for values n > 7. While higher ¹³C fields more effectively decouple the heteronuclear ¹H-¹³C interaction, shorter pulse lengths increase the relative impact of phase transients, decreasing the overall efficiency of recoupling [27,28]. Recent efforts to compensate for phase transients has shown an increase in performance for the C7 pulse sequence and could be applied to mitigate these effects [29,30].

Fig. 4.

Double quantum efficiency as a function of SPC symmetry number.

Next we tested whether any experimentally achievable level of ¹H decoupling field would perform better than the ¹³C field alone over the range of conditions studied (Fig. 5). DQF efficiency as a function of symmetry condition and ¹H power during decoupling exhibits a banded pattern that bears a striking resemblance to the theoretical predictions for $C{N}_2^1$ recoupling sequences presented in ref. [19] indicating that heteronuclear decoupling is the primary factor effecting the efficiency of SPC mixing. For all but the lowest symmetry conditions, the maximum efficiency is attained when the decoupling field is absent. This high ¹³C power, low ¹H power regime is advantageous as it lessens sample heating and facilitates experiments requiring DQ coherence for temperature sensitive samples, such as membrane proteins, and for experiments utilizing probes with low ¹H power handling capabilities.

Fig. 5.

Measured dependence of DQF efficiency as a function of the ¹H field strength and symmetry condition. For each sample the efficiency was normalized to the highest efficiency observed for that sample. Efficiency values were interpolated to generate a heat map. The three-fold symmetry condition was only tested at 40 kHz MAS frequency where 100 kHz ¹H power is only 2.5 ωr resulting in the blank region in the lower right corner of each plot.

Finally, we evaluated the performance of DQF for acquiring 2D ¹³C-¹³C correlation spectra. Such spectra are shown in Fig. 6 with SPC-7 at 16.667 kHz, SPC-5 at 24.000 kHz and SPC-3 at 40.00 kHz. All spectra demonstrate reasonable, broadband excitation of DQ coherence and reconversion to single quantum coherence. At 1 ms mixing the DQ coherence arising from the dipolar couplings of neighboring ¹³C nuclei is at a maximum; therefore, the two spectra primarily exhibit peaks corresponding to directly bonded carbons. In addition, in the SPC-7 spectrum (Fig. 6a) there are some peaks corresponding to two-bond correlations (threonine Cα-Cγ region (60 ppm, 20 ppm)) on both sides of the diagonal. These two-bond correlations show the opposite sign of the one-bond correlations, and at this mixing time three-bond correlations have negligible intensity. Therefore directly bonded carbons are unambiguously identified, making this mixing especially useful for chemical shift assignments where zero-quantum and spin-diffusion based mixing can crowd spectra with longer range correlations. Although the overall intensity of cross peaks in the SPC-3 spectrum is lower than those in the SPC-5 and SPC-7 spectra, the SPC-3 condition nevertheless generates useful correlations, especially in the Cα-C′ region. This observation is interesting, given that there is no explicit compensation for CSA and heteronuclear interactions [16]; we attribute this experimental observation to the combined effect of the 40 kHz MAS rate and the supercycled POST element.

Fig. 6.

2D SPC ¹³C-¹³C SQ-SQ correlations NMR spectra of U-¹³C,¹⁵N-alpha synuclein at 17.63 T magnetic field. A) Three-fold symmetric SPC mixing for 1 ms at 40 kHz MAS frequency. B) Eight-fold symmetric SPC mixing for 1 ms at 16.667 kHz MAS frequency. Both spectra show broadband recoupling of dipolar couplings. At 1 ms mixing DQ coherence from dipolar couplings between neighboring carbons are at a maximum, thus primarily one-bond correlations are seen in these spectra. Some two-bond peaks appear in the Threonine Cα-Cγ region (60 ppm, 20 ppm) and mirrored across the diagonal.

CONCLUSIONS

In summary, the SPC-n recoupling sequence has been demonstrated to be effective under MAS frequencies up to 40 kHz in the absence of ¹H decoupling. High-symmetry SPC-n recoupling is compatible with a large range of MAS rates. The experimental results demonstrated here indicate that SPC-n mixing is a robust and broadly applicable method for generating DQ coherence over a wide range of MAS frequencies extending higher than previously reported. Additionally, high symmetry SPC-n mixing does not require the high power ¹H decoupling required by SPC-5 and POST-C7 mixing schemes opening it as a possibility for many more challenging systems. These properties make SPC-n (with n > 7) a useful technique for general applicability from 13 to 40 kHz MAS rates, both as a longitudinal mixing scheme and for exciting DQ coherence for filtering. This mixing element can be incorporated into pulse sequences for the measurement of structural restraints and dynamics in proteins as well as other organic molecules at high magnetic field and MAS rate conditions that are conducive to the study of complex macromolecules.

HIGHLIGHTS.

• Experimental demonstration of heteronuclear decoupling interference

• Efficient ¹³C-¹³C double quantum filtering without a proton decoupling field

• New symmetry conditions explored experimentally for SPC-n mixing

• Strategies for double quantum excitation at MAS rates up to 40 kHz