Variability of the 15N chemical shielding tensors in the B3 domain of protein G from 15N relaxation measurements at several fields. Implications for backbone order parameters

Abstract

We applied a combination of 15N relaxation and CSA/dipolar cross-correlation measurements at five magnetic fields (9.4, 11.7, 14.1, 16.4, and 18.8 T) to determine the 15N chemical shielding tensors for backbone amides in protein G in solution. The data were analyzed using various model-independent approaches and those based on Lipari-Szabo approximation, all of them yielding similar results. The results indicate a range of site-specific values of the anisotropy (CSA) and orientation of the 15N chemical shielding tensor, similar to those in ubiquitin (Fushman, et al. J. Am. Chem. Soc. 1998, 120, 10947; J. Am. Chem. Soc. 1999, 121, 8577). Assuming a Gaussian distribution of the 15N CSA values, the mean anisotropy is -173.9 to -177.2 ppm (for 1.02 A NH bond length) and the site-to-site CSA variability is +/-17.6 to +/-21.4 ppm, depending on the method used. This CSA variability is significantly larger than derived previously for ribonuclease H (Kroenke, et al. J. Am. Chem. Soc. 1999, 121, 10119) or recently, using "meta-analysis" for ubiquitin (Damberg, et al. J. Am. Chem. Soc. 2005, 127, 1995). Standard interpretation of 15N relaxation studies of backbone dynamics in proteins involves an a priori assumption of a uniform 15N CSA. We show that this assumption leads to a significant discrepancy between the order parameters obtained at different fields. Using the site-specific CSAs obtained from our study removes this discrepancy and allows simultaneous fit of relaxation data at all five fields to Lipari-Szabo spectral densities. These findings emphasize the necessity of taking into account the variability of 15N CSA for accurate analysis of protein dynamics from 15N relaxation measurements.

Figure 1. Representative fits of the dependence of 2R₂′ - R₁′ on ω_N²

Shown are fits from the 2R₂-R₁ method for three residues in GB3. This plot also illustrates the variation in the ¹⁵N CSA values between these residues. The amides shown here have very similar values of J(0), as evidenced by the fact that they have the same intercept b (cf. Eq. 11), but exhibit strikingly different slopes reflecting the difference in their CSA values (Eq. 12). The plots of 2R₂′ - R₁′ versus ω_N² for all residues in GB3 can be found in the Supporting Material. The error bars here and in all other figures represent standard errors (corresponding to 68.3% confidence intervals).

Figure 2. Site-specific ¹⁵N CSA values in GB3 obtained using the three methods (2R₂-R₁, R/η, and LS-CSA)

(a) The site-specific ¹⁵N CSAs, from the 2R₂-R₁ method (black squares), R/η method (blue circles), and the LS-CSA method (green triangles) versus residue number. The secondary structure of GB3 is indicated at the top of the panel. (b) Correlation between ¹⁵N CSA values measured using the model-independent methods, 2R₂-R₁ and R/η. The Pearson’s correlation coefficient r for these two data sets is 0.79; 81% of these CSA data agree within the experimental uncertainties. These values improve to r=0.80 and 87% agreement if only those data (shown as solid squares) where the least-squares fits pass the 95%-confidence level χ²/df cutoff are considered. (c) Correlation between the CSAs from 2R₂-R₁ and LS-CSA methods. The correlation coefficient is 0.95; it decreases to r=0.93 if only those fits that pass the χ²/df cutoff (solid squares) are included, though the percent agreement improves from 94% to 96%. (d) Correlation between the results from R/η and LS-CSA methods. The correlation coefficient is 0.80 and remains unchanged when the χ²/df cutoff is applied (solid squares). The percent agreement increases from 84% for all considered residues to 88% for those residues with the χ²/df below the cutoff value. In all correlation plots (panels b-d) the solid symbols represent values obtained for least squares fits that passed the χ²/df cutoff while open symbols correspond to the remaining residues. Outliers and extreme values of the CSA are labeled. Note that those few residues that show significant differences in the CSA values between the methods are all located in the loops/termini. Also in the loops are all residues where only one out of the three methods resulted in an acceptable fit (panel a).

Figure 3. The agreement between the spectral density component, J(0), measured using the 2R₂-R₁ method and reconstructed from the LS parameters

The spectral density component J(0) obtained from the 2R₂-R₁ method directly (solid symbols) and calculated from the order parameters and local correlation times obtained in the LS-CSA method (open symbols). Throughout this paper, the factor 2/5 arising from the normalization of the spectral density of the overall rotational diffusion is explicitly included in the corresponding expression for J(ω).

Figure 4. The likelihood functions (Eq. 19) obtained from different methods and sets of data show significant site-so-site variability in the ¹⁵N CSA values

Contour plots of the likelihood functions p(μ, Λ) (Eq. 19) corresponding to the ¹⁵N CSA values from the three methods (2R₂-R₁ (black), R/η (blue), and LS-CSA (green)) (a) for all analyzed residues in GB3 and (b) for only those residues where χ²/df from the least-squares fits passed the goodness-of-fit test at a 95% confidence level. Also shown (in cyan), for comparison, is the analogous likelihood function obtained for the recently reported ¹⁵N CSAs in ubiquitin , scaled to a NH-bond length of 1.02 Å. The location of the maximum for each function is indicated by a dot (see also Table 1), the contour lines represent 68.3%, 90% and 95% bivariate confidence regions for μ and Λ. In panel a, the 95% joint confidence intervals (in ppm) for μ and Λ are (-165.7, -182.2) and (16.6, 28.6) from 2R2-R1, (-169.9, -184.6) and (13.2, 24.3) from R/η, and (-168.0, -185.7) and (14.3, 27.3) from LS-CSA methods. For a subset of residues (panel b) that pass the χ²/df cutoff, the corresponding confidence intervals for μ and Λ are (-172.7, -185.2) and (6.8, 17.1) from 2R2-R1, (-172.5, -183.9) and (6.4, 15.8) from R/η, and (-171.8, -184.7) and (8.5, 18.0) from LS-CSA methods.

Figure 5. The values of Δσ_g and the β_z angles from the R/η and 2η_xy-η_z methods

(a) Measured site-specific ¹⁵N Δσ_g values for GB3 from the R/η (black squares) and the 2η_xy-η_z methods (blue circles). The Δσ_g values range from -108.9 ppm (Ala20, 2η_xy-η_z) to -189.8 ppm (Phe52, 2η_xy-η_z). (b) Correlation between Δσ_g values measured using the R/η and 2η_xy-η_z methods. The correlation coefficient is 0.94 for all residues and 0.96 for only those fits that pass the χ²/df cutoff. (c) β_z angles (in degrees) determined from the R/η method (black squares) and by combining the Δσ_g values from the 2η_xy-η_z method with the Δσ values from 2R₂-R₁ (blue circles). The Pearson’s correlation coefficient for the agreement of the β angles from these two measurements is 0.94. The derivation of β_z assumed axial symmetry of the ¹⁵N chemical shielding tensor. The secondary structure of GB3 is indicated on the top of panels (a) and (c).

Figure 6. Backbone order parameters determined from ¹⁵N relaxation data at each field using different CSA models

Shown are backbone order parameters in GB3 derived from a LS analysis of the ¹⁵N relaxation data (R₁, R₂, NOE) at different fields (left panels). Right panels represent the differences, ΔS²=S² - S²(9.4T), between the S² values at a particular field and at 9.4 Tesla, where the ¹⁵N CSA contribution to ¹⁵N relaxation rates is the weakest. (a, f) The LS analysis was performed in a conventional way, i.e. assuming a uniform CSA of -160 ppm for all residues. (b, g) The LS analysis was performed assuming a uniform CSA of -174.2 ppm (the average of the site-specific CSAs in GB3, see Table 1) for all residues. (c, h) Site-specific ¹⁵N CSA values from the 2R₂-R₁ method were used as input parameters. (d, i) Site-specific ¹⁵N CSA values from the R/η method were used as input parameters. (e, j) The LS analysis was performed for each field separately using the site-specific CSAs derived from the global fit (LS-CSA) of all five fields. Also shown as open circles in panel (d) are the order parameters from the global fit. The coloring is as follows: the 18.8T data are shown in black, 16.4 T in red, 14.1 T in green, 11.7 T in blue, and 9.4 T data in cyan. The dashed horizontal lines represent the average estimated level (±0.029) of the experimental uncertainty in ΔS². Val39 has been removed from all panels because of the conformational exchange contribution . In order to exclude deviations in S² due to a change in the model selection for different fields in a few residues, all data presented here were obtained assuming a model of local motion (model 2 in , model “B” in 33) that includes S² and τ_loc as fitting parameters. Our model-selection analysis showed that for the majority of residues in the secondary-structure elements of GB3 this was the preferred model . Allowing freedom in the model selection led to even greater discrepancies between the order parameters from different fields, which, however, exhibit the same behavior as shown here (Supporting Fig. 2). As a measure of the discrepancy in order parameters, the rmsd from the average (over all five fields) S² value for each method is 0.024 (panel a), 0.015 (b), 0.010 (c), 0.012 (d), and 0.009 (e), calculated for the secondary structure elements only.

Figure 7. Illustration of the LS fit of the spectral density components determined at all five fields

Representative LS fit of all spectral density components from the five-field measurements for Phe30. Symbols depict the J(ω) values for ω = 0, ω_N, and 0.87ω_H derived from relaxation data for each field separately (Eqs. 15-17) assuming CSA of -160 ppm (open circles) or the CSA value of -199.1 ppm for Phe30 that optimizes the fit (solid circles). The corresponding fitting curves are shown as dashed and solid lines, respectively. Shown in the insets is a blow up of the regions corresponding to ω= ω_N and 0.87ω_H, indicated as “ω_N” and “ω_H”. The values of S² and τ_loc were 0.93 and 3.0 ps when using CSA of -160 ppm, and 0.81 and 10.3 ps for the fit CSA values. A 35-fold decrease in χ²/df was observed when using the CSA and the LS parameters from the LS-SDF fit. The Δσ value derived using the 2R₂-R₁ method (-194.3 ppm for Phe30) resulted in a fit which was practically indistinguishable from the LS-SDF fit shown here, as does the use of the CSA value (Δσ = -196.9 ± 2.93 ppm) from the LS-CSA fit for Phe30. For comparison, the result of this fit when the mean site-specific CSA of -174.2 ppm is used is shown in Supporting Fig.7.

Figure 8. Site-specific ¹⁵N CSA values, averaged over all three methods, show significant CSA variability in GB3

(a) Range of ¹⁵N CSAs for each backbone amide in GB3 from the three methods (2R₂-R₁, R/η, and LS-CSA) shown as solid vertical bars. The open symbols represent the average site-specific CSA, Δσ, from the three methods; the error bars represent the maximum error from the three methods for each residue. (b) A histogram of the average site-specific CSA values shown in panel (a). Including these average site-specific CSA values into the analysis of the derivation of the true CSA values (Eq.19) resulted in the true mean μ = -173.8 ppm and the site-to-site variability Λ = 21.2 ppm (Table 1). The black curve represents a Gaussian distribution with the mean of -174.2 ppm and the standard deviation of 22.2 ppm. The dashed curve is also a Gaussian, with the same mean but with a standard deviation of 13.0 ppm - this curve corresponds to the case when all seven outliers in panel (b) are taken out.