Conformational dynamics of an intact virus: Order parameters for the coat protein of Pf1 bacteriophage

Abstract

This study has examined the atomic-level dynamics of the protein in the capsid of filamentous phage Pf1. This capsid consists of ≈7,300 small subunits of only 46 aa in a helical array around a highly extended, circular single-stranded DNA molecule of 7,349 nt. Measurements were made of site-specific, solid-state NMR order parameters, 〈S〉, the values which are dimensionless quantities between 0 (mobile) and 1 (static) that characterize the amplitudes of molecular bond angular motions that are faster than microseconds. It was found that the protein subunit backbone is very static, and of particular interest, it appears to be static at residues glycine 15 and glutamine 16 where it had been previously thought to be mobile. In contrast to the backbone, several side chains display large-amplitude angular motions. Side chains on the virion exterior that interact with solvent are highly mobile, but surprisingly, the side chains of residues arginine 44 and lysine 45 near the DNA deep in the interior of the virion are also highly mobile. The large-amplitude dynamic motion of these positively charged side chains in their interactions with the DNA were not previously expected. The results reveal a highly dynamic aspect of a DNA–protein interface within a virus.

The Pf1 bacteriophage is a 2-μm-long filamentous virus that infects Pseudomonas aeruginosa strain K (1, 2). The virion consists of a circular single-stranded DNA genome of 7,349 nt (3) within a cylindrical capsid of ≈7,300 major coat protein subunits that have 1:1 stoichiometric interactions (4, 5) with nucleotides along the filament, as well as a small number of other proteins interacting with reverse turns of DNA at the ends. A variety of spectroscopic and diffraction studies of Pf1 have been carried out (5–19), including studies by solid-state NMR of the protein in the intact virion (16–19), as in the present study, and by solution NMR of the isolated protein in detergent micelles (8, 14) as a model of its structure in the membrane before virion assembly. Virion assembly occurs at the membrane in such a way that major coat protein subunits are packed in the filament as α-helices with their N-terminal regions on the outside and their C-terminal regions buried in the interior to interact with the DNA.

One of the studies of the Pf1 virion by solid-state NMR was on magnetically aligned hydrated virions, and it characterized the path and orientation of the backbone of the α-helical major capsid protein subunit by means of ¹H–¹⁵N polarization inversion spin exchange at the magic angle (PISEMA) (16, 17). It was proposed that the subunit consists of an N terminus that forms a double hook, a C terminus with an unraveled α-helix, and a central portion of three α-helices with two bends near the center. An assumed capsid helical symmetry for the high-temperature form of the virion (6, 20) was used to generate the intersubunit contacts for a model of the capsid (16, 17). In a more recent solid-state NMR study from our group (18, 19), magic angle spinning solid-state NMR (MAS SSNMR) was applied to nonaligned hydrated virions in polyethylene glycol precipitates. The assignment and analysis of the ¹³C and ¹⁵N isotropic chemical shifts for 92% of the carbon and nitrogen atoms demonstrated that the ≈7,300 major coat protein subunits are present in the virion as a single conformer, yet, despite this, the side chains of a few residues (e.g., T5 and M42) adopt more than one configuration. The single conformer must allow variable nucleotide contacts to accommodate the four nucleotide types in each of the two strand directions.

In addition to the high-resolution structural work, SSNMR can be used to obtain detailed site-specific information on dynamics. Multidimensional methods for characterizing the amplitude of bond vector dynamics on a submicrosecond time scale have been developed for SSNMR (21–23). These experiments measure a time-averaged dipolar-order parameter, which is expressed in Eq. 1.

The solid-state NMR order parameter tracks the amplitude of submicrosecond rotational motion for a bond vector such that an order parameter of unity indicates a static site and an order parameter of zero represents isotropic motion. The dynamic measurement is local to the bond being probed. By contrast, a distribution of static bond orientations in a crystal (static heterogeneity) produces order parameters of unity. Reduction of the order parameter from unity is the direct consequence of the motion of a bond.

This study addresses the dynamics of the backbone and side chains of the Pf1 major coat protein in the intact, infectious virion. There are contradictory data and unresolved questions in both aspects of the protein structure. For example, it has been recently proposed that there is a minor “outward-bulge” conformer in the backbone of residues 15–17 that is highly dynamic (16), but such a minor conformer was not observed in the¹³C and ¹⁵N chemical shift assignments (18). Is the backbone indeed dynamic in this region?

The DNA in Pf1 is known to be highly extended (4, 9), and it has been proposed to be highly twisted to follow the helical symmetry of the capsid (11) but the manner of the match between DNA and capsid helical symmetries remains a matter of debate (11, 15, 24–26). There is evidence supporting a P form DNA with exposed bases on the outside and ordered phosphates at the center (11, 15, 26, 27). How might such an unusual DNA conformation affect virion dynamics?

X-ray structure determinations of other viruses that provide information on dynamics, through temperature factors, and on nucleic acid structure are available for systems such as tobacco mosaic virus (TMV) (28), flock house virus (29), and satellite tobacco mosaic virus (30). Also, a few examples in the recent literature have elucidated localized dynamics in DNA interaction enzymes (31–33), including cases of rigidification (33) and flexibility (34) of the nucleic acid on binding. High-temperature factors, or the absence of interpretable data, are often diagnosed as disorder. Does such apparent disorder result from a static distribution of an ensemble of states or from dynamic disorder?

In this study we have the opportunity of studying an infectious virus at native conditions and addressing these questions. To this end, we have measured the backbone and side-chain dynamics of ¹³C¹H and ¹³C¹H₂ groups in the coat protein within the intact Pf1 bacteriophage. The protein backbone is highly static, including residues 15–17, and the side chains are highly mobile. The C terminus shows highly elevated side-chain dynamics, which presumably reflect interesting binding interactions with the DNA.

Results and Discussion

Eighty-three cross-peaks were resolved in the dipolar spectra, including redundant cross-peaks that report on the same site (see supporting information (SI) Table S1). Dipolar order parameters were determined for 25 Cα, 22 Cβ, 10 Cγ, and 1 Cδ unique sites. Dispersion between sites is not large for residues that are all α-helical, and therefore, many sites are missing in this dataset because of spectral congestion. The criterion for a peak to be isolated is more stringent for dynamic assignments than for chemical assignments because spectral congestion in the dipolar dimension can easily pollute the accuracy of the dipolar fit. In this study nonoverlapping cross-peaks within a window of ±0.25 ppm in both ¹³C dimensions were accepted. For reference, a 2D ¹³C–¹³C spectrum from the Lee–Goldburg cross-polarization with dipolar assisted rotational resonance (LGCP-DARR) experiment is provided in Figs. S1 and S2. Based on this criterion, conformers with different chemical shifts or dipolar splittings were not observed, and the major coat protein is therefore structurally homogeneous.

The data include dynamics results for the ¹³C¹H and the ¹³C¹H₂ types of spin systems, both of which have different spin physics and the modes of motion (22, 35). The dipolar order parameters of ¹³C–¹H systems track motions of their one bond, whereas the dipolar order parameters assigned to ¹³C¹H₂ systems track the combined motions of the two bonds, which are assumed to be the same in this analysis.

Backbone Dynamics.

Order parameters have been measured for 25 Cα backbone sites where well resolved peaks on the homonuclear spectra were observed. Fig. 1 shows the (¹³C¹H_x)α order parameters and Table 1 lists the order parameter averages. Most order parameters are between 0.95 and 1.0, which corresponds to diffusion cone angles of 0–10° (36). Compared with the backbone of microcrystalline ubiquitin (23), the Pf1 backbone is static, the average order parameter for the (¹³C¹H)α sites being 0.99 ± 0.04, whereas the corresponding value for microcrystalline ubiquitin is 0.80 ± 0.06 (23).

Fig. 1.

Solid-state NMR dipolar order parameters for the (¹³C¹H)α (black; filled circles) and (¹³C¹H₂)α (red; open circles) spin systems in uniformly labeled Pf1 coat protein. The primary sequence (3) is shown for convenience. Order parameters are calculated from the motionally narrowed dipolar coupling by using Eq. 1. Black lines connect order parameters for contiguous residues in primary sequence. The dotted reference line delineates the static limit (order parameter of 1.0). Order parameters of 1.0 represent sites that are completely static and order parameters of 0.0 represent sites with isotropic motion on a submicrosecond time scale. The Cα sites are mostly static, and Gly-1 is the most dynamic site with an order parameter of 0.38 ± 0.03, which corresponds to a diffusion in a cone angle of 59.3° (36).

Table 1.

Average solid-state NMR order parameters by side-chain position for the Pf1 virus

Spin system	Average	Minimum/maximum
(13C1H)α	0.99 ± 0.04	0.91/1.02
(13C1H)β	0.88 ± 0.10	0.72/1.00
(13C1H2)β	0.78 ± 0.17	0.60/1.00
(13C1H2)γ	0.52 ± 0.17	0.28/0.81

The (¹³C¹H₂)α positions of glycine are of particular interest, and three of the total of seven in Pf1 could be characterized. The (¹³C¹H₂)α of N-terminal Gly-1 is the most dynamic with a (¹³C¹H₂)α order parameter of 0.38 ± 0.03, which is understandable because of its unique end position. However, both of the two glycine residues within the chain are essentially static: Gly-15 has a static order parameter near 1.0, to be discussed below, and Gly-23 has an order parameter of 0.94 ± 0.03. By contrast, the two backbone glycine sites of microcrystalline ubiquitin that could be measured gave values of 0.50 and 0.45 (23). Even in crystalline glycine itself, temperatures lower than −45°C are required to produce an order parameter of 1 in the Cα methylene position (22). Therefore, based on these limited comparisons, these two immobile glycine residues in Pf1 are potentially unusual and interesting, and provide a useful case-in-point for the overall rigidity of the coat protein backbone.

The solid-state NMR PISEMA study (16, 17) reported qualitative dynamic observations for some of the sites in Pf1, but their overall conclusions on the path of the α-helical backbone are in implicit agreement with the present results. Had there been significant time-averaged dynamics present in the Pf1 coat protein backbone, the ¹H–¹⁵N couplings in the PISEMA data would have required scaling by nonunity order parameters, and a PISEMA structure would have been complicated by this fact. Therefore, that the PISEMA study produced an apparently self-consistent structure is in implicit agreement with our observation that the backbone is essentially static except for the N and C termini. Also, our data are in agreement with the claims that residues 2–6 are immobile; that residues Ile-3 and Asp-4 are completely immobile, and that Ser-6 has some motion (16).

However, Thiriot et al. (16) report that Gly-15, Gln-16, and Gly-17 are dynamic, whereas the present study found an essentially static backbone at Gly-15 and Gln-16. Our assignments here are linked to the chemical shift assignments for high-resolution MAS data for Pf1 (18), which have been confirmed in a number of ways (19). The dipolar splitting for Gly-15 shown in Fig. 2 corresponds to an order parameter near 1.0, even though the dipolar spectrum could not be fit because of attenuated intensity at lower frequencies. Gln-16 appears to be completely static in our dataset (Fig. 2). For comparison, Fig. 2 also shows the experimental and best-fit dipolar splittings for Gly-1. We point out that the comparison of our results with those of Thiriot et al. (16) is not direct because they used ¹⁵N¹H measurements and we used (¹³C¹H_x)α systems, which may have different motional modes. The details of the sample preparations were also not identical, although both samples were fully hydrated virus in the high-temperature form. These issues, therefore, remain to be resolved in future work.

Fig. 2.

Backbone (¹³C¹H_x)α dipolar spectra for Gly-1, Gly-15, and Gln-16 (Top, Middle, and Bottom). The simulated spectra (Right) were fit against the experimental spectra (Left) in the 2.3- to 10.8-kHz frequency range, and the zero-frequency region was not plotted. The Gly-1 (¹³C¹H₂)α dipolar spectrum order parameter is 0.38 ± 0.03, that for the Gly-15 (¹³C¹H₂)α appears to be ≈ 1.0 but was not successfully simulated, and that for the Gln-16 (¹³C¹H)α dipolar spectrum was 1.01 ± 0.03. Residue Gly-1 is the most dynamic backbone site in our dataset.

Side-Chain Dynamics.

The Cβ side-chain order parameters are plotted as a function of residue number in Fig. 3. The Cβ measurements include ¹³C¹H and ¹³C¹H₂ spin systems. The Cβ order parameters show many static sites (order parameters near 1) and many dynamic sites (order parameters of ≈0.5).

Fig. 3.

Solid-state NMR dipolar order parameters for the (¹³C¹H)β (black; filled circles) and (¹³C¹H₂)β (red; open circles) spin systems in uniformly labeled Pf1 coat protein, presented as described in Fig. 1 for Cα values. The Cβ sites have a large dynamic range, and many sites are static, including a few ¹³C¹H₂ sites.

Similar to the case for microcrystalline ubiquitin (23), the (¹³C¹H₂)β groups in Pf1 (0.78 ± 0.17 average 〈S〉) tend to be more mobile than (¹³C¹H)β groups (0.88 ± 0.10 average 〈S〉). However, there is considerable overlap in data points among all of the spin systems types, including many static (¹³C¹H)β and (¹³C¹H₂)β groups. The Ile-22 and Ile-32 (¹³C¹H)β sites have order parameters of 1, and the Asp-14, Leu-38, and Leu-43 (¹³C¹H₂)β sites all have order parameters >0.95. Among these residues with static side chains, there is no obvious pattern with respect to whether the side chains are neutral or acidic. By contrast, there are many dynamic (¹³C¹H)β and (¹³C¹H₂)β groups. The most dynamic (¹³C¹H)β sites are Val-2, Val-8, Ile-12, and Val-31, which have an order parameter of ≈0.75. The most dynamic (¹³C¹H₂)β sites are Glu-9, Asp-18, Lys-20, Arg-44, and Lys-45 with order parameters ≈0.60. An analysis of Cβ dynamics grouped by residue polarity yielded no clear correlation. From the Cβ side-chain dynamics alone, it is clear that the Pf1 coat protein assembly has a very large dynamic range, which is consistent with the elevated dynamics observed in other solid-state protein systems (23, 37).

Other side-chain sites show increased dynamics as well. Fig. 4 shows the backbone and side-chain order parameters for isoleucine and lysine residues. It has been shown that the mobility increases down the side chain for many different amino acid types in ubiquitin (23)—an analogous result to phospholipid studies (38).

Fig. 4.

Solid-state NMR (¹³C¹H_x) order parameters grouped by residue type for isoleucine (a) and lysine (b). The lines show average order parameter progressions for regions with order parameter values at adjacent sites. Similarities in dynamic patterns exist for residues of the same amino acid type.

Most of the isoleucine residues are similar in their side-chain dynamic behavior. However, residue Ile-26 shows an interesting deviation in the Cγ1 dynamics in that it has the most static methylene group at this position. This residue is located at the top interior of the coat protein assembly, which will be discussed in the next section.

Finally, the two lysine residues have very dynamic side chains. The Lys-45 residue has a more static backbone than that of Lys-20, and yet, its Cβ and Cγ positions are more dynamic. The elevated dynamics of the Cβ sites are a consequence of additional motion about the Cα–Cβ bond that is not tracked by the Cα–Hα bond, that is, rotomer changes. As will be discussed further, the elevated dynamics of the Lys-45 side chain compared with the Lys-20 side chain is of special interest with respect to structure and function.

Structural Relationships with the Side-Chain Dynamics.

The side-chain dynamics data must be viewed in the context of the Pf1 virion structure. Fig. 5 shows two models of Pf1 capsid structures that are colored by Cβ side-chain dynamics (11, 16). There is debate in the literature on the Pf1 capsid structure, and there are several atomic models in the databases. We have chosen two of them to show that the locations of dynamic and static regions in the models are not very different.

Fig. 5.

Views of Pf1 bacteriophage capsid structure models colored by Cβ side-chain order parameters. The views are of only a small section of the entire Pf1 virion. In the exploded views, the N termini of the subunits appear to be loose but they overlap either other major coat subunits along the filament contour or the minor coat proteins that initiate assembly at the end that emerges first from the cell. The two alternate structure models are displayed because a consensus structure has not been produced in the literature. The 1PFI model (11) and the 1PJF model (16) are for the low- and high-temperature forms, respectively, and they are based on different types of data. 1PJF was chosen because it was based primarily on NMR results, whereas 1PFI was chosen as the only model that includes DNA. Although the 1PJF model does not include DNA, the data on which it was based were for intact virions with DNA (17). The amino acid dynamics obtained in this study are for high-temperature conditions. We show here that the dynamics map onto the same regions of the subunit regardless of which structure model is considered. Both models show a mixture of dynamic (green and yellow) and static (blue) sites mapping to the outer surface of the virion exposed to solvent. The exploded views show progressively more static sites from the outside of the virion into the buried protein–protein interface between overlapping subunits. Of particular importance, the cutaway view of the 1PFI image shows that side chains near the DNA are dynamic (yellow), despite the dense packing in this region. In both images the capsid has been pulled apart and tilted to show other views of the unexpectedly dynamic side chains of the C termini in the core region (green, yellow, and orange). The remarkably dynamic side chains include the side chains of Arg-44 and Lys-45.

The solvent-exposed outer surface of the coat protein shows static and dynamic residues. Surface sites with dynamic side chains (based on Cβ order parameters) include residues Glu-9, Asp-18, and Lys-20. Static surface residues include Thr-13 and Asp-14. Hydrogen bonding between these two side chains could immobilize their Cβ positions.

The top interior and bottom exterior of the assembly that face each other both have static residues that could interact with each other. This is understandable in that within such a compact hydrophobic environment, side chains tightly packed next to each other might be expected to have low mobility. However, by contrast, the bottom interior of the assembly that faces the DNA shows a clustering of highly dynamic residues. The C-terminal side-chain residues have Cβ order parameters of ≈0.6. These residues include Arg-44 and Lys-45, and this patch shows the highly dynamic environment deep inside the coat assembly.

Fig. 6 shows the recoupled dipolar spectra for side-chain sites in Arg-44 and Lys-45. Even though both residues have very static backbones, their side chains are very mobile. The Arg-44 and Lys-45 Cβ bonds have submicrosecond order parameters of 0.65 ± 0.04 and 0.63 ± 0.04, respectively. If the diffusion in a cone model is assumed, the corresponding cone diffusion angle is ≈42°. The Lys-45 Cγ bonds become increasingly dynamic with an order parameter of 0.28 ± 0.04 and cone diffusion angle of 66°.

Fig. 6.

¹³C¹H_x recoupled dipolar spectra for residues Arg-44 and Lys-45. Arg-44 (¹³C¹H)α experimental data (Top Left) were simulated (Top, Right) best with 〈S〉 = 0.99 ± 0.04. Arg-44 (¹³C¹H₂)β experimental data (Second from Top, Left) were simulated (Second from Top, Right) best with 〈S〉 = 0.65 ± 0.04. Lys-45 (¹³C¹H)α experimental data (Third from Top, Left) were simulated (Third from Top, Right) best with 〈S〉 = 1.02 ± 0.04. Lys-45 (¹³C¹H₂)β experimental data (Fourth from Top, Left) were simulated (Fourth from Top, Right) best with 〈S〉 = 0.63 ± 0.04. Lys-45 (¹³C¹H₂)γ experimental data (Bottom Left) were simulated (Bottom Right) best with 〈S〉 = 0.28 ± 0.04. The simulated spectra were fit against the experimental spectra in the 2.3- to 10.8-kHz frequency range, and the zero frequency region was not plotted. Both Arg-44 and Lys-45 C-terminal residues have essentially staic protein backbones, but they have highly mobile side chains.

The elevated side-chain dynamics of the C-terminal Arg-44 and Lys-45 residues are of particular interest because they quantitate a relatively unexplored aspect of protein–nucleic acid interactions in viruses. Given that the major coat protein subunits interact with the nucleotides in a 1:1 ratio, the charges on these two residues can balance the phosphate charge of the DNA and a potential C-terminal carboxylate charge on Ala-46. All of these charges can be in close physical proximity, but exact distances have not yet been established, and, although the observed dynamics are related to static structure, they do not provide any information on static structure. However, the different types of interactions between the major coat protein and the different DNA bases, i.e., a presumed lack of specificity in this nucleic acid protein interface, may be consistent with the highly dynamic nature of residues Arg-44 and Lys-45.

We presume that the observed large-amplitude submicrosecond dynamics occur within a highly hydrated interior of the virus (39). To estimate the hydration of a cavity around the viral DNA, we used the coordinates of 1PFI, the only available Pf1 model with DNA coordinates, to calculate the possible number of explicit water molecules within the volume defined by the unison of all spheres with radius of 8 Å from each atom of the DNA by using GROMACS (40). The result was 14.4 water molecules per average nucleotide and its protein subunit. The side chains of Arg-44 and Lys-45 lie within this DNA hydration shell. This estimate of DNA hydration corresponds to a 40% mass ratio calculated as the mass of water over the mass of DNA and water together. Because 1PFI only gives coordinates for a single representative base (cytidine), and its orientation and those of the other three bases are not yet established, this is clearly an estimate. Nevertheless, the calculation demonstrates that there is ample solvent for rearrangements of hydrated side chains in the innermost interior of Pf1. Other studies have demonstrated that order parameters correlate to local contacts in a protein (41). The present findings show that the DNA–protein interface in Pf1 manifests itself as dynamic interaction on a submicrosecond time scale.

Furthermore, the DNA molecule itself could be dynamic in the hydrated form of the Pf1 virus, even though there is order in the phosphate backbone and nucleosides of the DNA (15). For instance, solid-state studies of a hydrated, Watson–Crick base-paired DNA molecule show considerable submicrosecond dynamics in the backbone and the deoxyribose ring (39, 42). By comparison, an extended DNA in Pf1 with bases directed outward toward the capsid (11, 15) may have additional dynamic modes or different amplitudes in the normal modes, such as greater torsional motion about the N-glycosidic bonds (43). Given the intimate contacts between the DNA and protein implicit in the unit stoichiometric ratio, increased motion in the Pf1 DNA molecule could further increase dynamics of the protein side chains in contact with the DNA.

By comparison, the structure of the protein–nucleic acid interface of TMV has been well characterized through fiber diffraction studies that have revealed an ordered RNA helix following the helical symmetry of the capsid with triplets of nucleotides accommodated in three different binding sites per subunit (28). In TMV there are 12 definable nucleotide–protein contacts (four nucleotide types in each of three binding sites). Crystallographic temperature factors for the protein side chains interacting with the RNA, which include both contributions from static structural heterogeneity and molecular motion, did not indicate remarkable dynamics at the RNA–protein interface. In fact, the temperature factors for the basic side chains deep in the interior of the TMV virion that interact with the nucleic acid were much lower than those of side chains on the virus exterior, in dramatic contrast to the present results for the Pf1 virion. Also, portions of the RNA genomes of flock house virus (29) and of satellite tobacco mosaic virus (30) have been seen in their interactions with their spherical capsids through high-resolution crystallographic studies, but here also the dynamic aspects cannot be appreciated (29, 30).

Conclusions

The site-specific amplitudes of motions in the coat protein assembly for the native-state Pf1 bacteriophage have been measured. Consistent with previous qualitative measurements, the protein backbone is rigid and immobile, including some glycine residues, which one might have expected to be dynamic. By contrast, the protein side chains show a large range of dynamic motion. Some residues at the surface of the coat assembly are mobile, and residues thought to interact with the viral DNA also show high mobility. This report shows the feasibility of determining experimentally the molecular dynamics of very large protein assemblies.

Materials and Methods

NMR Spectroscopy.

The NMR sample was prepared as described in ref. 18. A single sample of 7 mg of Pf1 in a polyethylene glycol-induced precipitate in ≈30 μl (≈230 mg/ml Pf1) (18) was loaded into the rotor of a wide-bore 4-mm MAS probe in the¹H/¹³C/¹⁵N configuration. The MAS sample rotation rate was set at 15.00 kHz, and the experiments lasted for a total of 10 days. After this exposure the sample gave normal static NMR spectra (18). LGCP-DARR 3D experiments were conducted on a Bruker 750-MHz wide-bore NMR spectrometer. The sample temperature was set at 21°C, which is corrected for heating from MAS, and the high-temperature form of the bacteriophage was studied. The average ¹H and ¹³C CP fields were 58.3 kHz and 51.8 kHz, respectively, based on intensities from Fourier transformed nutation spectra. Two-pulse phase modulated (TPPM) heteronuclear dipolar decoupling (44) with a ¹H field of 71 kHz was applied during ¹³C isotropic chemical shift evolution periods. A DARR field of 15 kHz (equal to the sample rotation velocity) was applied for a period of 50 ms during mixing.

The LGCP-DARR 3D pulse sequence (23) correlates the ¹H_x¹³C dipolar spectrum in the heteronuclear dipolar recoupling dimension (t₁) to the indirect ¹³C chemical shift dimension (t₂). The direct ¹³C chemical shift dimension (t₃) disperses the sites in the 3D spectrum. Data were collected with spectral widths of 32.542 kHz (44 points, zero-filled to 256 points), 13.600 kHz (212 points, zero-filled to 512 points), and 83.333 kHz (4096 points) in t₁, t₂, and t₃, respectively. Two 3D experiments of 16 scans each were added together, and the experiment duration for each 3D experiment was 5 days. Apodization with exponential decay functions were used in t₁ (1.5 kHz) and t₃ (40 Hz), and apodization with a sine-square bell with an offset of 23° and an end of 180° was used in t₂. Nonoverlapping cross-peaks within a ±0.25-ppm window were used in the analysis.

Dipolar Spectral Simulation and Fitting.

The data analysis was carried out according to published procedures (22, 23). The tensor asymmetry was assumed to be zero for all fits (45). The zero-frequency component was not included in the fit because cross-polarization dynamics and T_1ρ effects distort it (22, 23). The range of frequencies used in the χ² fits for 75 of the ¹³C¹H and ¹³C¹H₂ spin systems was 2.3 kHz to 10.8 kHz. Eight of the ¹³C¹H and ¹³C¹H₂ spin systems have reduced intensity at low frequencies and, consequently, a standard fit overestimates the dipolar coupling constant. Therefore, a reduced range fit was applied for these data points, by using frequency ranges of 4.8 kHz to 10.0 kHz for ¹³C¹H and 4.6 kHz to 10.8 kHz for ¹³C¹H₂. See Table S1 for a list of all 83 data points, including those fit with the reduced range.

The dipolar spectral simulations for ¹³C¹H and ¹³C¹H₂ spin systems were simulated with 256 crystallite orientations, a 2.1-μs time step, and fixed homonuclear couplings as reported previously (22). The exponential line broadening was varied from 1.5 to 8.5 kHz in 1-kHz increments. The heteronuclear dipolar coupling constants (DCC) were varied from 5.0 to 26.0 kHz in 0.2-kHz increments. To account for inhomogeneity effects in the analysis (22), the LGCP dipolar simulations were integrated over six ¹H fields and one ¹³C field from the intensities of the ¹H and ¹³C Fourier transformed nutation spectra, respectively (see Table S2 for the ¹H nutation profile used).

Protein ribbon and surface structure renderings were prepared with PyMOL (46).