Detection of Chemical Exchange in Methyl Groups of Macromolecules

Abstract

The zero- and double-quantum methyl TROSY Hahn-echo and the methyl ¹H-¹H dipole-dipole cross-correlation nuclear magnetic resonance experiments enable estimation of multiple quantum chemical exchange broadening in methyl groups in proteins. The two relaxation rate constants are established to be linearly dependent using molecular dynamics simulations and empirical analysis of experimental data. This relationship allows chemical exchange broadening to be recognized as an increase in the Hahn-echo relaxation rate constant. The approach is illustrated by analyzing relaxation data collected at three temperatures for E. coli ribonclease HI and by analyzing relaxation data collected for different cofactor and substrate complexes of E. coli AlkB.

Introduction

An important first step in characterizing micro-to-millisecond time scale dynamic processes in proteins and other biological macromolecules consists of identifying which sites are subject to significant chemical exchange broadening in NMR spectroscopic experiments¹. A very general approach relies on the scaling of chemical exchange broadening with the magnitude of the static magnetic field^2–4. Other approaches rely on high-power spin-locking radiofrequency fields to suppress chemical exchange broadening for comparison with a reference experiment in which exchange is minimally suppressed^5–7. For backbone ¹⁵N spins in {U-²H, U-¹⁵N} proteins, the TROSY Hahn-echo experiment is very efficient⁸. In this experiment, the exchange-free relaxation rate constant is estimated as R₂⁰ = κη_xy in which η_xy is the transverse ¹H-¹⁵N dipole/¹⁵N CSA transverse relaxation interference rate constant, which depends on physical parameters and can be calculated a priori, or more often measured empirically, for a subset of spins not subject to exchange^9,10.

Relaxation of ¹H and ¹³C spins in methyl groups is a powerful probe of side-chain conformational dynamics, and experimental methods for measurement of single- and multiple-quantum relaxation rate constants have been developed extensively by Kay and coworkers^11–19. We described zero- and double-quantum methyl TROSY Hahn-echo experiments²⁰ and subsequently used these experiments in an investigation of the role of conformational dynamics in gating activity of the E. coli DNA repair enzyme AlkB²¹. The Hahn-echo experiment minimally suppresses chemical exchange effects; consequently, exchange can be detected by comparison with a second experiment that either suppresses chemical exchange²² or that is independent of chemical exchange²³. Herein, the methyl ¹H-¹H dipole-dipole cross-correlation experiment developed by Tugarinov and Kay¹⁹ serves as the exchange-free reference experiment. The combination of methyl TROSY Hahn-echo and methyl ¹H-¹H dipole-dipole cross-correlation experiments allows facile identification of chemical exchange in methyl groups²³. The approach is illustrated for both E. coli ribonuclease HI (RNase H) and AlkB.

The expression for differential relaxation of zero- and double-quantum coherence (ΔR_MQ) measured in the Hahn-echo experiments is:

$$\Delta R_{MQ}=\left(R_{DQ}-R_{ZQ}\right)/2=\Delta R^0+\Delta R_{ex}/2$$ (1)

in which^14,20,24,25:

$$\begin{gathered} \Delta R^0=\frac{2}{5}{\left(\frac{{\mu }_0}{4\pi }\right)}^2\hslash {\tau }_c{\gamma }_c{\gamma }_H^3\left\{\frac{8{\gamma }_D^2}{3{\gamma }_H^2}\sum _{D^E}\langle \frac{P_2\left(\text{cos}{\theta }_{C{D}^{E}H}\right)}{{\left(r_{C{D}^E}{r}_{H{D}^E}\right)}^3}\rangle +\sum _{H^E}\langle \frac{P_2\left(\text{cos}{\theta }_{C{H}^{E}H}\right)}{{\left(r_{C{H}^E}{r}_{H{H}^E}\right)}^3}\rangle \right\} \\ =\frac{2}{5}{\left(\frac{{\mu }_0}{4\pi }\right)}^2{\hslash }^2{\tau }_c{\gamma }_c{\gamma }_H^3\Gamma \end{gathered}$$ (2)

$$\Delta R_{ex}=4p_1{p}_2\Delta {\omega }_C\Delta {\omega }_H/k_{ex}$$ (3)

μ₀ is the vacuum permeability, $\hslash$ is Planck’s constant divided by 2π, τ_c is the effective overall rotational correlation time of the macromolecule, γ_X is the magnetogyric ratio (X= C, D, and H to represent ¹³C, ²H, and ¹H, respectively), $r_{C{D}^E}$ and $r_{H{D}^E}$ are the distances from the methyl ¹³C and ¹H to remote ²H spins in the molecule, $r_{C{H}^E}$ and $r_{H{H}^E}$ are the distances from the methyl ¹³C and ¹H to remote ¹H spins in the protein, P₂(x) = (3ײ – 1)/2 is the second Legendre polynomial, and θ_CXH is the angle between the C-X-H atoms. The term in brackets has been denoted Γ for convenience. The first summation is over all the remote ²H spins and the second summation is over all the remote ¹H spins in the molecule; the relative size of these two summations depends upon the pattern and extent of deuteration of the protein and the fractional content of D₂O in the sample buffer (vide infra). Angle brackets indicate ensemble averaging to account for fast molecular dynamics. Rotation of the methyl group was treated by averaging distances for the three methyl H-atom positions. The expression for ΔR_ex is the fast-limit expression for two-site exchange for convenience; in this expression, p₁ and p₂ are the populations of the two states of the molecule, Δω_C and Δω_H are the differences in ¹³C and ¹H chemical shifts for a spin in the two states, k_ex = k₁ + k₋₁, and k₁ and k₋₁ are the forward and reverse reaction rate constants. Expressions for ΔR_ex for other time scales have been given in the literature²⁶. The ¹H-¹H dipole-dipole cross-correlated relaxation rate constant for pairs of ¹H spins in a methyl group is given by¹⁹:

$${\eta }_{HH}=\frac{9}{10}{\left(\frac{{\mu }_0}{4\pi }\right)}^2{\hslash }^2{\gamma }_H^4{P}_2{\left(\text{cos}{\theta }_{HH}\right)}^2{S}_{\mathit{\text{axis}}}^2{\tau }_c\langle r_{HH}^{-6}\rangle$$ (4)

in which θ_HH = π/2 is the angle between a vector of length r_HH between two ¹H spins in the methyl group and the methyl symmetry axis, and S_axis² is the generalized order parameter for a unit vector along the symmetry axis of the methyl group. Importantly, this rate constant is independent of any exchange contributions.

Experimental data reported below for RNase H suggest a linear correlation exists between ΔR⁰ and η_HH and hence between Γ and S_axis²:

$$\Gamma =\alpha S_{\mathit{\text{axis}}}^2+\beta$$ (5)

This correlation also is supported by molecular dynamics (MD) simulations (vide infra) and reflects the dependence of both Γ and S_axis² on packing density^27–29 Combining Eqs. 2, 4, and 5 yields:

$$\Delta R^0=\frac{4}{9}{P}_2{\left(\text{cos}{\theta }_{HH}\right)}^{-2}\langle r_{HH}^{-6}\rangle {\gamma }_c{\gamma }_H^{-1}\alpha {\eta }_{HH}+\frac{2}{5}{\left(\frac{{\mu }_0}{4\pi }\right)}^2{\hslash }^2{\tau }_c{\gamma }_c{\gamma }_H^3\beta =\kappa {\eta }_{HH}+\epsilon$$ (6)

The values of α and β, or κ and ε, can be estimated from MD simulations, or by examining the distribution of experimental values of ΔR_MQ relative to η_HH, because contributions from ΔR_ex will only increase ΔR_MQ. Combining Eqs. 1 and 6 yields ΔR_ex = 2(ΔR_MQ − η_HH − ε) as the key result for detection of chemical exchange contributions to multiple quantum relaxation in methyl spin systems.

Methods

Molecular dynamics simulations.

A full description of the MD simulations and comparison with NMR spin relaxation data for RNase H will be published elsewhere. Briefly, the system was prepared and simulations were performed using the Schrödinger Maestro Protein Preparation Wizard version 11.3.016^30,31, Schrödinger Multisim version 3.8.5.19³⁰, and Desmond version 5.5³¹. Hydrogen atoms were added to the x-ray crystal structure (PDB code 2RN2, 1.5 Å resolution) consistent with pH = 5.5 to mimic the conditions used in NMR experiments; solvated with TIP3P water in an orthorhombic box with a 10Å buffer region from solute to box boundary³²; and neutralized with Cl⁻ ions. The system was relaxed and energy-minimized prior to a 5 ns constant pressure and constant temperature (NPT) equilibration simulation. Twenty structures were extracted from the trajectory (structures were chosen roughly every 250 ps with the proviso that the box volume was close to the average box volume over the 5 ns of the simulation). These structures were ranked based on their MolProbity score^33,34 and the top two structures were chosen as the starting structures for two independent 1-μs constant volume and constant temperature (NVT) simulations. Volume and temperature reached equilibrium values in less than 100 ps in all simulations. A RESPA integrator was used with a time step of 1 fs for bonded and short-range non-bonded interactions, and 3 fs for long-range electrostatics³⁵. Electrostatics were calculated with the particle mesh Ewald method using a 9 Å cutoff^36–38. Simulations were performed at 300 K using a Nosé-Hoover thermostat^39,40. Additionally, the NPT ensemble used a Martyna-Tobias-Klein (MTK) barostat⁴¹. Coordinate sets were saved every 10 ps for NPT simulations and 4.5 ps for NVT simulations.

NMR spectroscopy.

¹³C^ϵ-methionine AlkB was expressed and purified and the NMR spin relaxation parameters were determined at 21.1 T as previously described²¹. The expression and purification of U-²H and [¹³C ¹H₃] Ile δ1 and stereospecifically labeled Val γ and Leu δ RNase H has also been described²⁰. For RNase H, all NMR experiments were performed on a Bruker Avance spectrometer with a triple resonance z-axis gradient cryoprobe and operating at 14.1 T. Each experiment was performed at 283, 300, and 310 K, and the Hahn echo data collected at 283 K have been previously reported²⁰. Temperature was calibrated using 98% ²H₄-methanol⁴². The zero- and double-quantum Hahn echo data collected at 300 and 310 K used 1024 × 188 (t₂ × t₁) complex points, 4.5 × 7.2 kHz spectral widths, and relaxation delays of n/(2J_CH) where J_CH = 128 Hz and n = {1, 25, 40} for 300 K and n = {1, 10, 25, 35, 40, 45} for 310 K. The ¹H-¹H cross correlated relaxation data were collected with 1024 × 256 complex points, 4.9 × 7.3 kHz spectral widths, and relaxation delays of 2, 8, 20, 40, and 50 ms at each of the three temperatures. Data were processed with NMRPipe⁴³ using a cosine bell function for apodization in the indirect dimension. Assignments were made using Sparky⁴⁴. Peak intensities for the Hahn Echo data acquired at 283 K were determined from ten iterative rounds of peak fitting performed in NMRPipe, as described previously²⁰. The remaining peak intensities were determined using Sparky. Further data analysis and visualization of results were performed using Python^45–51.

Results and Discussion

The bracketed term denoted Γ in Eq. 2 must be calculated from MD simulations or estimated empirically. In the present work, this term was calculated for Ile γ1, Leu γ1 and γ2, and Val γ1 and γ2 methyl groups in RNase H as the average value from two 1-μs MD simulations. The calculations included the 25 (out of 46) methyl groups for which the absolute differences between simulated and experimental values of S²_axis were less than 0.1; however, results were not substantially altered by changing the maximum difference to 0.05 or 0.15. The experimental values of S²_axis are described elsewhere⁵² and compared to simulated values in Figure 1a. The graph of Γ versus the simulated value of S²_axis is shown in Figure 1b. The calculated points cluster into two subsets with different slopes. The slopes were determined using the non-parametric Thiel-Sen estimator. The intercepts for both sets of data were set to the intercept determined for the subset of data with the smaller slope. The fitted values of α gave low and high estimates of κ_ILV = 0.030 and 0.080, respectively. The fitted value of β gave ε_ILV = 0.37 s⁻¹.

Figure 1.

(a) Comparison between experimental and MD simulated values of S²_axis for 25 methyl groups for which the absolute deviation is < 0.1. (b) Values of Γ determined from MD simulations are plotted versus the simulated values of S²_axis for the same methyl groups shown in (a). Two lines are plotted for the (solid symbols, solid line) subset of data with maximum slope and (empty symbols, dashed line) subset of data with minimum slope. The intercepts of the plotted lines are set equal to the fitted line for dashed line.

The calculations were validated by calculating ΔR⁰ from Eq. 1 for the same 25 methyl groups used for Figure 1 and comparing to the mean values of ΔR_MQ for protein L and malate synthase G reported by Kay and coworkers¹⁴. A graph of the experimental and predicted results is shown in Figure 2. The predicted slope differs from the fitted slope by ~10%, well within the spread of experimental values, and the standard deviation of the predicted slope is in good agreement with the experimental standard deviations shown in the figure. For the highly deuterated RNase H sample, the predicted relaxation contribution from remote ²H spins (the first sum in Eq. 2) is ~10-fold larger than from remote ¹H spins (the second sum in Eq. 2).

Figure 2.

Experimental and predicted values of ΔR⁰ versus τ_c. (solid, circles) Experimental values of ΔR_MQ measured for protein L (5° and 25° C) and malate synthase G (20° and 37° C), assuming minimal contributions from exchange¹⁴. (dashed) Average values calculated from the values of Γ determined from MD simulations of RNase H. The shaded region shows ± standard deviation of the calculations. Calculations were performed for the 25 methyl groups used in Figure 1.

The values of ΔR_MQ and η_HH for Ile γ1, Leu γ1 and γ2, and Val γ1 and γ2 methyl groups in RNase H at 283, 300, and 310 K are shown in Figure 3. Graphs of ΔR_MQ versus η_HH are shown in Figure 4. Lines plotted using the calculated values of κ_ILV and ε_ILV are shown. The differences between the lines shown for the two estimates of κ_ILV set a lower bound on the smallest exchange contribution that can be detected by this method. Note that ΔR_ex, and hence ΔR_MQ, can be negative depending on the relative signs of Δω_C and Δω_H, as shown by Eq. 3. Larger values of |ΔR_MQ| for Val 98 γ1, Val 101 γ1, and Leu 103 γ1 are consistent with significant conformational exchange; elevated values of |ΔR_MQ| also are observed for Ile 78 γ1 and Ile 82 γ1 at 283 K. Excluding these residues, a linear fit to ΔR_MQ versus η_HH using the ‘leiv’ Bayesian algorithm in the statistics program R gave κ_ILV = 0.094 ± 0.003 and ε_ILV = 0.01 ± 0.03, in good agreement with the larger of the two values of κ_ILV obtained from the MD simulations.

Figure 3.

(a) Differential relaxation rate of zero- and double-quantum coherence (ΔR_MQ) and (b) ¹H-¹H dipole-dipole cross-correlated relaxation rate constant (η_HH) for Ile, Leu, and Val residues of RNase H measured at (blue, circles) 283, (orange, squares) 300, and (reddish-purple, diamonds) 310 K, respectively.

Figure 4.

Values of ΔR_MQ vs. η_HH are shown for RNase H (a) Leu γ1 (circles) and γ2 (squares), (b) Val γ1 (circles) and γ2 (squares), and (c) Ile γ1 methyl groups at (blue) 283 K, (orange) 300 K, and (reddish-purple) 310 K. The solid line is the mean result calculated as κ_ILV η_HH. The shaded region shows ± the standard deviation in the mean of the calculation. (d) Arrhenius plot for (reddish-purple) Val 98 γ1, (orange) Val 101 γ1, (blue) Leu 103 γ1, and (black, circles) mean of all other Leu and Val residues. Solid lines for Val 98 γ1, Val 101 γ1, and Leu 103 γ1 show best single-exponential fits to the data to obtain $E_{app}^{†}$, given in Table 1.

The resonances of Val 98 γ1, Val 101 γ1, and Leu 103 γ1 are notably broadened, beyond that of the other residues in RNase H. Graphs of ΔR_ex versus 1/T for these residues are shown in Figure 4d. For fast-limit two-site exchange with site populations p₁ >> p₂, the apparent activation energy is⁵³:

$$E_{\mathit{\text{app}}}^{†}=E_1^{†}+\Delta E\left(1-3p_1^0\right)={\overline{E}}^{†}-\Delta E\left(p_1^0-p_2^0\right)$$ (7)

in which $E_1^{†}$, and $E_{-1}^{†}$ are the activation barriers in the forward and reverse reaction directions, $\Delta E=E_1^{†}-E_{-1}^{†}$, $p_1^0$ and $p_2^0$ are the site populations at a reference temperature T⁰, and ${\overline{E}}^{†}=p_2^0{E}_1^{†}+p_1^0{E}_{-1}^{†}$ is the apparent activation energy that would be obtained from dln(k_ex)/d(1/T) rather than dln(ΔR_ex)/d(1/T). Consequently, $E_{\mathit{\text{app}}}^{†}$ underestimates ${\overline{E}}^{†}\text{ by }\Delta E\left(p_1^0-p_2^0\right)\approx \Delta E$. Values of $E_{\mathit{\text{app}}}^{†}$ are given in Table 1 for Val 98 γ1, Val 101 γ1, and Leu103 γ1. Values of the activation barriers are consistent with results from $R_{1_{\text{ρ}}}$ measurements for backbone ¹⁵N spins⁵⁴. Each of these residues has been demonstrated to be directly involved in or located within the substrate-binding handle region associated with conformational transitions from open to closed states by ¹⁵N amide spin relaxation experiments and/or molecular dynamics simulations^54–56.

Table 1.

Apparent activation energies

Residue	Activation energy ($E_{\mathit{\text{app}}}^{†}$, kJ/mol)
Val 98 γ1	45.4 ± 1.6
Val 101 γ1	23.7 ± 1.9
Leu103 δ1	21.4 ± 3.0

Estimated apparent activation energies ($E_{\mathit{\text{app}}}^{†}$) as determined from the temperature dependence of ΔR_ex vs 1/T using Eq. 6, as shown in Figure 4d.

Figure 5 shows a graph of ΔR_MQ versus η_HH based on data previously reported (see Figure 5C&D in Ergel, et. al²¹) for the DNA repair enzyme AlkB in complex with Zn²⁺; Zn²⁺ and the co-substrate 2-oxoglutarate (2OG); and Zn²⁺, 2OG, and DNA substrate 5′-CAmAAT-3′. Results are shown for the four Met residues in AlkB: Met 49, Met 57, and Met 61 are located in the active site or nucleotide recognition lid (NRL) and Met 92 is located at a hinge between the core domain and the NRL. A number of residues in the various complexes exhibit conformational exchange broadening, with the largest ΔR_ex observed for M49 in the 2OG complex. Notably, the NMR spectra of the methyl groups of Met 49, Met 57 and Met 61 in the ternary complex show sharp resonance signals²¹, suggesting that exchange is absent for the active site residues in this complex. As shown above for RNase H, ε has a small effect on the analysis; accordingly, ε_Met was set to zero and the weighted-mean ratio ΔR_MQ/η_HH = 0.093 ± 0.009 for Met 49, Met 57 and Met 61 was set to κ_Met. These results are consistent with exchange between an open and closed conformer in the Zn and Zn/2OG enzyme complexes, and with significant line broadening of M49 in the 2OG complex due to nearly equal populations of open and closed conformations in the Zn/2OG complex and a relatively large chemical shift difference between the two states (Δω_C >= 2.1 ppm) for this residue^21,57,58.

Figure 5.

Chemical exchange in AlkB. (a) Ribbon diagram showing the crystal structure of AlkB-N11 with bound Fe(II) (red), 2-oxoglutarate (2OG, green), and methylated DNA substrate (blue) drawn from PDB code 2FD8. The Fe(II)/2OG core and nucleotide recognition lid are colored grey and magenta, respectively, and the residues used as spectroscopic probes are shown in orange stick representation. (b) Values of ΔR_MQ vs. η_HH are shown for AlkB. M49 (squares), M57 (circles), M61 (triangles) and M92 (diamonds) are shown for AlkB in successive complex with Zn²⁺ (reddish-purple), Zn²⁺/2OG (green), and Zn²⁺/2OG/DNA substrate (blue). The solid line is the mean empirical result calculated as κ_Metη_HH (see main text). The shaded region shows ± the standard deviation of the calculations. M49 and M57 are degenerate in the Zn²⁺ complex.

Conclusion

The combination of the zero- and double-quantum methyl TROSY Hahn-echo experiment²⁰ and the methyl ¹H-¹H dipole-dipole cross-correlation experiment¹⁹ provide a convenient experimental approach to determining ΔR_ex = 2(ΔR_MQ − κη_HH − ε) in a fashion that is analogous to the ¹H-¹⁵N TROSY Hahn-echo experiment. The proportionality constant κ can be calculated accurately from MD simulations or from empirical comparisons between ΔR_MQ and η_HH and depends on the labeling strategy employed; the intercept ε is small in the examples considered herein. Application of this approach to relaxation data collected at three temperatures identifies residues Val 98, Val 101, and Leu 103 as key probes of conformational dynamics of the substrate binding handle region of RNase H. A second application of this approach confirms previous observations that chemical exchange broadening reflects an open-closed equilibrium of nucleotide recognition lid of AlkB. These applications suggest that the proposed approach has wide application in studies of the conformational dynamics of proteins and other biological macromolecules²³.

Highlights.

Method for detecting chemical exchange in methyl groups of biological macromolecules.

Chemical exchange detected in key substrate-binding loop of the enzyme ribonuclease HI.

Confirmation of chemical exchange contributions in the enzyme AlkB.