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J Am Chem Soc. Author manuscript; available in PMC 2010 November 4.

Published in final edited form as:

PMCID: PMC2770885

NIHMSID: NIHMS152242

Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, and Chemical Sciences Laboratory, Department of Chemistry and Biochemistry and the National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32306

The publisher's final edited version of this article is available at J Am Chem Soc

See other articles in PMC that cite the published article.

^{2}H spin relaxation NMR experiments to study the dynamics of deuterated backbone α-positions, D^{α}, are developed. To date, solution-state ^{2}H relaxation measurements in proteins have been confined to side-chain deuterons - primarily ^{13}CH_{2}D or ^{13}CHD_{2} methyl groups. It is shown that quantification of ^{2}H 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-^{15}N,^{13}C,^{2}H]-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 ^{15}N 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 ^{2}H-derived squared order parameters of C^{α}-D^{α} bond vector motions, *S*^{2 }_{CαDα}, on average slightly higher than their N-H amides counterparts, *S*^{2 }_{NH}. For ubiquitin, the ^{2}H-derived backbone mobility compares well with that found in a 1-μs molecular dynamics simulation.

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 ^{15}N nuclei are the most commonly used spin probes of backbone motions in proteins, and ^{15}N-based NMR relaxation studies of fast dynamics at backbone ^{15}N-^{1}H amide positions of small- to medium-sized proteins are now largely routine.^{5}^{,}^{13}

The popularity of ^{15}N as a nuclear spin probe of motional processes in backbones of proteins stems from the ease and affordability of selective incorporation of ^{15}N into backbone amide positions (without concomitant ^{13}C-labeling of neighboring nuclear sites) as well as high sensitivity of ^{15}N relaxation measurements.^{5}^{,}^{13} The rates of decay of ^{15}N magnetization in amide moieties is expressed as the sum of dipolar (^{15}N-^{1}H) and ^{15}N chemical shielding anisotropy (CSA) contributions.^{5}^{,}^{13}^{,}^{14} Quantitative interpretation of conventional ^{15}N 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 ^{15}N-^{1}H bond lengths, (ii) amide ^{15}N CSA values, and (iii) contributions to the relaxation rates due to chemical exchange, *R _{ex}*, that, in principle, should be quantified independently. Although

In search of a `cleaner' spin probe of backbone order in protein molecules, we designed ^{2}H-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 ^{2}H 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 ^{13}CH_{2}D methyl groups of a 6.5-kDa protein L. The motional properties of ^{13}CHD methylene positions in N-terminal drk SH3 domain have been studied by ^{2}H relaxation.^{23} Comparisons of ^{2}H-derived and ^{13}C-derived methyl three-fold axis order parameters (*S*^{2 }_{axis}) in proteins have been provided.^{24}^{,}^{25} To date, however, ^{2}H relaxation measurements in proteins have been confined to side-chain deuterons, primarily methyl groups of the ^{13}CH_{2}D^{20}^{,}^{21}^{,}^{26}^{,}^{27} or ^{13}CHD_{2}^{27}^{,}^{28} variety. We show that the availability of increasingly sensitive NMR instrumentation allows the quantification of ^{2}H 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-^{15}N,^{13}C,^{2}H]-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 *R*_{2}/*R*_{1} ratios, with the extracted diffusion tensors in good agreement with those derived from ^{15}N 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, ^{2}H-derived *S*^{2}_{CαDα} values are similar to, but are on average slightly higher than their ^{15}N-derived *S*^{2}_{NH} counterparts. Importantly, D^{α} rates can sample protein backbone motions that are inaccessible through ^{15}N relaxation measurements. Although for sensitivity reasons the developed methodology is expected to be limited to small protein molecules, a number of advantages of using ^{2}H 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.

The following isotopically labeled samples of wild-type human ubiquitin and a variant of GB1 protein have been used in this work: (i) [U-^{15}N]-labeled (both proteins), (ii) [U-^{15}N,^{13}C,^{2}H]-labeled (both proteins), and (iii) a mixture of [U-^{15}N,^{13}C,^{2}H]-labeled and [U-^{15}N,^{13}C]-labeled GB1. The deuterated samples of both proteins have been obtained using [U-^{15}N,^{13}C]-glucose as the main carbon source in the 99.9% D_{2}O-based *E.coli* media. Since carbon α positions are completely deuterated in proteins obtained using D_{2}O 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-^{15}N,^{13}C,^{2}H]- and [U-^{15}N]-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% H_{2}O/10% D_{2}O sodium phosphate buffer (pH 6.8) containing 0.03% NaN_{3} and a cocktail of protease inhibitors. The [U-^{15}N,^{13}C,^{2}H]- and [U-^{15}N]-labeled samples of GB1 were 5.8 mM and 1.2 mM in protein concentration, respectively, and were dissolved in a 25 mM 90% H_{2}O/10% D_{2}O sodium phosphate buffer (pH 6.5) containing 50 mM NaCl, 0.03% NaN_{3} and a cocktail of protease inhibitors. A third sample of GB1 contained a mixture of the [U-^{15}N,^{13}C,^{2}H]- and [U-^{15}N,^{13}C]-labeled protein in the approximate ratio of 4.5:1 (final concentrations of [U-^{15}N,^{13}C,^{2}H]- and [U-^{15}N,^{13}C]-GB1 of 4.5 and 1 mM, respectively), and was dissolved in a 25 mM 90% H_{2}O/10% D_{2}O sodium phosphate buffer (pH 6.5) as above to enable the measurements of D^{α} quadrupolar splittings and ^{1}*D*_{Cα-Hα} residual dipolar couplings (RDCs) in the same protein solution (see below).

Figure 1 shows the pulse-schemes that have been designed for the measurements of *R*^{Q}(*D*_{+}), *R*^{Q}(*D _{z}*),

All ^{2}H and ^{15}N 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-^{15}N,^{13}C,^{2}H]-labeled samples) comprised [512, 40] complex points in the [^{1}HN,^{15}N] 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*_{z}*D*_{+}), *R*^{Q}(3*D*_{z}^{2}−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 programs^{43} and associated software. Rates were obtained by fitting peak intensities to a single exponential function of the form *I* = *I*_{0 }*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.

^{15}N *R*_{1ρ}, *R* and ^{1}H-^{15}N NOE measurements on [U-^{15}N]-labeled samples of both proteins have been performed using standard procedures.^{45}^{,}^{46} Typically, NMR data sets comprised [512, 64] complex points in the [^{1}HN,^{15}N] dimensions with corresponding acquisition times of [64 ms, 38 ms]. Recovery delays of 1.0s and 4.3s (including a 2s presaturation period) for ^{15}N *R*_{1ρ},*R* and ^{1}H-^{15}N 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 ^{15}N *R*_{1ρ} measurements. *R*_{1ρ} data have been subsequently corrected for resonance offset to obtain ^{15}N *R*_{2} rates.^{5} Error analysis of peak intensities and the extracted relaxation rates closely followed the procedure used for ^{2}H relaxation measurements at D^{α} positions.

The relaxation rates of N_{z}C'_{z}C^{α}_{z} 3-spin order, *R*(N_{z}C'_{z}C^{α}_{z}), have been measured using a pulse-scheme derived from the gradient sensitivity enhanced HN(COCA) experiment^{31} using the same acquisition parameters as for ^{2}H 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_{z}C'_{z}C^{α}_{z}) rates have been subsequently subtracted from the obtained D^{α }*R*^{Q}[D] rates before analysis (see text).

The relaxation rates of ^{2}H transverse and longitudinal magnetization are given by^{19}

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

(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 (*e*^{2}*qQ*/*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 ^{2}H 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, (*e*^{2}*qQ*/*h*) = *QCC*, enters into eq 1–2. Indeed, the asymmetry values of the ^{2}H 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 ^{2}H 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, *A*_{1}=(3/4)sin^{4}(α), *A*_{2}=3sin^{2}(α)cos^{2}(α), *A*_{3}=[(3/2)cos^{2}(α)−0.5]^{2}, τ_{1}=(4*D*_{||}+2*D*_{})^{−1}, τ_{2}=(*D*_{||}+5*D*_{})^{−1}, τ_{3}=(6*D*_{})^{−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} = (2*D*_{||} + 4*D*_{})^{−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 1ubq^{50} and 2qmt^{51}.

Diffusion tensors have been estimated by minimization of the error function χ^{2} expressed as,

$${\chi}^{2}=\sum _{i=1}^{N}{\left[\frac{{\left({R}_{2}^{expt}\u2215{R}_{1}^{expt}\right)}_{i}-{\left({R}_{2}^{calc}\u2215{R}_{1}^{calc}\right)}_{i}}{{\left({\sigma}_{{R}_{2}\u2215{R}_{1}}\right)}_{i}}\right]}^{2},$$

(4)

where the summation extends over all sites included in analysis, ${R}_{2}^{\mathit{expt}}$ and ${R}_{1}^{\mathit{expt}}$ are the experimentally measured ^{2}H/^{15}N rates, ${R}_{2}^{\mathit{calc}}$ and ${R}_{1}^{\mathit{calc}}$ are the rates calculated using diffusion tensor parameters (eq 3) and the expressions for ${R}_{2}^{Q}$, ${R}_{1}^{Q}(\mathrm{eq}\phantom{\rule{thickmathspace}{0ex}}1-2)\u2215{}^{15}\mathrm{N}{R}_{2}$, *R*_{1} rates, and σ_{R2 / R1} is the uncertainty in the experimental *R*_{2}/*R*_{1} ratios. A fit to a fully anisotropic diffusion tensor^{52} 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 χ^{2} (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), ^{1}H-^{15}N NOE<0.6 and the residues undergoing chemical exchange (^{15}N data only) have been excluded from analysis. Errors in the fitted diffusion parameters (polar angles θ, 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 simulations^{44} 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}(^{15}N) relaxation rates have been interpreted in terms of motional parameters using their corresponding ^{2}H-(^{15}N)-derived diffusion tensor characteristics. Motional parameters of D^{α} sites, *S*^{2}_{CαDα} and the corresponding τ_{f} values, were obtained by fitting the ^{2}H 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, *S*^{2 }_{NH} and τ_{f}, were obtained using the program Dynamics^{53}^{,}^{54} that models ^{15}N relaxation data selecting for the appropriate motional model (that can be different from the simplest form of eq 3) based on statistical criteria. ^{15}N relaxation data have been analyzed with standard expressions for ^{15}N relaxation in ^{15}N-^{1}H spin pairs. ^{15}N *R*_{2},*R*_{1} and ^{1}H-^{15}N 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, *S*^{2 }_{NH}, was used instead of *S*^{2 }_{CαDα} together with the corresponding N-H direction cosines. The N-H bond distance of 1.02Å and a uniform ^{15}N CSA of −170 ppm were used in all calculations.

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 ^{13}C^{methyl}-^{13}C RDCs measured in an oriented protein.^{55} The same approach can be used for α deuterons provided that ^{1}*D*_{Cα-Hα} RDCs are measured in the same sample. To enable the measurements of D^{α} splittings and ^{1}*D*_{Cα-Hα} RDCs in the same protein sample, a mixture of [U-^{15}N,^{13}C,^{2}H]-labeled and [U-^{15}N,^{13}C]-labeled GB1 was used (see `NMR samples' above). The use of the same sample with two different labeling schemes (one having ^{2}H nuclei and the other ^{1}H nuclei at α positions) ensures that the alignment characteristics and dynamical properties are exactly the same for the ν_{Q} and ^{1}*D*_{Cα-Hα} measurements. The `mixed' GB1 sample was aligned in 18 mg/ml pf1 bacteriophage^{56} (quadrupolar D_{2}O splitting of 24.7 Hz). ^{1}*D*_{Cα-Hα} RDCs have been obtained using the HNCO-type experiment of Yang *et al.*^{57} modified to eliminate the resonances of ^{13}C^{α} nuclei attached to deuterons arising from the (more concentrated) [U-^{15}N,^{13}C,^{2}H]-labeled protein. This experiment allows for convenient measurements of ^{1}*D*_{Cα-Hα} in H_{2}O protein solutions by recording the modulation of carbonyl chemical shifts by (^{1}*J*_{Cα-Hα} + ^{1}*D*_{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 ^{1}*D*_{Cα-Hα} and ν_{Q} measurements have been performed twice and the obtained ν_{Q}/^{1}*D*_{Cα-Hα} ratios have been averaged.

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 package^{59} with the AMBER99SB force field,^{60} which was shown previously to accurately reproduce the native state dynamics of ubiquitin.^{59}^{,}^{61}^{–}^{63} The SHAKE algorithm^{64} 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 method^{65} 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 *S*^{2 }_{CαHα} have been extracted using the iRED method^{66} averaged over time windows of 1 ns and 5 ns, *i.e.* on the order of the experimental global tumbling correlation time of ubiquitin.

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 experiment^{31} with additional delays at ^{13}C^{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 *t _{1},t_{2}* are acquisition times. A series of two-dimensional data sets is recorded as a function of

The *R*_{1} and *R*_{2} relaxation rates of D^{α} nuclei, *R ^{Q}*(

Figure 3 shows the profiles of experimental *R ^{Q}*(

Plots of D^{α} (shown with black rectangles and dashed lines) and ^{15}N (black circles and solid lines) relaxation rates in ubiquitin as a function of the protein sequence. *R*^{Q}(*D*) and ^{15}N *R*_{1} rates are shown at **a)** 10°C, **b)** 27°C, **c)** 40°C, **...**

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*_{+} and *D*_{z}, the relaxation rates of `rank-2' elements (*D*_{+}*D*_{z}+*D*_{z}*D*_{+}, 3*D*_{z}^{2} −2 and *D*_{+}^{2}) can be quantified in the same ^{2}H site. Indeed, one of the principal advantages of ^{2}H 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-workers^{69} 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 ^{2}H Larmor frequency, ω_{D}, (see `Materials and Methods') the following inequalities must hold: (5/3)*R*^{Q}(*D*_{+}*D*_{z}+*D*_{z}*D*_{+}) ≥ *R*^{Q}(*D*) ≥ (5/3)*R*^{Q}(3*D*_{z}^{2}−2) ≥ *R*^{Q}(*D*_{z}), where the relaxation rates of anti-phase ^{2}H magnetization, (*D*_{+}*D*_{z}+*D*_{z}*D*_{+}), and the quadrupolar order, (3*D*_{z}^{2}−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)

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

(7)

The pulse-scheme that can be used for *R*^{Q}(*D*_{+}*D _{z}*+

Consistency plots of D^{α} relaxation rates. **a)** (5/3)*R*^{Q}(3*D *^{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*_{z}*D*_{+}) (black rectangles; dashed lines) and *R*^{Q}(*D*_{+}) (black circles; solid **...**

As described above, fast ^{2}H spin-flips lead to on average 4-to-5-fold sensitivity losses in the *R*^{Q}(*D*_{+}*D*_{z}+*D*_{z}*D*_{+}) and *R*^{Q}(3*D*^{2}_{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 ^{2}H 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*_{z}*D*_{+}) and *R*^{Q}(3*D*^{2}_{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 ^{2}H coherence, *D*_{+}^{2}, at D^{α} sites.

Prior to obtaining the ^{2}H-derived measures of backbone order it is important to establish the diffusion parameters of the global molecular reorientation. In analogy to the case of ^{15}N relaxation in protein backbones, ^{2}H *R*_{2}/*R*_{1} 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}*(

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 sp^{3}-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 molecules^{72} - a situation that cannot be encountered in solution. In another low-temperature liquid crystal NMR study, the *QCC* value obtained for deuterons in a CD_{3} methyl group of toluene (165 kHz) has been compared to the *QCC* of deuterons in cyclohexane-d_{12} (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 ^{13}CH_{2}D methyl groups of proteins equal to 167 ± 1 kHz assuming θ = 109.5°.^{55} What is effectively determined in this study is the product *P*_{2}(cosθ)*QCC*, where *P*_{2}(*x*) = 0.5(3*x*^{2} − 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 √*S*^{2}*QCC*, 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 *S*^{2} is assumed to be equal to 0.95,^{75}^{,}^{76} then the measurements of Haeberlen and co-workers in α-glycine^{72} 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 ^{2}H magnetization evolves according to^{55}^{,}^{77}

$${D}_{y}\to {D}_{y}\mathrm{cos}\left(\pi {\nu}_{Q}T\right)-\{{D}_{x}{D}_{z}+{D}_{z}{D}_{x}\}\mathrm{sin}\left(\pi {\nu}_{Q}T\right),$$

(8)

, where the quadrupolar splitting ${\nu}_{Q}=\frac{3}{4}\mathit{QCC}\langle 3{\mathrm{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 (

$${D}_{y}\left(T\right)=\frac{A}{2}\mathrm{exp}\left\{-\frac{({R}_{1}+{R}_{A})}{2}T\right\}\left[(1-\Delta )\mathrm{exp}\left\{\frac{\Omega}{2}T\right\}+(1+\Delta )\mathrm{exp}\left\{-\frac{\Omega}{2}T\right\}\right],$$

(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

The value ^{1}*D*_{Cα-Hα} RDC measured as described in `Materials and Methods' is expressed as, ${}^{1}D_{C\alpha -H\alpha}=-({\mu}_{0}\u22154\pi )({\gamma}_{C}{\gamma}_{H}h\u22154{\pi}^{2}{r}_{C\alpha H\alpha}^{3})\langle 3{\mathrm{cos}}^{2}\theta -1\rangle $, where γ_{i} is the gyromagnetic ratio of nucleus *i*, μ_{0} is the vacuum permeability constant, and *r _{CH}* is the distance between C

$$QCC=\frac{1}{12}\frac{{\mu}_{0}{\gamma}_{C}{\gamma}_{H}h}{{\pi}^{3}{r}_{C\alpha H\alpha}^{3}}\left(\frac{{\nu}_{\mathrm{Q}}}{{}^{1}D_{C\alpha -H\alpha}}\right)$$

(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 ^{2}H quadrupolar splitting ν_{Q} with the ^{1}*D*_{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 ^{1}*D*_{Cα-Hα}. Using eq 10 and assuming a standard *r _{CH}* distance of 1.095 Å

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}/^{1}*D*_{Cα-Hα} ratios for 11 peaks in GB1 and from propagated errors in (fitted) ν_{Q} and ^{1}*D*_{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}/^{1}*D*_{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 sp^{3}-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).

Since, commonly, only two rates, *R*^{Q}(*D*_{+}) and *R*^{Q}(*D _{z}*), are available for the derivation of motional parameters of C

D^{α}-derived *S*^{2}_{CαDα} (blue rectangles and lines) and ^{15}N-derived *S*^{2}_{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 **...**

Ribbon diagrams of ubiquitin crystal structures with **a)** D^{α} and **b)** HN atoms represented as balls color-coded according to the values of *S*^{2}_{CαDα} and *S*^{2}_{NH} (27°C), respectively. The elements of the secondary structure are shown **...**

C^{α}-D^{α} bond vectors are motionally distinct from the N-H bond vectors, with ^{2}H-derived *S*^{2 }_{CαDα} values on average slightly higher than their *S*^{2 }_{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 *S*^{2 }_{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 *S*^{2 }_{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 *S*^{2 }_{CαDα} and *S*^{2 }_{NH} could be quantified, *S*^{2 }_{CαDα} values are higher than *S*^{2 }_{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 *S*^{2 }_{CαDα} and *S*^{2 }_{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 _{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 Leu^{71}, average *S*^{2 }_{CαDα}(*S*^{2 }_{NH}) of 0.61(0.63) have been obtained at 27°C, whereas in GB1 the average *S*^{2 }_{CαDα}(*S*^{2 }_{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 (*S*^{2 }_{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 *S*^{2 }_{CαDα} and *S*^{2 }_{NH} on a per-residue basis can be ambiguous since higher *S*^{2 }_{NH} values may result from the use of different motional models for the derivation of *S*^{2 }_{CαDα} and *S*^{2 }_{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 *S*^{2 }_{CαDα} and *S*^{2 }* _{NH}*, any small differences in these parameters (Table 1) can skew the differences between

Since different motional processes are sampled by D^{α} and ^{15}N 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, ^{15}N 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 Ile^{23}-Glu^{34}), *S*^{2 }_{CαDα} are noticeably higher for the residues whose C^{α}-H^{α}(D^{α}) bond vectors are directed towards a short 3_{10}-helical stretch the protein structure (Val^{26}, Ile^{30} or oriented towards the interior of the protein at the other face of the α-helix (Glu^{24}, Ala^{28}, Gln^{31}). 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 *S*^{2}_{CαDα} (27°C) shown for each D^{α} site. In GB1, the residues of the α-helix (Ala^{23}-Asp^{36}) facing the hydrophobic interior of the protein (Ala^{26}, Phe^{30}, Tyr^{33} and Ala^{34}) also tend to have elevated *S*^{2}_{CαDα}. The resulting alternating patterns of *R ^{Q}*(

To gain more confidence in the ^{2}H-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*^{2}_{CαHα} and experimental *S*^{2}_{CαDα} order parameters is achieved when the D^{α }*QCC* value is (slightly) lowered to 171 kHz. A comparison between experimental *S*^{2}_{CαDα} (*QCC* = 171 kHz) and MD-derived *S*^{2}_{CαHα} 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^{44}, Ala^{46}, Lys^{48} and Glu^{49}, whose side-chains point towards the solvent, is well reproduced by the MD simulation. Furthermore, the `zigzag' pattern displayed by the experimental *S*^{2}_{CαDα} values in the Tyr^{59}-Lys^{63} 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 *S*^{2} for inward oriented side-chains and higher *S*^{2} for more solvent exposed ones. Lys^{63} is a notable exception with a relatively high *S*^{2}_{CαHα} despite its high solvent accessibility. The close relationship between *S*^{2}_{CαDα} and the associated side chain properties is corroborated by the very close agreement between *S*^{2}_{CαDα} and *S*^{2}_{CαCβ} values found in the MD simulation of ubiquitin (see Supporting Information, Figure S6).

Experimental *S*^{2 }_{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 *S*^{2 }_{CαHα} values obtained from a 1 μs **...**

The comparisons of ^{15}N- and ^{2}H-derived measures of backbone order described here have been performed using their respective (^{15}N-derived or ^{2}H-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 *S*^{2}_{CαDα} and *S*^{2}*NH* 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 ^{2}H- and ^{15}N-derived backbone order' section above for ubiquitin at 27°C using common diffusion tensor parameters for ^{15}N and ^{2}H data with the averaged values of τ_{c,eff} = (2*D*_{||} + 4*D*_{})^{−1} = 4.05 ns; *D*_{||}/*D*_{} = 1.20; θ = 7°; ϕ = −12°, and the D^{α }*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*^{2 }_{CαDα}(*S*^{2 }_{NH}) values of 0.87(0.84) are obtained for all residues of ubiquitin, while *S*^{2 }_{CαDα}(*S*^{2 }_{NH}) 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*^{2 }_{CαDα} values higher than the theoretical limit of unity. When the D^{α }*QCC* value is `reset' to 174 kHz, the relationship between *S*^{2 }_{CαDα} and *S*^{2 }_{NH} still holds in both proteins although the average *S*^{2 }_{CαDα} values become only insignificantly higher than *S*^{2 }_{NH} in ubiquitin.

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 (*S*^{2 }_{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 ^{2}H 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-^{2}H,^{13}C,^{15}N]-labeled protein samples. Most of the D^{α} relaxation measurements described in this work have been performed on a 3.2 mM [U-^{2}H,^{13}C,^{15}N]-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 ^{2}H 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 ^{2}H spin-flips at the step when the magnetization is transferred from ^{13}C^{α} spins to D^{α} and back.

For sensitivity reasons, because of the requirement for [U-^{2}H,^{13}C,^{15}N] 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 ^{15}N *R*_{1}, *R*_{2} and ^{1}H-^{15}N NOEs) the developed methodology is not meant to substitute for the commonly used ^{15}N 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 ^{15}N-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 ^{13}C^{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 ^{15}N-based methods (the uncertainty in ^{13}C^{α}-H^{α} distances; site-specific ^{13}C CSA variation; contributions to ^{13}C relaxation from dipolar interactions with ^{13}C^{β} and ^{13}CO spins *etc*.). We have chosen to compare the D^{α}-derived motional parameters with more commonly used ^{15}N spin probes. An NMR study that quantifies ^{13}C^{α} relaxation rates in selectively ^{13}C^{α}-enriched protein samples^{95} and compares the measures of backbone order thus obtained with the D^{α}-derived data reported here, is in progress.

This work has been supported in part by the General Research Board (GRB) Award to V.T. from the University of Maryland. The authors are grateful to Dr. Pramodh Vallurupalli and Prof. Lewis Kay (University of Toronto, Canada) for useful discussions, to Dr. Andy Byrd (NCI, Federick, Maryland) for the generous gift of [U-^{15}N,^{13}C,^{2}H]-ubiquitin used in this work, Dr. Chenyun Guo (University of Maryland) for preparation of [U-^{15}N,^{13}C,^{2}H]-GB1 and [U-^{15}N]-GB1 samples, Prof. David Fushman (University of Maryland) for providing the sample of [U-^{15}N]-ubiquitin and the Matlab-based software for ^{15}N relaxation data analysis, and Prof. Nikolai Skrynnikov (Purdue University, West Lafayette, Indiana) for sharing with us some unpublished results of DFT calculations of quadrupolar coupling constants.

Supporting Information Available: One figure showing D^{α }*R*^{Q}(*D*_{+}), *R*^{Q}(*D*_{z}) relaxation rate profiles along with ^{15}N *R*_{1}, *R*_{2} profiles in GB1 at 22°C as a function of the protein sequence (Figure S1). One figure showing the dependence of *R*^{Q}(*D*_{+})/*R*^{Q}(*D*_{z}) on the angle α formed by C^{α}-D^{α} bonds and the principal axis of the diffusion tensor in GB1 at 22°C and ubiquitin at 27°C (Figure S2). One figure showing the correlation plot of the D^{α} quadrupolar splittings, ν_{Q}, and ^{1}D_{Cα-Hα} residual dipolar couplings measured for a subset of 11 peaks in the oriented sample of GB1 (Figure S3). One figure showing *S*^{2}_{CαDα} and *S*^{2}_{NH} as a function of sequence for GB1 at 22°C (Figure S4). One figure showing *S*^{2}_{CαDα} and *S*^{2}_{NH} for Ubiquitin at 27°C obtained using a common diffusion tensor and the *QCC* value of 171 kHz (Figure S5). One figure showing the agreement between *S*^{2}_{CαHα} and *S*^{2}_{CαCβ} values found in the 1-μs MD simulation of ubiquitin at 27°C (Figure S6). One Table listing *S*^{2}_{CαDα} and τ_{f} values obtained in ubiquitin at 10°C, 27°C and 40°C. This material is available free of charge via the Internet at http://pubs.acs.org.

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