A methyl ¹H double quantum CPMG experiment to study protein conformational exchange

Abstract

Protein conformational changes play crucial roles in enabling function. The Carr–Purcell–Meiboom–Gill (CPMG) experiment forms the basis for studying such dynamics when they involve the interconversion between highly populated and sparsely formed states, the latter having lifetimes ranging from ~ 0.5 to ~ 5 ms. Among the suite of experiments that have been developed are those that exploit methyl group probes by recording methyl ¹H single quantum (Tugarinov and Kay in J Am Chem Soc 129:9514–9521, 2007) and triple quantum (Yuwen et al. in Angew Chem Int Ed Engl 55:11490–11494, 2016) relaxation dispersion profiles. Here we build upon these by developing a third experiment in which methyl ¹H double quantum coherences evolve during a CPMG relaxation element. By fitting single, double, and triple quantum datasets, akin to recording the single quantum dataset at static magnetic fields of B_o, 2B_o and 3B_o, we show that accurate exchange values can be obtained even in cases where exchange rates exceed 10,000 s⁻¹. The utility of the double quantum experiment is demonstrated with a pair of cavity mutants of T4 lysozyme (T4L) with ground and excited states interchanged and with exchange rates differing by fourfold (~ 900 s⁻¹ and ~ 3600 s⁻¹), as well as with a fast-folding domain where the unfolded state lifetime is ~ 80 µs.

Introduction

Conformational dynamics are a ubiquitous feature of proteins and are essential for their function. A description of the conformations that are sampled by a protein, therefore, is important (Austin et al. 1975; Frauenfelder et al. 1991; Karplus and Kuriyan 2005; Rosenzweig et al. 2017; Xie 2002), yet in many cases such a description has proven elusive as key states are often sparsely populated and only transiently formed. In such cases the Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion NMR experiment (Carr and Purcell 1954; Meiboom and Gill 1958) is particularly powerful since conformational states that are populated to as low as 0.5% and with lifetimes ranging from ~ 0.5 to 5 ms can be detected and characterized at atomic detail. (Palmer et al. 2001; Sauerwein and Hansen 2015; Sekhar and Kay 2013; Zhuravleva and Korzhnev 2017). Indeed, atomic resolution structural models of minor states have been obtained in some cases from CPMG-based studies of exchanging systems (Bouvignies et al. 2011; Hansen et al. 2008b; Korzhnev et al. 2010; Neudecker et al. 2012; Vallurupalli et al. 2008), and CPMG analyses have provided insights into a diverse range of processes that include protein folding and aggregation, ligand binding and enzyme mechanism (Delaforge et al. 2018; Eisenmesser et al. 2005; Korzhnev et al. 2004, 2010; Kovrigin and Loria 2006; Neudecker et al. 2012; Sugase et al. 2007; Tugarinov et al. 2015). It is noteworthy that detection of such minor, short-lived (so called excited) states by conventional biophysical techniques is most often not possible, and in the case of NMR studies, only peaks derived from the highly-populated ground state conformer are observed.

The power of the CPMG experiment lies in the fact that excited states can be studied indirectly through the visible ground state. This is achieved by quantifying the relaxation of transverse magnetization during the course of a fixed interval where variable numbers of chemical shift refocusing pulses are applied (Mulder et al. 2001b). The resultant curve plotting the effective transverse relaxation rate, R_2,eff, versus ν_CPMG, where ν_CPMG = 1/(4τ_CPMG) and 2τ_CPMG is the spacing between successive refocusing pulses, is referred to as a relaxation dispersion profile that is analyzed using a model of chemical exchange to extract, in the case of a two-site exchange reaction, the exchange rate, k_ex, and the fractional minor state population, p_E, along with absolute values of chemical shift differences |Δω| (rad s⁻¹) between the major and minor state resonances. Often accurate exchange parameters (p_E, k_ex) and |Δω| values cannot be obtained from CPMG data collected at a single static magnetic field but require an analysis of data recorded at two well-separated fields. The improved fitting robustness when multiple field data are analyzed reflects the fact that Δω scales with field strength while the kinetic parameters do not change, reducing correlations between the extracted parameters.

¹³CH₃ methyl groups present an interesting and powerful probe of conformational exchange because it is possible to exploit the three equivalent protons in this spin system to record different classes of ¹H CPMG dispersion profiles that may obviate the requirement of multiple field data. For example, we have previously shown that single (SQ) (Tugarinov and Kay 2007) and triple (TQ) quantum (Yuwen et al. 2016) methyl ¹H CPMG dispersion profiles can be recorded that depend on Δω (SQ) and 3Δω (TQ), respectively, reflecting the fact that SQ and TQ transitions involve 1 and 3 quanta, respectively, Fig. 1. The TQ experiment increases the sensitivity of the dispersion technique to exchange processes that involve small chemical shift differences between converting states, as well as facilitating the study of faster exchange processes than would otherwise be possible using the more traditional SQ class of experiment (Yuwen et al. 2016). An additional advantage of the TQ experiment in relation to its SQ counterpart is one of sensitivity. As discussed in detail previously, the application of a ¹H 180° refocusing train during the CPMG period leads to artifacts in SQ experiments that do not eliminate signal from the 3/2 manifold (Korzhnev et al. 2005). This results from the fact that in methyl groups the fast and slowly relaxing ¹H transitions (Figs. 1, 3/2 manifold) are interconverted due to pulse imperfections that lead to non-flat dispersion profiles even in the absence of chemical exchange. As a result an experiment was developed that selects signal from only the spin ½ manifolds (Fig. 1) where such an effect cannot occur (Tugarinov and Kay 2007). The resulting dispersions are artifact-free but the sensitivity of the experiment is reduced considerably to approximately 1/10th that of the TQ CPMG (Yuwen et al. 2016). We were interested, therefore, in developing a double quantum (DQ) scheme that could be used in applications where the sensitivity of the SQ experiment was limiting. As DQ-CPMG profiles are sensitive to chemical shift differences of 2Δω it is expected that a combined analysis of DQ and TQ data sets would provide similar benefits to data obtained at multiple fields. This is of particular importance in NMR laboratories where only a single static magnetic field is available, such as is the case for a subset of the authors of the present paper (ABG and PV). We were also interested in establishing whether it would be possible to extend studies to faster exchange processes by a combined analysis of DQ and TQ CPMG data. Here we present a methyl ¹H DQ CPMG pulse scheme and demonstrate its utility using two cavity mutants of T4 lysozyme (T4L, 18 kDa) in which a hydrophobic residue interconverts between conformers that place it either inside or out of the cavity (Bouvignies et al. 2011; Vallurupalli et al. 2016). In the first cavity mutant a Leu at position 99 has been replaced by Ala, referred to as T4L L99A (Baase et al. 2010; Eriksson et al. 1992), while in the second construct the three mutations L99A, G113A, R119P are used (referred to as T4Ltm) (Bouvignies et al. 2011). A third system, the fast-folding peripheral subunit binding domain (PSBD) of the acetyl transferase from Bacillus stearothermophilus (4.7 kDa) that interconverts between folded and unfolded conformations (Vugmeyster et al. 2000) is studied as well. Our results establish that a combined analysis of DQ and TQ CPMG datasets provides more robust measures of exchange parameters for fast exchanging systems as PSBD (k_ex ~ 12,000 s⁻¹) than when TQ CPMG data from a single field exclusively is analyzed, removing the correlation between p_E and Δω values that is otherwise present.

Fig. 1

Energy level diagram of an X₃ spin system, separating levels according to the net spin angular momentum of each state |j〉 (indicated below) and highlighting ¹H SQ, DQ and TQ coherences. SQ (purple, red), DQ (green) and TQ (blue) coherences can be excited within the spin 3/2 manifold. Single quantum transitions relax very differently in the macromolecular limit (Kay and Torchia 1991; Tugarinov et al. 2003, 2006) and have been labeled as SQ_fast (purple, fast relaxing) and SQ_slow (red, slow relaxing). ZQ coherences are not depicted but are contained within the |2><2| and |3><3| elements of the 3/2 manifold, and within other elements in each of the ½ manifolds. However, as the DQ coherences are those of interest and these are only generated within the 3/2 manifold, only elements within this manifold need be considered as pulses cannot interconvert density elements in separate manifolds. Each of the levels depicted in the figure is further split due to scalar coupling involving the attached methyl ¹³C spin

Materials and methods

Sample preparation

U-[²H,¹⁵N], Ileδ1-[¹³CH₃], Leu,Val-[¹³CH₃,¹²CD₃]-labeled T4L wild-type (T4L), T4L L99A, T4Ltm and PSBD were expressed in E. coli BL21(DE3) cells grown in 100% D₂O M9 media with 1 g L^{−1 15}NH₄Cl and 3 g L⁻¹ U-[²H,¹²C] glucose as the sole nitrogen and carbon sources. Appropriate precursors were added to the media one hour before induction (Goto et al. 1999; Ollerenshaw et al. 2005; Tugarinov and Kay 2005). The proteins were purified by ion exchange chromatography followed by size exclusion chromatography as described previously (Gopalan and Vallurupalli 2018; Vallurupalli et al. 2009). The T4L samples comprised ~ 1.5 mM protein dissolved in a 50 mM NaH₂PO₄, 25 mM NaCl, 2 mM EDTA, 2 mM NaN₃, 10% D₂O, pH 5.5 buffer. The concentration of protein in the PSBD sample was under 0.5 mM, dissolved in 50 mM NaH₂PO₄, 25 mM NaCl, 2 mM EDTA, 2 mM NaN₃, 10% D₂O, pH 6.5 buffer.

NMR experiments

All experiments were performed on a Bruker Avance III HD 700 MHz spectrometer equipped with a cryogenically cooled probe. Methyl (¹³CH₃) ¹H SQ and TQ experiments were performed using published pulse sequences (Tugarinov and Kay 2007; Yuwen et al. 2016), while the DQ CPMG experiment was recorded as described below. A constant-time CPMG relaxation delay (T_relax) of 20 ms was used for methyl ¹H SQ, DQ and TQ CPMG experiments recorded on T4L L99A, along with ν_CPMG values in the range 50–1500 Hz. T_relax was set to 10 ms for the DQ and TQ CPMG experiments recorded on T4Ltm and PSBD samples and 15 ms for the SQ CPMG experiment recorded on the T4Ltm sample with ν_CPMG values between 100 and 2000 Hz. Amide ¹H^N and ¹⁵N CPMG data were recorded on PSBD at 41 °C to demonstrate the accuracy of exchange parameters extracted from the methyl ¹H DQ experiment, as described below. ¹H^N CPMG data were recorded using a pulse scheme that does not contain a P-element (Ishima and Torchia 2003; Vallurupalli et al. 2011) and the ¹⁵N TROSY CPMG experiment (Loria et al. 1999b; Vallurupalli et al. 2007) was used to record amide ¹⁵N data. T_relax was set to 15 ms, ν_CPMG values ranged between 133 and 2467 Hz in the ¹H^N CPMG experiment and between 67 and 1000 Hz in the ¹⁵N CPMG experiment.

Pseudo-3D CPMG datasets were recorded using 12–15 different ν_CPMG values in an interleaved manner with an inter-scan delay of 2.25 s and 2–3 repetitions for error estimation (Gopalan et al. 2018; Korzhnev et al. 2004). The total acquisition time for each dataset varied between 10 and 16 h except for measurements on the dilute PSBD sample that required up to 27 h.

Data analysis

All NMR data was processed using NMRPipe (Delaglio et al. 1995), spectra were visualized with SPARKY (Goddard and Kneller 2008; Lee et al. 2015) and the program PINT (Ahlner et al. 2013) was used for integrating peaks and computing intensities as a function of ν_CPMG, I(ν_CPMG). R_2,eff rates were calculated for each ¹H or ¹⁵N site according to (Mulder et al. 2001b),

$${R_{2,eff}}\left( {{\nu _{CPMG}}} \right)=\frac{{ - 1}}{{{T_{relax}}}}ln\left( {\frac{{I\left( {{\nu _{CPMG}}} \right)}}{{{I_o}}}} \right)$$

(1)

where I_o is the intensity of the peak in a reference plane recorded without the T_relax delay.

Exchange parameters were obtained from the experimental data via a standard best-fit procedure using the program ChemEx (Bouvignies 2011) that integrates the Bloch–McConnell equations (McConnell 1958) numerically (Korzhnev et al. 2004) to minimize the function ${\chi ^2}=\mathop \sum \nolimits_{{i=1}}^{N} {\left[ {\left( {I_{i}^{{Exp}} - I_{i}^{{Calc}}} \right)/{\sigma _i}} \right]^2}$, where $I_{i}^{{Exp}}$ are the experimentally measured peak intensities, $I_{i}^{{Calc}}$ are the intensities calculated by integrating the Bloch-McConnell equations numerically and ${\sigma _i}$ is the uncertainty in the experimentally measured intensity value. Uncertainties in the fitted parameters were estimated using 1000 trials of standard Monte Carlo or bootstrap analysis (Press et al. 1992). In the simplest version of the fitting procedure DQ data is analyzed in a manner similar to SQ data, but with the evolution frequencies and ¹J_CH (one bond ¹³C–¹H scalar coupling) values doubled (Yuwen et al. 2016) so that magnetization evolves under chemical exchange ($G{\mathop{\leftrightarrows}\limits^{k_{EG}}_{k_{GE}}}E$) according to

$$\frac{d}{{dt}}\left[ {\begin{array}{*{20}{c}} {M_{{AP}}^{G}} \\ {M_{{IP}}^{G}} \\ {M_{{AP}}^{E}} \\ {M_{{IP}}^{E}} \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} { - 2i{\Omega _G} - R_{{2\infty ,AP}}^{{DQ}} - {k_{GE}}}&{ - 2i{\pi ^1}{{\text{J}}_{{\text{CH}}}}}&{{k_{EG}}}&0 \\ { - 2i{\pi ^1}{{\text{J}}_{{\text{CH}}}}}&{ - 2i{\Omega _G} - R_{{2\infty ,IP}}^{{DQ}} - {k_{GE}}}&0&{{k_{EG}}} \\ {{k_{GE}}}&0&{ - 2i{\Omega _E} - R_{{2\infty ,AP}}^{{DQ}} - {k_{EG}}}&{ - 2i{\pi ^1}{{\text{J}}_{{\text{CH}}}}} \\ 0&{{k_{GE}}}&{ - 2i{\pi ^1}{{\text{J}}_{{\text{CH}}}}}&{ - 2i{\Omega _E} - R_{{2\infty ,IP}}^{{DQ}} - {k_{EG}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {M_{{AP}}^{G}} \\ {M_{{IP}}^{G}} \\ {M_{{AP}}^{E}} \\ {M_{{IP}}^{E}} \end{array}} \right].$$

(2)

In Eq. (2) $M_{{IP}}^{{}}=\frac{1}{2}\left( {H_{+}^{1}H_{+}^{2}+H_{+}^{2}H_{+}^{3}+H_{+}^{3}H_{+}^{1}} \right)$ and $M_{{AP}}^{{}}={C_Z}\left( {H_{+}^{1}H_{+}^{2}+H_{+}^{2}H_{+}^{3}+H_{+}^{3}H_{+}^{1}} \right)$ are methyl ¹H DQ coherences that are in-phase (IP) or anti-phase (AP) with respect to the methyl ¹³C spin, respectively, Ω_G (Ω_E) is the difference between the resonance frequency of a spin in the ground (excited) state and the carrier frequency (rad/s), and $R_{{2\infty ,IP}}^{{DQ}}$, $R_{{2\infty ,AP}}^{{DQ}}$ are the intrinsic relaxation rates of IP and AP DQ coherences, respectively. In the derivation of Eq. (2) we have not included cross relaxation between IP and AP DQ coherences that arises from intra-methyl ¹H–¹H, ¹H–¹³C cross-correlated dipolar interactions. Simulations show that such effects are small (see Supporting Information). Fitting parameters for the DQ experiment include the global values k_ex = k_GE + k_EG and the fractional population of the excited state p_E (p_G + p_E = 1), with residue specific chemical shift differences Δϖ (ppm) and $R_{{2\infty ,IP}}^{{DQ}}$ fit as well. In general, methyl ¹H DQ CPMG profiles are fit along with SQ and TQ curves that require additional fitting parameters $R_{{2\infty ,IP}}^{{SQ}}$ and $R_{{2\infty ,IP}}^{{TQ}}$. The differences in the relaxation rates between the IP and AP DQ and TQ coherences $\Delta R_{{IP - AP}}^{{DQ}}=R_{{2\infty ,IP}}^{{DQ}} - R_{{2\infty ,AP}}^{{DQ}}$ and $\Delta R_{{IP - AP}}^{{TQ}}=R_{{2\infty ,IP}}^{{TQ}} - R_{{2\infty ,AP}}^{{TQ}}$ are related to each other according to $\Delta R_{{IP - AP}}^{{DQ}} \approx \frac{1}{3}{{{\Delta}}}R_{{IP - AP}}^{{TQ}}$. $\Delta R_{{IP - AP}}^{{TQ}}$ can be measured, as described earlier (Yuwen et al. 2016), from which $\Delta R_{{IP - AP}}^{{DQ}}$ is obtained using the above relation. As $\Delta R_{{IP - AP}}^{{TQ}}$ values are small, ~ 0.6 s⁻¹ for T4Ltm at 15 °C and ~ 1.3 s⁻¹ for PSBD at 41 °C, we find that the same exchange parameters are obtained even when $\Delta R_{{IP - AP}}^{{TQ}}$ (or $\Delta R_{{IP - AP}}^{{DQ}}~$ in the case when only DQ data is analyzed) is treated as an additional fitting parameter or when it is set to a reasonable value (~ 1 s⁻¹).

Results and discussion

Figure 1 illustrates the energy level diagram for a spin system comprising three equivalent protons, as in a methyl group. For the case of ¹³CH₃ methyls, considered here, each of the energy levels is further split by the spin state of the ¹³C (not shown). Notably, there are a number of distinct ¹H transitions that can be distinguished on the basis of their relaxation properties or frequencies. These include SQ transitions that relax either rapidly (purple) or slowly (red) (Kay and Prestegard 1987; Tugarinov et al. 2003; Werbelow and Marshall 1973a, b) as well as the DQ (green) and TQ (blue) transitions that were mentioned in the Introduction. Previous pulse schemes have isolated either SQ_slow transitions from the spin ½ manifolds (Tugarinov and Kay 2007) or TQ transitions (Yuwen et al. 2016) in the context of ¹H CPMG experiments and we focus here on the corresponding ¹H DQ experiment.

Figure 2 illustrates the methyl ¹H DQ CPMG experiment that we have developed. In the brief description of the pulse scheme that follows we label each of the protons as 1, 2 or 3 to distinguish them and follow the trajectory of the coherences of interest throughout the sequence, neglecting the effects of pulse imperfections and spin relaxation. Starting from equilibrium, ¹H magnetization, $H_{z}^{1}+H_{z}^{2}+H_{z}^{3}$ (point A), is subsequently evolved during a refocused INEPT element (Morris and Freeman 1979) to generate $4\left( {H_{z}^{2}H_{z}^{3}+H_{z}^{1}H_{z}^{3}+H_{z}^{1}H_{z}^{2}} \right){C_z}$ at point B. The subsequent ¹H 90° pulse at point C converts the longitudinal order ¹H components into an equal combination of ZQ and DQ coherences at the start of the CPMG period that can be readily noted by considering the action of a ¹H pulse of phase ϕ₁ = x,

Fig. 2

Pulse sequence for measurement of methyl ¹H DQ CPMG relaxation dispersion profiles on highly deuterated, ¹³CH₃ labeled proteins. Narrow (wide) black bars denote 90° (180°) pulses, applied along the x-axis unless otherwise indicated, while grey bars indicate z-pulsed field gradients. All pulses are applied at the highest possible power level except for the ¹H pulses during the CPMG period where a ~ 22 kHz field was used. The ¹H carrier is set to the water resonance for the EBURP-1 pulse (Geen and Freeman 1991) at the start of the experiment (shaped pulse) and subsequently moved to the center of the ILV methyl resonance region ~ 0.8 ppm for the rest of the experiment. ²H and ¹³C carriers are placed at ~ 0.8 ppm and ~ 18 ppm, respectively. The delay τ_a is set to 1/(4¹J_CH) (2 ms). ¹³C and ²H WALTZ-16 decoupling (Shaka et al. 1983) elements are applied with B₁ field strengths of ~ 1.8 and ~ 0.55 kHz, respectively; ²H decoupling is required only when ν_CPMG values < 100 Hz are used (Yuwen et al. 2016). Phases are cycled as: ϕ₁ = − 45°, 45°; ϕ₂ = 45°, 135°; ϕ₃ = 2y, 2(− y); ϕ₄ = − 45°; ϕ₅ = 4x, 4(− x); ϕ₆ = x; ϕ₇ = x, − x; receiver = 2(x, − x), 2(− x, x). Phases of the CPMG pulses were incremented according to the XY-16 scheme (Gullion et al. 1990) by varying Ψ₁ and Ψ₂ as described previously (Yuwen et al. 2016). Briefly the phases of the (regular, i.e., not composite) π pulses in the first half of the CPMG train are incremented according to Ψ₁ = (x,y,x,y,y,x,y,x,− x,− y,− x,− y,− y,− x,− y,− x) followed by the central π_ϕ3 pulse, after which Ψ₂ is decremented in the reverse order of the increase in Ψ₁ and phases y and –y are inverted to reduce off-resonance effects (Hansen et al. 2008a). Thus the scheme is: ${\tau _{{\text{CP}}}}{\Pi _1}{\tau _{{\text{CP}}}}{\tau _{{\text{CP}}}}{\Pi _2}{\tau _{{\text{CP}}}} \ldots {\tau _{{\text{CP}}}}{\Pi _{{\text{k}} - 1}}{\tau _{{\text{CP}}}}{\tau _{{\text{CP}}}}{\Pi _{\text{k}}}{\tau _{{\text{CP}}}}{\Pi _{\Phi 3}}{\tau _{{\text{CP}}}}{\bar {\Pi }_{\text{k}}}{\tau _{{\text{CP}}}}{\tau _{{\text{CP}}}}{\bar {\Pi }_{{\text{k}} - 1}}{\tau _{{\text{CP}}}} \ldots {\tau _{{\text{CP}}}}{\bar {\Pi }_2}{\tau _{{\text{CP}}}}{\tau _{{\text{CP}}}}{\bar {\Pi }_1}{\tau _{{\text{CP}}}}$ where ${\Pi _1}$ is ${\Pi _{\text{x}}}$, ${\Pi _2}$ is ${\Pi _{\text{y}}}$ and so on according to the XY-16 scheme (Ψ₁). ${\bar {\Pi }_{\text{k}}}$ is obtained from ${\Pi _{\text{k}}}$ by replacing y with − y and − y with y. ¹³C t₁ evolution is carried out in a shared constant time manner (Grzesiek and Bax 1993; Logan et al. 1993), as indicated. Complex data in the indirect dimension is obtained by incrementing ϕ₆ and the receiver in a States-TPPI manner (Marion et al. 1989). Gradients (Strengths in G/cm: durations in µs) are: g₀ (10:1000), g₁ (12.5:300), g₂ (13.5:500), g₃ (15:300), g₄ (20:500), g₅ (25:500), g₆ (18.5:300), g₇ (− 25:500). Water suppression is achieved via the ~ 8 ms water selective EBURP-1 pulse followed by the g₀ gradient to destroy water magnetization at the start of the sequence and by the 3-9-19 WATERGATE scheme during the last INEPT (Sklenar et al. 1993)

$$\mathop \sum \limits_{{i < j}}^{{}} 4H_{z}^{i} H_{z}^{j} C_{z}^{{}} \xrightarrow{{{}_{{}}^{1} H~\left( {\frac{\pi }{2}} \right)_{x} }}\mathop \sum \limits_{{i < j}}^{{}} 4H_{y}^{i} H_{y}^{j} C_{z}^{{}} = \mathop \sum \limits_{{i < j}}^{{}} \left( {H_{ + }^{i} H_{ - }^{j} + H_{ - }^{i} H_{ + }^{j} - H_{ + }^{i} H_{ + }^{j} - H_{ - }^{i} H_{ - }^{j} } \right)C_{z}^{{}}$$

(3)

The relevant DQ terms $\left( {H_{+}^{i}H_{+}^{j}+H_{ - }^{i}H_{ - }^{j}} \right){C_z}$ are selected by a two-step cycle of ϕ₁ that filters out the ZQ coherences (Bain 1984; Cavanagh et al. 2006; Ernst et al. 1987; Gopalan and Vallurupalli 2018). After the T_relax delay ¹³C chemical shift is recorded during a t₁ interval with the subsequent transfer of magnetization back to ¹H for detection. Here, as in the methyl ¹H TQ CPMG experiment (Yuwen et al. 2016) and other ¹H CPMG experiments (Orekhov et al. 2004; Vallurupalli et al. 2011), we have chosen not to use a P-element (Loria et al. 1999a) to compensate for differential relaxation between DQ coherences that are in- and anti-phase with respect to ¹³C because the difference between the two rates is sufficiently small ($\Delta R_{{IP - AP}}^{{DQ}}$ < 1.5 s⁻¹, see Materials and methods section) that it can be readily accounted for in the fitting procedure after it is estimated from $\Delta R_{{IP - AP}}^{{TQ}}~$ (Yuwen et al. 2016) and because the extra delays introduced by the P-element reduce the sensitivity of the experiment.

The main sources of relaxation of methyl ¹H DQ coherences are dipolar interactions with external protons as well as interactions involving intra-methyl ¹³C–¹H and ¹H–¹H dipole pairs (see Supporting Information). External contributions can be minimized by using a highly ²H-enriched sample where only one of the two prochiral methyl groups of Leu and Val is labeled, as has been done here (see Materials and methods section). The ²H, ¹²C labelled background ensures the absence of homonuclear ¹H–¹H scalar couplings that would deteriorate the quality of the ¹H dispersion profiles; elimination of ¹³C–¹³C scalar couplings is also important to the sensitivity and resolution of the resulting dispersion datasets. Based on similar considerations, an identical labeling scheme has been used for methyl ¹H TQ CPMG experiments as well (Yuwen et al. 2016).

As a first test of the pulse scheme we wanted to establish that flat dispersion profiles are obtained for non-exchanging methyl sites. To this end we considered PSBD (~ 5 kDa) and identified eight methyl groups that were not sensitive to the exchange between folded and unfolded forms in this system, as established by flat dispersion curves from the TQ CPMG scheme ($R_{{2,eff}}^{{TQ}}\left( {100~{\text{Hz}}} \right) - R_{{2,eff}}^{{TQ}}\left( {2000~{\text{Hz}}} \right)$ ≤ 2 s⁻¹). As shown in Fig. 3a dispersion profiles are obtained with root-mean-squared-differences (RMSD) < 0.7 s⁻¹ between experimental R_2,eff values and values of the best fit horizontal lines. The replacement of ‘simple’ refocusing 180° pulses (referred to as ‘regular’) with composite pulses also results in flat dispersion profiles. The situation is different when the DQ experiment is recorded on a sample of wild-type T4 lysozyme, T4L (Baase et al. 2010), an 18 kDa protein that has been shown previously not to exchange within the millisecond time window. Although flat dispersion profiles were expected due to the absence of chemical exchange, we found small, non-flat $\Delta R_{{2,eff}}^{{DQ}}\left( {{\nu _{CPMG}}} \right)$ profiles for all peaks when composite pulses were used in the CPMG train (Fig. 3b). These apparent dispersions were significantly less pronounced with regular refocusing pulses. Simulations show that during a CPMG pulse, starting DQ coherence evolves into diagonal density elements that include ZQ and in addition, while net SQ magnetization does not build up, the density elements connecting the fast-relaxing single-quantum 1, 2 and 3, 4 transitions (Fig. 1) are also non-zero. In Fig. 3c we illustrate the evolution of different density elements during the course of a regular (left) or composite (right) pulse, with groupings of density elements that relax with similar rates considered together. The intrinsic relaxation rates ($R_{{2\infty }}^{{}}$ that does not include exchange contributions) of the DQ and individual SQ transitions are distinct, as is the relaxation of the on-diagonal density elements, with rates of DQ coherences ($R_{{2\infty }}^{{DQ}}$ ~ 120 s⁻¹) higher than for ZQ ($R_{{2\infty }}^{{ZQ}}$ ~ 6 s^− 1), SQ_fast ($R_{{2\infty }}^{{S{Q_{fast}}}}$ ~ 95 s^− 1), SQ_slow ($R_{{2\infty }}^{{S{Q_{slow}}}}$ ~ 12.5 s^− 1) and TQ ($R_{{2\infty }}^{{TQ}}$ ~ 60 s^− 1) coherences in the case of T4L at 15 °C where the tumbling time, τ_C is estimated to be ~ 14.3 ns from the measured value of 10.8 ns at 25 °C (Skrynnikov et al. 2001). Thus, R_2,eff values become a function of ν_CPMG and the pulse duration, decreasing for higher ν_CPMG values as the contribution from the ZQ elements (and the other diagonal density terms) that are generated during the pulse (Fig. 3c) becomes more significant. A similar phenomenon is observed in dispersion profiles recorded using ‘traditional’ SQ CPMG schemes when ${R_{2\infty }} \gg {R_1}$ that in this case results from off-resonance effects (Jiang et al. 2015; Yip and Zuiderweg 2004), leading to an interconversion between transverse and longitudinal magnetization during the course of the pulse; this can be readily taken into account in fitting software by including a basis set consisting of I_z, I₊ and I₋ operators (Hansen et al. 2008a). Similarly, the ‘apparent’ dispersions seen with the composite pulses can be accounted for by using a basis set that consists of all of the density elements in the spin 3/2 manifold, taking into account the appropriate intrinsic relaxation rates for the different terms (See Supporting information and Fig. S1). However, for the T4L data recorded using regular 180° refocusing pulses we find that essentially the same exchange parameters are obtained from an analysis that considers just the evolution of the DQ coherences (Eq. 2) rather than a more elaborate fit that accounts for all the transitions in the spin 3/2 manifold.

Fig. 3

Flat methyl ¹H DQ CPMG dispersions are obtained in the absence of exchange when regular π pulses are used during the CPMG element. a Flat dispersions at sites where Δϖ ~ 0 ppm in PSBD at 41 °C. RMSD values from the y = 0 line are shown. Here $\Delta R_{{2,eff}}^{{DQ}}\left( {{\nu _{{\text{CPMG}}}}} \right)=R_{{2,eff}}^{{DQ}}\left( {{\nu _{{\text{CPMG}}}}} \right) - R_{{2,eff}}^{{DQ}}\left( {{\nu _{{\text{CPMG}},{\text{max}}}}} \right)$ where ${\nu _{{\text{CPMG}},{\text{max}}}}$ is the maximum value of ${\nu _{{\text{CPMG}}}}$ used in the experiment. b Apparent dispersions are observed even in the absence of exchange with a dataset recorded on wild-type T4L at 15 °C (τ_C ~ 14.3 ns) using composite pulses but not when regular π pulses are used. c Evolution of coherences starting from DQ $\propto \left( {H_{+}^{1}H_{+}^{2}+H_{+}^{2}H_{+}^{3}+H_{+}^{3}H_{+}^{1}+H_{ - }^{1}H_{ - }^{2}+H_{ - }^{2}H_{ - }^{3}+H_{ - }^{3}H_{ - }^{1}} \right)$ during a regular π pulse of x phase and a composite 90_−y180_x90_−y π pulse (Levitt and Freeman 1979). The plots were calculated by propagating the Liouville-von Neumann equation for the spin 3/2 manifold (Fig. 1) using the basis functions for the 4 × 4 density matrix as shown in Fig. 1. In the starting density matrix $\rho (0)$, the elements corresponding to the DQ transitions are each set to ½, ${\rho _{1,3}}(0)={\rho _{3,1}}(0)={\rho _{2,4}}(0)={\rho _{4,2}}(0)=0.5$, and all other elements are set to 0. Relaxation is not included. Here we define $M_{{Diag}}^{2}=\rho _{{1,1}}^{2}+\rho _{{2,2}}^{2}+\rho _{{3,3}}^{2}+\rho _{{4,4}}^{2}$, $M_{{S{Q_{fast}}}}^{2}=\rho _{{1,2}}^{2}+\rho _{{2,1}}^{2}+\rho _{{3,4}}^{2}+\rho _{{4,3}}^{2}$, $M_{{S{Q_{slow}}}}^{2}=\rho _{{2,3}}^{2}+\rho _{{3,2}}^{2}$, $M_{{DQ}}^{2}=\rho _{{1,3}}^{2}+\rho _{{3,1}}^{2}+\rho _{{2,4}}^{2}+\rho _{{4,2}}^{2}$, $M_{{TQ}}^{2}=\rho _{{1,4}}^{2}+\rho _{{4,1}}^{2}~$and $\rho _{{i,j}}^{2}=\rho _{{i,j}}^{*}\rho _{{i,j}}^{{}}.$ $M_{{ZQ}}^{2}$ is subsumed within the $\rho _{{2,2}}^{2}+\rho _{{3,3}}^{2}$ terms of $M_{{Diag}}^{2}.~$Note that $M_{{Diag}}^{2}~+~M_{{S{Q_{fast}}}}^{2}+M_{{S{Q_{slow}}}}^{2}+M_{{DQ}}^{2}+M_{{TQ}}^{2}$ is constant throughout the pulse. SQ_slow and TQ coherences are not generated during these pulses

Having established that flat dispersion profiles can be obtained so long as regular CPMG refocusing pulses that are as short as possible are used we next recorded a ¹H DQ CPMG dataset on a sample of T4Ltm that has been shown previously to exchange between two compact conformers, including a major state where Phe114 is buried inside a cavity created by the L99A mutation and a minor conformer where the Phe114 sidechain is exposed to solvent (Bouvignies et al. 2011; Vallurupalli et al. 2016). Methyl ¹H DQ CPMG dispersion curves from 12 peaks with $R_{{2,eff}}^{{DQ}}\left( {100~{\text{Hz}}} \right) - R_{{2,eff}}^{{DQ}}\left( {2000~{\text{Hz}}} \right)>12\;{{\text{s}}^{ - 1}}$ were fit globally to a two-state process (Fig. 4a). Exchange parameters k_ex = 3548 ± 98 s^− 1, p_E = 4.8 ± 0.1%, extracted from analysis of the DQ CPMG data, are in good agreement with k_ex = 3775 ± 66 s⁻¹, p_E = 4.9 ± 0.1% obtained from a combined analysis of ¹H TQ and SQ CPMG datasets. Notably, flat dispersion profiles (Fig. 4a) were obtained when ZQ rather than DQ coherences were selected during the CPMG interval (RMSD < 1.0 s⁻¹). This is to be expected because methyl ¹H ZQ elements do not evolve under chemical shift; the result further confirms the robustness of the experiment. Finally, Fig. 4b shows a very good correlation between Δϖ values fit independently from analysis of the DQ or the SQ, TQ CPMG data, confirming that the DQ CPMG experiment is robust in this exchange regime.

Fig. 4

Selected methyl ¹H CPMG dispersion profiles recorded on T4Ltm at 15 °C. a DQ and ZQ relaxation dispersion profiles; although large DQ dispersions are observed the ZQ profiles are flat. The solid green lines derive from a global fit of the DQ CPMG data to a two-site exchange model. The RMSD between the ZQ CPMG data and the y = 0 line is also shown. b Correlation between Δϖ values obtained from the global analysis of the DQ CPMG dataset and a combined analysis of SQ/TQ CPMG profiles. Signs of Δϖ were obtained previously from exchange induced peak shifts between methyl ¹H SQ, DQ and TQ spectra (Gopalan and Vallurupalli 2018). c Site-specific combined analysis of SQ, DQ and TQ methyl ¹H CPMG data. d Distribution of the k_ex and p_E values obtained from site-specific fits of the CPMG data as indicated. Site-specific k_ex and p_E values (red) are very similar to the value obtained from a global analysis of all the CPMG data (blue). Data points with the same numbers in each panel derive from the same residue

It is well established that the accuracy of extracted exchange parameters generally improves upon analysis of CPMG profiles recorded at different static magnetic field strengths (Gopalan and Vallurupalli 2018; Korzhnev et al. 2004; Kovrigin et al. 2006; Millet et al. 2000; Vallurupalli et al. 2011). Recording ¹H SQ, DQ and TQ CPMG data is analogous to measuring SQ profiles at field strengths of B_o, 2B_o and 3B_o since the energy separation between levels connected by DQ and TQ transitions is two- and three-fold larger than for SQ transitions (Gopalan and Vallurupalli 2018; Yuwen et al. 2016). Notably, when ¹H SQ, DQ and TQ CPMG datasets were analyzed together (Fig. 4c) on a per-residue basis the resulting exchange parameters for 7 peaks with |Δϖ| ≥ 0.2 ppm clustered (Fig. 4d), consistent with a two-state chemical exchange process. This is an important result because it reinforces the fact that a comparison of (p_E, k_ex) values obtained on a per-residue basis from analysis of multiple datasets can be used to establish whether a global exchange process is occurring. Often only k_ex can be obtained reliably from analysis of per-residue CPMG data so that, in these cases, identification of multi-site exchange is based only on variations of k_ex (Vallurupalli and Kay 2006). Robust estimates of p_E values from single-site data improves the identification and characterization of multi-state chemical exchange occurring on the µs to ms timescale.

Next we explored the possibility of using the ¹H DQ CPMG experiment to characterize the folding reaction of the PSBD protein domain (Vugmeyster et al. 2000) that folds with a rate of ~ 13,000 s⁻¹ at 41 °C (Gopalan and Vallurupalli 2018). The low concentration of the sample (< 0.5 mM) and the short lifetime of the unfolded minor state precluded recording methyl ¹H SQ CPMG data but DQ and TQ CPMG profiles were obtained (Fig. 5a), as the corresponding DQ and TQ CPMG experiments are more sensitive than their SQ counterpart (Yuwen et al. 2016). The population of the minor state was not well defined based on analysis of TQ profiles (Fig. 5b, c) recorded at a single field yet exchange parameters from a combined analysis of DQ and TQ profiles from six sites, k_ex = 13,280 ± 779 s⁻¹ and p_E = 4.0 ± 0.2%, (Fig. 5b, c), could be estimated with confidence. These values are in reasonably good agreement with previously determined parameters, k_ex = 12,911 ± 300 s⁻¹ and p_E = 3.5 ± 0.1%, based on an analysis of amide ¹H^{N, 15}N and methyl ¹H TQ CPMG experiments along with exchange-induced peak shifts between ¹⁵N–¹H HSQC, HMQC spectra and between ¹³C–¹H SQ,DQ and SQ,TQ correlation maps recorded on a more concentrated sample (Gopalan and Vallurupalli 2018). The population of the unfolded state and consequently the unfolded state chemical shifts could not be estimated using amide ¹H^N and ¹⁵N CPMG data alone. Yet unfolded state amide ¹H^N and ¹⁵N chemical shifts could be obtained by analyzing the ¹H^N and ¹⁵N CPMG data when k_ex and p_E were fixed to values obtained from the present analysis. The good agreement between experimentally derived Δϖ values and those predicted (Tamiola et al. 2010) for an unfolded state (Fig. 5d) nicely confirms that the p_E value obtained from the joint analysis of DQ and TQ CPMG profiles is correct.

Fig. 5

Exchange processes on the order of 10,000 s⁻¹ can be studied using a combination of methyl ¹H DQ and TQ CPMG experiments. a The two largest experimental TQ and DQ CPMG relaxation dispersion profiles from the fast folding PSBD are shown in blue and green, respectively (41 °C). b 1D reduced χ² versus p_E profiles establishing that the unfolded state population cannot be defined by analysis of the single field TQ CPMG data alone (blue) but that a defined p_E value is obtained when the DQ and TQ CPMG data are analyzed together (green). (c) Scatter plot showing the extracted exchange parameters from 1000 bootstrap trials of the TQ CPMG data alone (blue) and in combination with DQ profiles (green). The scatter is reduced to a great extent when the DQ CPMG data is included in the analysis. (d) Differences between predicted unfolded state amide ¹H^N and ¹⁵N chemical shifts (Tamiola et al. 2010) and the corresponding chemical shifts of the folded state compared to Δϖ values obtained by analyzing amide ¹H^N or ¹⁵N CPMG data. In the analysis k_ex and p_E have been fixed to the values obtained from the combined analysis of the methyl ¹H DQ and TQ CPMG experiments. The good correlation between the values shows that the exchange parameters obtained from the analysis of DQ and TQ CPMG data are accurate. Signs of the amide ¹⁵N Δϖ values were determined previously (Gopalan and Vallurupalli 2018) by analyzing peak shifts between HSQC and HMQC spectra (Skrynnikov et al. 2002)

A limitation of the methyl ¹H DQ experiment is that the intrinsic relaxation rates of methyl ¹H DQ coherences are large, significantly higher than those of SQ_slow or TQ coherences (Fig. 6a). This is a consequence of the fact that intra-methyl ¹H-¹H dipolar interactions do not contribute spectral densities at zero-frequency to the relaxation rates of SQ_slow or TQ elements but do so for the relaxation of DQ coherences. The higher relaxation rates of DQ coherences do place limits on T_relax delays that can be used in this experiment. For the small protein PSBD $R_{{2\infty }}^{{DQ}}$ = 19 ± 4 s⁻¹ at 41 °C (τ_C ~ 2 ns, estimated from molecular weight) and for T_relax = 36 ms there is approximately 50% loss in signal. For T4L, that is approximately 3.5 fold larger than PSBD, $R_{{2\infty }}^{{DQ}}$ = 87 ± 18 s^− 1 at 22 °C (τ_C ~ 11.7 ns), while $R_{{2\infty }}^{{S{Q_{slow}}}}$ = 10 ± 3 s⁻¹ and $R_{{2\infty }}^{{TQ}}$ = 56 ± 16 s⁻¹ (Fig. 6a). In this case the signal to noise ratio (S/N) of the DQ CPMG experiment is 2.9 ± 0.9 times higher than for the SQ CPMG experiment when T_relax is 10 ms (when T_relax=0 the S/N of the DQ experiment is ~ eightfold higher), reflecting the fact that 50% of the starting magnetization is utilized in the DQ CPMG scheme as opposed to only 1/18th in the case of the SQ CPMG (Tugarinov and Kay 2007). For T_relax = 20 ms the S/N of DQ CPMG spectra are only marginally better than for the SQ datasets (1.6 ± 0.7). The significant decay of DQ coherences for T_relax = 20 ms for 20 kDa proteins (such as T4L) suggests that 20 ms may be an upper bound for the constant-time CPMG relaxation delay, limiting studies to exchanging systems with k_ex > ~ 300 s⁻¹. For larger proteins the utility of the DQ CPMG experiment will be restricted to studies of even faster exchanging systems because of more severe limitations on the maximum size of T_relax. By means of example, Fig. 6a, c plot relaxation rates and relative S/N values for cross peaks from datasets acquired on T4L at 5 °C (τ_C ~ 19.8 ns). For T_relax = 10 ms the relative S/N between the DQ and SQ CPMG experiments is reduced to 1.3 ± 0.6 (from 2.9 ± 0.9 at 22 °C). As expected, for all of the conditions explored here the TQ CPMG experiment has the highest sensitivity as 75% of the starting magnetization is preserved (neglecting relaxation) and $R_{{2\infty }}^{{TQ}}<R_{{2\infty }}^{{DQ}}.$

Fig. 6

Relative sensitivities of methyl ¹H SQ, DQ and TQ CPMG datasets recorded on a wild-type T4L sample (~ 18 kDa) that does not undergo chemical exchange. a Relaxation rates for DQ coherences are significantly larger than for the TQ and the SQ_slow coherences. b Relative intensities of peaks in the reference plane (T_relax = 0) and in planes with ν_CPMG = 2000 Hz and T_relax = 10 or 20 ms for the SQ, DQ and TQ CPMG experiments recorded at 22 °C (τ_C ~ 11.7 ns). The large sensitivity differences reflect, to a large extent, the fact that only coherences from the spin ½ manifolds are selected in the SQ experiment, whereas 1/2 and 3/4th of the starting ¹H magnetization is retained in the DQ and TQ CPMG experiments, respectively, in the absence of relaxation. c As in (b) but for data recorded at 5 °C where the rotational correlation time of T4L is ~ 19.8 ns

The above discussion establishes that the DQ experiment becomes increasingly insensitive as the size of the protein increases and as k_ex becomes slow since large T_relax values would then be required. We were interested, therefore, in demonstrating the utility of the DQ method for moderate exchange rates, on the order of 1000 s⁻¹, and for protein systems in the 20 kDa molecular mass range. To this end we have recorded a CPMG dataset on T4L L99A (as opposed to T4Ltm discussed above containing three mutations that exchanges much more rapidly). Here exchange is between a major conformer in which Phe114 is exposed outside a cavity in the protein and a minor state in which Phe114 is inserted inside, opposite to T4Ltm where the minor conformer is the one with Phe114 exposed and the major conformer is the one with Phe114 inserted in the cavity as described earlier. An exchange rate of ~ 900 s⁻¹ at 22 °C has been measured previously (Mulder et al. 2001a). Methyl ¹H DQ CPMG data were collected with T_relax = 20 ms (Fig. 7a) and the k_ex = 881 ± 60 s⁻¹, p_E = 2.9 ± 0.1% parameters obtained from the subsequent analysis of the data are in good agreement with k_ex = 943 ± 57 s⁻¹, p_E = 2.6 ± 0.1% fit independently from a combined analysis of SQ and TQ data (Fig. 7b, c). Additionally, extracted |Δϖ| values from the different methods are well correlated (Fig. 7d).

Fig. 7

Methyl ¹H DQ CPMG study of exchange in T4L L99A. a Selected ¹H DQ CPMG relaxation dispersion curves at 22 °C with T_relax = 20 ms, along with a global best-fit of the data to a two-site exchange model (solid lines). b Similar reduced χ² surfaces as a function of k_ex and p_E are obtained from a global analysis of the SQ and TQ CPMG data (left) or the DQ CPMG data (right). c Histograms of k_ex (left) or p_E (right) values from a bootstrap analysis of datasets as indicated. d Linear correlation plot of fitted |Δϖ| values from global analyses of SQ and TQ CPMG data or of DQ CPMG data

Conclusions

We have presented a methyl ¹H DQ CPMG relaxation dispersion experiment for studies of conformational exchange using ¹³CH₃-labeled methyl probes in highly deuterated protein systems. The experiment has been used to study proteins exchanging with rates varying between ~ 1000 and ~ 13,000 s⁻¹. Although the DQ CPMG experiment can be used in place of the SQ scheme, based on sensitivity considerations, perhaps its most important feature lies in the complementarity between SQ, DQ and TQ datasets that when fit together leads to a more accurate definition of exchange parameters than when only a single class of ¹H CPMG data recorded at a single static magnetic field is analyzed. This combined analysis can be important for identifying multiple exchange processes in the µs−ms time regime because k_ex and p_E values can vary substantially from site to site when there are different exchange process as opposed to a global process where similar k_ex and p_E values are obtained for every site. The faster ¹H DQ relaxation rate than for ¹H TQ coherences and the lower overall inherent sensitivity of the ¹H DQ CPMG scheme relative to the TQ counterpart does suggest, however, that if at least a pair of spectrometers operating at different magnetic fields is available for experiments, recording a pair of ¹H TQ datasets to obtain accurate exchange parameters is most likely the best option.