# The SOFAST-HMBC-HMQC experiment for pairing geminal methyl groups in valine and leucine side-chains

Ana Paula Aguilar Alva, Lucas Siemons, Ulric Le Paige, Coline Wiame, Florence Cordier, Nicolas Wolff, Guillaume Bouvignies, Philippe Pelupessy, Fabien Ferrage

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Ana Paula Aguilar Alva, Lucas Siemons, Ulric Le Paige, Coline Wiame, Florence Cordier, et al. The SOFAST-HMBC-HMQC experiment for pairing geminal methyl groups in valine and leucine side-chains. Journal of Biomolecular NMR, 2025, 79 (3), pp.163-170. 10.1007/s10858-025-00464-z. hal-05343602

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# The SOFAST-HMBC-HMQC experiment for pairing geminal methyl groups in Valine and Leucine side-chains.

Ana Paula Aguilar Alva *¹, Lucas Siemons *†,¹, Ulric B. le Paige ¹, Coline Wiame¹,² Florence Cordier ³,⁴, Nicolas
Wolff⁵, Guillaume Bouvignies¹, Philippe Pelupessy¹, Fabien Ferrage†,¹

* equal contribution authors

† corresponding authors

**Addresses and Affiliations:**

¹Laboratoire des Biomolécules, Département de Chimie, UMR 7203, École Normale Supérieure, 24 rue Lhomond,
75005 Paris Cedex 05, France

²University of Liège, 11, Allée du six Août, 4000 Liège, Belgium

³Biological NMR & HDX-MS Technological Platform, Institut Pasteur, Université Paris Cité, CNRS UMR 3528, Paris
(France)

⁴Structural Bioinformatics, Institut Pasteur, Université Paris Cité, CNRS UMR 3528, Paris (France)

⁵Signaling and Receptors Dynamics Unit, Institut Pasteur, Université Paris Cité, CNRS UMR 3571, Paris, France

**Abstract**

Methyl groups are essential probes for characterising interactions and dynamics in large proteins. HN-based triple-resonance NMR experiments are often too insensitive for methyl assignments, making a NOESY-based approach an efficient strategy. Linking geminal methyl groups in leucine and valine residues is a crucial step in such NOESY-based methyl resonance assignment strategies. This link can be established unambiguously with the 3D-HMBC-HMQC experiment, introduced for large U-[¹²C₂H] LV-[¹³CH₃]₂-labelled proteins. Here, we introduce the SOFAST variant of the 3D-HMBC-HMQC experiment which provides spectra with fewer artefacts arising from the water signal and a mean increase in signal-to-noise ratio per unit time of 16% compared to the original experiment with an optimised recovery delay.
Introduction

Methyl groups have been used for decades as some of the most effective probes to investigate large proteins (Sprangers and Kay 2007; Abramov et al. 2020; Shukla et al. 2023; Abayev-Avraham et al. 2023; Sever et al. 2023) as they are well dispersed throughout the protein, and their chemical shifts are sensitive to both the local environment and the conformation of the side-chain (Mulder 2009; Hansen and Kay 2011; Siemons et al. 2019b). Additionally, the fast rotation around the methyl three-fold axis combined with transverse-relaxation optimized (TROSY) pulse sequences that preserve the slow-relaxing components of the polarization, make methyl groups remarkably sensitive spin systems in large proteins and their assemblies (Tugarinov et al. 2003, 2007, 2023; Hansen et al. 2009).

A key challenge faced when deploying methyl-based approaches is the assignment of the resonances. For many proteins accessible to methyl-TROSY NMR, relaxation of coherences in conventional backbone-edited triple-resonance experiments is nevertheless too fast to obtain sufficient sensitivity, even in perdeuterated proteins. Historically, the first assignments were obtained from series of mutants (Sprangers et al. 2005; Amero et al. 2011). In some cases, a ‘divide and conquer’ approach can be applied where protein subunits are expressed and assigned separately and the individual assignments are transferred to the larger complex (Salzmann et al. 2000; Sprangers and Kay 2007). However, for many single-domain proteins this strategy is not feasible.

A variety of approaches have been developed to assign methyl resonances using distance information encoded in NOESY spectra and comparing them to distance information available from known structures (Pritišanac et al. 2017, 2019; Monneau et al. 2017; Nerli et al. 2021). In the case of Methyl Assignment by Graph MAtching (MAGMA) (Pritišanac et al. 2017), this problem is formalised as identifying a unique overlay between a graph generated from the NOESY cross peaks and a distance graph obtained from a known structure. If a unique mapping between the two can be found, information from the crystal structure can be transferred to the NOESY graph and so the assignment is obtained. This provides an important alternative to the ‘divide and conquer’ approach, as it can be applied directly to the full intact system without the need for insensitive HN backbone experiments, or in cases where the formation of the complex induces substantial chemical shift changes in the constituent domains.

To effectively apply these backbone-independent assignment methods, it is necessary to reduce the size of the solution space to search for assignment solutions effectively. In general, the number of possible solutions that describe the overlay between the NOESY graph and the methyl-distance graph scales approximately with n!, where n is the number of isotopically labelled methyl groups in the system (Pritišanac et al. 2017). For example, a medium-sized protein such as the Mitogen-Activated Protein Kinase (MAPK) p38γ (Aoto et al. 2016; Maisonneuve et al. 2016) with 147 labelled methyl groups in isoleucine, leucine and valine residues would yield 1.7x10²⁵⁶ candidate solutions. To reduce the number of candidate solutions two additional pieces of information can be included. The first is the residue type, yielding n<sub>Ile</sub>!n<sub>Val</sub>!n<sub>Leu</sub>! solutions, and the second is joining geminal valine and leucine residues into a single node, yielding n<sub>Ile</sub>! (n<sub>Val</sub>/2)! (n<sub>Leu</sub>/2)! solutions. The inclusion of both of these elements reduces the number of candidate solutions by over 150 orders of magnitude, greatly facilitating the methyl assignment by modern algorithms (Pritišanac et al. 2017, 2019; Monneau et al. 2017; Nerli et al. 2021). This approach can also be facilitated by including additional methyl bearing residues such as threonine (Ayala et al. 2020), alanine (Kerfah et al. 2015b) and methionine (Fischer et
al. 2007). Similar approaches can also be carried out using the distance information encoded in paramagnetic relaxation by introducing electron spin labels at multiple sites in the protein (Venditti et al. 2011).

The 3D-Heteronuclear Multiple Bond Correlation-Heteronuclear Multiple Quantum Coherence (3D-HMBC-HMQC) (Siemons et al. 2019a) is an efficient and unambiguous experiment that joins geminal methyl groups in leucine and valine residues, yielding exactly one cross peak for each methyl resonance in the absence of slow exchange. This experiment is designed for L/V-[¹³CH₃, ¹³CH₃] labelled samples, where both methyl groups are protonated and ¹³C labelled on an otherwise deuterated and ¹²C background. The pulse sequence consists of two HMQC-type blocks. In the first HMBC block, the polarization evolves under the three-bond scalar-coupling between the protons of one methyl group and the ¹³C nucleus of the second methyl group, while refocusing the intra-methyl coupling. In the second HMQC block, the spin system evolves under the intra-methyl coupling. This experiment provides three-dimensional spectra with peaks at frequencies (C₁, C₂, H₂) and (C₂, C₁, H₁). Pairing these two peaks using the two ¹³C chemical shifts allows the identification of pairs of geminal methyl groups in valine and leucine residues, greatly facilitating the backbone-independent assignment.

Alternatively pairing geminal methyl resonances can also be carried out by recording NOESY spectra in L/V-[¹³CH₃, ¹³CH₃] labelled samples with short mixing times. In this approach one can assume that the most intense/single peak is the geminal methyl resonance. However, multiple peaks are often present and it can be challenging to distinguish intra-residue NOEs from inter-residue NOEs. In the 3D-HMBC-HMQC this is made unambiguous as in the absence of slow exchange there is exactly one cross peak per methyl resonance. In general, the HMBC-HMQC and backbone independent assignment strategies are carried out when the backbone amide spectra are too insensitive due to relaxation in cases where they are available then a different overall assignment strategy can be used. (Tugarinov and Kay 2003a, b; Venditti et al. 2011; Mishra and Frueh 2015; Kerfah et al. 2015a).

Band-Selective Optimized-Flip-Angle Short-Transient (SOFAST) -HMQC (Schanda et al. 2005) and Band-selective Excitation Short-Transient (BEST) experiments are popular approaches that accelerate the acquisition of NMR spectra and improve experimental sensitivity (Schanda et al. 2006; Lescop et al. 2007). In this class of experiments, band-selective shaped protons radio frequency pulses are used to selectively excite and manipulate only the proton polarization of the HN or CH₃ groups of interest. The other protons from the protein and the solvent serve as a large reservoir of proton polarization, left along the z-axis. The coupling of the protons of interest to this reservoir through dipolar cross relaxation or chemical exchange can dramatically accelerate the return to equilibrium of the excited protons. This approach can be combined with Ernst-angle excitation (Ernst and Anderson 1966) to further speed up the rate at which free-induction decays can be acquired and improve the signal-to-noise ratio of NMR spectra obtained per unit time. This approach has given rise to a range of SOFAST and BEST experiments, including the aromatic SOFAST-HMBC (Vallet et al. 2019).

In this article, we introduce the SOFAST variant of the 3D-HMBC-HMQC experiment which combines the selective manipulation of the polarization of methyl protons of the SOFAST approach with the HMBC-HMQC experiment. The
absence of excitation of water protons provides clean spectra with excellent suppression of the water signal. Importantly, an improvement of 16% in signal-to-noise per unit time was obtained in our test sample: a specifically labelled L/V-[¹³CH₃, ¹³CH₃] sample of the kinase p38γ (42 kDa with an estimated τ_c ≈ 31ns) (Aoto et al. 2019), when compared to the original implementation with an optimised recovery delay.

## Methods

### Protein expression

The expression protocol was adapted from M. Cai et. al (Cai et al. 2016). Rosetta *E. coli* Rosetta2 (DE3) competent cells (NovaGen) were transformed with a pET15-b expression plasmid containing an N-terminal histidine tag (6xHis) tag, a TEV cleavage site (TEVc) and p38γ in the following sequence 6xHis-TEVc-p38γ. The transformed cells were incubated overnight at 37 °C on LB-agar Petri dishes with 34 µg/mL chloramphenicol (Cam) (Sigma Aldrich) and 100 µg/ml ampicillin (Amp) (Fisher Bioreagents). The pre-culture was made by transferring isolated colonies from the Petri dish in 5 mL of LB broth in H₂O with Cam + Amp in a 1:1000 proportion. *E. coli* cells were grown in a 37 °C shaker until the medium reached an O.D. of ~1. Then a gradual D₂O adaptation for the *E. coli* cells was carried out by transferring 200 µL from the LB-H₂O preculture into 2.5 mL of LB-D₂O and grown in a 37 °C shaker until the medium reached an O.D. of ~1. A fraction of the LB-D₂O preculture was transferred into 25 mL of M9 minimal medium in D₂O, yielding an O.D. ≈ 0.025 and grown in a 37 °C shaker overnight. Once the cells were adapted to D₂O, 25 mL was transferred into the final 730 mL M9 D₂O expression medium with ¹⁵NH₄Cl (Innova-Chem) and ¹²C-perdeuterated glucose (Innova-Chem). The M9-D₂O culture was incubated in a 37 °C shaker until an O.D. of 0.6-0.8 was obtained and then protein expression was induced by adding IPTG. To obtain the LV-[CH₃]₂ labelling scheme U-[¹²C,²H,¹⁵N]-[¹³CH₃]₂-α-ketoisovaleric acid (Cambridge Isotope Laboratories Inc.), was added 1 hour prior to induction (80 mg/L). Expression was carried out overnight at 18 °C. The cell pellet was collected by centrifuging at 4000 rpm at 4 °C for 20 min.

### Purification

The purification protocol for p38γ was based on and adapted from P. Maisonneuve, et. al. (Maisonneuve et al. 2014). The cell pellet was resuspended in a lysis buffer (50 mM TrisHCl pH = 7.5, 150 mM NaCl, 5 mM imidazole, 2 mM β-mercaptoethanol and a cOmplete™ EDTA-free Protease Inhibitor Cocktail tablet [Roche]). *E. coli* cells were lysed by sonication and the cell lysate was removed by centrifuging at 16000 g (RCF) at 4 °C for 25 min. The supernatant with the solubilized protein was filtered through a 0.45 µm pore membrane.

The purification process consisted of 3 steps. In the first step, the supernatant is loaded onto an Immobilized Metal Affinity Chromatography (IMAC) TALON Cobalt-based column (Cytiva) with a running Buffer (50 mM TrisHCl pH = 7.5, 150 mM NaCl, 5 mM imidazole and 2 mM β-mercaptoethanol). The protein is then eluted by applying a gradient of the elution buffer (50 mM TrisHCl pH = 7.5, 150 mM NaCl, 150 mM imidazole, 2 mM β-mercaptoethanol). The eluted fractions that contain p38γ were pooled and dialysed in the running buffer and TEV protease overnight, removing the 6xHis-tag. Then a reverse IMAC TALON Cobalt-based column, using the same running buffer and elution buffer gradient was carried out and the flow through was collected. The third step is gel filtration chromatography, using a Hiload Superdex 1660 75 pg column (Cytiva) with the final NMR buffer (20 mM HEPES pH = 7.5, 91 mM NaCl and 1
mM DTT) was used to elute p38γ. The fractions containing p38γ were collected and the sample was concentrated to reach a concentration of 250 µM. The final volume of the NMR sample was to 300 µL in a Shigemi tube with 10 % D₂O.

## NMR spectroscopy:

The 3D HMBC-HMQC and SOFAST-HMBC-HMQC experiments were performed at 294 K on a Bruker 950 MHz Neo spectrometer equipped with a Z-gradient TCI cryoprobe, using a 250 µM U-[¹²C,²H,¹⁵N]-(LV-[¹³CH₃]₂)-p38γ sample in NMR buffer. The 3D SOFAST-HMBC-HMQC experiment was acquired with 8 scans, a recycling delay of 0.4 s, a 60° tilt-angle and a total transfer time in the HMBC block of 3 × (2 × 3.91 ms), resulting in an experiment time of 44 hours. The conventional 3D HMBC-HMQC experiment was recorded with an optimized recycling delay of 0.69 s, yielding a total duration of 67 hours. Both experiments were recorded with acquisition times of 51 ms, 36 ms, and 25 ms and spectral widths of 12.53 ppm, 13 ppm and 13 ppm in the ¹H, ¹³C_HMQC and ¹³C_HMBC dimensions respectively. To optimize both experiments, a series of 1D spectra were collected for the SOFAST-HMBC-HMQC using tilt-angles of 30°, 60°, 90° and 120° for the initial PC9 pulse (Kupce and Freeman 1993). For both HMBC-HMQC variants the inter-scan delay was varied between 200 ms and 2 s. All spectra were processed with NmrPipe (Delaglio et al. 1995) and Nmrglue (Helmus and Jaroniec 2013), and the analysis was done using the software Poky (Lee et al. 2021).

Peak intensities were obtained by fitting lineshapes to the cross-peaks using PeakFit, an open-source Python program for extracting peak intensities in NMR spectra using analytical lineshape fitting. PeakFit models lineshapes by accounting for sine-bell apodization and truncation effects (Dudley et al. 2020) and fits user-provided peak lists via nonlinear least-squares minimization. Overlapping peaks are grouped into clusters based on contour levels, with all peaks in a cluster fitted simultaneously to generate a combined lineshape that accounts for their contributions. In a second iteration, contributions from other clusters fitted during the first iteration are included to further refine the accuracy, correcting for any residual effects from neighbouring clusters on the signal being fitted. Designed for multidimensional spectra, PeakFit enables robust quantification in crowded regions. The program is freely available at https://github.com/gbouvignies/PeakFit.

## Results:

The pulse sequence for the SOFAST-3D-HMBC-HMQC is presented in Figure 1. The selected coherence transfer pathways are the same as those in the original 3D-HMBC-HMQC (Siemons et al. 2019a). We consider two methyl groups with atom names [C₁, H₁] and [C₂, H₂]. During the first HMBC block the H₁ proton in-phase coherence evolves under the three-bond scalar coupling ³J(C₂, H₁) ≈ 4.8 Hz for a duration 2nτ. The C₂ chemical shift is labelled during the delay t₁. The evolution under the ³J(C₂, H₁) coupling for an integer number of full periods for the ¹J(C₁, H₁) coupling 2nτ ≈ n/¹J(C₁, H₁) ensures that the latter is rendered ineffective. In the second HMQC block, the C₁-H₁ correlations are recorded. In order to optimise the intensity of the C₂-C₁-H₁ cross peaks, n must be selected to balance the evolution under the ³J(C₂, H₁) coupling and the decay from transverse relaxation. Previous simulations and empirical evidence showed that n ∈ {3,4,5,6} yield good spectra for a 40 kDa proteins with transverse relaxation rates in the range of 10-
40 s⁻¹ (Siemons et al. 2019a). The geminal methyl peaks of valine and leucine residues can be paired using this experiment by matching the C₂-C₁-H₁ and C₁-C₂-H₂ cross peaks, as shown in Figure 2 & S1.

<figure><img src="image_2.png" /></figure>

Figure 1. The SOFAST-HMBC-HMQC pulse sequence. The ¹H excitation (with flip angle β) and refocusing pulses are PC9 and RE-BURP, respectively. Rectangles represent hard π/2 pulses. The PC9 and RE-BURP are centred on the carrier frequency, 0.4 ppm, and have a bandwidth of 2ppm. The delays t₁ and t₂ are incremented for evolution in the indirect dimensions, while τ = 1/(2¹J(CH)) = 3.91ms and τrec is the inter-scan recycling delay. The constant n is chosen in the interval {3-6}. The phase cycle employed is φ1 = x, -x, x, -x; φ2 = x, x, -x, -x; φrec = x, -x, -x, x; with all other pulses applied along the x axis of the rotating frame. All pulsed field gradients were applied for 1 ms with a sinc shape and amplitudes of 30.9, 7.2 and 11.2 G/cm, for G₁, G₂ and G₃ respectively. Composite-pulse decoupling is carried out during acquisition using the WALTZ-65 decoupling scheme (Shaka et al. 1983).

In the SOFAST-3D-HMBC-HMQC experiment, shown in Figure 1, the proton π/2 and π pulses of the original sequence were exchanged for PC9 (Kupce and Freeman 1993) and RE-BURP pulses (Geen and Freeman 1991) respectively. Compared to the original pulse sequence this modification offers three advantages. First, we can use a PC9 pulse with a variable pulse angle, allowing an Ernst-angle optimization for a selective range of frequencies and hence use shorter inter-scan relaxation delays. Second, shaped pulses centred on the ¹H methyl resonances avoid exciting the polarization of water and other buffer components, providing excellent water suppression and high-quality spectra for the methyl region. Third, residual non-methyl protons (NH, solvent protons, and residual protons due to imperfect labelling) stay along the z-axis, accelerating the return to equilibrium. This effect (SOFAST) is of course less pronounced than in a fully protonated sample.

This pulse sequence requires that two parameters are optimised in order to obtain the optimal signal-per-unit-time. These are the number *n*, which defines the duration of the HMBC transfer, and the inter scan-delay. In principle the optimal value of *n* can be determined from the transverse relaxation rate as the maximum of the function *I(n, R*₂*) = sin²[³J(C*₂*, H*₁*)] *π* *n* (2 *x*3.91 10⁻³ *s*)] *exp*[-2*R*₂ (2 *x*3.91 10⁻³ *s*)]. In practice the *R*₂ rates may vary from site to site due to anisotropic diffusion, local dynamics and chemical exchange. Nonetheless *I(n, R*₂*)* indicates that if *R*₂ = 20 s⁻¹ one could expect to obtain a signal intensity of ~6.5% (*n* = 6) compared to the initial polarisation, only decreasing to a signal intensity of ~1.8% (*n* = 3) as the *R*₂ increases to 40 s⁻¹. Full simulations of *I(n, R*₂*)* for *R*₂ = {10 s⁻¹, 20 s⁻¹, 40 s⁻¹} and optimal values of *n* for *R*₂ rates between 10 s⁻¹ and 100 s⁻¹ can be found in Figure 3 of the original HMBC-HMQC article (Siemons et al. 2019a). On the other hand, determining the optimal inter-scan delay can be challenging as it depends on the quantity of remaining aliphatic protons and overall deuteration level. In order to determine the optimal parameters a series of 1D experiments can be carried out to determine the optimal value of *n* and of the inter-scan delay.
<figure><img src="image_3.png" /><figcaption>Figure 2: SOFAST-HMBC-HMQC experiment recorded on a 200 µM sample of p38γ using a 60° excitation pulse and recycling delay of 0.4 s. (a) Projection on the HMQC plane, the HMBC projection is shown in Figure S2. (b) and (c) show two companion slices demonstrating how the cross peaks in the HMBC dimension are used to pair the geminal methyl groups, here for residue V161. The positions of the residual diagonal peaks, which are much smaller than cross peaks, are indicated by orange crosses.</figcaption></figure>

To determine the optimal excitation angle for the initial PC9 pulse and the inter-scan delay, a series of spectra were recorded with flip angles of 30°, 60°, and 90°. In addition, the original HMBC-HMQC experiment was recorded with various inter-scan delays. We compared the profiles in order to determine the maximum signal-to-noise ratio for a given unit of time, see Figure 3. The signal per square root of unit time for the original HMBC-HMQC indicates that for p38γ the optimal inter-scan delay is in the range of 0.6 to 0.8 s, which yields approximately 15% more signal than the original HMBC-HMQC commonly used inter-scan delays of ~1.5 s. Comparing the 4 tilt-angles shows that the optimal PC9 tilt-angle for the SOFAST experiment is 60° with an optimal inter-scan delay of 0.4 s. These optimizations were performed on the overall intensity of the 1D profiles. The optimum values may vary from one residue to another, in particular between rigid and highly flexible sites.
<figure><img src="image_4.png" /></figure>

Figure 3: Sum of the 1D signals divided by the square root of the experimental time as a function of the recovery delay, τ<sub>rec</sub>, for the SOFAST and original HMBC-HMQC experiments. (a) shows the increase in signal for the p38γ methyl groups obtained as the inter-scan delay is varied from 0.25 s (green) to 2 s (blue) with a 60° PC9 pulse. In (b) the profiles for the signal per unit time are shown for the SOFAST-HMBC-HMQC with tilt angles of 30°, 60° and 90° are shown with varying inter-scan delays. In addition to this the same profile is shown for the original HMBC-HMQC experiment with hard 90° pulses. In order to mitigate the effect from the solvent a linear baseline correction was applied to the methyl region of the original HMBC-HMQC experiment.

Based on these signal-per-unit-time profiles, a 3D-SOFAST-HMBC-HMQC experiment was recorded with a tilt angle of 60° and a recovery delay of 0.4 s and compared to an HMBC-HMQC experiment recorded with hard pulses and an inter-scan delay of 0.69 s, which corresponds to the optimal delay observed in Figure 3. On average, the SOFAST-HMBC-HMQC yields a signal enhancement per square-root unit time of 16% for isolated cross peaks compared to the original variant, as seen in Figure 4 & S2. Out of a total of 104 peaks, 80 peaks showed a signal enhancement. Notably peaks with the weakest intensity showed signal enhancements of up to 50 %, as seen in Figure 4. On the other hand, some of the more intense signals show a modest decrease in the peak intensity, but this has only a small impact on the overall ability to assign the methyl pairs as the peaks remained above the noise level. We note that the original HMBC-HMQC experiment is often recorded with a longer recovery delay, τ<sub>rec</sub> ≈ 1.5 s. Optimising the recovery time of the conventional HMBC-HMQC experiment provides a signal gain per unit time of 15% (Figure 3). Thus, combining the gains in sensitivity per unit time of 15% from the optimisation of the conventional HMBC-HMQC with the 16% improvement of the SOFAST variant leads to a total gain for the SOFAST-HMBC-HMQC experiment of approximately 33% more signal per unit time compared to the original HMBC-HMQC with commonly used recovery delays in the region of 1-2 s.
<figure><img src="image_5.png" /></figure>

Figure 4: Signal enhancement obtained from comparing the SOFAST-HMBC-HMQC sequence to the original implementation with an optimised recovery delay. (a) shows a histogram of the signal enhancement, for isolated peaks, obtained when comparing the SOFAST experiment to the original implementation. While (b) compares the enhancement to the peak intensity. The peak intensity per unit time is given as $I/(N * \sqrt{t})$. The intensity (I), time (t), and noise (N) for the SOFAST experiment are denoted by the SF superscript.

Comparing the original and SOFAST variants of the experiment highlights the need for a careful baseline correction when processing the original experiment. In particular, the application of the solvent filter and a polynomial baseline correction can have a substantial, systematic impact on the apparent noise in the spectra (Figure S3). For the original HMBC-HMQC recorded this would change the overall level of the noise from 2.6 AU to 3.0 AU thereby altering the signal-to-noise ratio by ~13%. In contrast, in the SOFAST experiment the baseline shows uniform noise as the band-selective pulses do not excite the water nor the HEPES buffer resonances. Unlike the original variant, the band-selective nature of the SOFAST-HMBC-HMQC make the baseline correction straightforward.

## Conclusion

We have introduced the SOFAST variant of the HMBC-HMQC experiment. By modifying this pulse sequence to use band-selective excitation of the methyl protons combined with Ernst-angle excitation and optimised inter-scan delays, we achieved a significant increase in sensitivity per unit time. In the case of the 42 kDa kinase p38γ, we obtained a 16% increase in signal per unit time compared to the original pulse sequence recorded with an optimal recovery delay. In addition, the SOFAST version provided a spectrum of higher quality, with better suppression of the water and buffer
signals. We anticipate the SOFAST-HMBC-HMQC will be used routinely for backbone-free assignments of methyl
resonances.

Acknowledgements

The authors acknowledge financial support by the European Commission through the FET-Open program, Grant agreement 899683 (HIRES-MULTIDYN). Financial support from the IR INFRANALYTICS FR2054 for conducting the research is gratefully acknowledged. The funders had no role in the design of the study, data collection or preparation of the manuscript.

Author Contributions

A.P.A.A., U.B.IP, F.C and N.W designed the expression and purification strategy for p38γ. A.P.A.A. expressed and purified the (LV-[¹³CH₃]₂) labelled sample. U.B.IP and P.P. wrote the pulseprogram for the SOFAST-HMBC-HMQC experiment. A.P.A.A. and P.P. recorded the experiments. A.P.A.A., L.S. and C.W. analysed the data. G.B. wrote PeakFit and extended it to fit nD lineshapes. L.S and F.F supervised the study. L.S and A.P.A.A. wrote the first draft of the manuscript and all authors discussed the results, provided feedback and approve the final manuscript.

Competing interests

There are not competing interests to declare.

References

Abayev-Avraham M, Salzberg Y, Gliksberg D, Oren-Suissa M, Rosenzweig R (2023) DNAJB6 mutants display toxic gain of function through unregulated interaction with Hsp70 chaperones. Nat Commun 14:7066

Abramov G, Velyvis A, Rennella E, Wong LE, Kay LE (2020) A methyl-TROSY approach for NMR studies of high-molecular-weight DNA with application to the nucleosome core particle. Proceedings of the National Academy of Sciences 117:12836–12846

Amero C, Asunción Durá M, Noirclerc-Savoye M, Perollier A, Gallet B, Plevin MJ, Vernet T, Franzetti B, Boisbouvier J (2011) A systematic mutagenesis-driven strategy for site-resolved NMR studies of supramolecular assemblies. J Biomol NMR 50:229–236

Aoto PC, Martin BT, Wright PE (2016) NMR Characterization of Information Flow and Allosteric Communities in the MAP Kinase p38γ. Sci Rep 6:28655

Aoto PC, Stanfield RL, Wilson IA, Dyson HJ, Wright PE (2019) A Dynamic Switch in Inactive p38γ Leads to an Excited State on the Pathway to an Active Kinase. Biochemistry 58:5160–5172

Ayala I, Chiari L, Kerfah R, Boisbouvier J, Gans P, Hamelin O (2020) Asymmetric Synthesis of Methyl Specifically Labelled *L*-Threonine and Application to the NMR Studies of High Molecular Weight Proteins. ChemistrySelect 5:5092–5098
Cai M, Huang Y, Yang R, Craigie R, Clore GM (2016) A simple and robust protocol for high-yield expression of perdeuterated proteins in Escherichia coli grown in shaker flasks. *J Biomol NMR* 66:85–91

Delaglio F, Grzesiek S, Vuister GW, Zhu G, Pfeifer J, Bax A (1995) NMRPipe: a multidimensional spectral processing system based on UNIX pipes. *Journal of biomolecular NMR* 6:277–293

Dudley JA, Park S, MacDonald ME, Fetene E, Smith CA (2020) Resolving overlapped signals with automated FitNMR analytical peak modeling. *Journal of Magnetic Resonance* 318:106773

Ernst RR, Anderson WA (1966) Application of Fourier Transform Spectroscopy to Magnetic Resonance. *Review of Scientific Instruments* 37:93–102

Fischer M, Kloiber K, Häusler J, Ledolter K, Konrat R, Schmid W (2007) Synthesis of a¹³ C-Methyl-Group-Labeled Methionine Precursor as a Useful Tool for Simplifying Protein Structural Analysis by NMR Spectroscopy. *ChemBioChem* 8:610–612

Geen H, Freeman R (1991) Band-selective radiofrequency pulses. *Journal of Magnetic Resonance* (1969) 93:93–141

Hansen DF, Kay LE (2011) Determining valine side-chain rotamer conformations in proteins from methyl 13C chemical shifts: application to the 360 kDa half-proteasome. *Journal of the American Chemical Society* 133:8272–81

Hansen DF, Vallurupalli P, Kay LE (2009) Measurement of methyl group motional parameters of invisible, excited protein states by NMR spectroscopy. *J Am Chem Soc* 131:12745–12754

Helmus JJ, Jaroniec CP (2013) Nmrglue: an open source Python package for the analysis of multidimensional NMR data. *J Biomol NMR* 55:355–367

Kerfah R, Hamelin O, Boisbouvier J, Marion D (2015a) CH3-specific NMR assignment of alanine, isoleucine, leucine and valine methyl groups in high molecular weight proteins using a single sample. *J Biomol NMR* 63:389–402

Kerfah R, Plevin MJ, Pessey O, Hamelin O, Gans P, Boisbouvier J (2015b) Scrambling free combinatorial labeling of alanine-β, isoleucine-δ1, leucine-proS and valine-proS methyl groups for the detection of long range NOEs. *J Biomol NMR* 61:73–82

Kupce E, Freeman R (1993) Polychromatic Selective Pulses. *Journal of Magnetic Resonance, Series A* 102:122–126

Lee W, Rahimi M, Lee Y, Chiu A (2021) POKY: a software suite for multidimensional NMR and 3D structure calculation of biomolecules. *Bioinformatics* 37:3041–3042

Lescop E, Schanda P, Brutscher B (2007) A set of BEST triple-resonance experiments for time-optimized protein resonance assignment. *Journal of Magnetic Resonance* 187:163–169
Maisonneuve P, Caillet-Saguy C, Raynal B, Gilquin B, Chaffotte A, Pérez J, Zinn-Justin S, Delepierre M, Buc H, Cordier F, Wolff N (2014) Regulation of the catalytic activity of the human phosphatase PTPN 4 by its PDZ domain. The FEBS Journal 281:4852–4865

Maisonneuve P, Caillet-Saguy C, Vaney M-C, Bibi-Zainab E, Sawyer K, Raynal B, Haouz A, Delepierre M, Lafon M, Cordier F, Wolff N (2016) Molecular Basis of the Interaction of the Human Protein Tyrosine Phosphatase Non-receptor Type 4 (PTPN4) with the Mitogen-activated Protein Kinase p38 γ. Journal of Biological Chemistry 291:16699–16708

Mishra SH, Frueh DP (2015) Assignment of methyl NMR resonances of a 52 kDa protein with residue-specific 4D correlation maps. J Biomol NMR 62:281–290

Monneau YR, Rossi P, Bhaumik A, Huang C, Jiang Y, Saleh T, Xie T, Xing Q, Kalodimos CG (2017) Automatic methyl assignment in large proteins by the MAGIC algorithm. Journal of Biomolecular NMR 69:215–227

Mulder FAA (2009) Leucine side-chain conformation and dynamics in proteins from 13C NMR chemical shifts. Chembiochem : a European journal of chemical biology 10:1477–1479

Nerli S, De Paula VS, McShan AC, Sgourakis NG (2021) Backbone-independent NMR resonance assignments of methyl probes in large proteins. Nat Commun 12:691

Pritišanac I, Degiacomi MT, Alderson TR, Carneiro MG, AB E, Siegal G, Baldwin AJ (2017) Automatic Assignment of Methyl-NMR Spectra of Supramolecular Machines Using Graph Theory. Journal of the American Chemical Society 139:9523–9533

Pritišanac I, Würz JM, Alderson TR, Günter P (2019) Automatic structure-based NMR methyl resonance assignment in large proteins. Nat Commun 10:4922

Salzmann M, Pervushin K, Wider G, Senn H, Wüthrich K (2000) NMR Assignment and Secondary Structure Determination of an Octameric 110 kDa Protein Using TROSY in Triple Resonance Experiments. Journal of the American Chemical Society 122:7543–7548

Schanda P, Kupče Ē, Brutscher B (2005) SOFAST-HMQC Experiments for Recording Two-dimensional Determinuclear Correlation Spectra of Proteins within a Few Seconds. J Biomol NMR 33:199–211

Schanda P, Van Melckebeke H, Brutscher B (2006) Speeding Up Three-Dimensional Protein NMR Experiments to a Few Minutes. J Am Chem Soc 128:9042–9043

Sever AIM, Alderson TR, Rennella E, Aramini JM, Liu ZH, Harkness RW, Kay LE (2023) Activation of caspase-9 on the apoptosome as studied by methyl-TROSY NMR. Proc Natl Acad Sci USA 120:e2310944120

Shaka AJ, Keeler J, Freeman R (1983) Evaluation of a new broadband decoupling sequence: WALTZ-16. Journal of Magnetic Resonance (1969) 53:313–340

Shukla VK, Siemons L, Hansen DF (2023) Intrinsic structural dynamics dictate enzymatic activity and inhibition. Proc Natl Acad Sci USA 120:e2310910120
Siemons L, Mackenzie HW, Shukla VK, Hansen DF (2019a) Intra-residue methyl-methyl correlations for valine and leucine residues in large proteins from a 3D-HMBC-HMQC experiment. Journal of Biomolecular NMR 73:749-757

Siemons L, Uluca-Yazgi B, Pritchard RB, McCarthy S, Heise H, Hansen DF (2019b) Determining isoleucine side-chain rotamer-sampling in proteins from 13 C chemical shift. Chemical Communications 55:14107-14110

Sprangers R, Gribun A, Hwang PM, Houry WA, Kay LE (2005) Quantitative NMR spectroscopy of supramolecular complexes: Dynamic side pores in ClpP are important for product release. Proc Natl Acad Sci USA 102:16678-16683

Sprangers R, Kay LE (2007) Quantitative dynamics and binding studies of the 20S proteasome by NMR. Nature 445:618-622

Tugarinov V, Baber JL, Clore GM (2023) A methyl-TROSY based 13C relaxation dispersion NMR experiment for studies of chemical exchange in proteins. J Biomol NMR 77:83-91

Tugarinov V, Hwang PM, Ollerenshaw JE, Kay LE (2003) Cross-Correlated Relaxation Enhanced 1H-13C NMR Spectroscopy of Methyl Groups in Very High Molecular Weight Proteins and Protein Complexes. Journal of the American Chemical Society 125:10420-10428

Tugarinov V, Kay LE (2003a) Ile, Leu, and Val Methyl Assignments of the 723-Residue Malate Synthase G Using a New Labeling Strategy and Novel NMR Methods. Journal of the American Chemical Society 125:13868-13878

Tugarinov V, Kay LE (2003b) Side Chain Assignments of Ile δ1 Methyl Groups in High Molecular Weight Proteins: an Application to a 46 ns Tumbling Molecule. J Am Chem Soc 125:5701-5706

Tugarinov V, Sprangers R, Kay LE (2007) Probing Side-Chain Dynamics in the Proteasome by Relaxation Violated Coherence Transfer NMR Spectroscopy. Journal of the American Chemical Society 129:1743-1750

Vallet A, Favier A, Brutscher B (2019) Aromatic SOFAST-HMBC for proteins at natural 13C abundance. Journal of Magnetic Resonance 300:95-102

Venditti V, Fawzi NL, Clore GM (2011) Automated sequence- and stereo-specific assignment of methyl-labeled proteins by paramagnetic relaxation and methyl-methyl nuclear overhauser enhancement spectroscopy. J Biomol NMR 51:319-328