Correction of field instabilities in biomolecular solid-state NMR by simultaneous acquisition of a frequency reference

Abstract

With the advent of faster magic-angle spinning (MAS) and higher magnetic fields, the resolution of biomolecular solid-state nuclear magnetic resonance (NMR) spectra has been continuously increasing. As a direct consequence, the always narrower spectral lines, especially in proton-detected spectroscopy, are also becoming more sensitive to temporal instabilities of the magnetic field in the sample volume. Field drifts in the order of tenths of parts per million occur after probe insertion or temperature change, during cryogen refill, or are intrinsic to the superconducting high-field magnets, particularly in the months after charging. As an alternative to a field-frequency lock based on deuterium solvent resonance rarely available for solid-state NMR, we present a strategy to compensate non-linear field drifts using simultaneous acquisition of a frequency reference (SAFR). It is based on the acquisition of an auxiliary 1D spectrum in each scan of the experiment. Typically, a small-flip-angle pulse is added at the beginning of the pulse sequence. Based on the frequency of the maximum of the solvent signal, the field evolution in time is reconstructed and used to correct the raw data after acquisition, thereby acting in its principle as a digital lock system. The general applicability of our approach is demonstrated on 2D and 3D protein spectra during various situations with a non-linear field drift. SAFR with small-flip-angle pulses causes no significant loss in sensitivity or increase in experimental time in protein spectroscopy. The correction leads to the possibility of recording high-quality spectra in a typical biomolecular experiment even during non-linear field changes in the order of 0.1 ppm h${}^{-1}$ without the need for hardware solutions, such as stabilizing the temperature of the magnet bore. The improvement of linewidths and peak shapes turns out to be especially important for ${}^1$H-detected spectra under fast MAS, but the method is suitable for the detection of carbon or other nuclei as well.

Figure 1

Without the magnetic-field drift, the values $S_x$ and $S_y$ , which form the Cartesian coordinates of the point $S$ , would be measured as the phase-sensitive signal in the indirect dimension under States or States–TPPI mode (red). During an experiment with a time-dependent magnetic field, the $x$ and $y$ coordinates of the points $S_k^{\ast }$ and $S_l^{\ast }$ are acquired, respectively (blue). $S_k^{\ast }$ and $S_l^{\ast }$ are images of the point $S$ after rotations by $\mathrm{\Delta }{{\mathit{\phi }}_k}^{\prime }$ and $\mathrm{\Delta }{{\mathit{\phi }}_l}^{\prime }$ , respectively.

Figure 2

Pulse programs for ${}^{\mathrm{1}}$ H-detected SAFR (red, flip angle $\mathit{\vartheta }$ ) before a 2D correlation experiment. (a) CP-based ${}^{\mathrm{1}}$ H-detected 2D hCH or hNH. (b) 2D ${}^{\mathrm{13}}$ C– ${}^{\mathrm{13}}$ C DARR. Filled black rectangles represent 90 ${}^{\circ }$ pulses, empty rectangles and curved shapes are CP transfers, and grey blocks indicate composite-pulse decoupling (CPD), MISSISSIPPI water suppression (MISS), and the DARR. Optionally, decoupling of the third nucleus can be turned on during $t_{\mathrm{1}}$ and $t_{\mathrm{2}}$ in (a).

Figure 3

1D  ${}^{\mathrm{1}}$ H spectra of dASC acquired by SAFR after a 0.5 ${}^{\circ }$ flip angle during hNH (green) and by a spin-echo pulse sequence (black). A total of 256 scans were recorded in both cases (850 MHz). (a) Full spectra scaled to match their maximal intensities. (b) The spectra in (a) multiplied 50-fold in intensities, showing negligible excitation of the amide region in the 0.5 ${}^{\circ }$ SAFR spectrum.

Figure 4

2D SAFR-hNH of dASC 36 min after the start of cooling down (850 MHz). (a) The spectrum without (blue) and with (red) the field-drift correction. 1D traces along the horizontal dashed lines are shown at the top. (b, c) Two selected details of the spectral regions indicated by the dashed rectangles in (a). (d) The evolution of the proton frequency correction.

Figure 5

2D SAFR-hNH of dASC during helium fill (850 MHz). (a) The spectrum obtained from summing raw data (before Fourier transform) of four experiments together before (blue) and after drift correction (red). 1D traces along the horizontal dashed lines are shown at the top. (b) A selected peak, indicated by the dashed lines in (a), shown separately for the 2D spectra numbered 1–4 and their sum ( $\mathrm{\Sigma }$ ) before (blue) and after the drift correction (red). Contours in all the panels are plotted at the same intensities per scan. (c) The frequency evolution in terms of H ${}_{\mathrm{2}}$ O chemical-shift difference measured by SAFR. Different colors correspond to the separate 2D experiments 1–4 (each taking 83 min with 512 rows, 8 scans per row). The magnet was depressurized around row 50, filling started after row 220, and ended before row 600.

Figure 6

3D SAFR-hCANH of dASC during and after helium fill (1200 MHz). (a) Two selected peaks and their surroundings viewed in three possible plane orientations before (blue) and after the drift correction (red). The perpendicular cross-sections are taken at the positions of the peaks after the correction, indicated by the dashed red lines. Differently to this, the ${}^{\mathrm{15}}$ N– ${}^{\mathrm{13}}$ C plane of the uncorrected spectrum is taken along the dashed blue lines. (b) The frequency evolution in terms of H ${}_{\mathrm{2}}$ O chemical shift difference measured by SAFR. Insets show details of the regions marked by rectangles (different aspect ratios). The helium filling started before the acquisition began.

Figure 7

2D SAFR-hCH of Rpo $\mathrm{4}/{\mathrm{7}}^{\ast }$ during nitrogen fill (1200 MHz) with processing-enhanced resolution (shifted squared sine bell with parameter $\mathrm{SSB}=\mathrm{5}$ in both dimensions). (a) C ${}_{\mathit{\alpha }}$ –H ${}_{\mathit{\alpha }}$ region of 2D hCH spectrum before (blue) and after the drift correction (red). (b) A detail of the 2D hCH spectrum outside of the region shown in (a). Peak maxima of the corrected spectrum are marked by red crosses. (c) The frequency evolution in terms of H ${}_{\mathrm{2}}$ O chemical-shift difference measured by SAFR. The nitrogen filling started around row 400.