Temperature Dependence of 1HNâ1HN Distances in Ubiquitin As

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Temperature Dependence of 1HN1HN Distances in Ubiquitin As Studied by Exact Measurements of NOEs Dominik Leitz,† Beat V€ogeli,† Jason Greenwald,† and Roland Riek*,†,‡ † ‡

Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-H€onggerberg, CH-8093 Z€urich, Switzerland The Salk Institute, 10010 North Torrey Pines Road, La Jolla, California 92037, United States

bS Supporting Information ABSTRACT: Although NMR relaxation phenomena provide a great deal of insight into local molecular dynamics, the dynamic picture of biomacromolecules is still largely incomplete, as no method is available to detect motions between atoms that are far apart in the sequence. Our recent investigations (V€ogeli et al. J. Am. Chem. Soc. 2009, 131 (47), 1721517225) indicate that extraction of exact effective distances from NOE rates might allow the determination of such motions. Using this approach, we measured exact effective distances between amide protons in 15N,13C,2H-labeled ubiquitin at three temperatures (284, 307, and 326 K). Comparisons among the three data sets reveal that, whereas the correlation-time-corrected cross-relaxation rates increase by 18% from 284 to 307 K, those at 326 K increase by 32% as compared to those at 284 K. Because theoretical considerations indicate that the NOE is largely insensitive to fast motion, as long as the local order parameter (e.g., SNH2) is larger than 0.5, the effective distance can be calculated from the NOE using its Ær6æ dependency. Doing so, the average NOE increases translate into effective distance changes of 2.4% and 4.0% in the temperature ranges measured. The data presented demonstrate that the determination of quantitative NOEs is a powerful tool for extracting small structural and dynamical changes in a biomolecule.

1. INTRODUCTION As motion is omnipresent in biological systems, it is not surprising that macromolecules such as proteins have evolved to take advantage of it.2,3 Although motion is therefore critical for the function of many biomolecules, the elucidation of the complete dynamics of a biomolecule has proven to be difficult. In routine NMR spectroscopy, local information on motion with time scales up to nanoseconds (fast motion) is obtained for 15 N1H bond vectors from measurements of the backbone nitrogen transverse and longitudinal relaxation times and heteronuclear 15N1H nuclear Overhauser effects (NOEs).46 Relaxation dispersion NMR experiments accurately sample the time scale on which very slow (i.e., millisecond to second range) local motions take place.7 The measurement of residual dipolar couplings (RDCs) allows the sampling of bond orientations over a time scale up to milliseconds.810 Recently, these local experimental restraints in combination with molecular dynamic simulations11,12 or structure prediction software13,14 were used toward a comprehensive dynamic picture of a biomolecule. Furthermore, cross-correlated relaxation NMR spectroscopy1518 can be used to study correlated motion in proteins. We recently proposed an alternative approach toward the aim of determining the structure and motion of a protein. We demonstrated that the measurement of NOE rates19,20 between amide protons in perdeuterated and protonated ubiquitin and GB3 enables the determination of time-averaged 1HN1HN distances up to 5 Å with high accuracy and precision.1,21 Because r 2011 American Chemical Society

the NOE-derived distance is a time-averaged parameter covering both fast and slow motions (faster or slower, respectively, than the rotational correlation time of the molecule), the potential of NOEs to provide information on fast and slow motions is evident, even though the relationship between NOEs, dynamics, and structure might be complex. Because of the abundance of protons in a protein, this collection of exact NOEs could lead to a rather complete map of the internal motion of a biomolecule. To explore the potential of exact NOE measurements for the determination of exact effective distances and motions, we measured NOE rates on human ubiquitin at three temperatures (i.e., 284, 307, and 326 K). Herein, we report that, whereas differences in the cross-relaxation constant of 18% can be observed between 284 and 307 K, the cross-relaxation rate increases by 32% when the temperature is raised from 284 to 326 K.

2. MATERIALS AND METHODS 2.1. Sample Expression and Purification. Ubiquitin with the human sequence was expressed recombinantly in E. coli in the triply labeled medium from Silantes E.coli-OD2 CDN (2H >95%, 13 C, 15N) and purified in H2O, giving a matrix-assisted laser Received: February 14, 2011 Revised: April 21, 2011 Published: May 19, 2011 7648

dx.doi.org/10.1021/jp201452g | J. Phys. Chem. B 2011, 115, 7648–7660

The Journal of Physical Chemistry B

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desorption/ionization time-of-flight (MALDI-TOF) mass of 9500.2 Da. The sample was measured in H2O with 3% D2O at a concentration of 4.3 mM and a pH of 5.8 in a 20 mM KPO4 buffer. The sample measured was nearly perdeuterated, with the exception of the exchangeable backbone and side-chain amide protons. 2.2. NMR Spectroscopy and Data Analysis. All experiments were performed on a Bruker 700 MHz spectrometer equipped with a triple-resonance cryoprobe at 284, 307, or 326 K. The resonances were assigned using a three-dimensional constanttime transverse relaxation optimized spectroscopy with amide proton-to-nitrogen-to-R-carbon correlation (ct-TROSY-HNCA) and a three-dimensional 15N-resolved heteronuclear multiplequantum coherence nuclear Overhauser enhancement spectroscopy (HMQC-NOESY) experiment.22 The three-dimensional 15 N-resolved HMQC-NOESY experiment1 was also used to measure NOE buildup rates. Spectra were acquired with the mixing times τm = 0.03, 0.06, 0.09, and 0.20 s at 284 K, τm = 0.03, 0.06, 0.09, and 0.12 s at 307 K, and τm = 0.06, 0.09, 0.12, and 0.15 s at 326 K, taking into account the decreasing rotational correlation time of ubiquitin with increasing temperature. The measurements at 284 K have been published previously.1 Furthermore, we recorded a [13C,1H] heteronuclear single-quantum coherence (HSQC) with a constant time of 54 ms with a 13C,15Nlabeled ubiquitin sample.22 T1 and T1F 15N-relaxation measurements were performed with relaxation delays of τm = 0.032, 0.128, 192, and 256 s for the T1 measurements and τm = 0.03, 0.06, and 0.09 s for the T1F measurements. To elucidate crosscorrelated relaxation delays, TROSY/anti-TROSY spectra were measured with a relaxation delay of τm = 0.06 s. All data were processed with the programs Prosa23 or nmrPipe24 and analyzed with the programs XEASY25 or nmrDraw,24 respectively. For the extraction of the cross-relaxation rates, the same procedure as described in ref 1 was followed, including the time-dependent spin diffusion analysis. The translation of NOEs into distances requires knowledge of the overall rotational correlation time of the molecule τc (eqs 2 and 3). 2.3. CD Spectroscopy and Data Analysis. CD spectra were measured on a JASCO J-815 instrument at 20 μM ubiquitin in a 0.1-cm-path-length cuvette in NMR sample buffer from 275 to 345 K in 5 K steps with an equilibration time of 1 h for each temperature measurement. Each spectrum is the average of three measurements for which the scan speed was 10 nm/min, the slit width was 1.5 nm, and the scan range was from 200 to 260 nm. 2.4. Conversion of NOE Rates into Distances. The homonuclear cross-relaxation rate is given by20,22 σ ¼

μ0 4π

2

γ4 h2 1 ½Jð0Þ 6Jð2ωÞ rigid 6 40π2 ðrHH Þ

ð1Þ

where μ0 is the permeability in a vacuum, γ is the gyromagnetic ratio, h denotes Planck’s constant, and ω is the Larmor frequency of the nuclei. rrigid HH is the internuclear distance in a hypothetically rigid structure, and J(ω) denotes the spectral density function sampled at the Larmor frequency ω. Under the assumption of isotropic molecular tumbling,21 J(ω) is given by JðωÞ ¼

2 ðSfast HH Þ

2 3 * + τc 1 τtot rigid 6 2 fast þ 4ðrHH Þ ðSHH Þ 5 rHH 6 1 þ ðτc ωÞ2 1 þ ðτtot ωÞ2

with 1 1 1 ¼ þ τtot τc τint

ð3Þ

where τc is the rotational correlation time of the molecule and τint is the correlation time for internal motion. The angle brackets denote a Boltzmann ensemble average. The order parameter for 2 fast internal motion (Sfast HH) used in this work depends on the mol polar and azimuthal angles (i.e., ϑmol HH and jHH, respectively), as well as the distances 2 ðSfast HH Þ

¼

rigid 4π ðrHH Þ6

5

*

2

∑

mol Y2q ðϑmol HH , jHH Þ

ðrHH Þ3

q¼ 2

+2 ð4Þ

An experimentally accessible order parameter is defined by the ratio of the experimentally derived cross-relaxation rate and that expected for a rigid molecule exp

ðSHH Þ2 ¼

σHH rigid

σHH

ð5Þ

For internal motion much faster than nanoseconds (τint , τc) under the assumption J(0) . J(ω) (which holds true at ω = 2π 700 MHz), (SHH)2 reduces to the order parameter of fast motion as defined in eq 4 2 ðSHH Þ2 ¼ ðSfast HH Þ

ð6Þ

The order parameter for fast motion introduced above can be approximately decomposed into an angular component 1 2 fast 2 [(Sfast HH )ang e 1] and a radial component [(S HH )rad g 1]. The definition of the radial order parameter is different from that in ref 26 (where it is the ratio of the fast and slow radial distance averaging), with the advantage that it is an absolute quantity rather than a relative one. Hence, depending on the 2 exact nature of the fast internal motions, (Sfast HH ) can be smaller or larger than 1. For motion much slower than the molecular tumbling (τint . τc), (SHH)2 becomes independent of angular coordinates * + rigid 6 1 2 ðSHH Þ ¼ ðrHH Þ ð7Þ r6 The simplest and most common way to extract a distance is to use eq 2 under the assumption of a rigid molecule. The distance has to be replaced by an effective one (reff HH) into which all motional effects are absorbed σ HH ¼

μ0 4π

2

γ4 h2 1 rigid J ð0Þ eff 6 40π2 ðrHH Þ

ð8Þ

The effective distances can be expressed with the distances in a rigid molecule and the order parameter (SHH)2 as follows from eq 5 rigid

rHH eff rHH ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffi 6 ðSHH Þ2

ð2Þ 7649

ð9Þ

dx.doi.org/10.1021/jp201452g |J. Phys. Chem. B 2011, 115, 7648–7660


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Table 1. Rotational Correlation Times τc of Ubiquitin at Four Different Temperatures Obtained from T1/T1F 15N-Relaxation Measurements5,30

Figure 1. Plot of the correlation times τc derived from our different measurements and literature values versus temperature.The orange circles indicate the correlation times measured in this study by T1/T1F 15 N-relaxation measurements, whereas the violet and turquoise symbols, reported in refs 28 and 29, were measured by conventional T1/T2 relaxation experiments. The pink circles indicate the correlation times derived from cross-correlated relaxation measurements (TROSY/antiTROSY). The black lines follow the τc values calculated based on the temperature-dependent viscosity changes of water with 298 K (upper line) or 300 K (lower line) as a reference temperature.

If only fast motion is present, the effective distance reff HH is

eff , fast rHH

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 * +2 31 u mol mol 2 6 u Y ðϑ , j Þ 4π 2q HH HH 5 ¼ t4 5 q¼ 2 ðrHH Þ3

∑

ð10Þ

The expression for the effective distance reff HH if only slow motion is present is much simpler rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 6 eff , slow ¼ ð11Þ rHH ÆrHH 6 æ In the present work, the change of NOE rates or distances with temperature is studied in detail. For this purpose, we introduce the reduced NOE rate termed NOE* using as a reference the NOEs derived at 284 K σ ¼ σ

τc ð284 KÞ τc ð307 or 326 KÞ

ð12Þ

3. RESULTS 3.1. Rotational Correlation Time τc. The extraction of order parameters from the cross-relaxation rates requires an accurate determination of τc, as an error in τc has a linear impact on the order parameter (eqs 27). For ubiquitin, τc was determined conventionally by T1/T1F 15N-relaxation measurements immediately before and after the NOESY measurements. The method was validated by application to a GB3 sample, for which τc deviated less than 1% from literature values27 (data not shown). To validate the determined τc value with an alternative approach, cross-correlated relaxation measurements between the chemical shift anisotropy (CSA) of 15N and 15N1H dipolar interaction were also measured. Although the correlation time τc cannot be extracted accurately with this method because of uncertainties in

T (K)

τc (ns)

284

7.72

298

5.20

307

4.32

326

3.02

the CSA tensor, it is instructive to compare the cross-correlated relaxation rates η for each of the three temperatures and correlate them with the temperature-dependent viscosity of water. Because there is an excellent temperature-sensitive correlation between the τc value determined by 15N-relaxation measurements, the cross-correlated relaxation rates, and the viscosity, the obtained τc value appears to be accurate. Figure 1 shows the correlation times derived from the T1/T1F 15N-relaxation measurements versus the temperature with comparison to literature values.28,29 The black lines represent the calculated τc values based on the temperature-dependent changes of the viscosity of the water, as implied by the StokesEinstein relationship.19 From this relationship, the correlation time at any temperature can be calculated by setting the τc value measured at 298 or 300 K as a reference. As shown in Figure 1, all correlation times follow the same temperature dependence. The offset in the curves is attributed to differences in concentration and buffer conditions used: Whereas refs 28 and 29 had relatively low sample concentrations at 2.3 and 1 mM, respectively, the sample used here had a higher concentration (4.3 mM) and was close to the solubility limit of ubiquitin. In a previous work,1 the rotational correlation time τc at 284 K on the same sample was not determined with the present accuracy, and correspondingly, the calculated distances presented here are more accurate (see below). For the correlation times, we obtained the values listed in Table 1. 3.2. Potential Sources of Error in Determination of NOEDerived Distances. In addition to small errors in determining the rotation correlation time τc (see above), a potential source of errors is the spin diffusion present in a multiple-spin systems. Within this effect, one has to distinguish between two different potential problems: (i) the principle presence of spin diffusion that has to be taken into account and, within this, (ii) the correction of spin diffusion using an inaccurate structural model. We consider first the presence of spin diffusion per se. If short mixing times are selected, most of the buildup curves for different secondary structure elements shown in Figure 2 indicate a good fit quality. Only for next-nearest neighbors in the R-helix (in the figure represented by residues 1HN 33 and 1HN 35) is the fit poor, even if only three instead of four time points are taken into account. These NOE transfers have a higher-order contribution (in addition to the two-spin solution) due to spin diffusion, preventing a satisfying two-spin fit. Figure 3 shows the spindiffusion-corrected intensities as calculated from the program DOMINO.21 The corrected intensities yield a much better fit than the uncorrected ones (compare to the corresponding buildup in Figure 2). However, even if spin diffusion pathways are taken into account, the inaccuracy of available structures needed for the calculation can lead to poor predictions. As described by refs 1 7650



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Figure 4. Cartoon illustrating the extraction of the order param2 2 eter (Sfast HH) of the NOE from local order parameters SHN of 15 1 15 N HN dipoles derived from N-relaxation measurements. First, the local order parameter SHN2 is translated into a 1HN Gaussian distribution within a cone as shown in the left panel. Second, as 2 illustrated in the middle and right panels, (Sfast HH) is determined by ensemble averaging, following eq 4.

Figure 2. Experimental NOE buildup curves for pairs of residues (i.e., shown are buildups for A f B as well as B f A) in various secondary structures: along β-strands (“Sequential Beta Sheet”), across β strands (“Across Beta Sheet”), and sequential and nonsequential within the helix and at the end of the helix and in loops. The x axis shows the mixing time (30, 60, 90, and 200 ms for 284 K; 30, 60, 90, and 120 ms for 307 K; and 60, 90, 120, and 150 ms for 326 K), whereas the normalized intensities (normalized with respect to the interpolated diagonal peak intensity at zero mixing time) are plotted on the y axis. Experimentally measured values are indicated by circles (blue, 284 K; green, 307 K; red, 326 K), and the fit of the data using the exact two-spin solution1,22 is illustrated by the black lines (without corrections for spin diffusion). Only for nonsequential NOEs in the R-helix (i.e., peaks 33/35) is a poor fit obtained because of strong spin diffusion (see text and Figure 3).

Figure 3. Spin-diffusion effects on fitting of the NOE buildups. The graph shows the fit of the spin-diffusion-corrected intensities shown in Figure 2 for the cross-peak between residues 33 and 35.

and 21, spin diffusion pathways are calculated by the software routine DOMINO using atomic-resolution structures such as those obtained from NMR or X-ray methods, both of which can be inaccurate representations of the protein structure. For example, although an X-ray structure at 1.8-Å resolution is available (pdb code 1Ubq31), the distance between 1HN of residue 34 and 1HN of residue 35 is 1.94 Å and therefore contradicts the average distance of 2.48 Å obtained from the high-resolution NMR structure (pdb code 1D3Z32). Although this disparity has no direct influence in determining the exact average distance by the cross-relaxation rates σ between 1HN of residue 34 and 1HN of residue 35, it has an impact on the distance between 1HN of residue 33 and 1HN of residue 35 because of the strong spin diffusion correction mediated by 1HN of residue 34. The correction for the NOE based on the distance obtained from the X-ray structure is 57%, whereas the correction for the spin diffusion derived from the product of the relevant NOEs measured experimentally is only 25% (data not shown). The overestimation of 32% ultimately yields an apparent effective distance of 4.25 Å instead of 3.87 Å (for 307 K, for example) as obtained from the NMR structure 1D3Z. Because the presented example is by far the largest error found, this potential source of error in determination of an exact effective distance from NOEs appears to be small because of the inverse relationship to the power of six between NOE rate and distance. Nonetheless, this source of error could be eliminated by the use of a full-relaxation matrix refinement,33 a method that is currently established in our group. Another potential source of error, especially for high temperatures, is a partial unfolding of ubiquitin. However, because its unfolding temperature under given buffer conditions is near 373 K (data not shown), very little of ubiquitin is unfolded. Furthermore, the unfolded ubiquitin should not contribute significantly to the NOE because of the low correlation time expected. 3.3. Conversion of NOE Rates into Distances. As described in the Materials and Methods section, the cross-relaxation rate has a complex relationship to the distance if motion is present. For slow internal motion (compared to the overall tumbling), the NOE depends on the average of the inverse sixth power of the distance (eq 11). In the presence of fast motion, however, the relationship is much more complex because both angular and distance fluctuations must be taken into account, as revealed in eqs 2, 4, and 10. Hence, the extraction of true distances in the presence of motion appears to be difficult. However, as 7651



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2 Figure 5. Relationship between calculated order parameters (Sfast HH) describing the influence of fast motion on the NOE and local order parameters 2 1 15 28 SNH of HN N spin vectors of relevance measured at 288 K. No local order parameters were available for residues 13, 19, 24, 25, 31, 37, 38, 53, 67, and 72. (A) Product of the local order parameters of ubiquitin determined experimentally28 versus the corresponding fast NOE order parameter. Consecutive residues in R-helices (Alpha), β-sheets (Beta), and loops (Loop) are represented by open circles, and nonconsecutive residues are 2 represented by solid circles. For large and small values of (Sfast HH) , the residues involved are labeled. Note that the relationship shown is valid only for a fast 2 temperature of 288 K. (B) Surface plot showing (SHH) versus the product of two corresponding SNH2 order parameters (having identical values) and the distance between the two cones in the interval from 2 to 5 Å. The two conformational scenarios, facing of the cones (top surface) or opposing each other (bottom surface), are illustrated. Facing yields an order parameter smaller than 1, whereas opposing yields an order parameter larger than 1. A figure with further sterical conformations can be found in the Supporting Information (Figure S3).

Table 2. Mean Values with Standard Deviations for the Fast 2 Order Parameters (Sfast HH) Derived from the NMR Bundle 2k3912 and the Simulations Discussed Herein and Presented in Figure 5 2 (Sfast HH)

mean value

β-strands

R-helix

2k39

Figure 5

2k39

Figure 5

0.99 ( 0.09

1.00 ( 0.02

0.99 ( 0.03

0.99 ( 0.01

explained in the following discussion, the presence of fast motion does not change the NOE significantly (in most cases in a protein backbone) and can therefore be neglected to a first approximation. 1 HN1HN NOE order parameters based on the NMR structure (pdb code 1Ubq) were simulated for ubiquitin following the idea illustrated in Figure 4. We assumed thereby that both 1 HN15N spin pairs undergo only fast motion that can be determined by conventional 15N-relaxation measurements and are described by the local LipariSzabo order parameters SHN2.4 From these local order parameters, a standard deviation σ for a two-dimensional Gaussian distribution of opening angles ϑ was calculated. Next, 5000 vector orientations were generated using a cutoff angle β for the distribution calculated from the local order parameters under the assumption of a ”diffusion in a cone” model,34 sampling the polar angle ϑ in 5 steps from 0 to β (see Figure 4) and the azimuthal angles in 20 steps from 0 to 360. Then, the order parameter of the NOE between the two 1HN spins of interest was calculated following eq 4. This procedure describes the entire rotational and translational fast motion between the two 1HN spins under the assumption that no correlated fast motion is present. Applying this approach to the 1 HN spins of ubiquitin with the use of published relaxation data kindly provided by Nico Tjandra,28 a correlation plot between 2 the local SHN2 and (Sfast HH) values is obtained (Figure 5). Note that the latter order parameter can be larger or smaller than 1 depending on the type of motion, whereas in a rigid structure, it would be equal to 1.

It is evident from Figure 5A, that the fast motion of the individual 1HN nucleus only slightly influences the corresponding NOE. This appears to be true irrespective of the secondary structure in which the spins are located (Table 2). Only for low values of SHN2, which are usually observed only in flexible regions of a protein such as the C-terminus of ubiquitin (i.e., residues 7376), might the influence of fast motion on the NOE become relevant. Following an example in Figure 5A, the product of two order parameters, SHN,x2SHN,y2 = 0.2 modifies the corresponding NOE by only 10%. This finding can be rationalized as follows: Whereas fast radial motion enhances the NOE by the Ær3æ2 dependence, the angular part of the motion results in a decrease of the NOE. Hence, the effect of fast motion is largely canceled. Inspection of Figure 5A shows that, for spin pairs that have individual local order parameters both above 0.6 (i.e., SHN, 2 2 x SHN,y > 0.36), the remaining influence of the fast motion is a truncation of the NOE on the order of less than 5%. This yields an uncertainty of less than 0.83% in the distance, which is well within the experimental error of the measurements. These observations of the ubiquitin backbone (Figure 5A) can be generalized as demonstrated in Figure 5B. Two conformational scenarios, facing or opposing of the two 15N1H cones, are illustrated [other scenarios are shown in the Supporting Information (Figure S3)]. If the two cones are facing each other, which is typically observed across a β-sheet, the order parameter 2 (Sfast HH) is smaller than 1, and hence, the corresponding NOE is quenched. In the other scenario, typically observed at consecutive positions within a β-strand, the NOE is enhanced with 2 (Sfast HH) > 1. These effects are more pronounced for small distances r. Overall, however, the influence for common scenarios with local order parameters of SNH2 > 0.5 is small (Table2). In other words, NOEs between spin systems with a product of local order parameters SHN,x2SHN,y2 > 0.25 are insensitive to fast motion. In such cases, the NOE appears to follow approximately eq 11 and is therefore dependent only on slow motions. However, if correlated motion of the whole spin system is present, (SHH)2 is accordingly reduced because of its angular motion. 7652


The Journal of Physical Chemistry B 2 To gain insight into the effect of partially correlated motion, (Sfast HH) 12 for the RDC-derived NMR bundle 2k39 was determined [Table2, Figure S1 (Supporting Information)]. Because the bundle includes both slow and fast motion, a pure fast motional averaging yields an overestimation of the fast 1HN1HN order parameters as evidenced by lower SHN2 values when compared to ref 28. As a 2 consequence, the (Sfast HH) value derived from the bundle can be regarded as a lower limit for fast motion present in the system.

Figure 6. τc-corrected normalized intensities of the representative cross-peaks 1HN421HN70 versus the mixing time for the three temperatures 284 K (blue), 307 K (green), and 326 K (red). Intensities were taken from the measurements and scaled by the ratio of the two correlation times (in accordance with eq 12).

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Nonetheless, as shown in Table 2, these fast order parameters 2 (Sfast HH) are, on average, very similar to those derived from the simulations and those presented in Figure 5. In summary, all of the calculations and simulations indicate that there is only a slight influence of fast motion on the order parameters (SHH)2. 3.4. Temperature-Dependent 1HN1HN NOE Rates of Ubiquitin. The NOE rates between pairs of 1HN spins in human ubiquitin were extracted from NOE buildups at three temperatures (284, 307, and 326 K) using the 15N-resolved HMQCNOESY experiment published in ref 1. Because of the magnetization pathway symmetry of a spin pair, two buildups can be evaluated as shown in Figure 2. These two buildups correspond to the magnetization transfers from 1HN of residue x to 1HN of residue y and vice versa. The differences between the two buildups arise from imbalances during the pulse sequences stemming from the WATERGATE element35 as well as small contributions from experimental uncertainties such as intensity readout. The data fit very well to theoretical curves, and the NOE rates can be extracted with confidence. This finding is supported by a repetition of the experiment at 307 K, which yielded very similar NOE rates, with an average deviation between the two measurements of 3%. At 284 K, a total of 140 NOE rates could be evaluated with 78 from both pathways and 62 from only one pathway (see Table S2 in the Supporting Information). Similarly, at 307 K, a total of 94 NOE rates were determined with 55 from both pathways and 39 from one pathway only. At 326 K, a smaller number of NOEs could be determined because of the smaller rotational correlation time that results in a decrease of cross-peak intensities (which was partially

Figure 7. Relative temperature-dependent changes of NOE rates σ*. The blue bars show the τc-corrected changes in NOE buildup rates in percentages between 284 and 307 K, whereas the red bars show the changes between 284 and 326 K. The 1HN nuclei involved are labeled with their corresponding residue number. 7653



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Table 3. Slopes s and Pearson’s Correlation Coefficient r between Experimental and Predicted Cross-Relaxation Rates σ for Ubiquitina temperature 284 K

326 K

s

r

s

r

s

r

X-ray structure (pdb code 1Ubq)

0.820

0.978

0.762

0.941

0.702

0.977

NMR pdb structure 1D3Z; HN distance set to dHN = 0.98 Å32

0.803

0.959

0.738

0.966

0.690

0.963

NMR pdb structure 1D3Z; HN distance set to dHN = 1.01 Å32 NMR bundle 2k39 (average distance b)12

0.814 0.978

0.968 0.949

0.743 0.908

0.974 0.945

0.699 0.827

0.971 0.981

GROMOS simulation (average distance b)

1.769

0.925

1.562

0.891

1.457

0.933

structural models used 31

a

307 K

For each temperature, all individually extracted distances were taken into account. b NMR bundle and GROMOS distances were linearly averaged.

Figure 8. NOE-derived effective distances, reff, between two 1HN nuclei in ubiquitin measured for three temperatures (blue, 284 K; green, 307 K; red, 326 K). The black circles show extracted distances from the X-ray structure (1Ubq). Error bars shown are based on the σ values determined individually from the two pathways. If only one pathway could be determined, no error bar is shown. The 1HN nuclei involved are labeled with their corresponding residue numbers.

countered by longer mixing times). Furthermore, several resonances were lost through fast exchange with water and the presence of motion. Thus, only 79 NOEs in total, 47 for both pathways and 32 for one pathway, could be determined. Inspection of Figure 2 indicates a decrease of the NOE buildups with temperature. This finding is only partially due to the decrease of the rotational correlation time τc, which changes by more than a factor of 2 between 284 K (τc = 7.72 ns) and 326 K (τc = 3.02 ns). Comparison of representative, τc-corrected NOE buildups between residues 42 and 70 (Figure 6) with the uncorrected one (Figure 2) shows that the buildup is smaller at

higher temperatures than expected for a protein with temperatureindependent conformation and dynamics. Similar findings are observed throughout the entire protein structure, including the β-sheets and the R-helix (Figure 7). These differences are attributed to a temperature-dependent change of motion and/ or the average distance between the two spins involved.

4. DISCUSSION 4.1. Comparison between Measured NOEs and Those Calculated from Various Structural Models. Before the 7654



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Table 4. Temperature-Dependent Changes of 1HN1HN Distances within the r-Helix of Ubiquitin Derived from NOE Measurements residues involved

a

Δr(307284 K) (Å)

Δr(326284 K) (Å)

ra (Å)

25

26

0.21

0.15

2.62

26

27

0.05

0.07

2.73

27

28

0.15

012

2.75

28

29

0.05

0.04

2.73

29 30

30 31

0.05 0.08

0.07 0.09

2.65 2.57

31

32

0.10

0.13

2.66

32

33

0.03

0.08

2.92

33

34

0.08

0.17

2.57

25

27

0.12

4.11

29

31

0.41

0.26

4.10

30 30

32 33

0.06 0.11

0.14 0.25

4.15 4.70

31

33

0.10

0.21

4.11

32

34

0.14

0.22

4.53

Distances extracted from the X-ray structure (pdb code 1Ubq31).

observed temperature-induced changes of the τc-corrected NOEs are discussed in detail, the data are first compared with corresponding values calculated from representative structures and structural bundles, including the X-ray structure (pdb code 1Ubq), the NMR structure (1D3Z) with the 15N1H bonds fixed at either 0.98 or 1.01 Å,32 the bundle 2k39 derived from RDCs and MD simulations,12 and MD simulation using the software package GROMOS.1 Table 3 shows the slope s providing an “average” experimental order parameter (eq 5), as well as the correlation coefficient r for a linear regression (experimental versus predicted σ). Concentrating on the comparison with the experimental data set at 284 K, it should be noted that, compared to the results in ref 1, this data set is an improvement, as the τc values was determined more accurately. The X-ray structure fits well with this data set, as previously documented1 (although a less accurate τc value was used therein). The NMR bundle 2k39 fits even better to the NOE data set for local interactions (i.e., intra and sequential NOEs), whereas across β-strands, it fits rather poorly when compared to the X-ray structure (Table S1, Supporting Information). Overall, the GROMOS simulation compares poorly with the experimental NOEs, apparently having too much internal motion (Table 3). However, whereas the correlation gets worse with increasing temperature for the X-ray structure, the NMR structure, and the Griesinger bundle (although the latter is based on experimental values measured at 298 K), the GROMOS MD simulation gets better. Most importantly for the context of interest is that, at 326 K, the cross-relaxation rates fit poorly with all of the structures and structural models listed, as exemplified by the slope s (Table 3). (Note that the apparent small improvement of the Pearson’s correlation coefficient r is not interpreted here because it might be due to the different extents of the data sets used.) The slopes s, which provide an “average” order parameter, range between 0.69 and 1.46, indicating an increase of internal motion of ubiquitin at high temperatures. 4.2. Temperature-Dependent 1HN1HN Distance in Ubiquitin. The comparison between NOE rates at the three temperatures of interest and corresponding calculated values from various

Figure 9. Temperature-dependent changes of the NOE-derived order parameters in ubiquitin. (A) Relative τc-corrected changes within the Rhelix (left) from 284 to 307 K and (right) from 284 to 326 K. (B) Changes of the NOE-derived order parameter within and between the first and last β-strands (top) between 284 and 307 K and (bottom) between 284 and 326 K. The backbone of the secondary structures is drawn by black lines and the residues are labeled according to the amino acid sequence position. The color code is as follows: gray: 40% < ΔS2 < 20%, violet: 20% < ΔS2 < 0%, blue: 0% < ΔS2 < 20%, yellow: 20% < ΔS2 < 40%, red: ΔS2 > 40%.

structural models (Table 3, Figures 6 and 7) strongly indicate a structural and/or dynamical change of ubiquitin with increasing temperature. To evaluate these temperature-dependent changes more quantitatively, the NOE rates were translated into effective distances (reff) using eq 11, because, in accordance with the findings above, the 1HN1HN NOEs appear to be insensitive to fast motions. This approach enables a detailed explanation of the temperature-dependent structural and dynamical changes of ubiquitin. As illustrated in Figure 8, the distances measured at 284 K are in excellent agreement with the X-ray structure 1Ubq, irrespective of whether the distances extracted are of sequential or longe-range nature or whether they are located in the R-helix, βstrands, or loop regions. This observation is in line with our previous comparison, although, at that time, the rotational correlation time τc was not accurately determined.1,21 Overall, for the temperature change from 284 to 307 K, an average decrease of the τc-corrected NOE rate on the order of 18% and a concomitant average increase of the distance by 2.4% is measurable throughout the protein structure, including the R-helical and β-sheet secondary structures (Figure 7). Another increase of 19 K to 326 K yielded changes on the same order, indicating structural and/or dynamical changes. An average decrease of the τc-corrected NOE rate on the order of 14% and concomitantly an average increase of the distance by 1.6% were measured. Again, these distance increases were observed throughout the protein structure (Figure 8). Comparing the data 7655



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Figure 10. Temperature-dependent 1HN chemical δ(1H) shifts versus τc-corrected NOE rates σ* measured at the temperatures 284 K (blue), 307 K (green), and 326 K (red). A complex correlation is observed as expected (see text). The 1HN nuclei involved are labeled with their corresponding residue numbers.

sets at 284 and 326 K, the average decrease of the NOE rates is 32%, translating into a distance change of 4.0%. A detailed inspection of the temperature dependence of the distance within the R-helix further reveals that the average distance increase in the temperature range 307326 K is more prominent toward the C-terminus of the R-helix, indicating a breathing of the helix from its C-terminus (Figure 8 and Table 4). To convert the distance increase into a dynamic picture, eq 5 can be used because it defines an order parameter that, depending on its type of motion, can be smaller or larger than 1 and equal to 1 if rigid (see text in the Materials and Methods section). Using eq 5 with the reduced cross-relaxation rate σ* under the assumption that the structure of ubiquitin at 284 K represents a compact conformation on top of which the protein breathes or partially unfolds, one obtains a ΔS2 for the two temperature ranges 284307 and 284326 K. As highlighted for the β-sheet (β1β5) and the R-helix in Figure 9, the dynamics is changing moderately between 284 and 307 K and increases further in a quasilinear manner with temperature. Hence, when compared with the data at 284 K a pronounced increase in motion is observed at 326 K (Figure 9). Whereas the helix seems to be mostly temperature insensitive at its N-terminal side, larger changes in the cross-relaxation rate, as well as in the distance, can be observed toward its C-terminal end. The changes in NOE and distance across β-sheets are also pronounced (Figures 8 and 9B). It appears that, for the loops overall, larger changes are observed, indicating a greater increase in flexibility than in secondary structural elements. These changes include, in particular, the termini of the secondary structural elements. It is not surprising that an increase of the temperature results in a less compact structure, because toward the melting temperature, the structure of ubiquitin should go toward a random-coil conformation because of the unfolding process. Overall, the increase of motion between 284 and 326 K as determined by the ΔS2 value is small but significant. 4.3. Comparison of the 1HN1HN NOE Rates to Other Temperature-Sensitive Probes. The presented study on temperature-sensitive 1HN1HN NOE rates is compared with corresponding measurements of 1HN, 13CR, and 13Cβ chemical

shifts, scalar couplings across hydrogen bonds36 and circular dichroism. Figure 10 shows representative correlation plots between the τc-corrected NOE rate changes and the corresponding 1HN chemical shift changes with temperature. Although there is a correlation present, it is of complex nature. This is expected because the chemical shift depends on the electronic environment of its spin whereas the NOE shows mostly a distance dependency. Although still of complex nature, the 13CR and 13Cβ shifts depend mainly on backbone angles and hence their deviation from random coil shifts can be used to investigate secondary structures and changes thereof. In order to correlate the NOE changes with the carbon shift changes, constant-time HSQC22 spectra at the three different temperatures (284, 307, and 326 K) with 15N,13C-labeled ubiquitin were recorded. To compensate for temperature induced offsets in the chemical shift reference, we calculated the difference of the 13CR and 13Cb shifts37 depicted in Figure 11. This difference is plotted versus the R corresponding NOE (δ13C(i) δ13Cβ(i) is plotted versus σ/(i,j)). Overall, the carbon chemical shifts change with increased temperature toward the value derived for “random-coil” configurations of the corresponding amino acid residue. Following the discussions above (Figures 79), the chemical shift changes of the C-terminus of the R-helix (residues 2837) and the end of β-strand 5 close to the C-terminus (residues 69 and 70) are of special interest. Whereas only slight chemical shift changes are observed at the center in the R-helix, more pronounced changes at its C-terminus are observed. Similarly, temperature-induced chemical shift changes are observed for the β-strand 5 with increased changes toward the C-terminus. As highlighted by Figure 11, analogous trends were found by the NOE measurements. Particular noteworthy is that the chemical shift differences and NOEs appear to change proportionally to each other with the temperature change for most examples shown (Figure 11). However, the temperature dependence of the NOEs appears to be much more sensitive than that of the carbon shifts. This finding is attributed to the proportionality between the deviation of the carbon shifts from the random coil and the secondary structure content,38 whereas the NOE shows a sixth-power dependency on the distance. 7656



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Figure 11. Correlation plots between differences in chemical shifts of 13CR and 13Cβ versus the corresponding τc- corrected NOE σ* for 284 K (blue circles), 307 K (green circles), and 326 K (red circles). The black lines indicate the difference δ13CR δ13Cβ in a “random-coil” entity calculated from ref 39. Glycines are not taken into account, as no 13Cβ shift is present. No error bars are included in the figure because the error is 2 orders of magnitude smaller than a typical chemical shift difference. The error in determining the chemical shifts can be estimated from the ratio between the line width (full width at half-maximum, fwhm) and 2 times the signal/noise (S/N) ratio.40 Typical values are fwhm = 20 Hz, N = 80000, and Smin = 107, resulting in an error of 5 104 ppm. The 1HN nuclei involved are labeled with their corresponding residue numbers.

An even more impressive correlation between NOEs and the scalar couplings across hydrogen bonds36 is attributed to the fact that both measurements are stronly dependent on distance changes (Figure 12). The only outlier is residue 42/70, for which the scalar coupling behaves atypically. Despite the good overall correlation between the NOE and scalar couplings, an estimation of the change of the hydrogen-bond distance based on a statistical relationship between scalar coupling and hydrogenbond length (0.03 Å)36 appears to be smaller than the effective distance increase between two corresponding amide protons as measured by NOEs [0.20 Å for Δr(326284 K), Figure S2 (Supporting Information)]. The nature of this apparent discrepancy is not known but might be attributed to the not entirely understood relationship between scalar coupling and hydrogen bond length.

Finally, for an independent measurement of the temperaturesensitivity of the secondary structure in ubiquitin, we turned to circular dichroism (CD) spectroscopy. The high thermal denaturation temperature of ubiquitin makes complete thermodynamic analysis difficult, so the change in the CD signal with temperature was measured instead. We found that there was a reversible change in the intensity of the 223-nm band at the same temperatures as used in the NMR measurements (Figure 13). The negative ellipticity in this region of the CD spectrum arises from the R-helix and, to a lesser degree, the β-sheet, and the shift toward less negative signal at higher temperature is indicative of a temperature-dependent decrease in the content of these secondary structural elements. Furthermore, the signal decrease of the negative ellipticity changes proportionally with the temperature, as can be seen from the inset of Figure 13. This observation is well 7657



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Figure 12. 3hJNC0 scalar coupling constants across hydrogen bonds extracted from ref 36 versus τc-corrected NOE rates σ* measured at the temperatures 284 K (blue), 307 K (green), and 326 K (red). The 1HN nuclei involved are labeled with their corresponding residue numbers.

Figure 13. CD spectra of ubiquitin at the three temperature used for this study (284 K, blue; 307 K, green; 326 K, red). The inset depicts the temperature dependence of the negative band at 223 nm that is characteristic of R-helices.

in line with the NOE rates, which also change linearly with temperature in the temperature range measured. In summary, all NMR probes and the CD measurements support the observation that, with a temperature increase within the ambient temperature range, conformational and dynamical changes appear in ubiquitin. 4.4. Unfolding Pathway of Ubiquitin. Whereas, with lowresolution techniques, ubiquitin appears to be a classical example for a simple protein folding pathway (two-state process41,42), high-resolution techniques show that the foldingunfolding equilibrium is more complex. For example, the temperaturedependent measurements of scalar couplings across hydrogen bonds indicate that, around loop 1 (residues 811), a rearrangement of hydrogen bonds is observed in the temperature range of 298328 K.36 Unfolding in urea indicates that a significant number of the ubiquitin molecules are still hydrogen-bonded

in the segment including residues 218 (β-strands 1 and 2) at 8 M urea,43 which implies a large stability of this segment. Fourier-transform infrared spectroscopy indicates that the protein segment following the R-helix unfolds first with temperature,44 which is in good agreement with the measured NOEs indicating an increase of motion toward the C-terminus of the R-helix (Figure 9, Table 4). Similarly, pressure-induced unfolding of ubiquitin suggests that the R-helix unfolds starting with a displacement of the C-terminal end of the helix and the connected loop. The pressure-induced unfolding also indicates that the flexibility of the C-terminus (i.e., residues 7276) is extended, which finds support in the NOE measurements at 326 K (Figures 8 and9).45,46 The presented structural changes with increasing temperature derived from NOE measurements are not only in good agreement with other data but also give quantitative insights into the breathing of ubiquitin with increasing temperature. This finding indicates that, before ubiquitin unfolds, it takes up the increasing thermal energy through partial opening of its structure by breathing.

5. CONCLUSIONS The NOESY technique provides dynamical and structural information from the chemical shifts, scalar couplings, line widths of cross-peaks, and most importantly NOEs. Whereas NOEs have most often been used only in a qualitative manner for structure determination19 or elucidation of dynamics,47 we recently demonstrated that the determination of NOE rates in a protein results in precise effective distances.1 One remaining problem was that the relationship between NOE and distance depends on the type of motion present. Here, we showed, first, that the NOE is insensitive to fast motion as long as the local order parameter is SNH2 > 0.5. Next, we demonstrated on the model protein ubiquitin that quantitative NOE rates can be used 7658


The Journal of Physical Chemistry B to highlight small conformational and dynamical changes of the protein backbone upon changes of the temperature. The measurements indicate that, at 326 K, the protein ubiquitin appears to breathe more than at 284 K, in agreement with molecular dynamics simulations on other systems.48 Hence, quantification of NOEs appears to provide an excellent probe for the characterization of both the protein three-dimensional structure and its motion.

’ ASSOCIATED CONTENT

bS

Supporting Information. Figure showing the influence of fast motion on the NOE, table presenting inverse slopes and correlation coefficients between predicted and experimental NOEs for ubiquitin, correlation plots between predicted and experimental NOEs for ubiquitin, table with extracted NOE rates before and after being corrected for spin diffusion and H/D 2 equilibrium, and surface plot showing (Sfast HH) versus the product 2 of two identical SNH order parameters and the distance between the two cones in the interval from 2 to 5 Å for different sterical conformations. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Address: Institute of Physical Chemistry, ETH Z€urich, CH-8093 Z€urich, Switzerland. Tel.: þ41 44 632 6139. E-mail: roland.riek@ phys.chem.ethz.ch.

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