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.


S3
Description and usage of pulse and AU programs

S3.1 Pulse programs
• All the pulse programs listed in Table S1 are available online (Římal, 2022).
• The pulse programs are compatible with and have been tested on Bruker Avance III, III+, and NEO with Bruker Topspin 3 or 4.
• Extensive comments and hints for preparation of the experiment and processing are present in the pulse programs.
• Acquisition parameters are explained in the pulse programs (available also in Topspin after ased command).
• Several control options can be used in the ZGOPTNS acquisition parameter: • -Dnosafr: turns off the SAFR block (no SAFR pulse, no additional acquisition); • -Donedim: makes the pulse program 1D (SAFR pulse present, but not its acquisition); • -DCdec for 2D hNH or -DNdec for 2D hCH: turn on decoupling on third channel.
• 1D variant of every pulse program (except for safr-hCH-hNH-DUMAS) is supplied as well, using the directive #define onedim and inclusion of the main pulse program.
• Pulse programs are intentionally written relatively simple and instructive on the use of SAFR.
• 2D and 3D pulse programs are available, but extension to more dimensions is straightforward.
• Homonuclear SAFR: st0 and st are used to store the FIDs into separate memory buffers, one ser file is produced.
• Heteronuclear SAFR: two receivers are active, two datasets (expnos) are used, two ser files are produced.
The heteronuclear SAFR needs a hardware support of multiple receivers, implemented routinely by Bruker since Avance NEO.
• Because of its limited compatibility with multiple acquisitions during one cycle of a pulse program, the mc macro is replaced by wr with a fixed States-TPPI loop scheme: • auxiliary delays acqTime (and acq2Time for heteronuclear SAFR), incrTime, and writeTime as well as a counter td1States (and td2States for 3D) are defined in order to facilitate and generalize the code; • for example, the mc statement 1m mc #0 to 2 F1PH(ip9, id0) in a 2D experiment with homonuclear SAFR is replaced by writeTime wr #0 if #0 zd ip9 lo to 3 times 2 incrTime id0 lo to 4 times td1States and the labels in the beginning of the pulse program are modified accordingly with appropriate delays that preserve the duration of each cycle; • a pulse program with heteronuclear SAFR, such as 2D 13C DARR, uses such commands to store the data from the two receiver on the disk: • as a consequence of avoiding the mc clause, it is not enough to switch the dimensionality of an experiment by the 1, 2, … button in eda, but adding or removing the -Donedim option is also necessary; • the absence of the mc macro makes implementation of NUS or other alternative schemes challenging.
• While D1 is still the duration of the repetition delay set by the user, D11 is used and calculated internally in the pulse programs.This conserves the overall timing regardless if SAFR is used or not.It also takes the delays introduced due to fixed States TPPI cycle into account.In a homonuclear SAFR 2D, D11 is calculated as follows: #ifdef nosafr "d11=d1-writeTime-incrTime" #else "d11=d1-writeTime-incrTime-p18-acqTime-incrTime-d12" #endif

S3.2 Preparation of experiments with SAFR -a typical workflow
We recommended here a way of preparing a new experiment using exclusively the pulse programs with SAFR: 1. optimizing all the pulse and delay parameters using a desired pulse sequence from Table S1 (or a sequential usage of several pulse programs, from a simple one to more complex ones) with -Donedim specified in ZGOPTNS (or, equivalently, using a <name>-1D pulse program), possibly with -Dnosafr as well; 2. SAFR pulse is set by P18 and PLW18 (a lower power than for a hard pulse is advisable); 3. experiment is switched to 2D or 3D in AcquPars and the -Donedim option is removed (or the pulse program is switched to the name without the -1D suffix); 4. parameters of the indirect dimensions are set as for normal experiment; 5. for an experiment with homonuclear SAFR, one of the indirect TD values needs to be doubled (described in the header of every pulse program); 6. in the heteronuclear variant, a second dataset must be prepared for the second receiver, e. g. using the button C in the AcquPars window.

S3.3 Pre-processing and drift correction
The recommended steps after acquisition are as follows: 1. spectral axis calibration by standard means according to the beginning of the experiment; 2. for homonuclear case, splitting of the spectrum into new datasets by Topspin native AU program split is needed (split creates experiments with increasing numbers, usage of the first one -the reference spectrum with SAFR -ending with "00" is recommended); 3. processing of the reference experiment in a pseudo-2D way (xf2 for 2D or xf2 nd2d for 3D) and a proper phasing by the user; 4. running safrcorr on the main experiment (i.e., ending with "01" if the recommendation in step 2 is followed); 5. standard processing (apodization, Fourier transform, etc.) of the corrected experiment under the new number.

S3.4 Description of the AU program safrcorr
• The program is available online (Římal, 2021).
• The user is prompted for several inputs, but the default values could usually be used: • "Intermediate expno for storing ser with 'int' format": if double data type of the ser file is detected (normally on Avance NEO), a conversion to int is done by sertoint and a new expno is required; • "Expno with the reference pseudo-2D SAFR spectrum": the expno of the reference spectrum with SAFR; • "Procno with reference pseudo-2D after xf2": for 3D experiments, the processing number (procno) of the reference spectrum (for 2D experiments, procno 1 is always used); • "The initial shift in Hz": the initial value of field drift: this can be used to process a row of identical experiments before they are added together, otherwise zero should be the input; positive value shifts the entire spectrum to higher frequencies; the units correspond to the direct dimension of the main experiment in Hz; • "New experiment number": the desired new expno for the corrected data.
• The core of the drift correction includes: • reading the processed data (file 2rr) of the reference experiment with SAFR; • finding global maximum and its parabolic interpolation from three adjacent data points (Press et al., 2016) of every row of SAFR data (equivalent result to the pp command in Topspin applied on every row, but much faster); • reading the raw data (ser) and the necessary parameters of the main 2D or 3D experiment;

Figure
Figure S1: 1D 13C DARR spectra of HETs(218 289) at various -289) at 1 H SAFR flip angle using pulse sequence in Fig. 2 (b) in the main text (1200 MHz).Acquisition parameters (128 scans, 64 dummy scans, relaxation delay 2.7 s), experimental time (8 min 49 s), and processing parameters (no apodization, common phase correction, automatic fifth-order polynomial baseline correction) of each spectrum were otherwise the same.All spectra were run immediately one after another from top to bottom.(a) A reference spectrum with no SAFR pulse.(b) Difference spectra between 1D 13C DARR spectra after 1H SAFR pulse with flip angle varying from 0.5° to 20.0° and the reference spectrum in (a).(c) Difference spectrum between another 1D DARR after 0.5° SAFR and the reference.(d) Difference between a control spectrum with identical parameters as in (a) and the reference spectrum in (a).The difference spectra in (b), (c), and (d) are scaled 50 times up relative to (a).

Figure S2 :
Figure S2: Comparison of 2D hNH experiments of dASC recorded with various options of the pulse program safr-hNH (850 MHz).Acquisition parameters (400 t1 increments, 16 scans per FID, SAFR flip angle 0.5°) and experimental time (2 h 35 min 8 s) of each spectrum were otherwise the same.No drift correction was applied.(a) The effect of SAFR while 13C decoupling was turned off: a spectrum with SAFR switched off (top) and two spectra with SAFR on (control 1 and control 2 shown in Fig. S11 as well) were recorded in order to show possible differences caused by SAFR as well as random changes.(b) 13C decoupling turned on: SAFR off (top) and on (bottom).(c) 1D traces along the horizontal dashed lines in (a) and (b).

Figure S3 :
Figure S3: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a 1H-detected 2D hCH or hNH correlation experiment with refocused INEPT transfers.Thin and thick filled black rectangles represent 90-degree and 180-degree pulses, respectively, and grey blocks show composite-pulse decoupling (CPD) and MISSISSIPPI water suppression (MISS).Optionally, decoupling of the third nucleus is turned on during t1 and t2.

Figure S4 :
Figure S4: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a CP-based 1 H-detected 3D hCNH correlation experiment.Thin and thick filled black rectangles represent 90-degree and 180-degree pulses, respectively, empty rectangles and curved shapes are CP transfers and grey blocks show composite-pulse decoupling (CPD) and MISSISSIPPI water suppression (MISS).

Figure S5 :
Figure S5: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a dual-acquisition MAS (DUMAS) 1H-detected 2D hCH (blue acquisition) and hNH (violet acquisition) correlation experiment with CP transfers.The number of increments of the indirect evolution periods t 1 C and t 1 N for the hCH and hNH experiments, respectively, is the same, but their maximum evolution times (hence resolutions) are set independently.Filled black rectangles represent 90-degree pulses, empty rectangles and curved shapes are CP or simultaneous-CP transfers and grey blocks show composite-pulse decoupling (CPD) and MISSISSIPPI water suppression (MISS).

Figure S6 :
Figure S6: Pulse program for 13 C-detected SAFR (red, flip angle ϑ) before a 2D 13 C DARR.A single channel is used for both acquisitions.Although the initial 1H-289) at 13C CP transfer in the main experiment prohibits CP and 1H decoupling during SAFR, because it would saturate protons before the main experiment starts, a 90-degree SAFR pulse (ϑ = 90°) can be employed to gain a stronger signal.Filled black rectangles represent 90-degree pulses, empty rectangle and curved shape is the CP transfer and grey blocks show high-power composite-pulse decoupling (CPD) and the DARR.

Figure S7 :
Figure S7: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a 13C-detected 2D 1H-289) at 13C correlation.Filled black rectangle represents a 90-degree pulse, empty rectangle and curved shape is the CP transfer and the grey block shows highpower composite-pulse decoupling (CPD).

Figure S8 :
Figure S8: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a CP-based 13C-detected 3D hNCC correlation experiment.Filled black rectangles represent 90-degree pulses, empty rectangles and curved shapes are CP and DREAM transfers, and grey blocks show high-power composite-pulse decoupling (CPD) and decoupling by a continuous-wave irradiation avoiding 1H recoupling conditions (without text).

Figure S9 :
Figure S9: Pulse program for 1H-detected SAFR (red, flip angle ϑ) before a 1H-detected 3D hCcNH correlation experiment with CP and 13C DREAM transfers (blue acquisition) with an additional 13 C detection of 2D hCC correlation exploiting orphan 13C polarization after CP to 15N (violet acquisition).Superscripts in the evolution periods mark whther they belong to the 13C-or the 1H-detected spectrum.The 13C-detected FID is stored after every complete cycle of t 2 H increments, yielding more scans per FID in the 2D than in the 3D.Thin and thick filled black rectangles represent 90-degree and 180-degree pulses, respectively, empty rectangles and curved shapes are CP or DREAM transfers and grey blocks show composite-pulse decoupling (CPD) and MISSISSIPPI water suppression (MISS).

Figure S10 :
Figure S10: Natural field drift of the 1200 MHz magnet (linear hardware correction turned on with a fixed drift value) observed by 13C CP on adamantane using a pseudo-2D pulse sequence.Positions of the methylene peak (38.5 ppm) were determined by safrcorr procedure.Non-linear field drift can be observed, as well as periodic oscillations on top of it.

Figure S11 :
Figure S11: 2D SAFR hNH of dASC 36 min after the start of cooling down with drift correction (Fig. 4 in the main text) and -289) at control experiments run at stable conditions with no correction applied (850 MHz).(a) Drift-corrected spectrum acquired during cooling down (red) and two control experiments (grey and dark blue).1D traces along the horizontal dashed lines are shown at the top.(b), (c) Two selected details at positions indicated by the dashed rectangles in (a).

Figure S12 :
Figure S12: 2D SAFR hNH of dASC during helium fill with drift correction ( -289) at Fig. 5 in the main text) and a control experiment during a negligible field drift (12 Hz in 1H) with no correction applied (850 MHz).(a) Drift-corrected spectrum during helium fill (sum of four datasets with 8 scans each, red) and a control experiment (one spectrum with 32 scans, grey).1D traces along the horizontal dashed lines are shown at the top.(b) Selected peak, indicated by dashed lines in (a), in detail.

Figure S13 :
Figure S13: Control 2D SAFR hNH experiments of dASC as in Fig. S11, but in overlay with the same spectra after the drift -289) at correction.Almost no differences are visible.The 1D traces through the indicated 15N frequency are shown together with the difference spectra between the corrected and uncorrected data (magnified 50-fold).The evolutions of the proton frequency drift are shown in parts per billion (ppb).

Figure S14 :
Figure S14: 2D SAFR-hNH of ASC with a linear field drift −0.638 ppm/h (850 MHz).(a) A detail of the spectrum after no correction, linear correction using lindriftcomp (Najbauer and Andreas, 2019), and full drift correction using safrcorr.1D traces along the dashed red lines (1H dimension) are shown at the top.(b) 1D traces of the spectra in (a) along the dashed red lines (15N dimension).(c) The differences of the spectra in (a) with the same contour levels, but scaled 10-and 100-fold as indicated.(d) The frequency drift as measured by 1H SAFR and calculated from the H2O peak maxima using safrcorr.

Figure S15 :
Figure S15: 2D 13C-DARR with 13C-SAFR (pulse program in Fig. S6, SAFR pulse 10°) of HET-s(218 289) during a sine drift -289) at (850 MHz).(a) The 2D spectrum before (top, blue) and after the drift correction (bottom, red).The black diagonal line indicates the spectral diagonal and the dashed line parallel to it marks the position of spinning side bands.(b) Detail of the region indicated by dashed rectangles in (a).(c) The frequency evolution in terms of the chemical shift difference of the carbonyl resonance at 173 ppm measured by 13C-SAFR.

Figure S16 :
Figure S16: 2D 13C DARR with 13C-SAFR of HET-s(218 289) during a sinusoidal field change as in Fig. S15, but with correction -289) at according to a function fitted to the measured drift and a control experiment run at stable conditions with no correction applied (850 MHz).(a) Drift-corrected spectrum acquired during sine drift and a control.(b) Details of the region indicated by dashed rectangles in (a).(c) A 13C SAFR spectrum acquired along the spectrum in (a).(d) The fit of the frequency evolution by a sine function and a constant value outside the sinusoidal part used for correction giving the spectrum in (a).

Figure S17 :
Figure S17: Partially Fourier-transformed 2D 13C DARR with 13C-SAFR of HET-s(218 289) during a sinusoidal field change -289) at before and after drift correction and a control experiment run at a stable field with no correction (fully transformed spectra shown in Fig. S15 and S16).(a) FT done along direct dimension only.(b) FT done along the indirect dimension only.

Figure S18 :
Figure S18: 2D SAFR-HC (13C detection of the main 2D with 1 H-detected SAFR, pulse program in Fig. S7) of 13C-adamantane (1200 MHz) during deliberate field manipulations by Z 0 shim current.Exponential line broadening by 2 Hz and 100 Hz was applied in the 13C (direct) and 1H (indirect) dimensions, respectively, in order to preserve the Lorentzian line shapes, in contrast to squared sine-bell apodization used in other spectra in this work.(a) The methylene peak without any correction.(b) Spectrum from (a) with linear drift correction by −25 Hz (−0.08 ppm, giving the best result) using lindriftcomp ( Najbauer and Andreas, 2019).(c) Fully corrected spectrum using safrcorr, the reference being the adamantane 1 H resonance acquired by SAFR.(d) Control spectrum measured without SAFR during a naturally drifting field with the linear hardware correction turned on.(e, f) 13C and 1H 1D slices, respectively, through the spectra in (a d) along the dashed red lines.(g) The fre -289) at quency drift as measured by 1H SAFR and calculated from the peak maxima using safrcorr.A fast jump in the field value was made during acquisition of row 23.An average shift appears in the plot, because the frequency change was smaller than the 1H linewidth.

Figure S19 :
Figure S19: 2D SAFR-HC of 13C-adamantane during deliberate field manipulations as in Fig. S18 with Fourier transform in 13C (direct) dimension only.The alternating sign (different colors) corresponds to the phase changes in the States TPPI -289) at phase cycle.The evolution of the methylene resonance is shown after no correction, linear correction by lindriftcomp (Najbauer and Andreas, 2019), full correction by safrcorr, and an uncorrected control experiment.The fast jump in the field value was made during acquisition of row 32 (4 scans).The frequency change was higher than the 13C linewidth, which caused a doubling of the spectrum that cannot be fully compensated in this particular row.
FnMODE in Topspin b Values for the four individual blocks as in Fig. 4 are shown; the control experiment had NS = 32 c Exponential line broadening shown for direct and indirect dimension, respectively

Table S2 : Acquisition and processing parameters of the 2D spectra
a Differently from all other spectra, DARR was acquired in TPPI mode and converted to States-TPPI by convdta, inverse Fourier transform by xtrfp followed by genser and modification of the acquisition status parameter