High-Resolution Solid-State NMR of Anisotropically Mobile Molecules Under Very Low Power ¹H Decoupling and Moderate Magic-Angle Spinning

Abstract

We show that for observing high-resolution heteronuclear NMR spectra of anisotropically mobile systems with order parameters less than 0.25, moderate magic-angle spinning (MAS) rates of ∼11 kHz combined with ¹H decoupling at 1-2 kHz are sufficient. Broadband decoupling at this low ¹H nutation frequency is achieved by composite pulse sequences such as WALTZ-16. We demonstrate this moderate MAS low-power decoupling technique on hydrated POPC lipid membranes, and show that 1 kHz ¹H decoupling yields spectra with the same resolution and sensitivity as spectra measured under 50 kHz ¹H decoupling when the same acquisition times (∼ 50 ms) are used, but the low-power decoupled spectra give higher resolution and sensitivity when longer acquisition times (> 150 ms) are used, which are not possible with high-power decoupling. The limits of validity of this approach are explored for a range of spinning rates and molecular mobilities using more rigid membrane systems such as POPC/cholesterol mixed bilayers. Finally, we show ¹⁵N and ¹³C spectra of a uniaxially diffusing membrane peptide assembly, the influenza A M2 transmembrane domain, under 11 kHz MAS and 2 kHz ¹H decoupling. The peptide ¹⁵N and ¹³C intensities at low power decoupling are 70-80% of the high-power decoupled intensities. Therefore, it is possible to study anisotropically mobile lipids and membrane peptides using liquid-state NMR equipment, relatively large rotors, and moderate MAS frequencies.

Introduction

Very fast magic-angle spinning (MAS) frequencies of greater than 40 kHz combined with low-field ¹H decoupling of 5 – 25 kHz has been shown to yield heteronuclear spectra of rigid organic solids with comparable linewidths and sensitivities to those measured under high-power ¹H decoupling [1-5]. The primary motivation for low power ¹H decoupling is to allow fast MAS frequencies to be used on high-field NMR spectrometers, so that the increased chemical shift anisotropy (CSA) sidebands can be removed without a concomitant increase in the ¹H decoupling field strength or the recoupling of the heteronuclear dipolar interaction by the rotary resonance phenomenon [6]. Low power decoupling also reduces the radio frequency (rf) load on the spectrometer and allows shorter recycle delays to be used, thus increasing the sensitivity per unit time. This fast MAS - low power decoupling approach has been demonstrated on small amino acids and large microcrystalline proteins [1; 3], all of which are rigid solids. However, a necessary cost of spinning at 40 kHz or higher is that very small rotors (< 2 mm outer diameter) with sample volumes of less than 5 μL must be used. This severely restricts the range of systems that can be investigated with this approach. In particular, membrane-bound peptides and proteins that are already diluted by the lipids cannot be easily studied in such small sample volumes.

Since the criterion for fast MAS is that the spinning rate is larger than the strength of the heteronuclear dipolar interaction to be suppressed, mobile semi-solids such as lipid bilayers and peptides embedded in them should benefit from low power decoupling at much lower MAS frequencies and rf irradiation fields than required for rigid solids. The fact that hydrated lipid membranes are also more susceptible to rf-induced sample heating and degradation gives further incentive to explore the regime of low power decoupling and fast MAS for hydrated biological membrane samples [7].

MAS frequencies of 10-15 kHz have been used before for ¹H NMR of lipids [8] and mobile proteins [9; 10] in lipid membranes. The narrowing of ¹H lines under these MAS frequencies in the absence of homonuclear decoupling allows high-resolution ¹H-¹³C or ¹H-¹⁵N heteronuclear correlation spectra to be measured with ¹H detection, as shown for cholesterol in deuterated DMPC bilayers [11], or with ¹⁵N detection, as shown for a membrane peptide in deuterated DMPC lipids [12]. However, to our knowledge, moderately fast MAS frequencies have not been combined with low power ¹H decoupling to obtain high-resolution heteronuclear spectra. Here we show that for anisotropically mobile lipids and membrane peptides with segmental order parameters of 0.25 and smaller, moderate MAS speeds achievable on 4 mm o.d. rotors (11-15 kHz) and very low ¹H decoupling fields of 1-2 kHz are sufficient to give similar spectral resolution and intensity as spectra measured under high decoupling fields. In practice, low power ¹H decoupling yields higher resolution than high power decoupling for hydrated lipids, due to the fact that longer acquisition times can be used without undesirable rf heating and sample degradation. The ability to measure high-resolution heteronuclear spectra of membrane systems using moderately fast MAS frequencies and low power ¹H decoupling allows dilute isotopically labeled membrane peptides to be studied without severe volume limitations, thus enhancing sensitivity.

Materials and Methods

Membrane samples

All lipids were obtained from Avanti Polar Lipids (Alabaster, AL) and used without further purification. POPC and POPC/cholesterol (3:2) membranes were prepared by dissolving the lipids in chloroform, drying them under nitrogen gas to remove the solvent, then dissolving the lipid film in cyclohexane and lyophilizing overnight. The dry and homogeneous lipid powder was suspended in water, subject to freeze-thawing five times, then centrifuged at 150,000 g for 3 hours to produce a membrane pellet. The pellet was lyophilized, packed into 4 mm rotors, then rehydrated to 35 wt % water. This procedure gives a low-salt membrane sample with a well defined hydration level.

In addition to lipids, the transmembrane peptide of the influenza A M2 protein (M2TMP), which forms a pH-gated proton channel [13], was used to demonstrate the validity of this moderate MAS - low power decoupling method on mobile membrane peptides [14]. The peptide contains uniformly ¹³C, ¹⁵N-labeled residues at V28, S31 and L36, and was reconstituted into DLPC bilayers by detergent dialysis as described previously [15]. The membrane peptide sample was prepared at pH 7.5, which corresponds to the closed state of the proton channel. The sample also contains amantadine, which gives higher resolution spectra than the apo peptide [16].

Solid-State NMR experiments

MAS experiments were carried out on a Bruker DSX-400 spectrometer (Karlsruhe, Germany) operating at Larmor frequencies of 400.49 MHz for ¹H, 100.70 MHz for ¹³C, and 40.58 MHz for ¹⁵N. A MAS probe equipped with a 4 mm spinner was used for all experiments. ¹H-¹³C and ¹H-¹⁵N cross polarization (CP) for the peptide-containing sample was carried out at a spin-lock field strength of 50 kHz for 0.5 ms. ¹³C chemical shifts were externally referenced to the α-Glycine ¹³C CO resonance at 176.49 ppm on the TMS scale and ¹⁵N chemical shifts were externally referenced to the ¹⁵N resonance of N-acetylvaline at 122 ppm on the NH₃ scale.

Low power decoupled spectra used the WALTZ-16 composite pulse sequence [17] to achieve broadband decoupling. The ¹H nutation frequencies ranged from 1 kHz to 11 kHz, and were measured by direct observation of the ¹H spectra of lipids. High power decoupled spectra used TPPM decoupling [18] with a field strength of 50 kHz for the lipid samples and 63 kHz for the peptide-containing sample.

Most ¹³C direct-polarization spectra of lipid-only samples used acquisition times of 51 ms with 4096 data points. The time-domain data were zero filled to 16,384 points and Fourier-transformed with 3 Hz Lorentzian broadening except when indicated otherwise. Longer acquisition times were not used in comparisons of high-power and low-powder decoupled spectra, since high power decoupling for more than 50 ms is deemed detrimental to the probe and the sample. To determine the ultimate resolution and sensitivity of the lipid membranes under 11 kHz MAS, we measured a 1 kHz ¹H decoupled ¹³C spectrum of POPC lipids with an acquisition time of 150 ms. For the peptide-containing sample, the ¹³C CP spectra were measured with an acquisition time of 25.7 ms and processed with 35 Hz Gaussian line broadening, and the ¹⁵N CP spectra were measured with an acquisition time of 17.6 ms with 70 Hz Gaussian line broadening.

Results and Discussion

Theory for low power decoupling and moderately fast MAS of uniaxially diffusive systems

The theory of fast MAS and low power ¹H decoupling has been described in detail by Ernst et al.[1]. Below we briefly summarize this theory and point out the differences between uniaxially mobile systems and rigid solids. Under fast MAS and low power decoupling, we consider the nuclear spin interactions to be averaged first by MAS and then by rf irradiation. For SI_N spin systems under infinite speed MAS, the average Hamiltonian collapses to the zero-order terms, which contain only interactions expected for an isotropic solution, namely isotropic chemical shifts (H^iCS) of the I and S spins, and the homonuclear (H^J_II) and heteronuclear (H^J_SI) J couplings:

$${\overline{H}}_{{\omega }_r\to \infty }^{\left(0\right)}={\frac{1}{{\tau }_r}}_0^{{\tau }_r}\mathit{\text{dt}}\cdot H(t)=H_S^{\mathit{\text{iCS}}}+H_I^{\mathit{\text{iCS}}}+H_{II}^J+H_{SI}^J$$ (1)

Under finite MAS frequencies, we need to consider the first order terms in the average Hamiltonian. Higher than first-order terms scale with the MAS frequency as (1/ω_r)² and higher powers, thus are not considered here. The first-order terms result from time-dependent commutators between the various interactions:

$${\overline{H}}^{(1)}=\frac{-i}{2{\tau }_r}\underset{0}{\overset{{\tau }_r}{\int }}{\mathit{\text{dt}}}_2\underset{0}{\overset{t_2}{\int }}{\mathit{\text{dt}}}_1\cdot \left[H(t_2),H(t_1)\right]$$ (2)

In general, there are three non-vanishing cross terms from the above commutator. They are the cross term between the I-I homonuclear dipolar coupling and the I-S heteronuclear dipolar coupling:

$${\overline{H}}_{\mathit{\text{II}},\mathit{\text{IS}}}^{(1)}={\frac{1}{{\omega }_r}}_{k\ne l}{\overline{\omega }}_{\mathit{\text{skl}}}{S}_z{I}_{\mathit{\text{kx}}}{I}_{\mathit{\text{ly}}},$$ (3)

the cross term between the I-I homonuclear dipolar coupling and I-spin CSA:

$${\overline{H}}_{\mathit{\text{II}},I}^{(1)}={\frac{1}{{\omega }_r}}_{k\ne l}{\overline{\omega }}_{\mathit{\text{kl}}}{I}_{\mathit{\text{kx}}}{I}_{\mathit{\text{ly}}},$$ (4)

and the cross term of the I-I homonuclear dipolar coupling with itself:

$${\overline{H}}_{\mathit{\text{II}},\mathit{\text{II}}}^{(1)}={\frac{1}{{\omega }_r}}_{i\ne k\ne l}{\overline{\omega }}_{\mathit{\text{ikl}}}{I}_{\mathit{\text{iz}}}{I}_{\mathit{\text{kx}}}{I}_{\mathit{\text{ly}}}$$ (5)

In these expressions, the coupling cross terms ω̄ have the unit of frequency squared (rad/s)² due to the commutation.

For uniaxially diffusive lipids and peptides in biological membranes, the I-I homonuclear coupling cross term (eq. 5) vanishes because all motionally averaged dipolar couplings within each lipid and between adjacent lipid molecules are parallel to the motional axis, the bilayer normal, thus they have the same orientation dependence. Analytically, the homonuclear dipolar coupling between spin i and k can be written as ω_ik(t) = δ̄_ik·ω(β, γ, t) where β and γ are the polar coordinates of the local bilayer normal with respect to the rotor axis and are the same for all spin pairs, and δ̄_ik is the motionally averaged coupling constant. As a result, the self commutation of the homonuclear dipolar coupling becomes:

$$\begin{array}{l}\left[H_{\mathit{\text{II}}}(t_2),H_{\mathit{\text{II}}}(t_1)\right]{=}_{i\ne k}{\overline{\delta }}_{\mathit{\text{ik}}}\cdot \omega (\beta ,\gamma ,t_2){(3I_z^i{I}_z^k-I^i\cdot I^k)}_{i\ne k}{\overline{\delta }}_{ik}\cdot \omega (\beta ,\gamma ,t_1)(3I_z^i{I}_z^k-I^i\cdot I^k)\\ =\omega (\beta ,\gamma ,t_2)\omega {(\beta ,\gamma ,t_1)}_{i\ne k}{\overline{\delta }}_{ik}{(3I_z^i{I}_z^k-I^i\cdot I^k)}_{i\ne k}{\overline{\delta }}_{ik}(3I_z^i{I}_z^k-I^i\cdot I^k)\\ =0\end{array}$$ (6)

The I-spin CSA and I-I dipolar cross term in equation 4 does not directly lead to S spectral broadening since it only involves the I spins. But the I-I and I-S dipolar cross term in equation 3 leads to S broadening through the heteronuclear dipolar coupling. To obtain narrow S spectra, one needs to decouple at a ω₁ nutation frequency either much higher than ω_r or much lower than ω_r but still adequate to remove the remaining S-I dipolar interaction. In the latter regime ω₁ ≪ ω_r, the rotary resonance recoupling condition ω₁ = nω_r (n=1,2) does not apply, thus no line broadening from rotary resonance will occur.

Under the condition that the decoupling field is lower than the spinning rate but higher than the MAS-averaged spin interactions in equations (3) and (4), transformation to an interaction frame defined by the rf field and a second averaging lead to the zero-order average Hamiltonian:

$${\overline{\overline{H}}}^{(0)}=H_S^{\mathit{\text{iCS}}}+H_{\mathrm{II}}^J.$$ (7)

Compared to the rigid solid case, no homonuclear dipolar coupling term remains for the uniaxially mobile system [1]. Comparing equations (1), (3) and (7), it can be seen that low power decoupling removes the I-S J-coupling and suppresses the cross term between the homonuclear and heteronuclear dipolar coupling.

For rigid solids, MAS rates ω_r/2π larger than 40 kHz and rf fields ω₁ /2π smaller than ∼20 kHz were found to be the fast spinning and low power decoupling regimes, respectively. We can estimate the prefactor ω̄_skl/ω_r in equation (3) as follows. Using the one-bond C-H dipolar coupling of 22 kHz and the geminal H-H dipolar coupling of 25 kHz, and assuming an MAS rate of 50 kHz, a CH₂ spin system has a prefactor of:

$$\frac{{\overline{\omega }}_{\mathit{\text{skl}}}}{{\omega }_r}\infty \frac{{\omega }_{\mathit{\text{IS}}}\cdot {\omega }_{\mathit{\text{II}}}}{{\omega }_r}\approx \frac{\left(2\pi \cdot 22\mathit{\text{kHz}}\right)\cdot \left(2\pi \cdot \mathit{25}\mathit{\text{kHz}}\right)}{2\pi \cdot \mathit{50}\mathit{\text{kHz}}}\approx 2\pi \cdot 11\mathit{\text{kHz}},$$ (8)

This prefactor matches well the experimental observation that at 50 kHz MAS, a ¹H decoupling field of less than 15 kHz causes broadening of the CH₂ signal [2]. For C-H spin systems, the prefactor is smaller, about 2.5 kHz, due to the weaker H-H dipolar coupling. Correspondingly, the measured threshold ¹H decoupling field decreases to ∼8 kHz, below which line broadening occurs.

For uniaxially mobile lipids where the segmental order parameters S_CH are in the range 0.02 – 0.25 [19], the spinning frequency and decoupling field requirements are correspondingly lower. Assuming an intermediate order parameter of 0.10 for a typical lipid group, the residual heteronuclear dipolar coupling prefactor for a CH₂ group under 11 kHz MAS can be estimated as:

$$\frac{{\overline{\omega }}_{\mathit{\text{skl}}}}{{\omega }_r}\infty \frac{{\overline{\omega }}_{\mathit{\text{IS}}}\cdot {\overline{\omega }}_{\mathit{\text{II}}}}{{\omega }_r}\approx \frac{\left(2\pi \cdot 22\cdot 0.1\mathit{\text{kHz}}\right)\cdot \left(2\pi \cdot \mathit{25}\cdot \mathit{0.1}\mathit{\text{kHz}}\right)}{2\pi \cdot 11\mathit{\text{kHz}}}\approx 2\pi \cdot 0.5\mathit{\text{kHz}},$$ (9)

Thus, a ¹H decoupling field of ∼1 kHz should be sufficient to suppress this residual coupling. This suggests that moderately fast MAS frequencies that are readily achievable on 4 mm rotors may allow lipid membranes and even membrane peptides to be studied under extremely low power ¹H decoupling. In this ω₁ regime, composite pulse sequences such as WALTZ-16 [17] are necessary to achieve broadband decoupling.

Low power decoupling of low-viscosity hydrated lipid membranes

Figure 1(a, b) shows the ¹³C direct polarization (DP) spectra of hydrated POPC membranes under 11 kHz MAS with 1 kHz WALTZ-16 decoupling (a) and 50 kHz TPPM decoupling (b). Both spectra were processed with 3 Hz of Lorentzian broadening to reduce truncation wiggles. It can be seen that the intensities and line widths of the low-power decoupled spectrum is comparable to or better than the high-power decoupled spectrum. For a clearer view of the intensities and linewidths, Figure 2 shows expanded regions of the ¹³C spectra of the lipid chain CH₂ resonance at 31 ppm (a) and the glycerol G2 peak at 71 ppm (b) as a function of the ¹H decoupling field. These two resonances are chosen because they are the most rigid segments in hydrated phosphocholine, as manifested by their relatively large C-H order parameters [20], and thus are the most difficult sites to decouple well. Figure 2 shows that both resonances broaden and decrease in intensities with increasing ¹H decoupling field ω₁/2π, with the minimum intensity at the rotary resonance condition of ω₁ = ω_r at 11 kHz. This is expected due to the recoupling of the C-H heteronuclear interaction. For all resonances, the maximum intensity is observed at the lowest decoupling field of 1 kHz.

Figure 1.

Direct polarization ¹³C spectra of hydrated POPC bilayers under 11 kHz MAS at 293 K with different ¹H decoupling methods. (a) 1.0 kHz WALTZ-16 decoupling, with a 50 ms acquisition time. (b) 50 kHz TPPM decoupling, with a 50 ms acquisition time. (c) 1.0 kHz WALTZ-16 decoupling with a 150 ms acquisition time. Spectra (a) and (b) were processed with 3 Hz Lorentzian broaderning, while spectrum (c) did not use any line broadening.

Figure 2.

Expanded regions of the ¹³C direct polarization spectra of hydrated POPC lipids. (a) Lipid chain CH₂ peaks. (b) Lipid glycerol G2 peak. The ¹H decoupling method and field strengths are indicated above the individual spectra. Dashed lines guide the eye for the maximum intensity.

At the HORROR condition of ω₁ = ω_r/2, it is known that recoupling of the homonuclear dipolar coupling I-I enhances I-spin spin diffusion and leads to line narrowing of the heteronuclear spectra by self decoupling [21]. This effect has been observed in rigid ¹³C-labeled model compounds [2]. We do not observe this HORROR line narrowing effect at ω₁/2π = 5.5 kHz for the lipids (Figure 2). This is consistent with the suppression of the I-I homonuclear dipolar coupling cross term by uniaxial motion as shown in equation (6). In addition, in contrast to rigid solids [2], we do not observe line broadening at low decoupling fields of ω₁/ω_r < 0.25. Down to 1 kHz decoupling, the intensity increased monotonically. This is again expected from the estimated prefactor for the residual dipolar interactions of lipids (eq. 9). When no ¹H decoupling is applied, the ¹³C spectrum of POPC membrane under 11 kHz MAS (Figure 3) shows ¹³C-¹H J-splittings with linewidths of 10-25 Hz, which are only slightly larger than the linewidths of the best decoupled spectra, which are 7 – 20 Hz. This means that 11 kHz MAS is already sufficient to suppress most of the residual heteronuclear interactions, and low power decoupling mainly serves to suppress the ¹³C-¹H scalar coupling in a broadband fashion.

Figure 3.

POPC ¹³C direct polarization spectra at 293 K under 11 kHz MAS. Both spectra were measured with an acquisition time of 150 ms. (a) WALTZ-16 ¹H decoupled spectrum with ω₁/2π = 1 kHz. (b) ¹H undecoupled spectrum. The FWHM linewidths of the peaks are 7 – 20 Hz in (a) and 10 – 25 Hz in (b).

A practical advantage of the very low power decoupling under moderately fast MAS is that it allows suitably long acquisition times to be used for hydrated membranes. With an acquisition time of 50 ms, the lipid spectra still exhibit truncation wiggles for many peaks such as the highly averaged headgroup Cγ at 54.6 ppm (Figure 1a, b). When a full acquisition time of 150 ms was used under 1 kHz decoupling, the linewidths of the lipid ¹³C spectrum are found to be 7 – 20 Hz (Figure 1c). This long acquisition time is not possible under high power decoupling conditions.

Limits of applicability: spinning speed, temperature, and mobility

To test whether the low-power decoupling and moderately fast MAS approach works for a wide range of membrane systems, we investigated the ¹³C spectral resolution and intensity as a function of MAS frequency, temperature, and lipid mobility. Figure 4 shows the glycerol G2 region of the ¹³C DP spectra of hydrated POPC lipids for a number of MAS frequencies under the same ¹H decoupling field of 1 kHz. At 9 kHz spinning the spectrum shows similar intensity to the 11 kHz MAS spectrum, but decreasing the spinning speed to 7 kHz and below clearly decreases the intensities under low power decoupling. Thus, for hydrated lipids, the minimum spinning rate necessary to achieve MAS averaging of the dipolar interaction is about 10 kHz.

Figure 4.

Low power decoupled POPC glycerol G2 intensity as a function of MAS frequency at293 K. All spectra were measured with 1.0 kHz WALTZ-16 ¹H decoupling. Spinning rates are (a) 11 kHz, (b) 9 kHz, (c) 7 kHz, and (d) 5 kHz.

The next two tests explore the effect of increased molecular rigidity on the low power decoupling efficiency. When the hydrated POPC membrane is cooled to below its phase transition temperature of 270 K, the ¹³C DP spectra showed higher intensities and narrower lines under higher power decoupling than low power decoupling (Figure 5). Although we did not measure the C-H order parameters of the gel-phase POPC lipids, ²H quadrupolar splittings from the literature suggest that the order parameters increase by a factor of 2 [22].

Figure 5.

¹³C direct polarization spectra of hydrated POPC membranes under 11 kHz MAS as a function of temperature and ¹H decoupling field strength. Top spectra: 293 K. Bottom spectra: 258 K. Left column: WALTZ-16 decoupling at 1.0 kHz. Right column: TPPM decoupling at 50 kHz field strength.

Cholesterol-containing membranes are of interest both for understanding the fundamental biophysics of domain formation in lipid membranes and for mimicking eukaryotic membranes. Addition of cholesterol to phospholipids is well known to make the lipid membrane less elastic, with order parameters increasing by about a factor of 2 [23]. Figure 6 shows three representative peaks of POPC and cholesterol in the mixed POPC/cholesterol (3:2) membrane under 11 kHz MAS and various ¹H decoupling fields. It can be seen that the moderately fast MAS rate is insufficient to narrow the cholesterol ring ¹³C peaks due to the rigidity of the sterol rings. However, the resolved aliphatic peaks of cholesterol such as C26 and C27 at 23.1 ppm vary in intensity with decoupling in a similar fashion as the POPC resonances. For the POPC lipids in this membrane mixture, the ¹³C intensities at low power decoupling are similarly narrow as the pure POPC sample.

Figure 6.

Expanded regions of POPC/cholesterol spectra at 293 K under 11 kHz MAS with different ¹H decoupling fields. (a) POPC glycerol G2 peak. (b) Cholesterol ring C14 and C17 peaks. (c) Cholesterol aliphatic C26 and C27 peaks and the POPC ω-1 peak. The assignment of cholesterol resonances is based on reference [31].

Uniaxially mobile membrane peptides under low power decoupling and moderate MAS

Since the basic requirement for moderate MAS and low power decoupling to yield high resolution heteronuclear spectra is the presence of large-amplitude fast motions that lead to sufficiently low order parameters, the approach should also be applicable to polypeptides that undergo fast uniaxial diffusion in lipid membranes. Several examples of such membrane protein diffusion have been reported [14; 24-26]. Hydrated membrane peptide samples often contain significant levels of associated salt, thus the reduction of rf irradiation and heating by low power decoupling is highly desirable.

We use the transmembrane domain of the influenza A M2 protein (M2TMP) to demonstrate the low power decoupling method. The M2 protein is a proton channel important for the influenza life cycle, and is effectively blocked by the drug amantadine [27]. The 25-residue transmembrane domain forms a tetrameric helical bundle in lipid bilayers [13; 28; 29]. In simple phosphocholine membranes such as DLPC, DMPC and POPC at physiological temperature, the M2TMP helical bundles undergo rotational diffusion around the bilayer normal at rates faster than the ²H quadrupolar interaction [14]. Typical C-H dipolar order parameters in M2TMP range from 0.4 to 0.6, while the variations in the N-H order parameters are larger due to their sensitivity to the helix orientation [16; 30]. Figure 7(a, b) show the ¹⁵N CP spectra of amantadine-bound M2TMP in DLPC bilayers. The spectra were acquired under 11 kHz MAS with 2 kHz WALTZ-16 decoupling and 63 kHz TPPM decoupling. The low-power decoupled spectra have 70-80% of the intensities of the high-power decoupled spectra. This is remarkable, considering that the overall oligomeric size of the protein is about 11 kDa. The rigid-limit one-bond N-H dipolar coupling is about 10 kHz, a factor of two smaller than the one-bond C-H dipolar coupling. The nearest neighbor H^N-H^α dipolar coupling is about 5.2 kHz for a distance of ∼2.5 Å. Thus, if we assume a local segmental order parameter of ∼0.5, the residual N-H dipolar coupling prefactor under 11 kHz MAS is estimated as:

Figure 7.

¹⁵N CP spectra of V28, S31, L36-labeled M2TMP at 313 K in DLPC bilayers under 11 kHz MAS with an acquisition time of 17.6 ms. (a) 2 kHz WALTZ-16 decoupled spectrum. (b) 63 kHz TPPM decoupled spectrum. Intensities in the low-power decoupled spectra are 70-80% of the high-power decoupled intensities. (c) 2 kHz WALTZ-16 decoupled spectrum measured with a recycle delay of 1.0 s and 23,040 scans. (d) 63 kHz TPPM decoupled spectrum measured with a 2.5 s recycle delay and 9216 scans. The fast-recycled low-power decoupled spectra have 1.3 times higher intensities than the high-power decoupled spectrum in the same total experimental time.

$$\frac{{\overline{\omega }}_{\mathit{\text{skl}}}}{{\omega }_r}\infty \frac{\left(2\pi \cdot 10\cdot 0.5\mathit{\text{kHz}}\right)\cdot \left(2\pi \cdot 5.2\cdot \mathit{0.5}\mathit{\text{kHz}}\right)}{2\pi \cdot 11\mathit{\text{kHz}}}\approx 2\pi \cdot 1.2\mathit{\text{kHz}},$$ (10)

which explains why the combination of 11-13 kHz MAS and 2 kHz decoupling is adequate to give reasonable lineshape.

With 2 kHz ¹H decoupling the recycle delay is no longer limited by the rf duty cycle, thus much faster signal averaging can be carried out. Indeed, the limiting factor in the low-power decoupled CP experiments is the ¹H T₁, which is usually in the hundreds of millisecond range for membrane samples. Figure 7(c, d) compares the M2TMP ¹⁵N CPMAS spectrum acquired with a recycle delay of 1.0 s and 23,040 scans under 2 kHz decoupling, with a spectrum acquired under regular high power decoupling but a recycle delay of 2.5 s and 9,216 scans. The low-power decoupled spectrum gave ∼1.3 times higher intensities than the high-power decoupled spectra in the same amount of experimental time.

To obtain similarly narrow ¹³C spectra should in principle require higher MAS rates and ¹H decoupling fields due to the stronger C-H dipolar couplings. Yet Figure 8 shows that the peptide ¹³C signals with 2 kHz ¹H decoupling still have 70-80% of the intensities of the high-power decoupled ¹³C spectrum. However, this comparison is limited by the fact that the M2TMP motional rates are not much faster than the C-H dipolar couplings at this temperature, so that the ¹³C resonances are broader than ¹⁵N peaks even in the high-power decoupled spectrum.

Figure 8.

¹³C CP spectra of V28, S31, and L36-labeled M2TMP in DLPC bilayers at 313 K under 11 kHz MAS. Black: TPPM decoupling at 63 kHz. Red: WALTZ-16 decoupling at 2 kHz. Peptide ¹³C peaks are assigned. The low-power decoupled intensities are 70-80% those of the high-power decoupled spectra. The two spectra used the same number of scans and recycle delays. Similar to Figure 7, if the low-power decoupled spectrum were measured with shorter recycle delays higher intensities would result in the same experimental time.

These ¹³C and ¹⁵N peptide spectra indicate that for low power decoupling to be useful for membrane peptides, the molecular motion needs to be well into the fast regime, and slightly higher MAS frequencies is also desirable to fully recover the intensity of the high power decoupled spectra. We predict that 3.2 mm rotors that allow spinning rates of 15-20 kHz will provide the best combination of sample volume and low-power decoupling efficiency for mobile membrane peptides.

Conclusion

We have shown that moderate MAS frequencies of 10-15 kHz combined with very low ¹H decoupling fields of 1-2 kHz are sufficient to yield high-resolution heteronuclear spectra of motionally averaged lipid membranes. The fast uniaxial diffusion removes the homonuclear dipolar coupling cross terms in the average Hamiltonian, thus suppressing spin diffusion. For lipids with order parameters of less than 0.25, the low power decoupled ¹³C spectra have equal intensities compared to the high power decoupled spectra at the same acquisition times. But by allowing much longer acquisition times to be used, low power decoupling in practice results in significant enhancement of sensitivity and resolution. For systems with order parameters of ∼ 0.5, MAS frequencies of 11 kHz combined with low power decoupling do not fully recover the high power intensities. Nevertheless, it is possible to obtain low-power decoupled ¹⁵N and ¹³C spectra with 70-80% intensity of the high power spectra on a membrane peptide assembly with an effective molecular weight of 11 kDa. This opens up the intriguing possibility of determining membrane peptide structures in lipid bilayers using liquid-state NMR spectrometers equipped with MAS probes.