A methyl-TROSY based ¹³C relaxation dispersion NMR experiment for studies of chemical exchange in proteins

Abstract

A methyl Transverse Relaxation Optimized Spectroscopy (methyl-TROSY) based, multiple quantum (MQ) ¹³C Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion NMR experiment is described. The experiment is derived from the previously developed MQ ¹³C–¹H CPMG scheme (Korzhnev in J Am Chem Soc 126: 3964–73, 2004) supplemented with a CPMG train of refocusing ¹H pulses applied with constant frequency and synchronized with the ¹³C CPMG pulse train. The optimal ¹H ‘decoupling’ scheme that minimizes the amount of fast-relaxing methyl MQ magnetization present during CPMG intervals, makes use of an XY-4 phase cycling of the refocusing composite ¹H pulses. For small-to-medium sized proteins, the MQ ¹³C CPMG experiment has the advantage over its single quantum (SQ) ¹³C counterpart of significantly reducing intrinsic, exchange-free relaxation rates of methyl coherences. For high molecular weight proteins, the MQ ¹³C CPMG experiment eliminates complications in the interpretation of MQ ¹³C–¹H CPMG relaxation dispersion profiles arising from contributions to exchange from differences in methyl ¹H chemical shifts between ground and excited states. The MQ ¹³C CPMG experiment is tested on two protein systems: (1) a triple mutant of the Fyn SH3 domain that interconverts slowly on the chemical shift time scale between the major folded state and an excited state folding intermediate; and (2) the 82-kDa enzyme Malate Synthase G (MSG), where chemical exchange at individual Ile δ1 methyl positions occurs on a much faster time-scale.

Methyl Transverse Relaxation Optimized Spectroscopy (TROSY) (Tugarinov et al. 2003; Ollerenshaw et al. 2003) has had a significant impact on studies of protein structure and dynamics (Tugarinov et al. 2004; Ruschak and Kay 2010; Rosenzweig and Kay 2014; Schütz and Sprangers 2020). Studies of chemical exchange processes at methyl sites of high molecular weight proteins have particularly benefited from the better sensitivity and resolution of NMR spectra afforded by methyl-TROSY based applications (Korzhnev et al. 2004a; Religa et al. 2010; Rosenzweig and Kay 2014). Exchange processes occurring on the micro-to-millisecond time-scale, are commonly characterized by Carr-Purcell-Meiboom-Gill (CPMG) (Carr and Purcell 1954; Meiboom and Gill 1958) pulse schemes that modulate the effects of chemical exchange by application of a variable number of refocusing (180°) radiofrequency pulses during a constant-time relaxation period (Mulder et al. 2000). The changes in effective transverse spin relaxation rates, R_2,eff, induced by exchange, are quantified as a function of the frequency of application of refocusing pulses, and analysis of the resulting relaxation dispersion profiles enable one quantitatively characterize the kinetics of the exchange in terms of rate constants and chemical shift differences between the major (ground) an minor (excited) states.

One of the first NMR experiments that relied on methyl-TROSY principles was the methyl multiple quantum (MQ) (Mueller 1979; Bax et al. 1983) ¹³C–¹H CPMG relaxation dispersion scheme for studying exchange processes at methyl-bearing side chains of high molecular weight proteins (Korzhnev et al. 2004a, b). As both methyl ¹H and methyl ¹³C magnetizations are present in the transverse plane during the CPMG relaxation period in this experiment, the resulting dispersion profiles depend on the differences in both methyl ¹H (Δω_H) and ¹³C (Δω_C) chemical shifts between the inter-converting states. The interplay between Δω_H and Δω_C may lead to a significant reduction in exchange contributions to R₂ rates, R_ex, such that, in extreme cases, virtually flat dispersion profiles are obtained, or R_ex becomes negative (i.e. the rates R_2,eff increase for higher CPMG frequencies) (Korzhnev et al. 2004a, b). These complications pose a challenge for the quantitative analysis of MQ ¹³C–¹H CPMG relaxation dispersion: in particular, profiles of superb quality, that may be especially difficult to achieve for large proteins, are required to extract with confidence Δω_H, Δω_C, and the exchange rate constants from this data. Although a methyl-TROSY based ¹H CPMG experiment (Yuwen et al. 2019) that enables one to extract Δω_H for methyl groups of large proteins has been developed, and combined analysis of methyl MQ ¹³C–¹H and single-quantum (SQ) ¹³C CPMG dispersions for obtaining reliable Δω_H values in small proteins has been suggested (Korzhnev et al. 2005), recording of ‘pure’ methyl ¹³C CPMG (i.e. one reporting on Δω_C exclusively and not contaminated by Δω_H) in a multiple quantum manner is, to the best of our knowledge, not accessible with existing NMR methodology. Note that even though the SQ ¹³C CPMG experiment with improved sensitivity developed by Lundstrom et al. (2007) gives the option of MQ ¹³C–¹H acquisition in the indirect dimension (t₁), the ¹³C CPMG dispersion proper is obtained on SQ ¹³C coherences.

Here we describe a methyl ¹³C CPMG relaxation dispersion experiment that is recorded in a multiple-quantum manner (denoted as ‘MQ ¹³C CPMG’ in the following) and thus takes advantage of methyl-TROSY acquisition. The experiment represents the MQ ¹³C–¹H CPMG scheme (Korzhnev et al. 2004a) supplemented with a CPMG train of refocusing ¹H pulses applied with constant frequency during the ¹³C CPMG period and synchronized with the latter. Accumulation of minor imperfections of the refocusing pulses in the ¹H pulse-train inevitably leads to creation of a portion of methyl magnetization that relaxes fast and/or is unobservable at the end of the experiment (Korzhnev et al. 2005; Yuwen et al. 2019). The main purpose of this work may therefore be viewed as the design of an optimal and robust ¹H ‘decoupling’ scheme that minimizes the amount of fast-relaxing methyl magnetization created during the CPMG intervals. While for large proteins, the MQ ¹³C CPMG experiment eliminates complications in interpretation of MQ ¹³C–¹H CPMG dispersions associated with contributions to exchange from Δω_H, for small-to-medium sized protein systems, it has the advantage of significantly reducing intrinsic, exchange-free transverse relaxation rates of methyl magnetization relative to its SQ ¹³C counterpart.

The pulse scheme for recording methyl ¹³C CPMG relaxation dispersion in a multiple-quantum manner is shown in Fig. 1. The experiment is derived from the methyl-TROSY MQ ¹³C–¹H CPMG scheme developed earlier for studies of chemical exchange in high molecular weight proteins (Korzhnev et al. 2004a), and employs synchronous ‘decoupling’ of methyl ¹H magnetization during the relaxation period T by a train of refocusing, composite 180° ¹H pulses (Levitt and Freeman 1981) phase-cycled according to the XY-4 scheme (Gullion et al. 1990; Yuwen et al. 2019). This train of ¹H pulses eliminates contributions to exchange of methyl ¹H nuclei, so that, effectively, only exchange at methyl ¹³C positions is monitored. Prior to the constant-time CPMG period of total duration T, active selection of the slow-relaxing methyl ¹³C–¹H MQ (methyl-TROSY) transitions is achieved by the element of duration 2ζ (Fig. 1). The number of ¹³C CPMG cycles (spin-echoes) n is variable and determines the spacing between ¹³C refocusing pulses, 2δ, and, hence, the ¹³C CPMG frequency, ν_CPMG = n/T. The number of ¹H CPMG spin-echoes (cycles) m is constant and determines the spacing between refocusing ¹H pulses, 2Δ, and the corresponding frequency of ¹H ‘decoupling’, ${\nu }_{\mathrm{C}\mathrm{P}\mathrm{M}\mathrm{G}}^{\mathrm{H}}=m/T$ (note that m should be a multiple of 4 to accommodate XY-4 phase-cycling; see the period T/2 for n = 1 zoomed at the bottom of Fig. 1). The trains of ¹H pulses in Fig. 1 (one for each T/2 period) are implemented as two separate synchronous composite decoupling schemes, with delays Δ carefully adjusted to ensure that the total duration of the train of m 180° ¹H pulses (including pulse lengths) is equal to one half of the CPMG period, T/2 (the Bruker code for the pulse scheme in Fig. 1 is provided in the Supplementary Information, SI).

Fig. 1.

Methyl MQ ¹³C CPMG relaxation dispersion pulse scheme for selectively protonated ¹³CH₃ methyl groups. All narrow and wide rectangular pulses are applied with flip-angles of 90° and 180°, respectively, along the x-axis unless indicated otherwise. The ¹H carrier is positioned in the center of the Ile^δ1-Leu-Val (ILV) methyl region (0.3–0.5 ppm), while the ¹³C carrier is positioned at 20 ppm for ILV-labeled samples and at 12 ppm for Ile^δ1-labeled samples. All ¹H and ¹³C pulses are applied with the highest possible power, with WALTZ-16 ¹³C decoupling (Shaka et al. 1983) achieved using a 2.5-kHz RF field. Delays are as follows: ${\tau }_{\mathrm{a}}=1/\left(4^1{J}_{CH}\right)=2.0\mathrm{m}\mathrm{s}$; $\zeta =1/\left(8^1{J}_{CH}\right)=1.0\mathrm{m}\mathrm{s}$; T is a constant-time relaxation delay; the delay δ is equal to 1/2 of the spacing between ¹³C 180° pulses. The phase cycling is as follows: ϕ1 = x, – x; ϕ2 = 2(y), 2(–y); ϕ3 = 4(y), 4(– y); ϕ4 = x; receiver = x, – x, x, – x. The durations and strengths of pulsed-field z-gradients in units of (ms; G/cm) are: g1 = (1; 40), g2 = (0.5; 40), g3 = (0.4; 30). Quadrature detection in F₁ is achieved via States-TPPI incrementation (Marion et al. 1989) of phase ϕ4. The first period T/2 is zoomed at the bottom of the figure for n = 1 and shows explicitly the phases of the composite ¹H pulses in the XY-4 scheme (Gullion et al. 1990). The delay Δ is equal to 1/2 of the spacing between ¹H pulses. In the second half of the relaxation period T, the phase y is inverted, and the phase-cycling of the composite ¹H pulses is as follows: (x, – y, x), (y, x, y), (x, – y, x), (y, x, y). Details of experimental parameters are provided in the SI, ‘Materials and Methods’

Even though a constant number m of refocusing radio-frequency ¹H pulses is employed during the constant-time relaxation delay T in Fig. 1, imperfections and/or mis-calibrations of these pulses will inevitably result in the creation of some amount of fast-relaxing methyl magnetization (Korzhnev et al. 2005; Yuwen et al. 2019; Tugarinov et al. 2022) (i.e. of the outer MQ ¹³C–¹H transitions in ¹³CH₃ groups or ‘anti-methyl-TROSY’ components (Tugarinov et al. 2003)) that would in turn increase the ‘base’ effective relaxation rates (i.e. intrinsic, exchange-free R₂ rates) in CPMG dispersion profiles. Keeping this in mind, we investigated in detail the behavior of different types of ¹H pulses and phase-cycling schemes for ¹H ‘decoupling’ for protein molecules of differing sizes. Figure 2 shows full density matrix simulations of ¹H ‘decoupling’ schemes in the MQ ¹³C CPMG experiment of Fig. 1 in the absence of exchange for proteins with rotational correlation times, τ_C, of ~ 11 (A) and ~ 45 (B) ns, with ¹H pulses mis-set by 6.7% (6° for a 90° pulse). The CPMG profiles in the Left panels (marked with ‘X’) are generated without phase-cycling of the 180°_x pulses (black circles) or composite pulses of the 90°_y180°_x90°_y (blue circles) or 90°_y240°_x90°_y (red circles) variety (Levitt and Freeman 1981), while the profiles in the Right panels are generated with the same pulses phase-cycled according to the XY-4 scheme (see Fig. 1). It should be noted that in the first category of pulses (no phase-cycling, ‘X’), the composite pulses 90°_y180°_x90°_y perform the best (providing the lowest effective R₂ rates)—in agreement with predictions of Levitt and Freeman (1981) for CPMG trains with relatively small off-resonance effects, as is the case when the carrier frequency for high power ¹H ‘decoupling’ is placed at the center of the methyl ¹H region (typically, 0.3–0.5 ppm for ILV methyl groups).

Fig. 2.

Full density matrix simulations of ¹H ‘decoupling’ schemes in the MQ ¹³C CPMG experiment of Figure 1 in the absence of exchange for (A) a protein with rotational correlation time ${\tau }_{\mathrm{C}}\sim 11$ ns (T = 60 ms; ${\nu }_{\mathrm{C}\mathrm{P}\mathrm{M}\mathrm{G}}^{\mathrm{H}}=1.33\mathrm{k}\mathrm{H}\mathrm{z}(m=80)$), and (B) a protein with ${\tau }_{\mathrm{C}}\sim 45\mathrm{n}\mathrm{s}\left(T=40\mathrm{m}\mathrm{s};{\nu }_{\mathrm{C}\mathrm{P}\mathrm{M}\mathrm{G}}^{\mathrm{H}}=1.30\mathrm{k}\mathrm{H}\mathrm{z}(m=52)\right)$. ν_CPMG = n/T. The effects of three different ¹H refocusing pulse schemes are simulated: a 180_x° pulse (black circles), composite 90_y°180_x°90_y° pulses (blue circles), and composite 90_y°240_x°90_y° pulses (red circles). ‘X’ and ‘XY-4’ denote the absence of phase cycling and the phase cycling of these pulses according to the XY-4 scheme (see Fig. 1), respectively. The following spin relaxation rates of MQ ¹³C–¹H coherences in a ¹³CH₃ methyl group are assumed: slow-relaxing, central zero-quantum (ZQ) transitions—6 and 14 s⁻¹ for (A) and (B), respectively; slow-relaxing, central double-quantum (DQ) transitions—8 and 17 s⁻¹ for (A) and (B), respectively; fast-relaxing (outer) ZQ transitions—45 and 140 s⁻¹ for (A) and (B), respectively; fast-relaxing DQ transitions—55 and 170 s⁻¹ for (A) and (B), respectively. For simplicity, the relaxation rates of the magnetization involving DQ and triple-quantum (TQ) ¹H coherences, were not differentiated with respect to ¹³C spins: the relaxation rates of coherences involving ¹H DQ magnetization were set to 100 and 300 s⁻¹ for (A) and (B), respectively, while those involving TQ ¹H terms were set to 50 and 100 s⁻¹ for (A) and (B), respectively. All simulations were performed for a methyl group located 160 Hz and 400 Hz off-resonance from the ¹H and ¹³C carrier frequencies, respectively. A one-bond scalar coupling ¹J_CH = 125 Hz was used. 90° ¹H pulses were mis-set by 6° (6.7%), with the mis-setting values scaled proportionately for 180° and 240° ¹H pulses

The artifacts of ¹H decoupling (outlying values of R_2,eff rates) in all these cases (Left panels in Fig. 2, ‘X’) can be traced to modulation of the signal due to one-bond ¹³C–¹H scalar couplings, ¹J_CH ~ 125 Hz. Although the slow-relaxing methyl MQ magnetization (central, methyl-TROSY MQ transitions), isolated before the CPMG period in Fig. 1, is ‘immune’ to evolution due to ¹J_CH couplings (Tugarinov et al. 2003; Korzhnev et al. 2005), the fast- relaxing (‘anti-methyl-TROSY’) coherences created by imperfections of refocusing ¹H pulses, are not, and evolve in time t as, $\mathrm{c}\mathrm{o}\mathrm{s}\left(2{\pi }^1{J}_{\mathrm{C}\mathrm{H}}t\right)\pm i\mathrm{s}\mathrm{i}\mathrm{n}\left(2{\pi }^1{J}_{\mathrm{C}\mathrm{H}}t\right)$. Note that completely flat CPMG profiles (as expected in the absence of exchange) are produced when the value of ¹J_CH is set to 0 in these simulations. As we verified experimentally, these artifacts only occur for those CPMG cycles n where the (composite) 180° ¹H pulses coincide with ¹³C 180° pulses for all CPMG spin-echoes or (less likely) for a relatively large number of spin-echoes (> ~ 10), leading to uninterrupted ¹J_CH evolution for the whole time period T or a significant fraction of it. The former case corresponds to the ratio of pulse spacings δ/Δ (Fig. 1) equal to odd integers to within the lengths of ¹H and ¹³C 180° pulses. For example, for the set of parameters in the Left panel of Fig. 2A (τ_C ~ 11 ns; T = 60 ms; ${\nu }_{\text{CPMG}}^{\text{H}}=1.33\mathrm{k}\mathrm{H}\mathrm{z}(m=80)$), odd integer δ/Δ ratios (to within pulse lengths) occur for n = 16, 25, 26, 27 and 28.

When the XY-4 phase cycling scheme is employed (Right panels in Fig. 2), the amount of fast-relaxing magnetization and, consequently, the relaxation rates R_2,eff, are reduced substantially, with similar results predicted for the refocusing ¹H pulses of any variety—in agreement with the observations by Yuwen et al. (2019) where the XY-4 scheme proved indispensible for recording high-quality methyl ¹H CPMG relaxation dispersions for very high molecular weight proteins. The origin of the artifacts in exchange-free CPMG profiles employing the XY-4 scheme is likewise related to the evolution of the fast-relaxing components due to ¹J_CH scalar coupling, but is more subtle in nature. After each pair of XY pulses in the XY-4 scheme, the fast-relaxing components of methyl magnetization are inverted (converted from phase x to -x and vice versa) that is equivalent to apparent evolution of the ¹J_CH coupling for a time-period of 1/(2¹J_CH) = 4.0 ms to form an angle of 180° with respect to the phase of the starting magnetization. The artifacts in the Right panels of Fig. 2 only occur if the end of an XY sub-cycle (two ¹H spin-echoes of total length 4Δ) coincides with the end of a ¹³C spin-echo (cycle), which occurs when the ratio of pulse spacings δ/Δ (Fig. 1) is equal (to within ¹H pulse lengths) to (4 k—2), where k is any positive integer (i.e. δ/Δ = 2, 6, 10, 14… The amplitude of these artifacts is determined by how many ¹H spin-echoes can be ‘squeezed’ inside a single ¹³C spin-echo of duration 2δ, and decreases rapidly for larger ratios δ/Δ. Experimentally, we verified that only for δ/Δ ≈ 2, the artifactual rates R_2,eff exceed the uncertainties in R₂ measurements. (If a unit-less measure of the amplitude is defined as the ratio of the time-period of J inversion and the duration of each ¹³C spin-echo, $\lambda ={\left(4{\delta }^1{J}_{\mathrm{C}\mathrm{H}}\right)}^{-1}$, significant artifacts are observed in practice only for λ > ~ 5). For the parameters in the Right panels of Fig. 2A and B, the artifacts are predicted for the sets of n values of {38–44} and {25–28}, respectively. These values of n have to be excluded from the set of CPMG cycles used for recording relaxation dispersion profiles. Note that, as expected, the relative amplitudes of these artifacts decrease for larger proteins (higher τ_C values; cf. Right panels in Fig. 2A and B), since the fast-relaxing components of methyl MQ magnetization relax too rapidly to contribute appreciably to the observed signal in larger proteins.

The experiment in Fig. 1 was applied first to the study of exchange in a {U-[¹⁵N,²H]; Ile δ1-[¹³CH₃]; Leu,Val-[¹³CH₃,¹²CD₃]}-(ILV)-labeled sample of a triple A39V/N53P/V55L (VPL) mutant of the Fyn SH3 domain (Fyn SH3^VPL) that was shown previously to unfold spontaneously through a well-defined intermediate state in a temperature-dependent manner (Neudecker et al. 2012). At 10 °C, the population of the unfolded state of Fyn SH3^VPL is too low to be detected, and exchange can be adequately described by a 2-site equilibrium between the folded (F) and intermediate (I) states, $F\underset{\underset{k_{\text{IF}}}{\leftharpoondown }}{\overset{k_{\text{FI}}}{\rightharpoonup }}\text{I}$ (Neudecker et al. 2012; Libich et al.2015). A comparison of the relaxation dispersion profiles for the methyl sites of Fyn SH3^VPL (10 °C; 600 MHz) that have significant differences in methyl ¹H chemical shifts, Δω_H, between folded and intermediate states obtained with the SQ ¹³C CPMG scheme (Lundstrom et al. 2007), the MQ ¹³C CPMG experiment of Fig. 1, and the MQ ¹³C–¹H scheme (Korzhnev et al. 2004a) is shown in Fig. 3A. Contributions to exchange from Δω_H leading to substantial decreases in R_ex for the MQ ¹³C–¹H CPMG profiles (shown in black; note that for two of the methyl sites in Fig. 3A, R_ex < 0) are effectively eliminated in the MQ ¹³C CPMG profiles obtained with the experiment of Fig. 1 (red), and R_ex is determined exclusively by exchange at methyl ¹³C positions. A comparison of the MQ ¹³C CPMG profiles (red) with those obtained from the SQ ¹³C CPMG experiment (blue) shows that the former are characterized by significantly lower (1.75-fold on average for all methyl sites in Fyn SH3^VPL) ‘base’ effective transverse relaxation rates, i.e. values in the limit ${\nu }_{\text{CPMG}}\to \mathrm{\infty }$, R_2,∞. This constitutes the principal benefit of the MQ ¹³C CPMG experiment in Fig. 1 for small-to-medium sized proteins, as slower intrinsic (exchange-free) relaxation generally leads to an increase in R_ex and, hence, the information content of relaxation dispersion profiles. As illustrated in SI Figure S1, R_ex is increased twofold for the two extreme cases at the sites of mutations in Fyn SH3^VPL (L55 δ1 and V39 γ2). In addition, an odd number of CPMG cycles n can be used in the MQ ¹³C CPMG experiment of Fig. 1, effectively doubling the number of ν_CPMG frequencies accessible in the SQ ¹³C CPMG experiments, where even numbers of cycles for each T/2 period are recommended. We note that in agreement with simulations in Fig. 2, as long as the XY-4 phase-cycling is employed, very similar results are obtained with composite ¹H pulses of the 90°180°90° and 90°240°90° variety, with the former providing an ever so slightly lower R_2,∞ (by 3% on average; the data obtained with the 90°180°90° pulses are shown in Fig. 3).

Fig. 3.

Chemical exchange in Fyn SH3^VPL (10 °C) studied by methyl CPMG relaxation dispersion. A Relaxation dispersion profiles for the methyl sites of Fyn SH3^VPL (600 MHz) with significant differences in methyl ¹H chemical shifts, Δω_H, acquired with the SQ ¹³C CPMG scheme (Lundstrom et al. 2007) (shown in blue), the MQ ¹³C CPMG experiment of Fig. 1 (shown in red), and the MQ ¹³C–¹H scheme (Korzhnev et al. 2004a) (black). The profiles for each experiment obtained at 500, 600 and 800 MHz (500 and 800 data not shown) are globally best-fit to a two-state exchange model (see Figure S2 and SI ‘Materials and Methods’ for parameters of NMR acquisition and details of data analysis). B Correlation plots comparing (Left panel) the absolute differences in 8 methyl ¹³C chemical shifts between the folded (F) and intermediate (I) states, $\mathrm{\Delta }{\omega }_{\mathrm{C}}=\left|\mathrm{\Delta }{\omega }_{\mathrm{F}\mathrm{I}}\right|=\left|{\omega }_{\mathrm{I}}-{\omega }_{\mathrm{F}}\right|\left(\mathrm{p}\mathrm{p}\mathrm{m}\right)$, and (Right panel) the fitted R₂ rates in the limit ${\nu }_{\text{CPMG}}\to \mathrm{\infty }$, R_2,∞(s⁻¹), for 11 methyl groups, obtained with the experiment in Fig. 1 (x-axes) and the SQ ¹³C CPMG scheme of Lundström et al. (2007) (y-axes). The parameters of linear regression and Pearson linear correlation coefficients R are indicated in the plots. The black dashed lines corresponds to y = x, while the red solid lines are drawn using the parameters of linear regression indicated at the right bottom corner of each panel. Uncertainties in the fitted R_2,∞ rates are smaller than the sizes of the circles

Global fitting of 8 SQ ¹³C CPMG profiles obtained at 3 spectrometer fields (500, 600 and 800 MHz; see ‘Materials and Methods’ in the SI for details of analysis) with R_ex > ~ 2 s⁻¹, yields values of k_FI = 4.9 ± 0.1 s⁻¹ and k_IF = 215 ± 20 s⁻¹, translating to a fractional population (p_I) of 2.2 ± 0.2% for the folding intermediate. These parameters are very similar to those extracted from the global fit of MQ ¹³C CPMG profiles obtained with the scheme in Fig. 1: k_FI = 5.3 ± 0.1 s⁻¹ and k_IF = 238 ± 18 s⁻¹, translating to p_I of 2.2 ± 0.2%. SI Figure S2 shows selected examples of ¹³C SQ and ¹³C MQ relaxation dispersion profiles best-fit simultaneously at the three spectrometer fields. Although in the case of Fyn SH3^VPL at 10 °C, exchange is slow on the chemical shift time-scale for the majority of methyl sites ($R_{\mathrm{e}\mathrm{x}}\sim p_{\mathrm{I}}{k}_{\mathrm{e}\mathrm{x}}$, where $k_{\mathrm{e}\mathrm{x}}=k_{\mathrm{F}\mathrm{I}}+k_{\mathrm{I}\mathrm{F}}$, and virtually independent of Δω_C chemical shift differences), recording relaxation dispersion at three static magnetic fields validates the robustness of the ¹H ‘decoupling’ for a wide range of resonance offsets from the carrier.

A very slight stabilization of the folded state can be noted in comparison of these exchange parameters with those reported by us previously for the sample of Fyn SH3^VPL with practically the same deuteration scheme but dissolved in H₂O: k_FI = 9.0 ± 0.2 s⁻¹; k_IF = 350 ± 20 s⁻¹, and p_I = 2.5 ± 0.15% (Libich et al. 2015). This slight stabilization may be attributed to an isotope effect of the D₂O solvent that is well documented in the literature (for example, see Stadmiller and Pielak 2018; Parker and Clarke 1997; Pica and Graziano 2018). The effect is small in Fyn SH3^VPL because the minor state represents a folding intermediate as opposed to a fully unfolded species, with both rate constants decreasing in different proportions in D₂O. We note that in our recent methyl ¹H relaxation dispersion study in D₂O solvent (Tugarinov et al. 2022), much larger effects were observed for the Fyn SH3 G48M mutant that completely unfolds (reaching the state U) through an on-pathway intermediate: (k_ex = k_FU + k_UF = 629 ± 25 s⁻¹; p_U = 1.2 ± 0.2%) in D₂O versus (k_ex = 472 ± 38 s⁻¹; p_U = 3.8 ± 0.1%) reported earlier in H₂O solvent (Tugarinov and Kay 2007).

Figure 3B shows the correlation plots comparing the absolute changes in methyl ¹³C chemical shifts between the folded (F) and intermediate (I) states, $\mathrm{\Delta }{\omega }_{\mathrm{C}}=\left|\mathrm{\Delta }{\omega }_{\mathrm{F}\mathrm{I}}\right|=\mid {\omega }_{\mathrm{I}}-{\omega }_{\mathrm{F}}\mid$, and the fitted R₂ rates in the limit ${\nu }_{\mathrm{C}\mathrm{P}\mathrm{M}\mathrm{G}}\to \mathrm{\infty }$, R_2,∞, obtained for methyl groups of Fyn SH3^VPL from the global fit of relaxation dispersion profiles at 500, 600, and 800 MHz with the MQ ¹³C CPMG experiment (Fig. 1) and the SQ ¹³C CPMG scheme. Excellent correlation between the two sets of data is obtained for Δω_C (Fig. 3B, Left panel). The correlation between the MQ ¹³C CPMG-derived methyl Δω_C values and those reported previously for Fyn SH3^VPL by (Neudecker et al. 2012) is likewise very strong (Pearson R = 0.995), with only the largest Δω_C for Ile28 δ1 site (3.8 ± 0.2 ppm) over-estimated by ~ 15% in the MQ ¹³C CPMG-derived dataset. A somewhat weaker correlation is observed between the two experiments for the values of R_2,∞, with the MQ ¹³C CPMG-derived rates systematically lower than their SQ ¹³C CPMG-derived counterparts (Fig. 3B, Right panel). It is worth underscoring that even for a protein as small as Fyn SH3, the rates of decay of the slow-relaxing methyl-TROSY components, which are almost attained in the MQ ¹³C CPMG experiment (8.4 s⁻¹ on average), are ~ 43% lower on average than those of a mixture of fast- and slow-relaxing SQ ¹³C transitions quantified in the SQ ¹³C CPMG experiment. We predict that even for methyl sites with very large Δω_H values (> 0.5 ppm), the MQ ¹³C CPMG experiment of Fig. 1 will provide relaxation dispersion profiles that are independent of Δω_H, although an increase in the rates R_2,∞ for such methyl sites may be expected, as the employed ¹H CPMG frequencies (1.30–1.33 kHz) will not be sufficiently strong to completely quench the exchange on the ¹H nuclei.

Next, we tested the MQ ¹³C CPMG experiment of Fig. 1 for the study of exchange at Ile δ1 sites of a {U-[¹⁵N,²H]; Ile δ1-[¹³CH₃]}-labeled sample of the 82-kDa enzyme Malate Synthase G (MSG; 37 °C; τ_C ~ 45 ns in D₂O). Although 14 ¹³C relaxation dispersions with R_ex > ~ 2 s⁻¹ are observed for Ile δ1 methyls of MSG at 800 MHz, no global exchange process can be detected at these methyl positions. Figure 4 compares CPMG relaxation dispersion profiles obtained with the MQ ¹³C CPMG scheme of Fig. 1, the MQ ¹³C–¹H CPMG experiment and the SQ ¹³C scheme at the Ile δ1 methyl sites of MSG (800 MHz) with significant contributions to exchange from differences in ¹H chemical shifts, Δω_H, between ground and excited states. The data obtained with the 90°180°90° ¹H refocusing pulses are shown in Fig. 4, as this decoupling scheme provided slightly lower R_2,∞ than those for the 90°240°90° variety (by 4% on average). The same trends as for Fyn SH3^VPL (Fig. 3A) are observed. Namely, contributions to exchange from Δω_H leading to decreases in R_ex in the MQ ¹³C–¹H CPMG profiles (shown in black) are effectively eliminated in the MQ ¹³C CPMG data (red). For larger proteins such as MSG, however, the SQ ¹³C CPMG experiment (blue) becomes significantly less sensitive (see below) and compromised by excessively high SQ ¹³C R_2,∞ relaxation rates (included here only for the sake of comparison with the MQ ¹³C CPMG profiles). SI Figure S3 compares relaxation dispersion profiles obtained with the MQ ¹³C–¹H and MQ ¹³C CPMG experiments (800 MHz) for selected Ile δ1 sites of MSG with negligible contributions from Δω_H. These MQ ¹³C CPMG profiles are generally characterized by slightly higher R_2,∞ relaxation rates than their MQ ¹³C–¹H counterparts (by 8% on average for all quantifiable Ile δ1 methyl sites in MSG with negligible Δω_H) indicating that the XY-4 ¹H ‘decoupling’ in the experiment of Fig. 1 is slightly imperfect in the sense that a small amount of the fast-relaxing MQ magnetization is created and present during the CPMG interval T due to non-idealities of the ¹H refocusing pulses. Exchange parameters obtained from individual fitting of MQ ¹³C and MQ ¹³C–¹H CPMG profiles obtained at 600 and 800 MHz for Ile δ1 sites of MSG shown in Figs. 4 and S3, are summarized in Table S1.

Fig. 4.

CPMG relaxation dispersion profiles obtained for the Ile δ1 methyl sites of Malate Synthase G (MSG; 37 °C; 800 MHz) with significant contributions from differences in ¹H chemical shifts, Δω_H, between ground and excited states. The profiles obtained with the MQ ¹³C CPMG scheme of Fig. 1 are shown in red, while those shown in black and blue are acquired with the MQ ¹³C–¹H CPMG experiment (Korzhnev et al. 2004a) and the SQ ¹³C scheme (Lundstrom et al. 2007), respectively. The profiles for each experiment are best-fit individually to a two-state model of exchange using the data at 600 (not shown) and 800 MHz (see SI ‘Materials and Methods’, for details of the fitting procedures, and Table S1 for the best-fit parameters of exchange)

Although the majority of MQ ¹³C–¹H CPMG profiles obtained for Ile δ1 sites of MSG can be fit with the assumption that Δω_H = 0 (Korzhnev et al. 2004a) yielding reliable sets of exchange parameters, this is not the case for the profiles shown in Fig. 4 (see the first 4 rows of Table S1). Simulations using synthetic MQ ¹³C–¹H CPMG profiles in differentexchange regimes show that the assumption Δω_H = 0 is approximately valid (does not compromise the extracted Δω_C and other exchange parameters significantly) as long as $\left|\mathrm{\Delta }{\omega }_{\mathrm{H}}\right|$ does not exceed ~ 1/5 of $\left|\mathrm{\Delta }{\omega }_{\mathrm{C}}\right|$ (if the chemical shifts are expressed in rad/sec, i.e. ~ 5% of $\left|\mathrm{\Delta }{\omega }_{\mathrm{C}}\right|$ if expressed in ppm). For larger relative values of Δω_H, the assumption Δω_H = 0 can no longer be tolerated and provides significantly compromised parameters of exchange, with the values of rate constants (and populations of excited states) biased to a somewhat larger extent than those of Δω_C.

It is of interest to compare sensitivities of the CPMG experiments used in this work for small-to-medium sized (such as Fyn SH3^VPL at 10 °C) and larger (such as MSG at 37 °C) proteins. In the absence of the relaxation period (T = 0), the MQ ¹³C CPMG experiment of Fig. 1 is on average ~ 17% less sensitive than the SQ ¹³C CPMG scheme (implemented with MQ acquisition during the t₁ period (Lundstrom et al. 2007)) for Fyn SH3^VPL—primarily, because 1/2 of the methyl MQ magnetization is filtered out prior to CPMG relaxation period by the element of duration 2ζ in the scheme of Fig. 1. With the relaxation period T of 60 ms included, however, the MQ ¹³C CPMG scheme becomes more sensitive than its SQ counterpart by approximately the same proportion (17% on average for 17 ILV methyl sites in Fyn SH3^VPL) due to the almost twofold lower R_2,∞ relaxation rates in the former. For 38 Ile δ1 sites in MSG, the MQ ¹³C CPMG experiment of Fig. 1 has 7% and 48% higher signal-to-noise than its SQ ¹³C CPMG counterpart for T = 0 and T = 40 ms, respectively. We note that when the relaxation period T is omitted (T = 0), the MQ ¹³C CPMG scheme of Fig. 1 becomes practically identical to the MQ ¹³C–¹H CPMG experiment, implemented with active selection for the slow-relaxing (methyl-TROSY) magnetization components prior to the CPMG interval, and therefore has the same sensitivity for both proteins. Inclusion of the relaxation period T of 40 ms (with the concomitant XY-4 ¹H ‘decoupling’), makes the MQ ¹³C CPMG scheme on average ~ 18% less sensitive in comparison to its MQ ¹³C–¹H counterpart, indicating that approximately that fraction of the slow-relaxing methyl MQ magnetization is ‘lost’ (converted to fast-relaxing and/or undetectable methyl coherences) due to imperfections of the ¹H refocusing pulses. Taking into account that the filtering element of 2ζ duration (Fig. 1) is not necessary (may be omitted) in applications of the MQ ¹³C–¹H CPMG experiment to proteins with correlation times τ_C exceeding ~ 12 ns (Korzhnev et al. 2004a), we estimate that a further ~ 5% and ~ 10% loss in sensitivity will be incurred by the inclusion of this element in the MQ ¹³C CPMG scheme applied to a protein tumbling with τ_C ~ 45 ns (such as MSG) and τ_C ~ 120 ns, respectively. The total loss of sensitivity on the order of ~ 25% is certainly a ‘small price to pay’ for making methyl CPMG relaxation dispersion profiles amenable to reliable and unambiguous interpretation in terms of exchange parameters.

In summary, we have described a methyl-TROSY based ¹³C CPMG relaxation dispersion experiment (MQ ¹³C CPMG) for probing exchanging processes at methyl group sites which exhibit differences in ¹³C_methyl chemical shifts between ground and excited states. The experiment is derived from the MQ ¹³C–¹H CPMG scheme (Korzhnev et al. 2004a) supplemented with a CPMG train of refocusing ¹H pulses applied with a constant frequency and synchronized with the ¹³C CPMG pulse train. Even minor imperfections of the refocusing pulses in the ¹H pulse-train inevitably lead to creation of methyl magnetization components that relax fast and/or are unobservable at the end of the experiment. The optimal ¹H ‘decoupling’ scheme that minimizes the amount of fast-relaxing methyl MQ magnetization present during the CPMG intervals, makes use of an XY-4 phase cycling of composite ¹H pulses. The experiment is applied to two protein systems: (1) the ILV-labeled triple mutant of Fyn SH3 domain (Fyn SH3^VPL) that, at 10 °C, interconverts slowly on the chemical shift time scale between the folded state and a folding intermediate, and (2) an 82-kDa enzyme Malate Synthase G (MSG; 37 °C), where exchange at Ile δ1 methyl sites does not represent a global process and generally occurs on a much faster time-scale. While for small-to-medium sized proteins, the MQ ¹³C CPMG experiment has the advantage over its SQ ¹³C counterparts of significantly reducing intrinsic, exchange-free relaxation rates (R_2,∞), for high molecular weight systems, it eliminates the major complications in interpretation of MQ ¹³C–¹H CPMG relaxation dispersion profiles arising from contributions to exchange from differences in ¹H chemical shifts, Δω_H, which can be, if needed, obtained from a separate methyl-TROSY based ¹H CPMG relaxation dispersion experiment (Yuwen et al. 2019).

Supplementary Material

The online version contains supplementary material available at https://doi.org/10.1007/s10858-023-00413-8.