Nano-Mole Scale Side-Chain Signal Assignment by 1H-Detected Protein Solid-State NMR by Ultra-Fast Magic-Angle Spinning and Stereo-Array Isotope Labeling

We present a general approach in 1H-detected 13C solid-state NMR (SSNMR) for side-chain signal assignments of 10-50 nmol quantities of proteins using a combination of a high magnetic field, ultra-fast magic-angle spinning (MAS) at ~80 kHz, and stereo-array-isotope-labeled (SAIL) proteins [Kainosho M. et al., Nature 440, 52–57, 2006]. First, we demonstrate that 1H indirect detection improves the sensitivity and resolution of 13C SSNMR of SAIL proteins for side-chain assignments in the ultra-fast MAS condition. 1H-detected SSNMR was performed for micro-crystalline ubiquitin (~55 nmol or ~0.5mg) that was SAIL-labeled at seven isoleucine (Ile) residues. Sensitivity was dramatically improved by 1H-detected 2D 1H/13C SSNMR by factors of 5.4-9.7 and 2.1-5.0, respectively, over 13C-detected 2D 1H/13C SSNMR and 1D 13C CPMAS, demonstrating that 2D 1H-detected SSNMR offers not only additional resolution but also sensitivity advantage over 1D 13C detection for the first time. High 1H resolution for the SAIL-labeled side-chain residues offered reasonable resolution even in the 2D data. A 1H-detected 3D 13C/13C/1H experiment on SAIL-ubiquitin provided nearly complete 1H and 13C assignments for seven Ile residues only within ~2.5 h. The results demonstrate the feasibility of side-chain signal assignment in this approach for as little as 10 nmol of a protein sample within ~3 days. The approach is likely applicable to a variety of proteins of biological interest without any requirements of highly efficient protein expression systems.


Fig. C.
A pulse sequence used for 13 C-detected 2D 1 H/ 13 C chemical-shift correlation spectroscopy in Fig. 2b. After excitation by a π/2-pulse, 1 H spin polarization evolved under 1 H chemical-shift interactions during the t 1 period under WALTZ-16 13 C decoupling with an RF field strength of 10 kHz. The t 1 period was incremented up to 5.1 ms with a t 1 increment of 0.15 ms. The 1 H polarization was transferred to the 13 C spins by adiabatic tangential double-quantum cross polarization (DQ-CP), which was identical to the first CP scheme in S2 Fig. The contact time for CP was 1.5ms. During the acquisition (t 2 ) period of 10.2 ms, SPINAL-64 1 H decoupling and WALTZ-16 2 H decoupling were applied with RF strengths of 10 kHz and 5 kHz, respectively. The t 2 dwell time was 5 µs. The phase cycles for the pulse sequence were as follows: ϕ 1 = y, -y; ϕ 2 = x, x, -x, -x; ϕ 3 = y; ϕ 4 = x, -x, -x, x. The phase ϕ 1 and the receiver phase were incremented along the t 1 points using the States-TPPI data collection mode.

Fig. D.
A pulse sequence used for 1 H-detected 3D 13 C/ 13 C/ 1 H correlation spectroscopy in Fig. 3. 13 C spin polarization was prepared by adiabatic double-quantum cross polarization (DQ-CP) using the same parameters as discussed in S2 Fig. During the t 1 period, SPINAL-64 1 H decoupling and WALTZ-16 2 H decoupling were applied with RF field strengths of 10 kHz and 5 kHz, respectively. After the t 1 period, a transverse component of the 13 C polarization was stored along the z-axis and the unnecessary component in the transverse plane is dephased during a zfilter period τ of 2 ms. Then, 13 C polarization transfer was achieved by 13 C-13 C dipolar couplings using the fpRFDR sequence without 1 H rf irradiation. A π-pulse train with the XY-16 phase cycle was rotor-synchronously applied to the 13 C channel so that a π-pulse was applied at the center of every rotor cycle. The π-pulse width in the fpRFDR mixing was 6.6 µs, and n = 96. After a z-filter and excitation by a π/2-pulse, 13 C signals were recorded during the t 2 period under SPINAL-64 1 H decoupling and WALTZ-16 2 H decoupling, as mentioned above for the t 1 period. Then, a transverse component of the 13 C polarization was transferred back to 1 H spins by an adiabatic DQ-CP scheme before the acquisition of 1 H signals in the t 3 period. The 1 H RF field strength was swept from 26.4 kHz to 66.0 kHz with the average rf field at 46.2 kHz (~3ν R /5) while the 13 C RF field amplitude was set kept constant at 32.0 kHz (~2ν R /5). The contact time of the second CP period was 0.5 ms. The t 1 and t 2 periods were both incremented up to 2.4 ms with an increment of 75 µs. The t 3 acquisition time was 10.2 ms with 5 µs dwell time. The phase cycles for the pulse sequence were as follows: ϕ 1 = y; ϕ 2 = x; ϕ 3 = x, x, -x, -x; ϕ 4 = y, y, y, y, -y,y, -y, -y; ϕ 5 = y; ϕ 6 = x, -x; ϕ 7 = x; ϕ 8 = x, -x, -x, x, -x, x, x, -x. The phases ϕ 3 and ϕ 5 and the receiver phase were incremented along the t 1 and t 2 points using the States-TPPI data collection mode.  fig.) from the 1 H and 13 C detected 2D 13 C/ 1 H correlation spectra are compared. The 1D slices and 1D spectrum in (c) are scaled so that all the 1D spectra show a common noise level for sensitivity comparisons. The experimental time was 5 min each. The pulse sequences used for (a) 13 C-detected and (b) 1 H-detected 2D 1 H/ 13 C chemical-shift correlation experiments are shown in S3 Fig. and S2 Fig., respectively. The CP and decoupling conditions for these experiments were similar to those for the data for the SAIL Ile labeled ubiquitin sample in Fig. 2. The 13 C detection/evolution periods was 10 ms, while 1 H detection/evolution periods was 6.5 ms for a) and b). These periods were matched to the inverse of the average line widths of 13 C and 1 H. Although 1 H T 1 value for this sample was ~3 s, the recycle delay was set to 0.3 s as sufficient signal-to-noise ratios can be obtained for all of (a-c). All the spectra in S5 Fig. were processed with 45-and 60-shifted sinebell functions on the 1 H and 13 C dimensions respectively without linear prediction. respectively. The long delays were employed to ensure that the signals were fully recovered. No window functions were applied to the spectra. The CP-transfer efficiency for C α , C β , C γ1 , C γ2 and C δ were 55%, 60%, 68%, 45% and 40%, respectively. The values were obtained by dividing the ratio of the integral peak intensity in (b) to that of the corresponding peak in (a) by γ H /γ C , where γ H and γ C are the gyromagnetic ratios of 1 H and 13 C, respectively.

Preparation of SAIL-Thr microcrystals
SAIL-Thr powder was recrystallized by dissolving 3.7 mg of the amino acid in 35 µL D 2 O followed by the addition of 55 µL d 4 -methanol. Precipitate was observed after the addition of d 4methanol and it was allowed to stand at room temperature for slow evaporation. The dry crystals were recovered after 2 weeks, and the sample was used for the SSNMR measurements. HiTrap SP column and then a gel filtration chromatography on a Superdex 200 column (All column materials from GE Healthcare, Uppsala, Sweden). The yield of SAIL-Ile labeled Ubq was ~14 mg, and the labeling efficiency of ~90 % was confirmed by mass spectroscopy.

Estimation of the α α-factors in eq. [1] for different window functions
Following ref. [3], the frequency-domain signal-to-noise ratio (S/N) per root of the experimental time in an one-dimensional (1D) direct detection of an X-nuclei with CP is expressed as where B 0 is a static magnetic field, γ A is a gyromagnetic ratio for nuclei A, f HX is the efficiency of CP transfer from 1 H to X (0 ≤ f HX ≤ 1), w X (t) is an apodization window function, t max is the length of the acquired time-domain signal for the X nuclei, and <z(t)> denotes the time average of z over the interval [0, t max ]. The normalized 1D time-domain NMR signal of the X nuclei is assumed to be of the form s X (t)exp(-iω X t), where s X (t) is a non-negative envelope function with S8 s X (0) = 1. Here, Q X is a quality factor of the sample coil for X detection; C X is a constant that includes properties such as temperature, coil geometry, filling factor, receiver noise figure, spin density, and repetition rate for signal averaging. The frequency-domain S/N per root of the experimental time in a two-dimensional (2D) 1 H indirect detection of X nuclei (i.e. 1 H-detected H/X HETCOR) is expressed as where f XH is the efficiency of CP transfer from X to 1  experiments are performed at the same repetition rate and at the same temperature using a probe with a single double-tuned sample coil for X and 1 H nuclei, we can assume C H ~ C X . The factor 1 / 2 in eq. [S2] is attributed to quadrature detection in the t 1 period. When the 2D signal can be separated as s ID (t 1 , t 2 ) = s X (t 1 )s H (t 2 ) and w(t 1 , t 2 ) = w X (t 1 )w H (t 2 ), eq. [S2] can be rewritten as Similarly, the frequency-domain S/N per root of the experimental time in a 2D 1 H/X HETCOR via direct X detection is expressed as where s DD (t 1 , t 2 ) is the normalized envelope function of the 2D time-domain signal for the direct detection, s DD (0, 0) =1, and w DD (t 1 , t 2 ) is a window function for the 2D data. Here, the time average for <z(t 1 , t 2 )> is over the intervals [0, t 1H max ] and [0, t 2X max ].
First, we compare the sensitivity of 2D 1 H indirect detection with that of 1D X direct detection. In case that C X ~ C H and t max = t 1X max , the sensitivity enhancement factor ξ 1D by 2D 1 H indirect detection over 1D X-detection is given by Assuming where τ max denotes the maximum length of τ. For a Lorentzian line shape, W A is reduced to the conventional half-width-at-half-height (HWHH) width after applying a Lorentzian window function assuming that s A (τ max ) w A (τ max ) ~ 0. Then, Thus, the α factor in eq. [1] depends on s H (t 2 )w H (t 2 ) / w H (t 2 ) 1/2 . Now, we evaluate sensitivity enhancement factor by 2D indirect detection over 2D direct detection ξ 2D as Hence, α = 1 in eq. [1] in this case when t 2H max / t 2 X max = W X /W H . In case that t 2 X max = t 1X max , the ratio of ξ 2D to ξ 1D (ζ) is given by It is noteworthy that ζ = (S/N) DD_2D /(S/N) DD_1D . In general, the ratio ζ reflects the 1 H signal envelope and window functions as well as a factor of 1 / 2 due to quadrature detection. When a matched window function of w H (t 2 ) = s H (t 2 ) is used, [S10] b) The S/N values were estimated from the sum spectrum of two separate 13 C-detect 2D spectra collected with 5 min each, and the S/N values were divided by 2. The S/N values are not reported for the peaks noted by * as these peaks were under the detection limit.
c) The S/N values were estimated from the sum spectrum of four separate 13 C 1D CPMAS spectra collected with 5 min each, and the values were divided by 2. Only 3 peaks were analyzed as other peaks were overlapping in the 1D spectrum.
d) The S/N value here is defined by the peak intensity (S) divided by twice the root-mean-square noise level σ N (S/2σ N ). The relative S/N of 1/p means that 1 H-detected scheme enhances S/N by a factor of p. a) The values in the parentheses denote relative S/N with respect to the corresponding S/N ratio for the 1 H detected 2D correlation experiment.
b) The data are shown in S5 Fig. The S/N value here is defined by the peak intensity divided by twice the root-mean-square noise level σ N (S/2σ N ).  Fig. 3. Once the connectivity of the signals were established, the signals were assigned to each Ile residue based on 13 C α and 13 C β assignments in previous SSNMR studies of microcrystalline human ubiquitin. [4,5] All chemical shifts were calibrated based on DSS standard. b) Not observed presumably for dynamics and/or scrambling.