TROSY in tripleresonance experiments: New perspectives for sequential NMR assignment of large proteins
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Contributed by Kurt Wüthrich
Abstract
The NMR assignment of ^{13}C, ^{15}Nlabeled proteins with the use of triple resonance experiments is limited to molecular weights below ∼25,000 Daltons, mainly because of low sensitivity due to rapid transverse nuclear spin relaxation during the evolution and recording periods. For experiments that exclusively correlate the amide proton (^{1}H^{N}), the amide nitrogen (^{15}N), and ^{13}C atoms, this size limit has been previously extended by additional labeling with deuterium (^{2}H). The present paper shows that the implementation of transverse relaxationoptimized spectroscopy ([^{15}N,^{1}H]TROSY) into triple resonance experiments results in severalfold improved sensitivity for ^{2}H/^{13}C/^{15}Nlabeled proteins and approximately twofold sensitivity gain for ^{13}C/^{15}Nlabeled proteins. Pulse schemes and spectra recorded with deuterated and protonated proteins are presented for the [^{15}N, ^{1}H]TROSYHNCA and [^{15}N, ^{1}H]TROSYHNCO experiments. A theoretical analysis of the HNCA experiment shows that the primary TROSY effect is on the transverse relaxation of ^{15}N, which is only little affected by deuteration, and predicts sensitivity enhancements that are in close agreement with the experimental data.
In the standard protocol for protein structure determination by NMR spectroscopy, sequencespecific resonance assignment plays a pivotal role (1). Several different assignment strategies are available, and one of the established procedures for obtaining sequential assignments (2) involves uniform ^{13}C/^{15}N labeling and delineation of heteronuclear scalar couplings with tripleresonance experiments (3–7). In these experiments, the transfer of magnetization along networks of scalarcoupled spins includes long delays during which ^{13}C and ^{15}N magnetization evolve in the transverse plane. Fast transverse relaxation during these delays and during ^{1}H acquisition, limits the application of tripleresonance NMR experiments with larger proteins. For experiments that exclusively correlate ^{1}H^{N}, ^{15}N, and ^{13}C, the situation has been improved by ^{2}Hlabeling of the ^{13}CH_{n} moieties, which eliminates dipolar ^{13}C relaxation by the directly attached protons (8) and reduces ^{1}H^{N} line broadening by dipole–dipole (DD) coupling with remote protons. However, uniform deuteration also imposes stringent limitations on the structural information that can be obtained by NMR (8,9) and does not significantly reduce ^{15}N relaxation during the delays when this spin is in the transverse plane. Here, we propose to extend the application of tripleresonance experiments by using the principle of transverse relaxationoptimized spectroscopy (TROSY) (10). TROSY suppresses transverse relaxation in ^{15}N–^{1}H^{N} moieties by constructive use of interference between dipole–dipole coupling and chemical shift anisotropy (CSA) (10) and thus results in improved sensitivity of tripleresonance experiments by minimizing ^{15}N transverse relaxation during ^{15}N evolution periods and ^{1}H^{N} transverse relaxation during detection. Because part of the gain achieved with TROSY stems from the reduced T_{2} relaxation rate of ^{15}N, TROSY will benefit tripleresonance experiments with deuterated as well as protonated proteins. In this paper, we present experimental schemes for the implementation of TROSY in the amide protontonitrogentoα carbon correlation (HNCA) and amide protontonitrogentocarbonyl carbon correlation (HNCO) experiments, which correlate the ^{15}N–^{1}H(i) group with ^{13}C^{α}(i) and ^{13}C^{α}(i − 1), and with ^{13}CO(i − 1), respectively (11, 12). For a quantitative evaluation of the sensitivity gain that can be achieved, we compare [^{15}N, ^{1}H]TROSYHNCA with conventional HNCA (13).
METHODS
Tripleresonance experiments use coherence transfers along a network of scalar coupled ^{15}N, ^{13}C, and ^{1}H spins (3–7). Thereby, coherence transfer from ^{15}N to either ^{13}C^{α} or ^{13}CO requires long delays due to the small ^{1}J(^{15}N, ^{13}C^{α}) and ^{1}J(^{15}N, ^{13}CO)coupling constants. Because the ^{15}N magnetization is in the transverse plane throughout these transfer periods, the ^{15}N chemical shift evolution is recorded in a constanttime (ct) fashion during the magnetization transfer (14, 15), and relaxation of ^{15}N due to DD coupling with the directly bound ^{1}H^{N} and to ^{15}N CSA leads to severe loss of coherence. Using the TROSY principle (10), transverse relaxation during these critical ^{15}N evolution periods can be efficiently suppressed. Similarly, ^{1}H^{N} transverse relaxation during detection due to ^{1}H^{N} CSA and to DD coupling with ^{15}N can be suppressed with the use of TROSY.
In the following product operator analysis (16) of the [^{15}N, ^{1}H]TROSYHNCA experiment (Fig. 1), we describe the ^{13}C magnetization (C) with Cartesian operators, whereas for the ^{1}H^{N} (H) and ^{15}N (N) magnetizations singletransition operators (17) are used. For both ^{13}C/^{15}N and ^{2}H/^{13}C/^{15}Nlabeled proteins, the ^{1}H as well as the ^{15}N steady–state magnetizations are used at the outset, and the density matrix after the first insensitive nuclei enhanced by polarization transfer (INEPT) step at time point b in Fig. 1 becomes 1 where the constant factors u and v represent the relative magnitudes of the steady–state ^{1}H and ^{15}N magnetizations (18, 19), and the singletransition operators N_{r}^{±} and N_{s}^{±} represent the ^{15}N magnetization associated with the rotating frame transition frequencies ω_{s}^{N} = ω^{N} + πJ_{HN} and ω_{r}^{N} = ω^{N} − πJ_{HN}, respectively (20). Only the N_{s}^{−} and N_{s}^{+} terms are transferred to detectable magnetization after the single transitiontosingle transition polarization transfer (ST2PT) element (18) (time points e–f in Fig. 1). During the ct period T/2 between time points b and c, the N_{s}^{±} spin operators evolve due to the ^{15}N chemical shift and the Jcouplings to the two neighboring αcarbons, ^{13}C^{α}(i) and ^{13}C^{α}(i − 1). The resulting antiphase terms N_{s}^{±} C_{z}^{α}(i) and N_{s}^{±} C_{z}^{α} (i − 1) are converted to multiplequantum coherences by the 90° (^{13}C^{α}) pulse at time point c. During t_{2}, these terms evolve due to the ^{13}C^{α} chemical shift because carbonyl carbons and deuterons or protons are decoupled (Fig. 1). The 90° (^{13}C^{α}) pulse at time point d completes the ^{13}C^{α} evolution period. During the second half of the ct ^{15}N evolution period, the N_{s}^{±} C_{z}^{α} (i) and N_{s}^{±} C_{z}^{α} (i − 1) terms again evolve due to the ^{15}N chemical shift (21), 2 Two signals in the ^{13}C(t_{2}) dimension exhibit the intraresidual correlation ω_{1}(^{15}N_{i})/ω_{2}(^{13}C_{i}^{α}) modulated by cos(ω^{C}(i)t_{2}) and the sequential correlation ω_{1}(^{15}N_{i})/ω_{2}(^{13}C_{i−1}^{α}) modulated by cos(ω^{C}(i − 1)t_{2}). Transverse ^{15}N relaxation during the ct period T = 1/^{1}J_{NCα} is given by (see Appendix): 3 where the term p_{HKj}^{2}J(0) represents the relaxation of ^{15}N due to DD interactions of ^{1}H^{N} (H) with remote protons K^{j} (see Appendix) and R_{s}^{N} is the ^{15}N relaxation rate due to DD coupling with ^{1}H^{N} and to ^{15}N chemical shift anisotropy CSA. Auto and crossrelaxation terms due to ^{13}C^{α}–^{15}N and ^{13}CO–^{15}N DD coupling were neglected because they contribute <10% to the overall relaxation rate of ^{15}N (see Appendix). The ST2PT element (18) (Fig. 1, ef) transfers the magnetization from ^{15}N to ^{1}H^{N} (N_{s}^{+} → H_{s}^{−}), resulting in the following coherence being acquired during t_{3}: 4 In Eq. 4, the transition H_{s}^{−} is associated with the resonance frequency ω_{s}^{H} = ω^{H} + πJ_{HN}, and the ^{1}H^{N} relaxation is given by Eq. 5 (10): 5 where R_{s}^{H} is the ^{1}H^{N} relaxation rate due to DD coupling with ^{15}N and to ^{1}H^{N} CSA (10).
EXPERIMENTAL PROCEDURES
NMR spectra were recorded with two 23kDa globular proteins, i.e., uniformly ^{2}H/^{13}C/^{15}Nlabeled gyrase23B (95% H_{2}O/5% D_{2}O, pH 6.5 at 20°C) (22–24) and uniformly ^{13}C/^{15}Nlabeled FimC (90% H_{2}O/10% D_{2}O, pH 5.0 at 20°C) (25). A Bruker DRX750 spectrometer equipped with four radiofrequency channels was used. Data processing included zerofilling and sine bell filtering (26), using the program prosa (27), and the spectra were analyzed with xeasy (28). For gyrase23B and FimC at 20°C, the isotropic rotational correlation time, τ_{c}, was estimated from the T_{1}/T_{2} ratio of the backbone ^{15}N nuclei (29) to be 15 ns.
RESULTS
The pulse sequence of Fig. 1 was applied with ^{2}H/^{13}C/^{15}Nlabeled gyrase23B (22–24) and ^{13}C/^{15}Nlabeled FimC (25). Fig. 2a shows [ω_{2}(^{13}C), ω_{3}(^{1}H)] strips from a threedimensional (3D) [^{15}N, ^{1}H]TROSYHNCA spectrum of gyrase23B, and Fig. 2b shows the corresponding strips from a conventional HNCA experiment (13) recorded with identical conditions. Using TROSY, all sequential ^{1}H^{N}^{13}C^{α} connectivities could be identified, as indicated by the broken lines (Fig. 2a), whereas with conventional HNCA no reliable sequential assignment was possible (Fig. 2b). A more quantitative assessment of the gain in signaltonoise is afforded by the cross sections in Fig. 2a′ and b′. Data of this type were collected in Fig. 3 for the complete sequence of gyrase23B. In [^{15}N, ^{1}H]TROSYHNCA (Fig. 3a), nearly all sequential cross peaks were present with sufficient intensity to allow sequential assignments, which was feasible only for a fraction of the sequence when conventional HNCA is used (Fig. 3b). TROSY also yielded greatly increased intensities of the intraresidual correlation peaks [ω_{1}(^{15}N_{i})/ω_{2}(^{13}C_{i}^{α})/ω_{3}(^{1}H_{i}^{N})] (Fig. 3a′ and b′). In line with theoretical considerations (10), the highest sensitivity gains were obtained for the immobilized core of the protein, with values of 2.9 for the αhelices and 3.4 for the βsheets. The average sensitivity gain for sequential and intraresidual correlation peaks of the entire protein was 2.4fold.
Measurements corresponding to those in Figs. 2 and 3 also were performed with uniformly ^{13}C/^{15}Nlabeled FimC in order to evaluate the performance of [^{15}N, ^{1}H]TROSYHNCA with protonated proteins. The experimental scheme of Fig. 1 was used with ^{1}H^{α} decoupling. The average sensitivity enhancement for the entire protein was 1.5fold, with a sensitivity gain of 1.7 for the regular secondary structures, which in FimC consist exclusively of βsheets.
The pulse scheme of the [^{15}N, ^{1}H]TROSYHNCO experiment (Fig. 4a) was applied to ^{2}H/^{13}C/^{15}Nlabeled gyrase23B with identical conditions to those described for the HNCA experiment in Fig. 2. As an illustration of the results obtained, Fig. 4b and c compares corresponding crosssections from [^{15}N, ^{1}H]TROSYHNCO and conventional HNCO (30). From a corresponding data set to Fig. 3, the average gain in sensitivity for the entire protein was found to be 2.4fold, with values of 2.5 and 2.9 for the αhelices and the βsheets, respectively.
DISCUSSION
The HNCA and HNCO measurements (Figs. 2–4) showed that significant improvement of triple resonance experiments can be achieved by suppression of transverse ^{15}N and ^{1}H^{N} relaxation with TROSY. In this section, the origins of the enhanced sensitivity of [^{15}N, ^{1}H]TROSYHNCA are further analyzed.
In Eq. 5, the ^{1}H^{N} relaxation can be represented by a single exponential, with the rate constant 6 where R_{2}^{T}(^{1}H^{N}) denotes the transverse ^{1}H^{N} relaxation rate in [^{15}N, ^{1}H]TROSYHNCA. To a good approximation for the molecular size range of interest, the ^{15}N relaxation in [^{15}N, ^{1}H]TROSYHNCA (Eq. 3) may similarly be represented by a single exponential decay, with the rate constant R_{2}^{T}(^{15}N): 7 The approximation of Eq. 7 assumes that p_{HKj}^{2}J(0)T ≪ 1, which is satisfied for commonly used ct periods, T, over the τ_{c} range 1–80 ns. For the conventional HNCA experiment, corresponding transverse relaxation rates, R_{2}^{C}(^{15}N) and R_{2}^{C}(^{1}H^{N}), were evaluated as the average of the relaxation rates in the individual components of the ^{15}N and ^{1}H^{N} doublets, respectively. Using Eqs. 6 and 7 for a 23kDa protein with τ_{c} = 15 ns at 750 MHz, and the corresponding formalism for conventional HNCA, one predicts for the protonated protein that TROSY yields 2.9fold and 1.5fold reductions of the ^{15}N and ^{1}H^{N} relaxation rates, respectively, when compared to conventional HNCA (Table 1). For conventional HNCA, one expects further that deuteration reduces the ^{1}H^{N} relaxation rates 2.5fold and 1.6fold for βsheets and αhelices, respectively, and that deuteration yields only a small reduction, by less than a factor 1.3, of the ^{15}N relaxation rate. For [^{15}N, ^{1}H]TROSYHNCA, deuteration has approximately the same absolute effects on R_{2}^{T}(^{15}N) and R_{2}^{T}(^{1}H^{N}), but because of the greatly reduced R_{s}^{N} and R_{s}^{H} rates the relative improvement is larger, i.e., up to 6.5 for ^{1}H^{N} and up to 2.9 for ^{15}N (Table 1).
We calculated a theoretical sensitivity gain for [^{15}N, ^{1}H]TROSYHNCA relative to conventional HNCA by using Eq. 8, 8 where A^{T} and A^{C} are the peak amplitudes in corresponding [^{15}N, ^{1}H]TROSYHNCA and conventional HNCA experiments, respectively. The amplitudes are linearly proportional to the ^{1}H^{N} relaxation rates, whereas the dependence on the ^{15}N transverse relaxation rates is exponential because of the ct evolution in the ^{15}N dimension (15). For a 23kDa protein, Eq. 8 predicts an 8fold sensitivity gain for the hypothetical isolated ^{15}N–^{1}H^{N} moiety. When allowing for DD coupling with remote protons, the gain for βsheets and αhelices amounts to 4.7 and 2.9 in deuterated proteins and to 1.8 and 2.0 in protonated proteins, respectively. Sensitivity gains measured for the ^{2}H/^{13}C/^{15}Nlabeled gyrase23B were 3.4 for βsheets and 2.9 for αhelices, and for ^{13}C/^{15}Nlabeled FimC, a gain of 1.7 was measured for the βsheet regions. These experimental data are in good agreement with the theoretical predictions (Table 1).
The sensitivity gain (Eq. 8) depends on the molecular size. Fig. 5 shows the relative peak amplitudes calculated for [^{15}N, ^{1}H]TROSYHNCA (bold lines) and for conventional HNCA (thin lines) as a function of the rotational correlation time, using the parameters listed in Table 1. The thick and thin solid lines indicate the peak intensities for ^{15}N–^{1}H^{N} moieties located in βsheet regions of a ^{2}H/^{13}C/^{15}Nlabeled protein. The dashed lines show the corresponding intensities expected for a ^{13}C/^{15}Nlabeled protein. The rapid decrease of the peak amplitude with increasing molecular size limits the application of the conventional HNCA experiment to much smaller proteins than [^{15}N, ^{1}H]TROSYHNCA (Fig. 5). Actually, for deuterated proteins similar peak amplitudes are expected for τ_{c} = 15 ns with HNCA and τ_{c} = 50 ns with [^{15}N, ^{1}H]TROSYHNCA. For τ_{c} values above 15 ns, [^{15}N, ^{1}H]TROSYHNCA with protonated proteins is predicted to yield similar sensitivity as conventional HNCA with deuterated proteins (see Fig. 5).
Similar results to those obtained here with [^{15}N, ^{1}H]TROSYHNCA are predicted for the use of [^{15}N, ^{1}H]TROSY with other tripleresonance experiments that use coherence pathways with ct ^{15}N evolution periods. For HNCO this is born out by the experiment in Fig. 4, and similar results have been obtained for HN(CO)CA (15), HNCACB (31, 32), and HN(CO)CACB (7,33) (M.S., G.W., K.P., H.S., and K.W., unpublished results). Overall, the present investigation predicts that TROSYtype tripleresonance experiments (Figs. 1 and 4) will be applicable for the assignment of significantly larger proteins than the corresponding conventional tripleresonance experiments. The predictions of Fig. 5 may serve as a platform for estimating the feasibility of resonance assignments and the instrument time needed for particular proteins in the size range 10–250 kDa. Thereby, one has to take into account that these curves can only provide a general guideline, since the CSA parameters may be somewhat variable in the individual amino acid residues (34–38).
Appendix
The transverse ^{15}N relaxation rate is calculated for a fourspin system HNCK representing the backbone atoms ^{1}H^{N}, ^{15}N, and ^{13}C^{α} and a remote proton K, with scalar couplings ^{1}J_{HN}, ^{1}J_{NC}, and J_{KN}. ^{13}CO, which is not considered (see below), would be treated in the same way as ^{13}C^{α}. The following single spin transition basis operators (47) were selected to evaluate the transverse relaxation of the ^{15}N singlequantum coherences that evolve in [^{15}N, ^{1}H]TROSYHNCA: A1 In this basis, the Liouville matrix in the rotating frame has the diagonal form given by Eq. A2: A2
with ω_{r}^{N} = Ω^{N} − Ω_{0} + π^{1}J_{HN} and ω_{s}^{N} = Ω^{N} − Ω_{0} − π^{1}J_{HN}, where Ω_{0} is the reference frequency and Ω^{N} the Larmor frequency of N. In calculating the relaxation matrix, Γ, the DD interactions HN, NC, CK, and HK, the CSA of H and N, and all crosscorrelation terms between these relaxation interactions are taken into account. Not included are the very small NC DD interactions (48). In the slowtumbling approximation, only terms in J(0) need to be retained: A3 where the Γ_{ii} represent the relaxation rates of individual transitions of the N multiplet. Γ_{25}, Γ_{52}, Γ_{47}, and Γ_{74} represent the crossrelaxation between different nondegenerate transitions of the N multiplet with resonance frequencies separated by π^{1}J_{HN}. The individual relevant matrix elements are: A4 A5 A6 A7 A8 A9 A10 A11 A12 f_{ki} = 0.5(3cos^{2}Θ_{kl} − 1), p_{ij} = (2r_{ij}^{3})^{−1}ћγ_{i}γ_{j} and δ_{N} = (3)^{−1} γ_{N}B_{0}Δσ_{N}, where ћ is the Planck constant divided by 2π, Θ_{kl} the angle between the unique tensor axes of the interactions k and l, γ_{i} the gyromagnetic ratio of spin i, r_{ij} the distance between the spins i and j, B_{0} the polarizing magnetic field, and Δσ_{N} the difference between the axial and perpendicular principal components of the ^{15}N chemical shift tensor, which is assumed to be axially symmetric. Numerical calculations using Eqs. A4–A12 showed that the terms (p_{CN}^{2} ± 2f_{pCN}_{δN}p_{CN}δ_{N} ± 2f_{pCN}_{pHN}p_{CN}p_{HN})⋅4J(0) contribute <10% to the overall relaxation of ^{15}N and can be neglected. This applies for both ^{13}C^{α} and ^{13}CO. The Eqs. A2 and A3 show that there is no interference between the group of basis operators B_{1}^{±}, B_{3}^{±}, B_{6}^{±}, and B_{8}^{±} and the other four basis operators. Thus, for these operators, the time evolution can be calculated individually, resulting in singleexponential relaxation determined exclusively by interactions within the HN spin subsystem. Because of the pairwise linkage of B_{2}^{±} with B_{5}^{±}, and of B_{4}^{±} with B_{7}^{±}, the relaxation of the corresponding transitions is in general biexponential. However, since Γ_{ij} ≪ π^{1}J_{HN} (i ≠ j) the offdiagonal elements can be neglected, so that a singleexponential decay is obtained for all basis operators: A13 The sum of the operators B_{2}^{±}, B_{4}^{±}, B_{6}^{±}, and B_{8}^{±} represents the magnetization of the TROSY ^{15}N multiplet component, so that the transverse ^{15}N magnetization at time t can be described by: A14 where N_{s}^{±} = N^{±} (1/2 − H_{z}) and R_{s}^{N} = (p_{HN}^{2} − 2f_{pHN}_{δN}p_{HN}δ_{N} + δ_{N}^{2})⋅4J(0). Eq. A14 can be further simplified by assuming that J_{NK} = 0. Furthermore, since N^{±} K_{z} does not result in an observable signal, the evolution of the ^{15}N magnetization can be described by A15: A15 This treatment can be expanded to n mutually noninteracting remote protons, K^{1}, K^{2}, …, K^{n}, resulting in Eq. A16: A16 Eq. A16 was used for the derivation of Eq. 3 in the main text.
ABBREVIATIONS
 ct,
 constanttime;
 DD,
 dipole–dipole;
 CSA,
 chemical shift anisotropy;
 HNCA,
 amide protontonitrogentoα carbon correlation;
 HNCO,
 amide protontonitrogentocarbonyl carbon correlation;
 ST2PT,
 single transitiontosingle transition polarization transfer;
 TROSY,
 transverse relaxationoptimized spectroscopy;
 3D,
 threedimensional
 Accepted September 10, 1998.
 Copyright © 1998, The National Academy of Sciences
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