Protein Backbone Dynamics and 15N Chemical Shift Anisotropy from Quantitative Measurement of Relaxation Interference Effects

Cross-correlation between 15N-1H dipolar interactions and 15N chemical shift anisotropy (CSA) gives rise to different relaxation rates of the doublet components of 15N-{1H} peptide backbone amides. A simple scheme for quantitative measurement of this effect is described which yields information on the magnitude of the CSA from the relative intensities of 1H-15N correlations obtained with two slightly different pulse schemes. The method is applied to a sample of uniformly 15N-enriched ubiquitin and measurements conducted at two field strengths (8.5 and 14 T) yield identical results. The degree of relaxation interference correlates with the isotropic 15N chemical shift and results indicate that the sum of the most shielded principal components of the CSA tensor is nearly invariant to structural differences in the polypeptide backbone. The relaxation interference is directly proportional to the generalized order parameter, S2, of the peptide backbone amides, and this relation can be utilized to obtain approximate values for these order parameters. There is a renewed interest in understanding the relation between protein structure and 13C and 15N chemical shifts.1-3 Indeed, recent ab initio calculations show considerable promise for providing an accurate correlation between chemical shift and the structure of the peptide backbone. In proteins, the results of calculations could only be compared with the value of the isotropic chemical shift, as accurate values for the individual chemical shift anisotropy (CSA) tensor elements in proteins are not easily measured. Here we demonstrate that a measure for the magnitude of the CSA of individual peptide backbone 15N nuclei can be obtained from quantitative measurement of interference effects between the CSA and dipolar relaxation mechanisms. The magnitude of the interference effect is expected to be directly proportional to the generalized order parameter, S2,4,5 and this correlation is confirmed experimentally. Inversely, the simple relaxation interference measurement can be used to obtain the relative S2 values of the backbone amides. Relaxation of peptide backbone 15N nuclei in proteins is dominated by CSA and by the dipolar interaction between 15N and its directly attached proton. Based on solid-state NMR studies of model compounds containing peptide bonds, the 15N CSA tensor is nearly axially symmetric and its unique axis makes a relatively small angle of ca. 20-24° with the N-H bond vector.6-9 As a result, for a 15N nucleus attached to a proton in the |â〉 spin state the sum of the dipolar and CSA tensors is much smaller than for 15N nuclei attached to a 1H in the |R〉 spin state, and the two types of 15N nuclei relax at very different rates. This differential relaxation is commonly referred to as a cross-correlation or relaxation interference effect10-15 and a simple treatment of this effect, directly applicable to the case of peptide 15N-1H amide pairs, has been presented by Goldman.13 Although cross correlation forms the basis of several elegant heteronuclear magnetization transfer experiments,16,17 more often it is considered a nuisance as it can alter the outcome of relaxation measurements if no precautions are taken to eliminate the effect.18-20 Here we demonstrate that the effect can be used advantageously to obtain information on the 15N CSA tensor and on the internal dynamics of the peptide backbone. The method is demonstrated for human ubiquitin, a small globular protein of 76 residues which is well-characterized by both X-ray crystallography21 and numerous NMR studies.22-27 X Abstract published in AdVance ACS Abstracts, July 1, 1996. (1) de Dios, A. C.; Pearson, J. G.; Oldfield, E. Science 1993, 260, 14911496. (2) Pearson, J. G.; Oldfield, E.; Lee, F. S.; Warshel, A. J. Am. Chem. Soc. 1993, 115, 6851-6862. (3) Oldfield, E. J. Biomol. NMR 1995, 5, 217-225. (4) Lipari, G.; Szabo. A. J. Am. Chem. Soc. 1982, 104, 4546-4558, 4559-4570. (5) Elbayed, K.; Canet, D. Mol. Phys. 1989, 68, 1033-1046. (6) Oas, T. G.; Hartzell, C. J.; Dahlquist, F. W.; Drobny, G. P. J. Am. Chem. Soc. 1987, 109, 5962-5966. (7) Hiyama, Y.; Niu, C.-H.; Silverton, J. V.; Bavoso, A.; Torchia, D. A. J. Am. Chem. Soc. 1988, 110, 2378-2383. (8) Lumsden, M. D.; Wasylishen, R. E.; Eichele, K.; Schindler, M.; Penner, G. H.; Power, W. P.; Curtis, R. D. J. Am. Chem. Soc. 1994, 116, 1403-1413. (9) Shoji, A.; Ozaki, T.; Fujito, T.; Deguchi, K.; Ando, S.; Ando, I. Macromolecules 1989, 22, 2860-2863. (10) McConnell, H. M. J. Chem. Phys. 1956, 25, 709-711. (11) Mackor, E. L.; MacLean, C. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 3, 129-157. (12) Gueron, M.; Leroy, J. L.; Griffey, R. H. J. Am. Chem. Soc. 1983, 105, 7262-7266. (13) Goldman, M. J. Magn. Reson. 1984, 60, 437-452. (14) Wimperis, S.; Bodenhausen, G. Mol. Phys. 1989, 66, 897-919. (15) Werbelow, L. G. Encyclopedia of Nuclear Magnetic Resonance; Grant, D. M., Harris, R. K., Editors-in-Chief; Wiley: London; Vol. 6, pp 4072-4078. (16) Dalvit, C. J. Magn. Reson. 1992, 97, 645-650. (17) Tolman, J. R.; Prestegard, J. H. J. Magn. Reson. Ser. B 1995, 106, 97-100. (18) Boyd, J.; Hommel, U.; Campbell, I. D. Chem. Phys. Lett. 1990, 175, 477-482. (19) Palmer, A. G., III; Skelton, N. J.; Chazin, W. J.; Wright, P. E.; Rance, M. Mol. Phys. 1992, 75, 699-711. (20) Kay, L. E.; Nicholson, L. K.; Delaglio, F.; Bax, A.; Torchia, D. A. J. Magn. Reson. 1992, 97, 359-375. (21) Vijay-Kumar, S.; Bugg, C. E.; Cook, W. J. J. Mol. Biol. 1987, 194, 531-544. (22) Di Stefano, D. L.; Wand, A. J. Biochemistry 1987, 26, 7272-7281. (23) Weber, P. L.; Brown, S. C.; Mueller, L. Biochemistry 1987, 26, 7282-7290. (24) Schneider, D. M.; Dellwo, M.; Wand, A. J. Biochemistry 1992, 31, 3645-3652. (25) Wang, A. C.; Grzesiek, S.; Tschudin, R.; Lodi, P. J.; Bax, A. J. Biomol. NMR 1995, 5, 376-382. (26) Wang, A. C.; Bax, A. J. Am. Chem. Soc. 1996, 118, 2483-2494. 6986 J. Am. Chem. Soc. 1996, 118, 6986-6991 S0002-7863(96)00510-0 This article not subject to U.S. Copyright. Published 1996 by the American Chemical Society Experimental Section All NMR experiments were carried out at 27 °C on a sample of commercially obtained (U-15N)-ubiquitin (VLI Research, Southeastern, PA), 1.4 mM, pH 4.7, 10 mM NaCl. Experiments were carried out on Bruker AMX-360 and AMX-600 NMR spectrometers operating at 1H resonance frequencies of 360 and 600 MHz, respectively. Both spectrometers were equipped with pulsed field gradient 1H/15N probeheads, optimized for 1H detection. Data matrices acquired at both 360 and 600 MHz consisted of 128*(t1) × 768*(t2) data points, with acquisition times of 64 (t1) and 83 ms (t2). A total of 32 scans per complex t1 increment was collected in experiment B (Figure 1) at both 360 and 600 MHz, whereas 384 and 128 scans were accumulated in experiment A (Figure 1) at 360 and 600 MHz, respectively. All experiments were performed with the 1H carrier positioned on the H2O resonance and the 15N carrier at 116.5 ppm. Durations for the dephasing delay, 2∆, were 46.7, 68, and 132 ms at 600 MHz and 132 ms at 360 MHz. All data sets were processed using 45° shifted sine-bell apodization and zero filling in both dimensions to yield a digital resolution of 2.3, 3.9 Hz (F1) and 2.7, 4.5 Hz (F2) for 360 and 600 MHz data respectively. Data were processed using nmrPipe28 and analyzed with the program PIPP.29 Resonance intensities were obtained from peak heights using three-data-point interpolation,29 and resonance assignments are taken from Wang et al.25 Results and Discussion Assuming an axially symmetric 15N chemical shift tensor with an angle θ between the orientation of its unique axis and the N-H bond vector, the 15N transverse relaxation rates for the two doublet components of an isolated 15N-1H spin pair are given by5,13-15 where the + sign applies to the upfield 15N doublet component (JNH < 0) and λ and η are given by where d ) γHγNh/(80πrHN), R ) -4π/3Bo(σ| σ⊥)rHN/ (hγH), and rNH is the 15N-1H internuclear distance, assumed to be 1.02 Å. Jdd(ω), Jcc(ω), and Jcd(ω) are the spectral densities for dipolar autocorrelation, CSA autocorrelation, and dipolarCSA cross correlation, respectively. For an axially symmetric CSA tensor, these spectral densities are given by where μp(t) is the unit vector describing the orientation of the axially symmetric interaction p at time t, and P2(x) ) (3x2 1)/2. Assuming isotropic rotational diffusion of a rigid body, one has where θ is the angle between the unique axes of the CSA and dipolar tensors, i.e., θ ) cos(μd(t)‚μc(t)). Although eq 3 is no longer rigorous in the presence of internal motion, results of calculations shown in the Appendix indicate it remains a very good approximation provided θ is small. Therefore, the superscripts in the spectral density function may be dropped and eq 1c is then rewritten as For the case of isotropic rotational diffusion and additional rapid internal motions, occurring on a time scale τe and described, in the model-free approach of Lipari and Szabo,4 by a generalized order parameter S2, the spectral density function is defined as with τ-1 ) τc + τe. The time constant τc is the rotational correlation time, assuming isotropic diffusion. However, rotational diffusion of ubiquitin is slightly anisotropic, and to a good approximation is described by an axially symmetric diffusion tensor, D, with D|/D⊥ ) 1.17.27 In this case, calculation of the cross-correlation term becomes considerably more complex,30,31 unless θ ) 0°. For θ ) 0°, one may simply use eq 1 in combination with the spectral density function applicable for axially symmetric rotational diffusion with internal motion:32,33 with k ) 1, 2, 3 and A1 ) 0.75 sin4 â, A2 ) 3 sin2 â cos2 â, A3 ) (1.5 cos2 â 0.5)2, where â is the angle between the N-H bond vector and the unique axis of the rotational diffusion tensor; τ1 ) (4D| + 2D⊥), τ2 ) (D| + 5D⊥), τ3 ) (6D⊥), and τ-1 ) τe + (2D| + 4D⊥), where D| and D⊥ are the rotational diffusion constants parallel and perpendicular to the unique axis of the diffusion tensor. For peptide 15N nuclei θ is small (20-24°), and use of eqs 1 and 6 provides a reasonable approximation. (27) Tjandra, N.; Feller, S. E.; Pastor, R. W.; Bax, A. J. Am. Chem. Soc. 1995, 117, 12562-12566. (28) Delaglio, F.; Grzesiek, S.; Vuister, G. W.; Zhu, G.; Pfeifer, J.; Bax, A. J. Biomol. NMR 1995, 6, 277-293. (29) Garrett, D. S.; Powers, R.; Gronenborn, A. M.; Clore, G. M. J. Magn. Reson. 1991, 94, 214-220. (30) Chung, J.; Oldfield, E.; Thevand, A.; Werbelow, L. J. Magn. Reson. 1992, 100, 69-81. (31) Szabo, A. J. Chem. Phys. 1984, 81, 150-167. (32) Woessner, D. E. J. Chem. Phys. 1962, 3, 647-654. (33) Barbato, G.; Ikura, M.; Kay, L. E.; Pastor, R. W.; Bax, A. Biochemistry 1992, 31, 5269-5278. Figure 1. Pulse scheme for quantitative measurement of cross correlation. In the reference experiment (scheme B), the open 1H 90° and composite (90y-220x-90y) 180° pulses are not applied, whereas they are applied in scheme (A), where all resonances are the result of cross correlation effects during the period 2∆. Narrow and wide pulses correspond to flip angles of 90° and 180°, respectively. The two low power pulses immediately preceding and following the last non-selective 1H 180° pulse have a width of 1 ms each and correspond to flip angles of 90°. With the carrier positioned on the H2O resonance, they are part of the WATERGATE water suppression scheme.39 The radio-frequency phase of all pulses is assumed x, unless indicated. Delay durations: τ ≈ 2.4 ms; δ ) 2.67 ms, T2/8 < ∆ < T2/2. Phase cycling: φ1 ) y,-y; φ2 ) x,x,-x,-x; φ4 ) 4(x),4(y),4(-x),4(-y); φ5 ) -x; Receiver ) x,2(-x),x,-x,2(x),-x. Quadrature detection in the t1 dimension is accomplished by incrementing φ3 in the States-TPPI manner. All gradients are sine-bell shaped, with an amplitude of 25 G/cm at their center. Durations: G1,2,3,4,5 ) 2.75, 2, 1, 1.5, and 0.4 ms. R2 ) λ ( η (1a) λ ) d[4J(0) + 4RJ(0) + 3J(ωN) + 3R J(ωN) + J(ωN ωH) + 3J (ωH) + 6J (ωN + ωH)] (1b) η ) 2Rd{4J(0) + 3J(ωN)} (1c) J(ω) )∫0〈P2(μp(0)‚μq(t)〉 cos(ωt) dt (2) J(ω) ) J(ω) ) J(ω)/P2(cos θ) (3) η ) 2Rd{4J(0) + 3J(ωN)}P2(cos θ) (4) J(ω) ) Sτc/(1 + ω τc ) + (1 S)τ/(1 + ωτ) (5)