TROSY-selected ZZ-exchange experiment for characterizing slow chemical exchange in large proteins

Abstract

A TROSY-selected ZZ-exchange experiment is described for measuring slow chemical exchange rates by monitoring the TROSY component of ¹⁵N longitudinal magnetization. Application of the proposed pulse sequence to the cadherin 8 N-terminal extracelluar domain demonstrates that enhanced sensitivity is obtained, compared to a previously described TROSY-detected ZZ-exchange sequence (Sahu et al. (2007) J Am Chem Soc 129: 13232–13237), by preserving the TROSY effect during the mixing period as well as the frequency encoding periods.

ZZ-exchange experiments (Montelione and Wagner 1989; Wider et al. 1991; Farrow et al. 1994; Hwang and Kay 2005) have been used extensively to study slow chemical exchange processes in ¹⁵N-labeled biological macromolecules. For large molecular weight systems, significant gain in resolution and sensitivity can be obtained by utilizing the slowly relaxing component or the TROSY component for measuring dynamic parameters, as previously demonstrated by TROSY-selected (TS) Carr-Purcell-Meiboom-Gill (Loria et al. 1999; Korzhnev et al. 2004), TS Hahn Echo (Wang et al. 2003) and TS R_1ρ experiments (Igumenova and Palmer 2006). In these experiments, to take full advantage of the TROSY effect, the narrow component of the ¹⁵N magnetization is maintained during both the frequency encoding periods and the spin relaxation period. In contrast, TROSY-detected (TD) experiments record evolution of “classical” longitudinal and transverse magnetizations during relaxation periods and monitor the narrow TROSY magnetization component only during frequency encoding periods (Zhu et al. 2000; Kempf et al. 2003). A recent study (Sahu et al. 2007) presented a TD ¹⁵N ZZ-exchange experiment, in which the narrow magnetization component is detected, but the TROSY effect is eliminated during the mixing period by interconverting the narrow and broad components of the longitudinal magnetization. Here, we present a TS ZZ-exchange experiment that obtains enhanced sensitivity by preserving the narrow magnetization component throughout the mixing period.

Figure 1 shows the pulse sequence of the TS ZZ-exchange experiment. The sequence includes an S³E element (Meissner et al. 1997) before the mixing period to selectively excite the S_zI^β spin operator (I = ¹H and S = ¹⁵N) and to dephase the S_zI^α spin operator and an S³CT element (Sorensen et al. 1997) in the middle of the mixing period to selectively invert the β spin state. The S³E element creates a favorable initial condition by dephasing the unwanted coherence and the S³CT element eliminates the cross relaxation between α and β spin states to first order (Kroenke et al. 1998; Igumenova and Palmer 2006). As shown in the Supplementary Information, in the absence of chemical exchange, the evolution of the spin system during the mixing period can be described by the following equations, to a first-order approximation,

Figure 1.

Pulse sequence diagram for the TS ZZ-exchange experiment. Open and filled bars represent 90° and 180° pulses, respectively. The shorter bars represent water-selective 90° pulses (~ 1.5 ms) with a rectangular shape. The hatched bar represents a 3-9-19 pulse (Sklenar et al. 1993). All pulse phases are x unless indicated otherwise. The delays are Δ = 2.7 ms and Δ′= 1.35 ms. The phase cycle is φ1 = 4 (x, −x, −y, y), φ2 = 2 (135°, 315°, 45°, 225°), 2 (315°, 135°, 225°, 45°), φ3 = 4 (x, −x, −y, y), φ4 = 4 (x, −x, y, −y), φ5 = 2 (y, y, y, y, −y, −y, −y, −y), φ6 = 2 (−y, −y, −y, −y, y, y, y, y), φ7 = 4 (−x, x, −y, y), φ8= 2 (x, x, x, x, −x, −x, −x, −x), φ_rec = (x, −x, y, −y, x, −x, −y, y, −x, x, −y, y, −x, x, y, −y). The phase cycle is for Bruker spectrometers. For Varian spectrometers, y and y phases should be swapped. Quadrature detection in the indirect dimension is achieved by incrementing φ4 using States-TPPI. Gradients along the z-axis have sine amplitude profile, with peak strengths and durations as follows: G1 = 7.5 G/cm, 1.5 ms; G2 = 10 G/cm, 0.5 ms; G3 = 10 G/cm, 1.5 ms; G4 = 10 G/cm, 0.5 ms; G5 = 22.5 G/cm, 1.0 ms.

$$\frac{d}{dt}\left[\begin{array}{c}{I}_z\\ S_z{I}^{\alpha }\\ S_z{I}^{\beta }\end{array}\right]=-\left[\begin{array}{ccc}{R}_{1H}& {\eta }_H+\sigma & 0\\ \frac{{\eta }_H+\sigma }{2}& {\overline{R}}_1+{\eta }_z& 0\\ 0& 0& {\overline{R}}_1-{\eta }_z\end{array}\right]\left[\begin{array}{c}{I}_z\\ S_z{I}^{\alpha }\\ S_z{I}^{\beta }\end{array}\right]$$ (1)

in which R_1H is the ¹H longitudinal relaxation rate, R̄₁ = (R_1N + R_1HN)/2 is the average of the relaxation rates of ¹⁵N longitudinal magnetization and two-spin order, σ is the ¹H-¹⁵N heteronuclear cross relaxation rate, η_z is the longitudinal ¹⁵N-¹H dipole/¹⁵N CSA cross-correlated relaxation rate, η_H is the longitudinal ¹⁵N-¹H dipole/¹H CSA cross-correlated relaxation rate. The phase of the last ¹⁵N 90° pulse in the S³CT element should be set to invert the β spin state, which ensures that the effects of ¹H-¹⁵N heteronuclear cross relaxation and ¹⁵N-¹H dipole/¹H CSA cross-correlated relaxation are eliminated to first order. The presence of both S³E and S³CT elements ensures that the evolution of the selected TROSY component is nearly mono-exponential during the mixing period in the absence of population exchange, which allows the same data analysis procedure to be used as for the conventional ZZ-exchange experiment (Farrow et al. 1994), in which the longitudinal ¹⁵N magnetization is utilized for monitoring exchange rates and the magnetization is subsequently transferred back to ¹H for detection by an INEPT scheme. Numerical simulations (Figure 2) show that omitting either element results in appreciable deviation from the ideal mono-exponential decay profile for the S_zI^β spin operator.

Figure 2.

Simulated trajectories of S_zI^β operator during the mixing period when only the S³E element (green), only the S³CT (blue), both S³E and S³CT elements (red), and no S³E or S³CT elements (cyan) are included in the pulse sequence of Figure 1. The black line represents a mono-exponential function with the decay rate equal to R̄₁−η _z. The relaxation parameters used for the simulations are the following: R_1H = 2.5 s⁻¹; R_1N = 1.8 s⁻¹; R_1HN = 3.8 s⁻¹; η_z = 1.2 s⁻¹; η _H = 1.0 s⁻¹; σ = 0.03 s⁻¹. A rotational correlation time of 10 ns was used to estimate the relaxation parameters.

The advantage of the TS ZZ-exchange experiment over the TD ZZ-exchange experiment (Sahu et al. 2007) is the slower decay of the selected coherence during the mixing period. We compared the performance of these two experiments, as well as the conventional ZZ-exchange experiment (Farrow et al. 1994), using a sample of ¹⁵N, ²H-labeled cadherin 8 N-terminal extracellular (EC1) domain, whose dynamic properties have been characterized previously (Miloushev et al. 2008). The NMR sample contains 0.9 mM protein in 50 mM D₁₃-morpholino-ethane-sulfonate (MES), 500 mM D₅–Gly at pH 6.0 and 10% D₂O. The cadherin 8 EC1 domain has a molecular weight of 10 kDa and forms dimers with affinity in the μM to mM range, depending on solution pH and ionic strength. The kinetic rates for exchange between monomeric and dimeric species under equilibrium conditions are in the slow-exchange regime suitable for ZZ-exchange experiments. NMR experiments were performed on a Bruker DRX spectrometer operating at 600 MHz ¹H frequency and equipped with a triple-resonance z-axis gradient CryoProbe. The sample temperature was 306.6 K, which was calibrated using 99.8% D₄-methanol (Findeisen et al. 2007). We recorded the first row of each 2D experiment at 10 mixing times and compared the decay of total integrated intensity of signals in the amide ¹H region. As shown in Figure 3, under current sample and experimental conditions, the decay is significantly slower in the TS ZZ-exchange experiment than in the TD experiment and is comparable to the conventional experiment. The additional loss in sensitivity resulting from the S³E element in the TS experiment compared to the TD experiment was estimated from the total integrated signal intensities at 10 ms mixing time to be ~ 10 %. Overall, the TS experiment gave approximately a factor of 2 enhancement in sensitivity at the longest mixing time (1 s). While both TS and TD experiments enhance spectral resolution to the same extent, the TS experiment is particularly beneficial for measuring relatively slow exchange rates, which requires utilization of long mixing times. The superior performance of the TS experiment over the TD experiment results solely from the effect of longitudinal ¹⁵N-¹H dipole/¹⁵N CSA cross-correlated relaxation during the mixing period. Both the TD and TS experiments are affected identically by the increased apparent relaxation rate R̄₁, compared with R_1N, caused by ¹H-¹H dipolar interactions with remote spins (eq. 1). The resolution and sensitivity enhancement of both TD and TS experiments over the conventional experiment relies on the deuteration of nonexchangeable sites in the protein, which attenuates the dipolar interactions between amide and remote ¹H spins. The enhanced resolution is important particularly for resolving exchange cross peaks when the resonance frequencies of exchanging spins are close (Sahu et al. 2007).

Figure 3.

Decay curves of the total integrated intensity of signals in the amide ¹H region during the mixing periods of TS ZZ-exchange (black, circle), TD ZZ-exchange (red, square) and conventional ZZ-exchange (blue, triangle) experiments performed on ¹⁵N, ²H-labeled cadherin 8 EC1 domain at 306.6 K. The lines connecting data points only serve as guide for the eye and do not represent fits to the data.

To measure kinetic rate constants, a set of 2D data was recorded at seven mixing times (5, 200, 300, 400, 500, 600, 800 ms) using the TS ZZ-exchange sequence. A composite ratio of auto- and cross-peak intensities, which has quadratic time dependence, was employed to extract kinetic on- and off-rate constants as described previously (Miloushev et al. 2008). The expression is given below

$$\mathrm{\Xi }(T)=\frac{I_{MD}(T)I_{DM}(T)}{I_{MM}(T)I_{DD}(T)-I_{MD}(T)I_{DM}(T)}\cong 4k_{\mathit{off}}{k}_{on}[M]T^2$$ (2)

where I_ij is the auto- or cross-peak intensity with i and j standing for initial and final states, respectively, monomers and dimers are denoted by M and D, respectively, [M] represents the equilibrium concentration of monomers, and the factor of 4 arises from the dimerization reaction. The main benefit of using the composite ratio is to cancel the effects of differences in R₁ relaxation rates of monomeric and dimeric species, as well as differences in the transfer efficiencies during the preparation period and linewidths during the detection period. Figure 4 shows the composite ratio of peak intensities as a function of the mixing time for three residues (G41, Q49 and A69), which give well-resolved auto- and cross-peaks. The data were globally fit to eq. 2 using the nonlinear least-squares fitting procedure implemented in Mathematica (Wolfram Research, Inc.). The best-fit value for 4k_off k_on [M] is 0.21 ± 0.01 s⁻¹. Uncertainties in the fitting parameter were determined by the jackknife procedure (Mosteller and Tukey 1977) and reflect the grouping of data on a residue basis. Values of K_D and [M] were calculated from the relative equilibrium populations of monomers and dimers determined from a ¹H-¹⁵N TROSY spectrum with a pulse delay of 6 s, which is long enough for both monomeric and dimeric species to be fully relaxed, and the total protein concentration determined from absorbance at 280 nm. Using these results, the measured off-rate constant was 0.79 ± 0.08 s⁻¹ and the bimolecular on-rate constant was 86 ± 8 s⁻¹ M⁻¹ at 306.6 K. The differences between these rate constants and values reported previously (Miloushev et al. 2008) arise primarily from the larger monomer-dimer equilibrium dissociation constant for the present sample, evident in Figure 4a.

Figure 4.

(A) Typical ZZ-exchange spectra of ¹⁵N, ²H-labelled cadherin 8 EC1 domain, showing the buildup of cross-peaks. Monomers and dimers are denoted by m and d, respectively. (B) Buildup curve of the composite ratio of auto- and cross-peak intensities of residues G41 (green), Q49 (red) and A69 (blue). The solid line indicates the fit of the data to eq. 2.

In summary, we have presented a TS ZZ-exchange experiment with sensitivity enhanced by preserving the slowly relaxing TROSY ¹⁵N magnetization component in the mixing period. The performance of this experiment has been demonstrated on a cadherin 8 EC1 domain that is in slow exchange, on the chemical shift time scale, between monomeric and dimeric states. The TS ZZ-exchange experiment is useful both for application to larger proteins and for situations in which exchange cross peaks must be detected between nearly degenerate resonances.