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Attenuated T_{2} relaxation by mutual cancellation of dipole–dipole coupling and chemical shift anisotropy indicates an avenue to NMR structures of very large biological macromolecules in solution

Contributed by Kurt Wüthrich
Abstract
Fast transverse relaxation of ^{1}H, ^{15}N, and ^{13}C by dipoledipole coupling (DD) and chemical shift anisotropy (CSA) modulated by rotational molecular motions has a dominant impact on the size limit for biomacromolecular structures that can be studied by NMR spectroscopy in solution. Transverse relaxationoptimized spectroscopy (TROSY) is an approach for suppression of transverse relaxation in multidimensional NMR experiments, which is based on constructive use of interference between DD coupling and CSA. For example, a TROSYtype twodimensional ^{1}H,^{15}Ncorrelation experiment with a uniformly ^{15}Nlabeled protein in a DNA complex of molecular mass 17 kDa at a ^{1}H frequency of 750 MHz showed that ^{15}N relaxation during ^{15}N chemical shift evolution and ^{1}H^{N} relaxation during signal acquisition both are significantly reduced by mutual compensation of the DD and CSA interactions. The reduction of the linewidths when compared with a conventional twodimensional ^{1}H,^{15}Ncorrelation experiment was 60% and 40%, respectively, and the residual linewidths were 5 Hz for ^{15}N and 15 Hz for ^{1}H^{N} at 4°C. Because the ratio of the DD and CSA relaxation rates is nearly independent of the molecular size, a similar percentagewise reduction of the overall transverse relaxation rates is expected for larger proteins. For a ^{15}Nlabeled protein of 150 kDa at 750 MHz and 20°C one predicts residual linewidths of 10 Hz for ^{15}N and 45 Hz for ^{1}H^{N}, and for the corresponding uniformly ^{15}N,^{2}Hlabeled protein the residual linewidths are predicted to be smaller than 5 Hz and 15 Hz, respectively. The TROSY principle should benefit a variety of multidimensional solution NMR experiments, especially with future use of yet somewhat higher polarizing magnetic fields than are presently available, and thus largely eliminate one of the key factors that limit work with larger molecules.
NMR spectroscopy with proteins based on observation of a small number of spins with outstanding spectral properties, which either may be present naturally or introduced by techniques such as sitespecific isotope labeling, yielded biologically relevant information on human hemoglobin (M = 65,000) as early as 1969 (1), and subsequently also for significantly larger systems such as Igs (2). In contrast, the use of NMR for de novo structure determination (3, 4) so far has been limited to relatively small molecular sizes, with the largest NMR structure below molecular weight 30,000. Although NMR in structural biology may, for practical reasons of coordinated use with xray crystallography (5), focus on smaller molecular sizes also in the future, considerable effort goes into attempts to extend the size limit to bigger molecules (for example, see refs. 6–8). Here we introduce transverse relaxationoptimized spectroscopy (TROSY) and present experimental data and theoretical considerations showing that this approach is capable of significantly reducing transverse relaxation rates and thus overcomes a key obstacle opposing solution NMR of larger molecules (7).
At the high magnetic fields typically used for studies of proteins and nucleic acids, chemical shift anisotropy interaction (CSA) of ^{1}H, ^{15}N, and ^{13}C nuclei forms a significant source of relaxation in proteins and nucleic acids, in addition to dipole–dipole (DD) relaxation. This leads to increase of the overall transverse relaxation rates with increasing polarizing magnetic field, B_{0}. Nonetheless, transverse relaxation of amide protons in larger proteins at high fields has been reduced successfully by complete or partial replacement of the nonlabile hydrogen atoms with deuterons and, for example, more than 90% of the ^{15}N, ^{13}C^{α}, and ^{1}H^{N} chemical shifts thus were assigned in the polypeptide chains of a proteinDNA complex of size 64,000 (6). TROSY uses spectroscopic means to further reduce T_{2} relaxation based on the fact that crosscorrelated relaxation caused by DD and CSA interference gives rise to different relaxation rates of the individual multiplet components in a system of two coupled spins ½, I and S, such as the ^{15}N–^{1}H fragment of a peptide bond (9, 10). Theory shows that at ^{1}H frequencies near 1 GHz nearly complete cancellation of all transverse relaxation effects within a ^{15}N–^{1}H moiety can be achieved for one of the four multiplet components. TROSY observes exclusively this narrow component, for which the residual linewidth is then almost entirely because of DD interactions with remote hydrogen atoms in the protein. These can be efficiently suppressed by ^{2}Hlabeling, so that in TROSYtype experiments the accessible molecular size for solution NMR studies no longer is primarily limited by T_{2} relaxation.
Theory
We consider a system of two scalar coupled spins ½, I and S, with a scalar coupling constant J_{IS}, which is located in a protein molecule. T_{2} relaxation of this spin system is dominated by the DD coupling of I and S and by CSA of each individual spin, because the stereochemistry of the polypeptide chain restricts additional interactions of I and S to weak scalar and DD couplings with a small number of remote protons, I_{k}. The relaxation rates of the individual multiplet components of spin S in a single quantum spectrum then may be widely different (9, 11, 12). They can be described by using the singletransition basis operators S_{34}^{±} and S_{12}^{±} (13), which refer to the transitions 1→2 and 3→4 in the standard energylevel diagram for a system of two spins ½, and are associated with the corresponding resonance frequencies, ω_{S}^{12} = ω_{S} + πJ_{IS} and ω_{S}^{34} = ω_{S} − πJ_{IS} (13–16): 1
ω_{S} and ω_{I} are the Larmor frequencies of the spins S and I, T_{2}_{S} and T_{1}_{I} account for the transverse relaxation of spin S and the longitudinal relaxation time of spin I, respectively, by all mechanisms of relaxation except DD coupling between the spins S and I and CSA of the spins S and I. and where γ_{I} and γ_{S} are the gyromagnetic ratios of I and S, ℏ is the Planck constant divided by 2π, r_{IS} the distance between S and I, B_{0} the polarizing magnetic field, and Δσ_{S} and Δσ_{I} are the differences between the axial and the perpendicular principal components of the axially symmetric chemical shift tensors of spins S and I, respectively. R_{1212} and R_{3434} are the transverse relaxation rates of the individual components of the S doublet (11) given by Eqs. 2 and 3, 2 3 where J(ω) represents the spectral density functions at the frequencies indicated: 4 In deriving Eqs. 2 and 3, parallel orientation of the principal symmetry axis of the chemical shift tensor and the vector r_{IS} was assumed. These equations show that whenever CSA and DD coupling are comparable, i.e. p ≈ δ_{S}, the resonance at frequency ω_{S}^{12} may exhibit slow transverse relaxation even for very large molecules.
For a treatment of the relaxation of spin I by Eq. 1 the symbols I and S simply can be interchanged. The singletransition operators I_{13}^{±} and I_{24}^{±} then refer to the transitions between the energy levels 1→3 and 2→4, respectively, which are associated with the frequencies ω_{I}^{13} = ω_{I} + πJ_{IS} and ω_{I}^{24} = ω_{I} − πJ_{IS}, and the relaxation rates R_{1313} and R_{2424} are determined by equations obtained by permutation of the S and I indices in Eqs. 2 and 3, respectively.
To evaluate the contributions from other mechanisms of relaxation we identify I and S as the ^{1}H^{N} and ^{15}N spins in a ^{15}N–^{1}H moiety. The relaxation of ^{15}N then is mainly determined by the CSA of ^{15}N and the DD interactions with the directly attached proton (17), so that the contributions from other interactions, 1/T_{1}_{S} and 1/T_{2}_{S}, to a good approximation can be neglected. For ^{1}H^{N}, 1/T_{1}_{I} and 1/T_{2}_{I} are dominated by DD interactions with other protons I_{k} at distance r_{k}. These can be accounted for by spectral density functions J_{k}(ω), which describe the motions of the vectors joining the individual ^{1}H^{N}–^{1}H_{k} spin pairs (17): 5 6 Here, Eqs. 16 were used to calculate theoretical lineshapes of spin multiplets for given sets of the relaxation parameters, which subsequently were compared with the experimental NMR data. In particular, the inphase absorptive spectrum was calculated using Eq. 7 (14), 7 where V = (1,1), and the relaxation matrix A is the (2×2) matrix on the right side of Eq. 1, and E is the unity matrix.
Experimental Procedures
NMR spectra were recorded on Bruker DRX 750 and Varian Unityplus 400 spectrometers with a 2 mM solution of the specific 1:1 complex formed between a uniformly ^{15}Nlabeled 70residue fushi tarazu (ftz) homeodomain polypeptide and an unlabeled 14bp DNA duplex (18, 19) in 95% ^{1}H_{2}O/5% ^{2}H_{2}O at pH 6.0 and 4°C.
The isotropic rotational correlation time, τ_{c}, of the complex was estimated from the T_{1}/T_{2} ratio of the relaxation times of the backbone ^{15}N nuclei (20). The experimental schemes of Farrow et al. (21) were used for measurements of T_{1} (^{15}N) and T_{2} (^{15}N) for backbone nitrogen atoms.
The TROSY approach (Fig. 1) and conventional [^{15}N,^{1}H]correlation spectroscopy (COSY) (22, 23) experiments were used to correlate ^{1}H and ^{15}N resonances. For all spectra t_{1max} = 90 ms and t_{2max} = 171 ms were used. In TROSY the evolution of the I,S spin system due to the ^{1}J_{IS} scalar coupling was not refocused during t_{1} and t_{2}, thus avoiding suppression of crosscorrelated relaxation during these periods. To obtain the pure absorptive spectrum containing only the most slowly relaxing component of the twodimensional multiplets, the scheme of Fig. 1 was used (see also Appendix: Quantitative Analysis of TROSY).
Results
The NMR experiments with the uniformly ^{15}Nlabeled ftz homeodomain complexed with a 14bp DNA duplex were performed at 4°C. The T_{1}/T_{2} ratio of ^{15}N was used to estimate the effective global correlation time, τ_{c}, of the complex (20). For the backbone amide groups, average T_{1} (^{15}N) and T_{2} (^{15}N) values of 0.720 ± 0.03 and 0.042 ± 0.005 s, respectively, were measured at 400 MHz, resulting in a global rotational correlation time of τ_{c} = 20 ± 2 ns. This τ_{c} value corresponds to that expected for a spherical protein of size 40 kDa in H_{2}O solution at 35°C.
Fig. 2 shows a small region from ^{15}N–^{1}H correlation spectra of the ftz homeodomainDNA complex that contains the resonance of the indole ^{15}N–^{1}H moiety of Trp48, which is buried in the core of the protein (19). In the conventional [^{15}N,^{1}H]COSY experiment (22, 23), decoupling of ^{1}H and ^{15}N during the time periods t_{1} and t_{2}, respectively, leads to detection of a single correlation peak per ^{15}N–^{1}H moiety (Fig. 2a). If the same [^{15}N,^{1}H]COSY spectrum is recorded without decoupling, four crosspeaks are observed per ^{15}N–^{1}H moiety, which show largely different linewidths (Fig. 2b). The crosspeak at (ω_{1} = 130.7 ppm, ω_{2} = 10.78 ppm) exhibits the broadest linewidths in both dimensions, which shows that it originates from the rapidly relaxing components of both ^{1}H^{N} and ^{15}N. Onedimensional crosssections taken along ω_{2} and ω_{1} at the positions indicated by arrows in the spectra presented in Fig. 2 show that the two crosspeaks at (ω_{1} = 132.1 ppm, ω_{2} = 10.78 ppm) and (ω_{1} = 130.7 ppm, ω_{2} = 10.65 ppm) are broadened either along ω_{1} or along ω_{2} (Fig. 3). The crosspeak at (ω_{1} = 132.1 ppm, ω_{2} = 10.65 ppm) displays narrow linewidths in both dimensions, showing that it originates from the two slowly relaxing components of the ^{15}N–^{1}H doublets. The TROSYtype correlation experiment, which does not use decoupling either during t_{1} or t_{2}, contains only this narrowest correlation peak (Fig. 2c), which shows about 60% and 40% decrease in the linewidths of the ^{15}N and ^{1}H resonances, respectively, when compared with the collapsed crosspeak in the conventional, broadbanddecoupled spectrum (Fig. 2).
The fits of the experimental line shapes shown in Fig. 3 were obtained with lineshape calculations using the parameters τ_{c} = 20 ns and ^{1}J(^{1}H,^{15}N) = 105 Hz, where the chemical shift anisotropies, Δσ_{H} and Δσ_{N}, were adjusted for the best fit. Because there was an otherwise unaccountable deviation from the Lorentzian lineshape we included a longrange scalar coupling ^{2}J(^{1}H^{δ1},^{15}N^{ɛ1}) = −5 Hz (24) in the calculations, and T_{1} and T_{2} relaxation of ^{1}H^{N} because of DD coupling with other protons was modeled by placing three protons at a distance of 0.24 nm from ^{1}H^{N}. Application of one or a series of 180° pulses on spin I during the evolution of spin S interchanges the slowly and rapidly relaxing components of the S multiplet, which results in averaging of the slow and fast relaxation rates and elimination of the CSA/DD interference (25, 26). Indeed, the line shapes of the ^{1}H^{N} and ^{15}N resonances measured with conventional [^{15}N,^{1}H]COSY are well reproduced if the average of the two relaxation rates is used in the simulation (Fig. 3 a1 and b1). The bestfit values of Δσ_{H} = −16 ppm and Δσ_{N} = −160 ppm correspond closely to the experimentally measured chemical shift anisotropies of ^{1}H and ^{15}N in ^{15}N–^{1}H moieties. With solidstate NMR studies of ^{15}N–^{2}D moieties, values for Δσ_{D} near −14 ppm (27) and for Δσ_{N} of −160 ppm (28) were determined. Independently, solution NMR experiments yielded values for Δσ_{H} of backbone amide protons in the range 3 to 15 ppm (37) and Δσ_{N} near −170 ppm (10).
Discussion
In the experiments with the ftz homeodomainDNA complex the overall transverse relaxation rates of ^{15}N and ^{1}H^{N} in the indole ^{15}N–^{1}H moiety of a buried tryptophan were reduced by 60% and 40%, respectively, when using a TROSYtype [^{15}N,^{1}H]correlation experiment instead of the conventional [^{15}N,^{1}H]COSY scheme. At a first glance this may appear to be a modest improvement, but a closer look reveals that DD coupling with remote protons, which could be nearly completely suppressed by replacement of the nonlabile hydrogen atoms with ^{2}H (e.g., refs. 6 and 8), accounts for 95% of the residual T_{2}(^{1}H^{N}) relaxation and 75% of the residual T_{2}(^{15}N) relaxation. In a corresponding DNA complex with the perdeuterated ftz homeodomain the reduction of the T_{2} relaxation rates of the ^{15}N–^{1}H moieties by the use of TROSY at 750 MHz would be about 40fold for ^{1}H^{N} and about 10fold for ^{15}N.
Using Eqs. 1–6 with Δσ_{H} = −16 ppm, Δσ_{N} = −160 ppm, r_{HN} = 0.101 nm and parallel orientation of the principal axis of the CSA tensor with the vector r_{HN}, we evaluated the dependence of the residual T_{2} relaxation rates of ^{15}N and ^{1}H in TROSYtype experiments on the polarizing magnetic field B_{0} and the molecular size. These calculations showed that nearly complete compensation of T_{2} relaxation because of DD and CSA within the ^{15}N–^{1}H moieties is obtained at a B_{0} strength corresponding to a ^{1}H frequency near 1,100 MHz, i.e., at this field strength (p − δ_{S}) ≅ 0 and (p − δ_{I}) ≅ 0 in Eq. 2. Theory further predicts that the residual TROSY T_{2} relaxation rates because of DD and CSA interactions within the ^{15}N–^{1}H fragment are practically independent of the molecular size. For perdeuterated proteins the size limit for TROSYtype [^{15}N,^{1}H]correlation experiments thus is not critically determined by T_{2} relaxation, but one needs nonetheless to consider that the effect of deuteration of the nonlabile proton sites in the protein is dependent on conformation. For the ^{15}N–^{1}H moieties in βsheet secondary structure, DD and CSA interactions within the ^{15}N–^{1}H^{N} fragment are the only sources of transverse relaxation that need to be considered, whereas in αhelices the two sequentially adjacent ^{1}H^{N} protons (3) contribute significantly to the transverse relaxation of the ^{15}N and ^{1}H^{N} spins.
To provide a tangible illustration (Fig. 4) we calculated the ^{1}H^{N} and ^{15}N line shapes for two perdeuterated spherical proteins in ^{1}H_{2}O solution with rotational correlation times τ_{c} of 60 and 320 ns, which corresponds to molecular masses of 150 and 800 kDa, respectively. A magnetic field B_{0} corresponding to a resonance frequency 750 MHz for protons was assumed. To account for the worst possible situation for DD interaction with remote protons, two protons were placed at 0.29 nm from ^{1}H^{N}. The linewidth of the narrow component of the ^{15}N doublet increases only slightly with molecular mass and is about 5 Hz at 150 kDa and 15 Hz for a 800kDa protein (Fig. 4). The ^{1}H^{N} linewidth depends more strongly on the residual DD interactions with remote protons and is about 15 Hz at 150 kDa and 50 Hz for a 800kDa protein. For the 150kDa protein these numbers correspond to 10 and 4fold reduction of the ^{15}N and ^{1}H^{N} TROSY linewidths, respectively, when compared with a conventional [^{15}N,^{1}H]COSY experiment with broadband decoupling of ^{15}N and ^{1}H. For large molecular sizes the experimental scheme of Fig. 1 may, in principle, be further improved by elimination of the 180° refocusing radio frequency (rf)pulses during the insensitive nuclei enhanced by polarization transfers (INEPTs), because during the INEPT mixing times these pulses mix the multiplet components with slow and fast T_{2} relaxation in a similar way as during the entire experiment in conventional [^{15}N,^{1}H]COSY. The elimination of decoupling sequences and 180° pulses from TROSYtype NMR pulse sequences also may have implications for future probe designs, because the constraints by the requirements for minimal radio frequency heating and maximal B_{1} homogeneity then may be relaxed, permitting a better optimization of other parameters such as sensitivity or sample diameter.
The TROSY principle drastically reduces all major sources of relaxation throughout the entire NMR experiment, including signal acquisition, and is clearly distinct from the use of heteronuclear multiplequantum coherence to reduce dipolar relaxation between heteronuclei (29), which previously was used for measurements of ^{3}J_{HαHβ} scalar coupling constants in proteins (30). Heteronuclear multiplequantum coherences are subject to dipolar relaxation with remote spins as well as to CSA relaxation, which limits the use of these coherences at high polarizing magnetic fields. Moreover, the slow relaxation of the multiplequantum coherences cannot be used during signal acquisition (14), which is critical for large molecules.
The following are some initial considerations on practical applications of the TROSY principle: (i) Because only one of the four multiplet components of ^{15}N–^{1}H moiety is retained in TROSYtype experiments, the conventional [^{15}N,^{1}H]COSY is intrinsically more sensitive. However, for measurements with proteins at ^{1}H frequencies higher than 500 MHz, TROSY will provide a much better ratio of signal height to noise. (ii) TROSYtype [^{13}C,^{1}H]correlation experiments with the ^{13}C–^{1}H moieties of the aromatic rings of Tyr, Phe, and Trp yield comparable results to those for ^{15}N–^{1}H moieties (unpublished results). (iii) Twodimensional nuclear Overhauser effect spectroscopy (NOESY) experiments correlating amide protons and aromatic protons can be relayed by TROSYtype heteronuclear correlation experiments. In favorable cases this might result in low resolution structures for severalfold larger proteins than have been accessible so far. (iv) We anticipate that a wide variety of NMR experiments currently used for resonance assignments and collection of conformational constraints can be optimized for larger molecular sizes by use of the TROSY approach in one or several dimensions.
Acknowledgments
We thank M. Wahl for the preparation of the ftz homeodomainDNA complex and Dr. R. Brüschweiler for critical reading of the manuscript. Financial support was obtained from the Schweizerischer Nationalfonds (Project 31.49047.96).
Quantitative Analysis of TROSY
The coherence transfer during the pulse sequence of Fig. 1 was evaluated using the product operator formalism (31) as implemented in the program poma (32), and the resulting phases of the rfpulses and the receiver were transferred into the experimental pulse program according to (33). The transverse proton magnetization after the first 90° pulse on protons (a in Fig. 1) then is given by Eq. 8: 8 During the delay 2τ_{1} the scalar coupling ^{1}J(^{1}H,^{15}N) evolves, so that the first 90°(^{15}N) pulse generates twospin coherence. With τ_{1} = 1/(4^{1}J(^{1}H,^{15}N)) we have at time b for the first step of the phase cycle (Fig. 1): 9 The evolution of these terms during t_{1}, including relaxation, was evaluated using the singletransition basis operators S_{12}^{±} and S_{34}^{±}: 10 11 The time evolution of the expectation values of these operators can be obtained by integration of Eq. 1 with initial conditions derived from Eq. 9 and the assumption that 1/T_{1}_{I} ≪ ^{1}J(^{1}H,^{15}N), which results in the following density matrix at time c: 12 The relaxation factors R_{ij} are related to the individual relaxation rates of the multiplet components by Eqs. 13 and 14: 13 14 The subsequent polarization transfer step (time period c to d in Fig. 1) links the evolution period t_{1} with the acquisition period t_{2}. The density matrix at time point c is represented by Eq. 15, where only those I^{−} and I^{−}S_{z} coherences are retained that result in detectable signals during data acquisition: 15 The other steps in the phase cycle of Fig. 1 can be analyzed in an analogous fashion. Accumulation of the eight transients of the pulse sequence results in the following density matrix for the real part of the interferogram: 16 Incrementation of the phase ψ_{1} by 90° at each discrete value of t_{1} leads to the corresponding imaginary part: 17 Eqs. 16 and 17 are combined to the hypercomplex interferogram that represents pure phase correlation in the ω_{1} dimension.
The treatment of the relaxation of the ^{1}H^{N} coherences during the acquisition period t_{2} is similar to the treatment of ^{15}N during t_{1} (see Theory). The signals generated by I^{−} and I^{−}S_{z} coherences that are received during t_{2} are described by Eqs. 18 and 19, respectively: 18 19 where A is a proportionality coefficient. Substitution of Eqs. 18 and 19 into Eqs. 16 and 17 results in the hypercomplex interferogram corresponding to the 1→2 and 2→4 transitions of the ^{1}H,^{15}N spin system: 20 Finally, the Fourier transformation of the hypercomplex interferogram represented by Eq. 20 results in the pure absorptive correlation spectrum, with resonance frequencies in ω_{1} and ω_{2} corresponding to the desired individual component of the ^{15}N–^{1}H multiplet.
ABBREVIATIONS
 rf,
 radio frequency;
 DD,
 dipole–dipole;
 CSA,
 chemical shift anisotropy;
 COSY,
 correlation spectroscopy;
 TROSY,
 transverse relaxationoptimized spectroscopy;
 ftz homeodomain,
 fushi tarazu homeodomain polypeptide of 70 amino acid residues, with the homeodomain in positions 3–62
 Accepted September 3, 1997.
 Copyright © 1997, The National Academy of Sciences of the USA
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