Deuterium Spin Probes of Backbone Order in Proteins: A ²H NMR Relaxation Study of Deuterated Carbon α Sites

Abstract

²H spin relaxation NMR experiments to study the dynamics of deuterated backbone α-positions, D^α, are developed. To date, solution-state ²H relaxation measurements in proteins have been confined to side-chain deuterons - primarily ¹³CH₂D or ¹³CHD₂ methyl groups. It is shown that quantification of ²H relaxation rates at D^α backbone positions and the derivation of associated order parameters of C^α-D^α bond vector motions in small [U-¹⁵N,¹³C,²H]-labeled proteins is feasible with reasonable accuracy. The utility of the developed methodology is demonstrated on a pair of proteins - ubiquitin (8.5 kDa) at 10°C, 27°C, and 40°C, and a variant of GB1 (6.5 kDa) at 22°C. In both proteins, the D^α-derived parameters of the global rotational diffusion tensor are in good agreement with those obtained from ¹⁵N relaxation rates. Semi-quantitative solution state NMR measurements yield an average value of the quadrupolar coupling constant, QCC, for D^α sites in proteins equal to 174 kHz. Using the uniform value of QCC for all D^α sites, we show that C^α-D^α bond vectors are motionally distinct from the backbone amide N-H bond vectors, with ²H-derived squared order parameters of C^α-D^α bond vector motions, S² _CαDα, on average slightly higher than their N-H amides counterparts, S² _NH. For ubiquitin, the ²H-derived backbone mobility compares well with that found in a 1-μs molecular dynamics simulation.

Introduction

It is becoming increasingly apparent that protein function is oftentimes predicated upon the character and amplitudes of motions undergone by protein structures - that is molecular dynamics.^1–4 As a result, the past decade has witnessed an up-surge in the development of both experimental and theoretical approaches for studying motional processes in proteins on a variety of time scales. NMR spectroscopy is a particularly powerful experimental method for studying dynamics in proteins because it provides site-specific information that covers a wide range of motional time scales.^5–12 The amide ¹⁵N nuclei are the most commonly used spin probes of backbone motions in proteins, and ¹⁵N-based NMR relaxation studies of fast dynamics at backbone ¹⁵N-¹H amide positions of small- to medium-sized proteins are now largely routine.^5,13

The popularity of ¹⁵N as a nuclear spin probe of motional processes in backbones of proteins stems from the ease and affordability of selective incorporation of ¹⁵N into backbone amide positions (without concomitant ¹³C-labeling of neighboring nuclear sites) as well as high sensitivity of ¹⁵N relaxation measurements.^5,13 The rates of decay of ¹⁵N magnetization in amide moieties is expressed as the sum of dipolar (¹⁵N-¹H) and ¹⁵N chemical shielding anisotropy (CSA) contributions.^5,13,14 Quantitative interpretation of conventional ¹⁵N NMR relaxation data in terms of microdynamic characteristics of fast (pico- to nanosecond) motions requires, however, prior knowledge of a number of parameters, such as (i) exact ¹⁵N-¹H bond lengths, (ii) amide ¹⁵N CSA values, and (iii) contributions to the relaxation rates due to chemical exchange, R_ex, that, in principle, should be quantified independently. Although ¹⁵N relaxation rates in small- to medium-sized proteins can be usually measured with high accuracy, the uncertainties in any or all of the above parameters leads to ambiguities in the obtained measures of backbone order expressed as generalized order parameters (amplitudes) of N-H bond vector fluctuations, S_NH.^15,16 That is why significant efforts have been dedicated recently to development of NMR methodology that would provide `exchange-free' and `CSA-free' amide ¹⁵N relaxation data in proteins.^17,18

In search of a `cleaner' spin probe of backbone order in protein molecules, we designed ²H-based spin relaxation experiments for the studies of dynamics at deuterated backbone α-positions, D^α. Deuterium relaxation is dominated by a strong and local quadrupolar interaction,¹⁹ and the knowledge of only a single parameter, the anisotropy of ²H quadrupolar tensor or quadrupolar coupling constant (QCC), is needed to quantitatively describe D^{α 2}H relaxation data in terms of order parameters of C^α-D^α bond motions, S_CαDα. Since the seminal introduction of deuterium relaxation measurements to the field of protein NMR by Kay and co-workers,²⁰ deuterium has been recognized as a particularly favorable probe for the studies of dynamics. Millet et al.²¹ and Skrynnikov et al.²² have demonstrated the utility of deuterium spin probes of side-chain dynamics by the measurement of five relaxation rates per deuteron in ¹³CH₂D methyl groups of a 6.5-kDa protein L. The motional properties of ¹³CHD methylene positions in N-terminal drk SH3 domain have been studied by ²H relaxation.²³ Comparisons of ²H-derived and ¹³C-derived methyl three-fold axis order parameters (S² _axis) in proteins have been provided.^24,25 To date, however, ²H relaxation measurements in proteins have been confined to side-chain deuterons, primarily methyl groups of the ¹³CH₂D^20,21,26,27 or ¹³CHD₂^27,28 variety. We show that the availability of increasingly sensitive NMR instrumentation allows the quantification of ²H relaxation rates at D^α positions of protein backbones as well as the associated order parameters of C^α-D^α bond vector motions in small [U-¹⁵N,¹³C,²H]-labeled protein molecules.

The developed NMR methodology has been applied to a pair of small proteins - an 8.5-kDa ubiquitin at three temperatures and a variant of a 6.5-kDa protein GB1. The parameters of the global molecular reorientation can be reproduced using D^{α 2}H R₂/R₁ ratios, with the extracted diffusion tensors in good agreement with those derived from ¹⁵N data in both proteins. Relying on a number of previous solid-state NMR measurements and our own semi-quantitative solution state results we propose the use of a uniform QCC value of 174 kHz for D^α sites in proteins. Using this QCC value, it is shown that C^α-D^α bond vectors are motionally distinct from the backbone amide N-H bond vectors. In particular, ²H-derived S²_CαDα values are similar to, but are on average slightly higher than their ¹⁵N-derived S²_NH counterparts. Importantly, D^α rates can sample protein backbone motions that are inaccessible through ¹⁵N relaxation measurements. Although for sensitivity reasons the developed methodology is expected to be limited to small protein molecules, a number of advantages of using ²H relaxation of D^α sites turn it into a useful complement to the existing array of NMR techniques for quantitative studies of motional order in proteins.

Materials and Methods

NMR Samples

The following isotopically labeled samples of wild-type human ubiquitin and a variant of GB1 protein have been used in this work: (i) [U-¹⁵N]-labeled (both proteins), (ii) [U-¹⁵N,¹³C,²H]-labeled (both proteins), and (iii) a mixture of [U-¹⁵N,¹³C,²H]-labeled and [U-¹⁵N,¹³C]-labeled GB1. The deuterated samples of both proteins have been obtained using [U-¹⁵N,¹³C]-glucose as the main carbon source in the 99.9% D₂O-based E.coli media. Since carbon α positions are completely deuterated in proteins obtained using D₂O as the solvent in bacterial medium,^29,30 residual protonation of some aliphatic and aromatic sites is of no consequence for the present study. All samples of GB1 have been obtained using a co-expression vector where the sequence of GB1 serves as a removable tag, resulting in the addition of seven residues (-Ser-Ser-Gly-Leu-Val-Pro-Arg) to the C-terminus of the protein.

The [U-¹⁵N,¹³C,²H]- and [U-¹⁵N]-labeled NMR samples of human ubiquitin were 3.2 mM and 1.0 mM in protein concentration, respectively, and were dissolved in a 20 mM 90% H₂O/10% D₂O sodium phosphate buffer (pH 6.8) containing 0.03% NaN₃ and a cocktail of protease inhibitors. The [U-¹⁵N,¹³C,²H]- and [U-¹⁵N]-labeled samples of GB1 were 5.8 mM and 1.2 mM in protein concentration, respectively, and were dissolved in a 25 mM 90% H₂O/10% D₂O sodium phosphate buffer (pH 6.5) containing 50 mM NaCl, 0.03% NaN₃ and a cocktail of protease inhibitors. A third sample of GB1 contained a mixture of the [U-¹⁵N,¹³C,²H]- and [U-¹⁵N,¹³C]-labeled protein in the approximate ratio of 4.5:1 (final concentrations of [U-¹⁵N,¹³C,²H]- and [U-¹⁵N,¹³C]-GB1 of 4.5 and 1 mM, respectively), and was dissolved in a 25 mM 90% H₂O/10% D₂O sodium phosphate buffer (pH 6.5) as above to enable the measurements of D^α quadrupolar splittings and ¹D_Cα-Hα residual dipolar couplings (RDCs) in the same protein solution (see below).

Experimental NMR pulse sequence details

Figure 1 shows the pulse-schemes that have been designed for the measurements of R^Q(D₊), R^Q(D_z), R^Q(D₊D_z+D_zD₊), R^Q(3D_z²−2) at D^α sites of deuterated proteins. The scheme derives from a gradient sensitivity enhanced HN(COCA) experiment³¹ and involves additional magnetization transfers to and from D^α nuclei whose relaxation is measured by parametrically varying delay T. Insets A and B correspond to the measurement of R^Q(D₊) and R^Q(D_z), respectively. The part of the scheme that is enclosed in a dashed rectangle should be modified as it is shown in the figure to measure the relaxation of the D₊D_z+D_zD₊(3D_z²−2) elements in insets C(D). All narrow (wide) rectangular pulses are applied with the flip angles of 90°(180°) along the x-axis unless indicated otherwise. The ¹H(²H; ¹⁵N) carriers are positioned at 4.7(4.5; 119) ppm. The ¹³C carrier is placed at 177 ppm, switched to 57 ppm before the first 90° ¹³C^α pulse (after the gradient g5), and switched back to 177 ppm after the last 90° ¹³C^α pulse (after the gradient g5). ¹⁵N WALTZ-16³² decoupling during acquisition is achieved using a 1.25 kHz field, while ²H GARP-1³³ decoupling uses a 0.9 kHz field. ²H decoupling is interrupted for the application of gradients g6 and g8 (insets A,B).³⁴ SEDUCE^{35 13}C^α decoupling is implemented with 300 μs seduce-shaped pulses applied at ¹³C^α frequency by phase-modulation of the carrier.^{36,37 1}H WALTZ-16³² decoupling is applied with a 7 kHz field. All ¹H, ²H and ¹⁵N pulses are applied with maximum possible power, while 90°(180°) ¹³C pulses shown with filled rectangles are applied with a field strength of Δ/√15(Δ/√3) where Δ is the difference in Hz between the ¹³C^α and ¹³CO chemical shifts.³⁸ Vertical arrows at the beginning and the end of 2τ_c periods indicate the position of the ¹³CO Bloch-Siegert shift compensation pulses.^{38 13}C^α shaped pulses marked with asterisks in the middle of 2τ_d periods are 350 μs RE-BURP³⁹ pulses centered at 43 ppm by phase modulation of the carrier and cover the range of all ¹³C aliphatic chemical shifts. The ²H pulses shown with open rectangles in inset C have a flip angle of 45°. The ¹³C^α pulses shown with open dashed rectangles (insets A–C) are optional. All the experiments described in this work have been performed with these pulses included. The ¹H pulse shown with an arc (preceding the gradient g3) is implemented as a water-selective 1.5 ms pulse of rectangular shape. Delays are: τ_a = 2.7 ms; τ_b = 12.5 ms; τ_c = 4.5 ms; τ_d = 14 ms; δ = 5.4 ms; ε = 11 ms; ζ = 7 ms; Δ = 0.4 ms. The phase-cycle is: φ1 = x,−x; φ2 = 2(x),2(−x) (insets A,B) and 4(x),4(−x) (insets C,D); φ3=x; φ4=8(x),8(−x); φ5=x; φ6=4(x),4(−x) (inset A,C) and 2(0°),2(45°),2(90°),2(135°) in inset D; φ7=2(x),2(y),2(−x),2(−y) (inset A) and 8(x),8(−x) (inset C); φ8=x,−x,y,−y (inset C); rec.=2(x,−x), 2(−x,x) (inset A), x,2(−x),x,−x,2(x),−x (inset B), x,2(−x),x,−x,2(x),−x,−x,2(x),−x,x,2(−x),x (inset C), x,2(−x),x,−x,2(x),−x (inset D). Quadrature detection in t₁ is achieved via the Rance-Kay scheme: for each t₁ value a pair of spectra is recorded with (φ5=x; g11) and (φ5=−x; −g11) and manipulated post-acquisition.^40,41 The phase φ3 is inverted for each t₁ point.⁴² Durations and strengths of pulsed-field gradients in units of (ms; G/cm) are: g1 = (1; 15); g2 = (0.25; 5); g3 = (1.2; 12); g4 = (0.5; 8); g5 = (0.6; 10); g6 = (0.3; 5); g7 = (0.7; 15); g8 = (0.35; 5); g9 = (0.5; 12); g10 = (0.4; 10); g11 = (1.25; 20); g12 = (0.25; 8); g13 = (0.3; 5); g14 = (0.0625; 20); g15 = (0.0625; −20); g7′ = (0.6; 10); g8′ = (0.8; 12).

Figure 1.

The HN(COCA)D pulse scheme for the measurement of relaxation rates of α-deuterons in proteins. See `Materials and Methods' for the pulse-sequence details.

D^α and ¹⁵N Relaxation Measurements

All ²H and ¹⁵N spin relaxation experiments were performed on a 600 MHz Bruker Avance III spectrometer equipped with a room temperature triple-resonance z-gradient probe. NMR data sets recorded with the pulse scheme of Figure 1 (D^α, [U-¹⁵N,¹³C,²H]-labeled samples) comprised [512, 40] complex points in the [¹HN,¹⁵N] dimensions with corresponding acquisition times of [64 ms, 24 ms]. Typically, a recovery delay of 1.5 s was used along with 128 scans/FID giving rise to net acquisition times of ~4.8 hr./experiment. R^Q(D₊) rates in ubiquitin samples were recorded with parametrically varied delays T (inset A in Figure 1) of (0.02; 0.2; 0.4; 0.6; 0.8; 1.2; 1.6) ms, (0.02; 0.3; 0.6; 0.9; 1.2; 1.6; 2.0) ms, and (0.02; 0.2; 0.4; 0.6; 0.8; 1.2; 1.6) ms at 10°C, 27°C and 40°C, respectively, while R^Q(D_z) rates (Figure 1, inset B) were recorded with parametrically varied delays T of (0.02; 2.0; 4.0; 6.0; 8.0; 10.0; 12.0; 14.0) ms, (0.02; 1.0; 2.0; 3.0; 4.0; 6.0; 8.0; 10.0) ms, and (0.02; 1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 8.0) ms at 10°C, 27°C and 40°C. R^Q(D₊), R^Q(D_z), R^Q(D₊D_z+D_zD₊), R^Q(3D_z²−2) relaxation rates of α deuterons in GB1 have been measured at 22°C using the delays T of (0.02; 0.2; 0.4; 0.6; 0.8; 1.2; 1.6; 2.0) ms, (0.02; 2.0; 4.0; 6.0; 8.0; 10.0; 13.0) ms, (0.02; 0.2; 0.4; 0.6; 0.8; 1.2; 1.6; 2.0) ms, and (0.02; 1.0; 2.0; 3.0; 4.0; 6.0; 8.0; 10.0) ms, respectively. All NMR spectra were processed using the NMRPipe/NMRDraw suite of programs⁴³ and associated software. Rates were obtained by fitting peak intensities to a single exponential function of the form I = I₀ exp(−RT), where I is the measured intensity and R is the relaxation rate. Errors in peak intensities have been estimated from duplicate measurements or from the noise-floor level of the spectra, whichever was the highest, and subsequently propagated to the errors in the extracted rates using Monte-Carlo analysis.⁴⁴ The estimated errors in R^Q(D₊)(R^Q(D_z)) measurements are on the order of 2.0%(1.5%) on average in ubiquitin.

¹⁵N R_1ρ, R and ¹H-¹⁵N NOE measurements on [U-¹⁵N]-labeled samples of both proteins have been performed using standard procedures.^45,46 Typically, NMR data sets comprised [512, 64] complex points in the [¹HN,¹⁵N] dimensions with corresponding acquisition times of [64 ms, 38 ms]. Recovery delays of 1.0s and 4.3s (including a 2s presaturation period) for ¹⁵N R_1ρ,R and ¹H-¹⁵N NOE measurements respectively, along with 16 scans/FID gave rise to respective net acquisition times of ~0.7 and 2.5 hr./experiment. The spin-lock field strength of 1.9 kHz was used in ¹⁵N R_1ρ measurements. R_1ρ data have been subsequently corrected for resonance offset to obtain ¹⁵N R₂ rates.⁵ Error analysis of peak intensities and the extracted relaxation rates closely followed the procedure used for ²H relaxation measurements at D^α positions.

The relaxation rates of N_zC'_zC^α_z 3-spin order, R(N_zC'_zC^α_z), have been measured using a pulse-scheme derived from the gradient sensitivity enhanced HN(COCA) experiment³¹ using the same acquisition parameters as for ²H relaxation measurements. A recovery delay of 1.0 s was used along with 16 scans/FID giving rise to net acquisition times of ~30 min./experiment. The relaxation delays T of (0.01; 50; 100; 150; 200; 300; 350; 400; 450; 500; 600) ms have been typically used for both proteins at all temperatures. The extracted R(N_zC'_zC^α_z) rates have been subsequently subtracted from the obtained D^α R^Q[D] rates before analysis (see text).

Data Analysis

The relaxation rates of ²H transverse and longitudinal magnetization are given by¹⁹

$$R^Q\left(D_{+}\right)=R_2^Q=\frac{{\pi }^2}{20}{\left(\frac{e^{2}qQ}{h}\right)}^2[9J\left(0\right)+15J\left({\omega }_D\right)+6J\left(2{\omega }_D\right)]$$ (1)

$$R^Q\left(D_Z\right)=R_1^Q=\frac{3{\pi }^2}{10}{\left(\frac{e^{2}qQ}{h}\right)}^2[J\left({\omega }_D\right)+4J\left(2{\omega }_D\right)],$$ (2)

where (e²qQ/h) is the quadrupolar coupling constant, QCC, and J(ω_D) is the spectral density function evaluated at ω_D frequency. A uniform value of QCC = 174 kHz has been used for α deuterons in this work (see text). It is usually assumed that the ²H electric field gradient tensor is axially symmetric with its principal axis parallel to the direction of the deuteron bond, so that only the anisotropy of the tensor, (e²qQ/h) = QCC, enters into eq 1–2. Indeed, the asymmetry values of the ²H tensor, η, in aliphatic deuterons are known to be <0.04.^47,48 If the assumption of axial symmetry is dropped, the relaxation rates in eq 1–2 above should be multiplied by $(1+\frac{{\eta }^2}{3})$, that would contribute <0.06 % to R(D₊) and R(D_z). Clearly, such small contributions are well within the errors of the relaxation rate measurements and can be safely neglected.

All ²H data have been analyzed using the following Lipari-Szabo model-free spectral density function for the axially symmetric molecular tumbling,^15,16,49

$$J\left(\omega \right)=S_{C\alpha D\alpha }^2\left(\frac{A_1{\tau }_1}{1+{\left(\omega {\tau }_1\right)}^2}+\frac{A_2{\tau }_2}{1+{\left(\omega {\tau }_2\right)}^2}+\frac{A_3{\tau }_3}{1+{\left(\omega {\tau }_3\right)}^2}\right)+(1-S_{C\alpha D\alpha }^2)\frac{\tau \prime }{1+{(\omega \tau \prime )}^2},$$ (3)

where S_CαDα is the generalized order parameter describing the fluctuations of C^α-D^α bond vectors, A₁=(3/4)sin⁴(α), A₂=3sin²(α)cos²(α), A₃=[(3/2)cos²(α)−0.5]², τ₁=(4D_||+2D_⊥)⁻¹, τ₂=(D_||+5D_⊥)⁻¹, τ₃=(6D_⊥)⁻¹, D_|| and D_⊥ are the parallel and perpendicular components of the molecular diffusion tensor, α is the angle between the C^α-D^α bond vector (assumed collinear with C^α-H^α bond vector in protein structures) and the unique diffusion axis, and 1/τ' = 1/τ_f + 1/τ_c,eff with τ_c,eff = (2D_|| + 4D_⊥)⁻¹ the effective correlation time of overall rotation and τ_f the correlation time of fast local motions. Direction cosines for the C^α-H^α vectors of ubiquitin and GB1 have been obtained from the x-ray structures with the respective PDB accession codes 1ubq⁵⁰ and 2qmt⁵¹.

Diffusion tensors have been estimated by minimization of the error function χ² expressed as,

$${\chi }^2=\sum _{i=1}^N{\left[\frac{{\left(R_2^{expt}∕R_1^{expt}\right)}_i-{\left(R_2^{calc}∕R_1^{calc}\right)}_i}{{\left({\sigma }_{R_2∕R_1}\right)}_i}\right]}^2,$$ (4)

where the summation extends over all sites included in analysis, $R_2^{\mathit{expt}}$ and $R_1^{\mathit{expt}}$ are the experimentally measured ²H/¹⁵N rates, $R_2^{\mathit{calc}}$ and $R_1^{\mathit{calc}}$ are the rates calculated using diffusion tensor parameters (eq 3) and the expressions for $R_2^Q$, $R_1^Q(\mathrm{eq}1-2)∕{}^{15}\mathrm{N}{R}_2$, R₁ rates, and σ_{R2 / R1} is the uncertainty in the experimental R₂/R₁ ratios. A fit to a fully anisotropic diffusion tensor⁵² was not warranted for either protein because of relatively high errors in extracted D^α R^Q[D] relaxation rates that preclude a statistically significant differentiation between the axially symmetric and fully anisotropic models. The diffusion tensor parameters obtained by minimization of χ² (eq 4) are sensitive to the choice of residues whose dynamics is properly described by the first term of eq 3. Therefore, in both proteins only the residues in the secondary structure elements have been used. Likewise, the residues with missing coordinates (C-terminus of GB1), ¹H-¹⁵N NOE<0.6 and the residues undergoing chemical exchange (¹⁵N data only) have been excluded from analysis. Errors in the fitted diffusion parameters (polar angles θ, φ describing the orientation of the unique axis of the diffusion tensor with respect to the inertial frame, and D_||, D_⊥) were estimated using 300 Monte-Carlo simulations⁴⁴ with random additions of experimental errors to the measured rates. The standard deviations in the fitted parameters were used as uncertainties in diffusion parameters.

D^α(¹⁵N) relaxation rates have been interpreted in terms of motional parameters using their corresponding ²H-(¹⁵N)-derived diffusion tensor characteristics. Motional parameters of D^α sites, S²_CαDα and the corresponding τ_f values, were obtained by fitting the ²H relaxation data to the corresponding expressions for relaxation rates (eq 1–2) using eq 3 for the spectral density function (see `Results and Discussion'), whereas the motional parameters of N-H bond vectors, S² _NH and τ_f, were obtained using the program Dynamics^53,54 that models ¹⁵N relaxation data selecting for the appropriate motional model (that can be different from the simplest form of eq 3) based on statistical criteria. ¹⁵N relaxation data have been analyzed with standard expressions for ¹⁵N relaxation in ¹⁵N-¹H spin pairs. ¹⁵N R₂,R₁ and ¹H-¹⁵N NOE data were included in analysis that used the spectral density function of eq 3 where the squared order parameter describing the fluctuations of the backbone amide N-H bond vector, S² _NH, was used instead of S² _CαDα together with the corresponding N-H direction cosines. The N-H bond distance of 1.02Å and a uniform ¹⁵N CSA of −170 ppm were used in all calculations.

D^α quadrupolar splitting and ¹D_Cα-Hα measurements in oriented GB1

Analysis of D^α QCC closely followed the work of Mittermaier and Kay where QCC values have been determined for methyl deuterons using the ratios of quadrupolar splittings, ν_Q, and ¹³C^methyl-¹³C RDCs measured in an oriented protein.⁵⁵ The same approach can be used for α deuterons provided that ¹D_Cα-Hα RDCs are measured in the same sample. To enable the measurements of D^α splittings and ¹D_Cα-Hα RDCs in the same protein sample, a mixture of [U-¹⁵N,¹³C,²H]-labeled and [U-¹⁵N,¹³C]-labeled GB1 was used (see `NMR samples' above). The use of the same sample with two different labeling schemes (one having <sup>2</sup>H nuclei and the other <sup>1</sup>H nuclei at α positions) ensures that the alignment characteristics and dynamical properties are exactly the same for the ν<sub>Q</sub> and <sup>1</sup>D<sub>Cα-Hα</sub> measurements. The `mixed' GB1 sample was aligned in 18 mg/ml pf1 bacteriophage⁵⁶ (quadrupolar D₂O splitting of 24.7 Hz). ¹D_Cα-Hα RDCs have been obtained using the HNCO-type experiment of Yang et al.⁵⁷ modified to eliminate the resonances of ¹³C^α nuclei attached to deuterons arising from the (more concentrated) [U-¹⁵N,¹³C,²H]-labeled protein. This experiment allows for convenient measurements of ¹D_Cα-Hα in H₂O protein solutions by recording the modulation of carbonyl chemical shifts by (¹J_Cα-Hα + ¹D_Cα-Hα) couplings (see ref. 57). The quadrupolar splittings ν_Q in α deuterons have been obtained using the scheme of Figure 1 (inset A) with parametrically varied delays T of (0.02; 0.4; 1.0; 1.1; 1.6; 2.0; 2.3; 2.8; 3.1; 3.5; 4.0; 4.3; 4.8; 5.1; 5.5; 6.0; 6.3; 6.8; 7.1; 7.6; 8.0; 8.6) ms. The ¹D_Cα-Hα and ν_Q measurements have been performed twice and the obtained ν_Q/¹D_Cα-Hα ratios have been averaged.

Molecular dynamics simulations

A 1 μs molecular dynamics (MD) trajectory of ubiquitin was performed as described elsewhere.⁵⁸ Briefly, the MD simulation was performed using the AMBER 9 package⁵⁹ with the AMBER99SB force field,⁶⁰ which was shown previously to accurately reproduce the native state dynamics of ubiquitin.^59,61–63 The SHAKE algorithm⁶⁴ was employed to constrain all bonds involving hydrogen atoms, and a time step of 2 fs was used. Non-deuterated ubiquitin was embedded in a cubic box with SPC/E water models and long-range electronic interactions were handled using the PME method⁶⁵ with an 8 Å cutoff. The starting coordinates were taken from the crystal structure of ubiquitin (PDB entry 1ubq), and the simulation was run for 1000 ns at 300 K under NPT conditions after application of standard minimization and heating protocols. The values of S² _CαHα have been extracted using the iRED method⁶⁶ averaged over time windows of 1 ns and 5 ns, i.e. on the order of the experimental global tumbling correlation time of ubiquitin.

Results and Discussion

NMR experiments for the measurement of ²H relaxation rates at D^α sites of proteins

Figure 1 shows the HN(COCA)D experiment used for the measurements of relaxation rates at D^α sites. The pulse scheme is derived from the gradient sensitivity-enhanced HNCOCA experiment³¹ with additional delays at ¹³C^α nuclei to allow the magnetization to evolve to and from D^α positions whose relaxation is measured during time period T (see `Materials and Methods' for the pulse-scheme details). The transfer of magnetization can be summarized by,

$${}^1\mathrm{HN}_i\to {}^{15}\mathrm{N}_i\to {}^{13}\mathrm{CO}_{i-1}\to {}^{13}\mathrm{C}^{\alpha }{}_{i-1}\to {{\mathrm{D}}^{\alpha }}_{i-1}\left(T\right)\to {}^{13}\mathrm{C}^{\alpha }{}_{i-1}\to {}^{13}\mathrm{CO}_{i-1}\to {}^{15}\mathrm{N}_i\left(t_1\right)\to {}^1\mathrm{HN}_i\left(t_2\right),$$ (5)

where the transfer from one spin to the next is achieved via one-bond scalar couplings and t₁,t₂ are acquisition times. A series of two-dimensional data sets is recorded as a function of T. The cross-peaks obtained at the frequencies (ω_Ni; ωHNi) decay with the relaxation rates of α-deuterons belonging to the previous residue, D^α_i−1. A region of such a 2D spectrum recorded on ubiquitin at 27°C using the pulse scheme of Figure 1 (inset A, T = 0) is shown in Figure 2a. Relaxation rates can be extracted directly by fitting the intensity of each correlation to a single-exponential decay curve (Figures 2b–c). Since in glycines the magnetization is transferred from α carbons to both α-deuterons, the relaxation rates of the two (non-equivalent) Gly D^α positions can not be separated. Therefore, glycine residues (i.e. the amide correlations of the residues following glycines) have been excluded from analysis in this work. Likewise, D^α relaxation rates of residues preceding prolines can not be quantified using the experiment of Figure 1. The relaxation rates of proline D^α sites can be measured, however, through the amide correlation of the following (non-proline) residue. Although, as shown below, robust measures of backbone dynamics can be obtained from D^α relaxation rates, the D^α relaxation rate measurements using the scheme of Figure 1 are associated with very significant sensitivity losses compared to conventional ¹⁵N relaxation experiments. Taking into account different sample concentrations and acquisition times used for each time-point in the D^α/¹⁵N rate measurements (see `Materials and Methods'), we estimate that the scheme of Figure 1 is approximately 20 times less sensitive than ¹⁵N relaxation experiments necessitating the use of more concentrated protein samples and/or cryogenically cooled probes for data collection.

Figure 2.

a) A region of the ¹HN-¹⁵N correlation map of the [U-¹⁵N,¹³C,²H]-labeled 3.2 mM ubiquitin (27°C; 600 MHz) acquired as the first measurement point using the experiment of Figure 1 (inset A, T = 0). Assignments of the cross-peaks are shown according to their ¹HN-¹⁵N frequencies (located at position i if i−1 is the position of the decaying D^α nucleus). Typical decay curves of b) D_z and c) D₊ magnetization are shown for Asp⁵⁸ (dashed curves) and Gln⁶² (solid curves) of ubiquitin.

D^α relaxation rates

The R₁ and R₂ relaxation rates of D^α nuclei, R^Q(D⁺) and R^Q(D_z), have been measured using the experiments shown in insets A and B of Figure 1, respectively. Both experiments measure the relaxation rates of magnetization terms N_zC'_zC^α_z[D], where [D] is any deuterium spin operator and A_z is a longitudinal spin operator of nucleus A (carbonyl/carbon-α of residue i−1 and nitrogen of residue i). As is the case in the previous deuterium relaxation studies,^20,21,67 it can be shown that to a very good approximation R(N_zC'_zC^α_z[D]) = R(N_zC'_zCα_z + R[D], and to obtain a `pure' deuterium relaxation rate it is sufficient to subtract R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>) from the rates obtained in the experiments of Figure 1. In practice, however, the rates R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>) are very small compared to R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>[D]). For example, the R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>D<sub>+</sub>) rates measured in ubiquitin vary between 372 and 1042(321 and 675; 370 and 569) s<sup>−1</sup> at 10(27;40)°C, whereas R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>D<sub>z</sub>) rates in ubiquitin at 10(27;40)°C vary between 62 and 115(90 and 129; 119 and 153)s<sup>−1</sup>. The rates R(N<sub>z</sub>C'<sub>z</sub>C<sup>α</sup><sub>z</sub>) measured as described in `Materials and Methods' vary between 2.1 and 2.8(2.1 and 3.8; 1.9 and 4.0) s⁻¹ at 10(27;40)°C. Clearly, these rates are within measurement errors of R(N_zC'_zC^α_zD₊). This is, however, not necessarily the case for R(R(N_zC'_zC^α_zD_z) measurements - although the corrections remain small. To avoid introduction of systematic errors to the quantified deuterium relaxation rates, the (R(N_zC'_zC^α_z) values have been subtracted on a residue-specific basis from all measured D^α rates in this work. It is important to emphasize that ²H relaxation of backbone D^α sites is completely dominated by the strong quadrupolar interaction, as is also the case in the previous ²H relaxation studies of ¹³CH₂D^20,21,27,68 and ¹³CHD₂^27,28 methyl groups, ¹³CHD methylene sites in proteins²³ as well as deuterated sugars and bases of RNA molecules.⁶⁷ For example, calculations using typical sets of motional parameters obtained in this work for proteins tumbling with isotropic correlations times in the range between 2 and 10 ns show that the maximal contribution of the dipolar interaction of D^α deuterons with the directly bonded ¹³C^α spins to transverse(longitudinal) D^α relaxation rates D₊(D_z) is 1.0(0.25) s⁻¹. Evidently, such small contributions are within the errors of D^α relaxation rate measurements and can be safely ignored.

Figure 3 shows the profiles of experimental R^Q(D_z) and R^Q(D₊) values obtained in ubiquitin at 10°C (Figure 3a,d), 27°C (Figure 3b,e) and 40°C (Figure 3c,f). For comparison, ¹⁵N R₁ and R₂ rate profiles are included in the same plots. The average R^Q(D₊) rates measured at 10(27;40)°C in ubiquitin are 880(597;500) s⁻¹, whereas average R^Q(D_z) rates are 72(107;132) s⁻¹. Higher than average degree of backbone flexibility is manifested in decreased R^Q(D₊) values in (i) the loop between residues Thr⁷ and Lys¹¹ with average R^Q(D₊) of 813(571)s⁻¹ at 10(27)°C (Figures 3d and 3e; the residues in this region could not be reliably quantified at 40°C); (ii) near the Lys⁴⁸ polymerization site (residues Ala⁴⁶-Lys⁴⁸) at all temperatures with average R^Q(D₊) values of 855(566;467)s⁻¹ at 10(27;40)°C, and (iii) the C-terminus starting from Arg⁷² (Figures 3 d–f). These trends are largely mirrored by ¹⁵N R₂ rates. Interestingly, R^Q(D_z) profiles show that higher disorder at the C-terminus is accompanied by an increase in R^Q(D_z) rates while ¹⁵ R₁ rates decrease for the same residues (Figures 3a–c; some R^Q(D_z) rates could not be quantified at the C-terminus at 40°C because of resonance overlap). Notably, the R^Q(D_z) and R^Q(D⁺) rates of Gly D^α positions have to be excluded from the plots in Figure 3 resulting in a loss of information as some of Gly residues in ubiquitin (e.g. Gly¹⁰ and Gly⁴⁷) fall in the regions of increased backbone flexibility according to ¹⁵N data. It is apparent from Figures 3d–f that chemical exchange on the micro-to-millisecond time-scale - most notably affecting the amide of Asn²⁵ with ¹⁵N R₂ rate of 17.2(8.6;5.8)s⁻¹, while the average ¹⁵N R₂ rates in ubiquitin are 9.0(6.0;4.6)s⁻¹ at 10(27;40)°C - does not affect the D^α rates to any significant extent. Large exchange contributions to R₂ relaxation rates can significantly complicate ¹⁵N relaxation analysis, while D^α relaxation data (with the exception of double-quantum coherences, D²₊, vide infra) remain unaffected by contributions from chemical exchange.

Figure 3.

Plots of D^α (shown with black rectangles and dashed lines) and ¹⁵N (black circles and solid lines) relaxation rates in ubiquitin as a function of the protein sequence. R^Q(D) and ¹⁵N R₁ rates are shown at a) 10°C, b) 27°C, c) 40°C, while R^Q(D₊) and ¹⁵N R₂ rates are shown at d) 10°C, e) 27°C, f) 40°C. The lines connecting the symbols on the plots are intended solely to guide the eye. Schematic representation of the secondary structure of ubiquitin is shown on top: β-sheets are depicted with arrows, while α-helices are represented with cylinders.

Because the deuteron is a spin 1 nucleus, a total of five relaxation rates can be measured at D^α sites. As described by Millet et al.²¹ for the case of methyl groups, in addition to `rank-1' coherences D<sub>+</sub> and D<sub>z</sub>, the relaxation rates of `rank-2' elements (D₊D_z+D_zD₊, 3D_z² −2 and D₊²) can be quantified in the same ²H site. Indeed, one of the principal advantages of ²H spin relaxation lies in the possibility to assess the self-consistency of the obtained rates prior to analysis in terms of motional parameters. Jacobsen and co-workers⁶⁹ have shown that so long as J(0) ≥ J(ω_D) ≥ J(2ω_D), where J(ω_D) is the spectral density function evaluated at the ²H Larmor frequency, ω_D, (see `Materials and Methods') the following inequalities must hold: (5/3)R^Q(D₊D_z+D_zD₊) ≥ R^Q(D) ≥ (5/3)R^Q(3D_z²−2) ≥ R^Q(D_z), where the relaxation rates of anti-phase ²H magnetization, (D₊D_z+D_zD₊), and the quadrupolar order, (3D_z²−2), are given by,

$$R^Q(D_{+}{D}_Z+D_Z{D}_{+})=\frac{{\pi }^2}{20}{\left(\frac{e^{2}qQ}{h}\right)}^2[9J\left(0\right)+3J\left({\omega }_D\right)+6J\left(2{\omega }_D\right)]$$ (6)

$$R^Q(3D_Z^2-2)=\frac{3{\pi }^2}{10}{\left(\frac{e^{2}qQ}{h}\right)}^2\left[3J\left({\omega }_D\right)\right]$$ (7)

The pulse-scheme that can be used for R^Q(D₊D_z+D_zD₊) and R^Q(3D_z²−2) measurements at D^α positions of proteins are shown in insets C and D of Figure 1, respectively. In contrast to ²H relaxation studies of methyl deuterons, however, the R^Q(D₊D_z+D_zD₊) and R^Q(3D_z²−2) measurements at backbone D^α sites suffer from very poor sensitivity because of fast ²H spin-flips occurring during prolonged ¹³C^α_i−1→D _i−1(T)→¹³C^α_i−1 magnetization transfer steps (two time periods τ_d+ζ in Figure 1, insets C–D). As a result, it was not possible to measure R^Q(D₊D_z+D_zD₊ and R^Q(3D_z²−2) of D^α nuclei in ubiquitin within a reasonable time frame. Nevertheless, we have been able to quantify the R^Q(D₊D_z+D_zD₊) and R^Q(3D²_z−2) rates in a more concentrated sample of a smaller protein GB1. Figure 4 shows that the inequalities (5/3)R^Q(3D²_z−2)≥R^Q(D_z) (Figure 4a) and (5/3)R^Q(D₊D_z+D_zD₊)≥R^Q(D₊) (Figure 4b) are indeed satisfied without a single exception in GB1 at 22°C representing a useful semi-quantitative consistency test of the experimental raw data. The profiles of R^Q(D₊),R^Q(D_z) and ¹⁵N R₂,R₁ rates measured in GB1 are compared in Figure S1 of the Supporting Information. Notably, the flexibility of the backbone in the loop between Gly⁹ and Leu¹³ and the C-terminus of GB1 is `picked-up' by D^α relaxation data with decreased R^Q(D₊) and R^Q(D₊D_z+D_zD₊) rates in these regions (Figure 4b and Figure S1 of the Supporting Information). Unfortunately, the presence of two glycine residues (Gly³⁸ and Gly⁴¹) prevents the quantification of D^α rates in another flexible loop of GB1 extending from Asn³⁷ to Gly⁴¹ as it is apparent from ¹⁵N R₁,R₂ rate profiles (Figure S1b).

Figure 4.

Consistency plots of D^α relaxation rates. a) (5/3)R^Q(3D ²_z−2) (shown with black rectangles and dashed lines) and R^Q(D_z) (black circles; solid lines); b) (5/3)R^Q(D₊D_z+D_zD₊) (black rectangles; dashed lines) and R^Q(D₊) (black circles; solid lines) rates measured in GB1 at 22°C (600 MHz) are plotted as a function of GB1 sequence. Schematic representation of the secondary structure of GB1 is shown on top.

As described above, fast ²H spin-flips lead to on average 4-to-5-fold sensitivity losses in the R^Q(D₊D_z+D_zD₊) and R^Q(3D²_z−2) experiments (Figure 1, insets C–D) compared to the R^Q(D₊) measurements (Figure 1, inset A) in GB1 at 22°C. This situation is similar to ²H relaxation measurements in the sugar and base moieties of RNA reported earlier.⁶⁷ Because of low sensitivity of `rank−2' relaxation measurements and, as a result, substantial errors in the derived R^Q(D₊D_z+D_zD₊) and R^Q(3D²_z−2) rates, these data have not been used in further analysis. Mainly for the same reasons, no attempt has been undertaken to measure the relaxation rate of the fifth double-quantum ²H coherence, D₊², at D^α sites.

D^α relaxation derived diffusion tensor parameters

Prior to obtaining the ²H-derived measures of backbone order it is important to establish the diffusion parameters of the global molecular reorientation. In analogy to the case of ¹⁵N relaxation in protein backbones, ²H R₂/R₁ ratio, R^Q(D₊)/R^Q (D_z), is, to a good approximation, independent of the amplitude and time-scale of rapid internal motions.^13,52 It therefore serves as a good measure of the rate at which the C^α-D^α vector reorients with global tumbling.⁷⁰ Table 1 compares the parameters of the (axially symmetric) diffusion tensors derived from D^α R^Q(D₊)/R^Q(D_z) and ¹⁵N R₂/R₁ ratios for ubiquitin at three temperatures (see `Materials and Methods'). Since the diffusion tensor of ubiquitin has a relatively low diffusion anisotropy, we have chosen to test whether the R^Q(D₊)/R^Q(D_z) ratios can reproduce a significantly more anisotropic reorientation on the sample of GB1 modified at the C-terminus (Table 1). Figure S2 of the Supporting Information shows the plots of R^Q(D₊)/R^Q(D_z) as a function of the angle α that each of the C^α-D^α bond vectors subtends with respect to the unique axis of the diffusion tensor, along with the best fits of the data for GB1 (22°C) and ubiquitin (27°C). Although the D^α-derived orientations of the principal axes (polar angles θ and ϕ in the inertial coordinate frame) are less well defined in comparison to ¹⁵N-derived values, a good agreement between the ¹⁵N- and D^α-derived tensors is observed in all cases. The ratios of τ_c,eff = (2D_∥ + 4D⊥)⁻¹ values obtained at 10, 27 and 40°C in ubiquitin are very close to those expected based on the Stokes-Einstein relationship. Despite the fact that D^α relaxation rates in ubiquitin have been obtained using a 3-fold more concentrated protein sample than ¹⁵N rates, the D^α-derived values of τ_c,eff in ubiquitin are somewhat lower (3.6%, 5.6% and 2.8% at 10°C, 27°C and 40°C, respectively) than their ¹⁵N-derived counterparts at the same temperature (Table 1). Interestingly, in a recent study exchange-free, purely dipolar contributions to ¹⁵N relaxation rates, R_dd, in ubiquitin have been derived.¹⁷ These exchange-free rates indicated the presence of non-zero R_ex contributions to ¹⁵N R_1ρ rates for many residues in ubiquitin.¹⁷ This implies that D^α R^Q(D₊)/R^Q(D_z) ratios that are not affected by chemical exchange to any significant degree might serve as more robust estimates of the global reorientation parameters in small proteins.

Table 1.

Comparison of D^α R^Q(D₊)/R^Q(D_z)- and ¹⁵N R₂/R₁-derived Diffusion Tensor Parameters of Ubiquitin (10°C, 27°C, 40°C) and GB1 (22°C).^a)

	τc,effb)	D||/D⊥	θc)	φc)
Ubiquitin (10 °C)	6.68 ± 0.03 (6.92 ± 0.02)	1.28 ± 0.04 (1.23 ± 0.02)	12 ± 4 (6 ± 2)	−22 ± 12 (−19 ± 5)
Ubiquitin (27 °C)	3.94 ± 0.03 (4.16 ± 0.01)	1.22 ± 0.03 (1.18 ± 0.02)	8 ± 3 (6 ± 2)	−8 ± 12 (−16 ± 4)
Ubiquitin (40 °C)	2.90 ± 0.02 (2.98 ± 0.01)	1.26 ± 0.03 (1.23 ± 0.01)	16 ± 2 (6 ± 1)	−34 ± 14 (−48 ± 8)
GB1 (22 °C)	4.43 ± 0.02 (4.42 ± 0.01)	1.45 ± 0.03 (1.39 ± 0.02)	20 ± 6 (24 ± 1)	−61 ± 26 (−99 ± 8)

^a)15N R₂/R₁-derived diffusion parameters are shown in parentheses and italics below the D^α R^Q(D₊)/R^Q(D_z)-derived values. The orientation of the unique axis of the axially symmetric diffusion tensor is specified in the inertial frame for both proteins. The inertia tensors and direction cosine values for C^α-H^α and N-H bond vectors have been calculated using the coordinates of protonated x-ray structures of ubiquitin and GB1 with respective pdb accession codes 1ubq.pdb⁵⁰ and 2qmt.pdb.⁵¹ Seven C-terminal residues of GB1 do not have crystallographic coordinates and have been excluded from the derivation of the diffusion tensor. See 'Materials and Methods' for the details of diffusion tensor determination.

^b)τ_c,eff is given in units of nanoseconds (ns).

^c)Angles are given in degrees. The angle γ between the D^α and ¹⁵N-derived diffusion axes can be estimated using the relationship cosγ = cosθ₁cosθ₂ + sinθ₁sinθ₂cosϕ₁−ϕ₂), where {θ_i,ϕ_i} are the polar angles that define the mean orientations of the unique axes of the two compared diffusion tensors. These angles are equal to 6(2,10)° for ubiquitin at 10(27,40)°C and 14.5° for GB1 (22°C).

The choice and estimation of D^α QCC values

Although the value of D^α QCC is not needed for determination of the diffusion tensor, the knowledge of its accurate value is of paramount importance for interpretation of D^α relaxation rates in terms of motional parameters. Several solid-state NMR studies have reported the values of QCC for aliphatic deuterons attached to sp³-hybridized carbons ranging from 168 ± 2 to 174 ± 2 kHz.⁷¹ Solid-state NMR measurements of Haeberlen and co-workers provided the QCC values of the two α-deuterons in zwitterionic glycine equal to 159.9 and 169.4 kHz.⁷² The authors explained the large difference between the two values by formation of weak C-H^…O hydrogen bonds leading to a decrease of QCC in one of the two α-deuterons. Notably, oxygen acceptors are located in an adjacent layer of glycine molecules⁷² - a situation that cannot be encountered in solution. In another low-temperature liquid crystal NMR study, the QCC value obtained for deuterons in a CD₃ methyl group of toluene (165 kHz) has been compared to the QCC of deuterons in cyclohexane-d₁₂ (174 ± 2 kHz). The two values can be brought into exact agreement if the tetrahedral angle θ of the methyl group is assumed to be equal to 111° instead of 109.5°.⁷³ Interestingly, using solution NMR techniques Mittermaier and Kay determined the QCC value of deuterons in ¹³CH₂D methyl groups of proteins equal to 167 ± 1 kHz assuming θ = 109.5°.⁵⁵ What is effectively determined in this study is the product P₂(cosθ)QCC, where P₂(x) = 0.5(3x² − 1) is the second order Legendre polynomial. If the value of θ is increased by only 1°,⁷⁴ the methyl QCC increases to 174 kHz. We note here that what is normally determined in single-crystal NMR measurements (unless they are performed at very low temperatures) is the product √S²QCC, where S is the order parameter of local motions. Here, local motions are assumed to be axially symmetric, and S includes the effects of slow motions and (potentially small) contributions from `rocking' motions of the molecule relative to the crystal lattice. If S² is assumed to be equal to 0.95,^75,76 then the measurements of Haeberlen and co-workers in α-glycine⁷² yield the value of QCC = 173.8 kHz for the non-hydrogen bonded deuteron.

To obtain an independent estimate of QCC of α-deuterons in proteins we followed the approach of Mittermaier and Kay.⁵⁵ Briefly, in an oriented protein, during the period T in the pulse-scheme of Figure 1 (inset A) the ²H magnetization evolves according to^55,77

$$D_y\to D_y\cos \left(\pi {\nu }_{Q}T\right)-\{D_x{D}_z+D_z{D}_x\}\sin \left(\pi {\nu }_{Q}T\right),$$ (8)

, where the quadrupolar splitting ${\nu }_Q=\frac{3}{4}\mathit{QCC}\langle 3{\cos }^2\theta -1\rangle$, θ is the angle between the principal axis of the electric field gradient tensor and the magnetic field, and the brackets <> denote ensemble averaging. The relaxation rates of D_y and (D_zD_x+D_xD_z) coherences are described by eq 1 (the rate of in-phase ²H magnetization, R_I) and eq 6 (the rate of anti-phase ²H magnetization, R_A), respectively. Including relaxation during the period T, the evolution of the D_y magnetization (that is detected in the end of the experiment) is described by⁵⁵

$$D_y\left(T\right)=\frac{A}{2}\exp \left\{-\frac{(R_1+R_A)}{2}T\right\}\left[(1-\Delta )\exp \left\{\frac{\Omega }{2}T\right\}+(1+\Delta )\exp \left\{-\frac{\Omega }{2}T\right\}\right],$$ (9)

where $\Omega =\sqrt{{(R_1-R_A)}^2-4{\pi }^2{\nu }_Q^2}$ and Δ = (R_I − R_A)/Ω. In contrast to the study of methyl groups,⁵⁵ here, the average rate of magnetization decay, (R_I + R_A)/2, is 2-to-3 fold higher than the maximal achievable quadrupolar splitting ν_Q, making the analysis of the decay of D_y (eq 9) extremely unreliable except for a (small) subset of residues where ν_Q is close to its maximal value and the zero-crossing of the magnetization decay can be achieved experimentally. In pf1 phage-aligned, highly concentrated sample of GB1 (see `Materials and Methods'), a small subset of 11 peaks has been chosen where the zero-crossing of the D_y magnetization decay is apparent and where the extraction of a reliable albeit inexact value of ν_Q is still feasible. Although for this subset of residues the condition (2πν_Q)² >> (R_I − R_A)² is always satisfied, simulations using synthetic data and average R_I, RA rates and ν_Q values for GB1 showed that the fitting of the decay function D_y to a simpler 3-parameter expression with a single effective (R_I + R_A)/2 rate⁷⁸ would produce errors in the derived ν_Q values of 5 to 8%. We have chosen therefore to fit the decay curves to the full expression in eq 9 above with four variable parameters (R_I, R_A, A and ν_Q). Two examples of such fits for Leu¹² and Asp⁴⁰ from the chosen subset of 11 peaks in GB1 are shown in Figures 5a–b.

Figure 5.

Examples of the decay curves are shown for a) for Leu¹² and b) Asp⁴⁰ of GB1(22°C) from the chosen subset of 11 peaks in GB1 that show clear-cut zero-crossing. The decay curves are fit to eq 9. Zero normalized intensity is shown with a dashed line. The ¹HN-¹³CO correlations obtained in the experiment of Yang et al.⁵⁶ that allows the measurement of ¹D_Cα-Hα residual dipolar couplings for c) for Leu¹² and d) Asp⁴⁰. The measured frequency differences (¹J+¹D_Cα-Hα) are shown for each pair of peaks.

The value ¹D_Cα-Hα RDC measured as described in `Materials and Methods' is expressed as, ${}^{1}D_{C\alpha -H\alpha }=-({\mu }_0∕4\pi )({\gamma }_C{\gamma }_{H}h∕4{\pi }^2{r}_{C\alpha H\alpha }^3)\langle 3{\cos }^2\theta -1\rangle$, where γ_i is the gyromagnetic ratio of nucleus i, μ₀ is the vacuum permeability constant, and r_CH is the distance between C^α and H^α nuclei. Figures 5c–d show the results of ¹D_Cα-Hα measurements for the same pair of residues in GB1 as in Figures 5a and 5b, respectively. As shown by Mittermaier and Kay for methyl groups, the ratio of ν_Q/¹D_Cα-Hα taken for the same α position, is independent of magnetic alignment (<3cos²θ −1>) and local motions.⁵⁵ QCC value can then be obtained from the ν_Q/¹D_Cα-Hα ratio following the relationship,

$$QCC=\frac{1}{12}\frac{{\mu }_0{\gamma }_C{\gamma }_{H}h}{{\pi }^3{r}_{C\alpha H\alpha }^3}\left(\frac{{\nu }_{\mathrm{Q}}}{{}^{1}D_{C\alpha -H\alpha }}\right)$$ (10)

Note that unlike in the case of methyl groups,⁵⁴ according to eq 10, D^α QCC does not depend on dihedral angles. The correlation of the ²H quadrupolar splitting ν_Q with the ¹D_Cα-Hα dipolar coupling for the subset of 11 peaks in GB1 is shown in Figure S3 of the Supporting Information. Linear regression analysis of this correlation provided a slope of −5.66 ± 0.34 (Pearson R = 0.979) when the (statistically insignificant) intercept was fixed at zero. The sign of ν_Q can not be determined using this procedure, and ν_Q values have been assumed to have a sign opposite to that of the measured ¹D_Cα-Hα. Using eq 10 and assuming a standard r_CH distance of 1.095 Å^79–81 we obtain the D^α QCC value of 173.7 kHz. Notably, any effects of local dynamics are cancelled out by taking the ratio of ν_Q and ¹D_Cα-Hα allowing one to use the value of r_CH distance `uncorrected' for any type of local motions.⁸¹

The procedure described above for the derivation of QCC values of D^α deuterons is only semi-quantitative due to large uncertainties associated with the derivation of ν_Q. From the variation of individual ν_Q/¹D_Cα-Hα ratios for 11 peaks in GB1 and from propagated errors in (fitted) ν_Q and ¹D_Cα-Hα values we estimate the uncertainty obtained in D^α QCC measurements on the order of 6–8% (~10–14 kHz). However, on average we have been able to obtain the value of D^α QCC that agrees quantitatively with the results of solid-state measurements in α-glycine if dynamics is taken into account (see above). In what follows, we therefore used a uniform value of D^α QCC equal to 174 kHz in all calculations. It is unlikely that the variation in individual ν_Q/¹D_Cα-Hα ratios in GB1 reflects the actual variation in D^α QCC values in a protein rather than the uncertainties of the measurement. Although hydrogen bonding is known to significantly affect quadrupolar couplings of deuterons,⁷⁶ α-deuterons in proteins are unlikely to participate in sufficiently strong hydrogen bonds. Of note, DFT calculations of QCC values of aliphatic deuterons bound to sp³-hybridized carbons show that QCC is a highly local parameter whose value is dependent almost exclusively on the choice of the r_CD bond length (N.R. Skrynnikov, personal communication).

Comparison of ²H- and ¹⁵N-derived backbone order

Since, commonly, only two rates, R^Q(D₊) and R^Q(D_z), are available for the derivation of motional parameters of C^α-D^α vectors in proteins, caution must be exercised in a modelfree-type analysis of D^α relaxation data to avoid over-interpretation when the results are compared to ¹⁵N-derived dynamics parameters. Therefore, we have chosen to fit the R^Q(D₊) and R^Q(D_z) rates first to the simplest possible motional model that excludes the term describing local motions in the spectral density function of eq 3 (τ' = 0). The majority of the residues in ubiquitin could be fit using such a single-parameter (S² _CαDα) spectral density function with 5% probability of exceeding χ².⁸² If the χ² of the fit exceeded this level of confidence, the R^Q(D₊) and R^Q(D_z) rates have been fit to the full expression in eq 3 with 2 variable parameters (S² _CαDα; τ_f). The resulting values of S² _CαDα in ubiquitin at 10°C, 27°C and 40°C versus residue numbers are shown with blue rectangles in Figures 6a–c. For convenience of comparison we have included in the plots the values of S² _NH derived from ¹⁵N relaxation data (red circles in Figures 6a–c). Table S1 in the `Supporting Information' lists all the dynamics parameters obtained at D^α positions of ubiquitin at the three temperatures. Figure 7 shows the ribbon structure of ubiquitin where the H^α(D^α) atoms (Figure 7a) and HN atoms (Figure 7b) are color-coded according to the values of S² _CαDα and S² _NH, respectively. Overall, lower S² _CαDα and S² _NH values are observed in the loop region between residues Thr⁷ and Lys¹¹, in the bend near the polyubiquitination site (residues Ala⁴⁶-Lys⁴⁸) and in several C-terminal residues.

Figure 6.

D^α-derived S²_CαDα (blue rectangles and lines) and ¹⁵N-derived S²_NH (red open circles and lines) in ubiquitin at a) 10°C, b) 27°C and c) 40°C plotted as a function of protein sequence. Schematic representation of the secondary structure of ubiquitin is shown on top: β-sheets are depicted with arrows, while α-helices are represented with cylinders.

Figure 7.

Ribbon diagrams of ubiquitin crystal structures with a) D^α and b) HN atoms represented as balls color-coded according to the values of S²_CαDα and S²_NH (27°C), respectively. The elements of the secondary structure are shown in blue. The placement of a number of residues discussed in the text is indicated with residue numbers. c) Schematic representation of the α-helical stretch of ubiquitin (residues Ile²³-Glu³⁴) viewed from the top along the helical axis. The color-coded balls represent D^α atoms. The values of S²_CαDα are listed along with residue numbers.S²_CαDα values of residues with C^α-D^α vectors directed towards a short 3₁₀-helical stretch (Pro³⁸-Gln⁴⁰) are shown in bold, whereas those directed towards the interior of the protein core on the other side of the α-helix are shown in italics. The color-coding scale is shown to the right of panel (b). The diagrams have been generated using the program Molmol.⁸⁹

C^α-D^α bond vectors are motionally distinct from the N-H bond vectors, with ²H-derived S² _CαDα values on average slightly higher than their S² _NH counterparts in N-H amides in agreement with several earlier molecular dynamics simulations^83,84 as well as NMR spin relaxation^85,86 and liquid crystal studies.⁸¹ In particular, the average S² _CαDα values of 0.86(0.85;0.84) are obtained in ubiquitin at 10(27;40)°C for the full protein and 0.89(0.87;0.85) when the flexible C-terminal residues are excluded from analysis, while the respective average S² _NH values are 0.82(0.81;0.81) for the full protein and 0.84(0.83;0.82) when the C-terminus is excluded. For those residues where both S² _CαDα and S² _NH could be quantified, S² _CαDα values are higher than S² _NH on average, with their respective average values of 0.86(0.86;0.85) and 0.82(0.81;0.80) at 10(27;40)°C. The difference in order parameters is even more pronounced in GB1. The values of S² _CαDα and S² _NH in GB1 at 22°C are plotted as a function of the protein sequence in Figure S4 of the Supporting Information. The higher rigidity of the C^α-H^α (C^α-D^α) bond vectors in proteins is a consequence of the high correlation of their motions with those of the C^α-C^β bond vector of the same amino acid.⁸⁷ The latter anchors the side-chain to the backbone, and thereby any reorientational motion will need to involve the bulk of the side chain. By contrast, the N-H^N amides are strongly affected by local crank-shaft-type motions of the peptide bond plane,^84,88 which involve anti-correlated modulations of the associated backbone φ_i and ψ_i−1 dihedral angles. There are notable exceptions to this general trend, however. For example, in the C-terminal region of ubiquitin following Leu⁷¹, average S² _CαDα(S² _NH) of 0.61(0.63) have been obtained at 27°C, whereas in GB1 the average S² _CαDα(S² _NH) of the C-terminal residues are 0.22(0.24). Interestingly, the D^α rates of the C-terminal residues in both proteins can not be fit to the simplest (S² _CαDα only) Lipari-Szabo model because the increased R^Q(D_z) rates at the C-terminus (Figure 3a–c) can not be explained without invocation of fast local motions. In principle, direct comparison of S² _CαDα and S² _NH on a per-residue basis can be ambiguous since higher S² _NH values may result from the use of different motional models for the derivation of S² _CαDα and S² _NH as well as significantly different time-scales of N-H and C^α-D^α bond vector fluctuations. Furthermore, since their respective diffusion tensor parameters have been used for the derivation of S² _CαDα and S² _NH, any small differences in these parameters (Table 1) can skew the differences between S² _CαDα and S² _NH (S² _CαDα - S² _NH) in favor of somewhat smaller values adding additional uncertainty to direct comparisons of backbone order at the amide and D^α sites (vide infra).

Since different motional processes are sampled by D^α and ¹⁵N relaxation rates, it would be of interest to compare the degree of backbone order in the elements of protein secondary structure where C^α-H^α(D^α) and N-H bond vectors are oriented in different directions. For example, ¹⁵N relaxation data do not sample fast local motions that occur around the helical axis, such as a rolling motion of an α-helical shaft,⁹⁰ because in α-helices all N-H bonds lie approximately parallel to the helical axis forming hydrogen bonds with a carbonyl oxygen acceptor of residue i−4. In contrast, C^α-H^α(D^α) bond vectors are directed outward making angles of up to ~70° with the α-helical axis. Interestingly, in the α-helical segment of ubiquitin (residues Ile²³-Glu³⁴), S² _CαDα are noticeably higher for the residues whose C^α-H^α(D^α) bond vectors are directed towards a short 3₁₀-helical stretch the protein structure (Val²⁶, Ile³⁰ or oriented towards the interior of the protein at the other face of the α-helix (Glu²⁴, Ala²⁸, Gln³¹). Figure 7c shows a schematic representation of the α-helix in ubiquitin viewed from its N-terminal end approximately along the axis of the helix, with S²_CαDα (27°C) shown for each D^α site. In GB1, the residues of the α-helix (Ala²³-Asp³⁶) facing the hydrophobic interior of the protein (Ala²⁶, Phe³⁰, Tyr³³ and Ala³⁴) also tend to have elevated S²_CαDα. The resulting alternating patterns of R^Q(D₊) rates (Figures 3d–f and Figures S1 of the Supporting Information) and S²_CαDα values (Figures 6a,b, Figure S4 of the Supporting Information) are apparent in the helical regions of both proteins indicating that the backbone order as probed by ²H spin relaxation at D^α positions is likely to be related to the tightness of hydrophobic packing in protein cores. Specifically, the values of S²_CαDα in the α-helix of ubiquitin (Figure 7c) are weakly but statistically significantly correlated with the buried surface area and the hydrophobic contact potential^91,92 at C^α positions (Pearson R > 0.5). We note that the `zigzag' patterns of R^Q(D₊) rates and the resulting S²_CαDα values cannot be explained by the anisotropy of the global molecular tumbling, as the unique diffusion axis of ubiquitin subtends an angle of only ~10° relative to the α-helical axis.

Molecular dynamics simulations and alternative analyses of D^{α 2}H rates

To gain more confidence in the ²H-derived measures of backbone order, we have performed molecular dynamics simulations for ubiquitin at 27°C (see `Materials and Methods'). Interestingly, the best agreement between MD-derived S<sup>2</sup><sub>CαHα</sub> and experimental S<sup>2</sup><sub>CαDα</sub> order parameters is achieved when the D<sup>α</sup> QCC value is (slightly) lowered to 171 kHz. A comparison between experimental S<sup>2</sup><sub>CαDα</sub> (QCC = 171 kHz) and MD-derived S<sup>2</sup><sub>CαHα</sub> values obtained using a 1 μs MD trajectory of ubiquitin averaged over 1 ns and 5 ns time windows, is shown in Figure 8. A good agreement is found for the loop region of the N-terminal β-hairpin and the flexible C-terminus. The experimentally observed decrease in the order parameters of loop residues Ile<sup>44</sup>, Ala<sup>46</sup>, Lys<sup>48</sup> and Glu<sup>49</sup>, whose side-chains point towards the solvent, is well reproduced by the MD simulation. Furthermore, the `zigzag' pattern displayed by the experimental S²_CαDα values in the Tyr⁵⁹-Lys⁶³ loop is also clearly observable in the simulation profile (Figure 8). For this region, the order parameters directly reflect the orientation of the associated side-chain, with lower S² for inward oriented side-chains and higher S² for more solvent exposed ones. Lys⁶³ is a notable exception with a relatively high S²_CαHα despite its high solvent accessibility. The close relationship between S²_CαDα and the associated side chain properties is corroborated by the very close agreement between S²_CαDα and S²_CαCβ values found in the MD simulation of ubiquitin (see Supporting Information, Figure S6).

Figure 8.

Experimental S² _CαDα order parameters of ubiquitin at 27°C (black line with closed circles) determined using a uniform QCC value of 171 kHz, in comparison with the MD-derived S² _CαHα values obtained from a 1 μs MD trajectory of ubiquitin averaged over 1 ns (green line with `x' symbols) and 5 ns (red line with `+' symbols) time windows. See `Materials and Methods' for the details of MD simulations.

The comparisons of ¹⁵N- and ²H-derived measures of backbone order described here have been performed using their respective (¹⁵N-derived or ²H-derived) overall diffusion tensor parameters (Table 1). Obviously, there is a unique diffusion tensor that characterizes the rotational reorientation of a molecule. Therefore, it would be of interest to ascertain that the relation between S²_CαDα and S²NH noted above holds if analysis is performed using a common set of diffusion tensor parameters for both nuclei. We have repeated the analysis as described in the `Comparison of <sup>2</sup>H- and <sup>15</sup>N-derived backbone order' section above for ubiquitin at 27°C using common diffusion tensor parameters for <sup>15</sup>N and <sup>2</sup>H data with the averaged values of τ<sub>c,eff</sub> = (2D<sub>||</sub> + 4D<sub>⊥</sub>)<sup>−1</sup> = 4.05 ns; D<sub>||</sub>/D<sub>⊥</sub> = 1.20; θ = 7°; ϕ = −12°, and the D<sup>α</sup> QCC value of 171 kHz as obtained from MD simulations. The results of this analysis are presented in Figure S5 of the Supporting Information. The main conclusions obtained in the case when separate diffusion tensors have been used, remain in force. In particular, the average S<sup>2</sup> <sub>CαDα</sub>(S<sup>2</sup> <sub>NH</sub>) values of 0.87(0.84) are obtained for all residues of ubiquitin, while S<sup>2</sup> <sub>CαDα</sub>(S<sup>2</sup> <sub>NH</sub>) values of 0.89(0.86) are obtained when the flexible C-terminal and loop regions are excluded from analysis. However, when the same analysis (common diffusion tensor, QCC = 171 kHz) is performed for GB1, a number of residues give S<sup>2</sup> <sub>CαDα</sub> values higher than the theoretical limit of unity. When the D<sup>α</sup> QCC value is `reset' to 174 kHz, the relationship between S² _CαDα and S² _NH still holds in both proteins although the average S² _CαDα values become only insignificantly higher than S² _NH in ubiquitin.

Concluding remarks

In summary, we have shown that deuterium relaxation rates measured at deuterated carbon-α positions (D^α) serve as robust measures of backbone order in proteins. D^α relaxation rates are straightforward to interpret in terms of motional parameters (S² _CαDα; τ_f) provided that a uniform quadrupolar coupling constant (QCC) is assumed for all D^α sites in the protein molecule. To the best of our knowledge, this is the first attempt to use ²H relaxation as a probe of backbone dynamics in proteins. Clearly, the experiments developed for D^α relaxation rate measurements are not sufficiently sensitive for routine applications requiring the use of concentrated [U-²H,¹³C,¹⁵N]-labeled protein samples. Most of the D^α relaxation measurements described in this work have been performed on a 3.2 mM [U-²H,¹³C,¹⁵N]-ubiquitin using a room-temperature probe. Obviously, at such high protein concentrations, potential aggregation of protein molecules in NMR samples is of concern. The data on diffusion tensor characteristics summarized in Table 1 show that this is apparently not the case for both proteins studied in this work. With the increased sensitivity of NMR measurements due to the continuing development of cryogenically-cooled detection devices and the availability of higher magnetic fields, we anticipate that R^Q(D₊), R^Q(D_z) measurements would become feasible on protein samples with regular protein content (0.5–1.0 mM). Moreover, with the increasing molecular weight of a protein under study ²H spin-flipping rates would decrease (Figures 3a–c). Therefore, the methods described in this work may be applicable to well-behaved medium-sized proteins (up to ~200 residues), as the sensitivity of the experiment in Figure 1 is primarily determined by the rate of ²H spin-flips at the step when the magnetization is transferred from ¹³C^α spins to D^α and back.

For sensitivity reasons, because of the requirement for [U-²H,¹³C,¹⁵N] labeling, and because less data is available per nuclear probe in the case of D^α measurements at a single spectrometer field (R^Q(D₊), R^Q(D_z) rates versus ¹⁵N R₁, R₂ and ¹H-¹⁵N NOEs) the developed methodology is not meant to substitute for the commonly used ¹⁵N amide nuclei as NMR spin probes of backbone dynamics. Rather, it can be envisaged to serve as a useful complement to existing more sensitive techniques. Indeed, it should be kept in mind that the D^α relaxation rates measured in this work sample motions occurring in the protein backbone at positions that are distinct - chemically, structurally and motionally - from those normally sampled by conventional ¹⁵N-based techniques. This work represents an attempt to get an alternative view of dynamic processes in protein molecules and to establish the range of applicability and utility of the described NMR methodology. In this context, it is noteworthy that, in principle, the measurements of ¹³C^α relaxation in proteins^93,94 would provide the same information about backbone dynamics in a protein molecule as D^α methodology described here. The use of (protonated) carbon-α probes would, however, suffer from the same set of shortcomings and uncertainties as ¹⁵N-based methods (the uncertainty in ¹³C^α-H^α distances; site-specific ¹³C CSA variation; contributions to ¹³C relaxation from dipolar interactions with ¹³C^β and ¹³CO spins etc.). We have chosen to compare the D^α-derived motional parameters with more commonly used ¹⁵N spin probes. An NMR study that quantifies ¹³C^α relaxation rates in selectively ¹³C^α-enriched protein samples⁹⁵ and compares the measures of backbone order thus obtained with the D^α-derived data reported here, is in progress.