Paramagnetic shifts in solid-state NMR of proteins to elicit structural information

Abstract

The recent observation of pseudocontact shifts (pcs) in ¹³C high-resolution solid-state NMR of paramagnetic proteins opens the way to their application as structural restraints. Here, by investigating a microcrystalline sample of cobalt(II)-substituted matrix metalloproteinase 12 [CoMMP-12 (159 AA, 17.5 kDa)], it is shown that a combined strategy of protein labeling and dilution of the paramagnetic species (i.e., ¹³C-,¹⁵N-labeled CoMMP-12 diluted in unlabeled ZnMMP-12, and ¹³C-,¹⁵N-labeled ZnMMP-12 diluted in unlabeled CoMMP-12) allows one to easily separate the pcs contributions originated from the protein internal metal (intramolecular pcs) from those due to the metals in neighboring proteins in the crystal lattice (intermolecular pcs) and that both can be used for structural purposes. It is demonstrated that intramolecular pcs are significant structural restraints helpful in increasing both precision and accuracy of the structure, which is a need in solid-state structural biology nowadays. Furthermore, intermolecular pcs provide unique information on positions and orientations of neighboring protein molecules in the solid phase.

Solid-state NMR (SSNMR) on biomolecules is a rapidly growing technique, with an increased interest based on its ability to determine protein structures in the solid phase (1, 2) and to permit the study of noncrystalline biomolecular systems such as membrane proteins (3) and fibrils (4, 5).

Limitations in biomolecular structural determination through SSNMR are due to the difficulties in obtaining a large number of restraints to be used for structural purposes (4, 6–9). Most of the structural information is obtained through distance restraints, analogous to nuclear Overhauser effects (NOE) in solution NMR, which in the solid state are obtained through experiments such as proton-driven spin diffusion (PDSD) (1, 6, 10), and CHHC (11), whereas specifically designed sequences can be applied on short peptides (4, 12–14). The ability to obtain a large number of distance restraints is hampered by the reduced resolution of SSNMR spectra, which increases the amount of ambiguities in the assigned restraints (15), whereas relayed transfer (10, 16) and the effects of the dipolar truncation (17) affect the accuracy of these restraints. These problems have been tackled by working on samples prepared with selective labeling schemes (1, 6) and, more recently, on uniformly labeled proteins with the help of software able to provide automated PDSD/CHHC assignment and on dealing with a large number of ambiguous restraints (10, 15, 18). However, even when additional dihedral angle restraints from backbone chemical shifts—through Chemical Shift Index (CSI) (19) or TALOS (20) programs—are used, the size of the affordable proteins has been, up to now, limited to small systems (<100 aa) (10, 15, 18). In this work, we show how SSNMR paramagnetic restraints such as pseudocontact shifts (pcs) can be used as additional sources of restraints for protein structural determination, even providing information about the relative arrangement of protein molecules in the solid phase.

Paramagnetic NMR restraints as relaxation times, pcs, and residual dipolar couplings (RDC) (21)—the latter two originating from anisotropy in the magnetic susceptibility tensor—are routinely used in solution NMR to refine structures (22), to investigate protein–protein interactions (23, 24), or to monitor dynamics (25, 26). Small paramagnetic molecules have been studied through magic angle spinning (MAS) SSNMR for decades (27–33). Paramagnetism in the solid state causes problems connected with the large shift anisotropy, inhomogeneous broadening (34), and the difficulties in obtaining efficient proton decoupling (30, 32). Pioneering works have shown that paramagnetic proteins are also affordable by SSNMR by using either perdeuterated substrates (35) or selective labeling (36). More recently, uniformly labeled paramagnetic proteins have also been studied (37–39), taking advantage of the absence of paramagnetic relaxation mechanisms related to the molecular tumbling (as Curie relaxation terms) (40). The prospective availability of fast and ultrafast MAS probes should allow one to reduce the limits posed by the presence of metals inducing large shift anisotropies (33, 40, 41).

In a recent paper, we reported the first observation of pcs in the ¹³C SSNMR of a uniformly ¹³C-labeled paramagnetic protein, i.e., cobalt(II)-substituted matrix metalloproteinase 12 (CoMMP-12), and we proposed that pcs could constitute additional structural restraints for SSNMR (38). From the known high-resolution X-ray structure (42), we were able to show that the pcs observed for each of 246 assigned ¹³C nuclei are very well accounted for by a sum of contributions arising from the intramolecular cobalt(II) ion and from cobalt(II) ions belonging to neighboring molecules. We concluded that if it were possible to separate intra- from intermolecular pcs, even for cases where the structure was not available, intramolecular pcs would constitute valuable restraints to obtain the protein structure in the solid state. On the other hand, intermolecular pcs could provide information on the relative arrangement of different protein molecules in the solid phase.

Here, we show that by using an approach based on the dilution of the paramagnetic species (30, 38) in combination with 2 different labeling strategies, it is effectively possible to experimentally separate intra- and intermolecular pcs. Then, we show that intramolecular pcs, together with a relatively small number of distance restraints from PDSD and CHHC spectra, permit the determination of the 3-dimensional structure in the solid state even for a 159-aa protein. Finally, we show that intermolecular pcs provide information on the arrangement of the nearest protein neighbors. The present approach is general and independent of the information coming from X-ray diffraction techniques. Even if the present method is demonstrated on a metalloprotein, it can, in principle, be extended to diamagnetic proteins once a paramagnetic metal is attached to them by using specifically designed tags (43, 44).

Results and Discussion

Paramagnetic Dilution Strategy.

To separate the intra- and intermolecular pcs contributions without previous knowledge of the protein structure, the preparation of 2 samples with 2 different combinations of protein labeling and dilution of the paramagnetic species is proposed. In the first scheme (diluted CoMMP-12), ¹³C,¹⁵N-enriched* CoMMP-12 (paramagnetic species) is diluted with unlabeled ZnMMP-12 (native diamagnetic protein). By crystallizing this mixture in an appropriate dilution ratio in the same conditions previously used for the uniformly labeled samples (ZnMMP-12 or CoMMP-12) (38, 45) a sample is obtained where each ¹³C-labeled paramagnetic protein molecule is—on average—surrounded by unlabeled diamagnetic protein molecules. Because the ¹³C-labeled molecules are the only species observable in ¹³C–¹³C correlation NMR experiments, the paramagnetic species, which is affected only by the intramolecular pcs, can be selectively observed. The second scheme is based on the “inverse dilution”: a mixture is crystallized in which ¹³C,¹⁵N-enriched ZnMMP-12 (diamagnetic) is diluted with unlabeled CoMMP-12 (paramagnetic). Because only the labeled species can be observed in this sample, intramolecular pcs are absent, and only intermolecular pcs are observed.

In both cases, the cleanest effects are, of course, expected for very high dilutions of the labeled species, which would, however, produce signal-to-noise ratios that are too small. In practice, a reasonable compromise should be found between sensitivity and the increased probability that 2 labeled molecules crystallize adjacent to one another, giving rise to unwanted peaks. Although the best dilution ratio should be determined for each sample on the basis of the nature of the sample and of the actual sensitivity (which depends on several parameters like amount of sample, probe sensitivity, magnetic field used, etc.), in the present case, it is found that the separation among intra- and intermolecular pcs can be afforded by using only a factor-three dilution [see supporting information (SI) Text for a further discussion of different cases]. For the first dilution scheme, in a typical situation where the intermolecular effects are generated by only 1 neighbor at a time, as in the present case (38), each pair of connected nuclei gives rise to 2 cross-peaks, arising from molecules affected by only intramolecular pcs or by both intra- and intermolecular contributions. Fig. S1A reports the calculated intensities of both peaks as a function of the dilution ratio (x), showing that by using a 33% dilution ratio, the intensity of the peaks affected only by intramolecular pcs is sizably higher than those of the peaks affected by both contributions. Similar considerations hold for the second dilution scheme (Fig. S1B). Details on the derivation of the relevant equations are also reported in SI Text.

Solid-State NMR Spectra.

The ¹³C-¹³C PDSD spectra obtained with the 2 dilution schemes (diluted CoMMP-12 and diluted ZnMMP-12 samples) were recorded, assigned, and compared with those of fully enriched CoMMP-12 and ZnMMP-12 (38, 45), respectively. Representative portions of these spectra are shown in Fig. 1, to illustrate the clear separation of the observed pcs into their intra- and intermolecular components. Residues, such as Thr-154, which are affected by both intra- and intermolecular pcs, show different shifts in the spectra of the fully labeled CoMMP-12 and diluted CoMMP-12 samples (purple and green in Fig. 1B, respectively). Likewise, the same shift difference is observed when the spectra of the diluted ZnMMP-12 sample (where only intermolecular pcs are expected) and diamagnetic fully labeled ZnMMP-12 (cyan and orange, respectively, in Fig. 1D) are compared. Conversely, for residues such as Val-217, which are essentially affected only by the intramolecular term, the same shift in both fully labeled CoMMP-12 and diluted CoMMP-12 samples (Fig. 1A) is observed, and no pcs in the diluted ZnMMP-12 sample (Fig. 1C), because the intermolecular term is negligible here. Table S1 summarizes the number of meaningful pcs that could be collected from each spectrum. The complete sets of pcs values are reported in Table S2. Compared with the previous report (38), the number of assigned pcs in the present fully enriched CoMMP-12 sample could be nearly doubled (401 vs. 246) by a subsequent careful analysis of the 3D NCOCX and NCACX spectra (see details in SI Text). Even the 2 diluted samples (labeled CoMMP-12 and labeled ZnMMP-12) provided a relatively large number of pcs (318 intra- and 231 intermolecular, respectively), the smaller number for the intermolecular pcs arising from the fact that relatively fewer protein nuclei are exposed to nonnegligible paramagnetic effects from the neighboring molecules.

Fig. 1.

Representative parts of the PDSD spectra of fully labeled ZnMMP-12 (orange), fully labeled CoMMP-12 (purple), diluted CoMMP-12 (green), and diluted ZnMMP-12 (cyan). (A and C) The peaks of Val-217, which is affected only by intramolecular pcs, and thus the shifts observed in full-labeled samples are analogous to those observed in diluted samples. (B and D) The peaks of Thr-154, which is strongly affected only by intermolecular pcs, and the shifts observed in fully-labeled samples differ from those observed in diluted samples by the intermolecular contributions.

The intramolecular pcs measured in the diluted CoMMP-12 sample are in excellent agreement with the pcs measured in solution (Fig. S2), because in both cases, they depend only on the presence of the internal metal and are given by the same equation (Eq. 1) (21, 38):

where Δχ_ax and Δχ_rh are the axial and rhombic components of the magnetic susceptibility tensor anisotropy (χ), r is the metal-nucleus distance, and θ and ϕ are, respectively, the polar and azimuthal angles describing the orientation of the metal-nucleus vector with respect to the principal axes of the χ tensor.

Thus, from the experimental intramolecular pcs and the known crystal structure^† (42) (PDB ID code 1RMZ), the 2 anisotropy parameters Δχ_ax and Δχ_rh as well as the 3 Euler angles defining the orientation of the principal axes of the magnetic susceptibility tensor of the cobalt(II) ion in the MMP-12 molecular frame can be determined.

Figs. 2 A–C shows, respectively, the experimental total pcs (as measured in the fully labeled CoMMP-12 sample), the intramolecular pcs, and the intermolecular pcs (blue lines) plotted together with the calculated values (green lines).^‡ In the calculated total pcs (Fig. 2A), the contributions from the internal and from all of the external metals within a radius of 80 Å were summed up, whereas for the intramolecular pcs (Fig. 2B) and the intermolecular pcs (Fig. 2C), only the contributions of the internal and external metals, respectively, were considered. The agreement between calculated and experimental values (see also Fig. S3) is very good in all 3 cases. For the total pcs, the RMSD between calculated and experimental values is 0.19 ppm, which represents a very reasonable value, because it is of the order of the experimental error in the measured pcs (≈0.2 ppm). This indicates that the calculated values agree with the experimental ones within the error limits.

Fig. 2.

¹³C pcs observed (blue lines) for fully labeled CoMMP-12 (A), diluted CoMMP-12 (B), and diluted ZnMMP-12 (C). The green lines are calculated as the sum of contributions from the internal and external cobalt(II) ions (A), from the internal cobalt(II) ion only (B), and from the external cobalt(II) ions only (C).

In conclusion, by using diluted samples^§, 2 high-quality sets of intra- and intermolecular pcs values can be made experimentally available, thus allowing the potential use of the former for structural determination (as is routinely done in solution) and of the latter to obtain structural information on neighboring molecules.

Pcs are long-distance restraints: In the present case, pcs up to 20–22 Å from the metal could be measured. On the other side, the limits posed by shift anisotropy (30) and/or by insufficient decoupling (32) make the nuclei closer than 9–10 Å to the metal unobservable; the perspective of investigating samples at higher MAS frequency suggests that this lower limit could be reduced (40, 41), but this aspect deserves further investigation.

Use of the Intramolecular pcs for Structural Determination.

To demonstrate the affordability of protein structural determination supported by pcs, structural calculations were performed by using experimental intramolecular pcs, distance restraints determined on the zinc form of the protein from the analysis of PDSD and CHHC spectra at different mixing times (see Materials and Methods), and angle restraints derived from TALOS analysis (20).

Fig. 3 shows the significant structural refinement obtained by using pcs in the structural calculation: by using 318 experimental intramolecular pcs, 284 distance restraints (Table S3 and PDB ID code 2K9C), and 152 angle restraints obtained from TALOS analysis, it was possible to arrive to a reasonably good structural family (Fig. 3C; PDB ID code 2K9C) even for a protein significantly larger than those studied in the solid state until now. The overall backbone RMSD (secondary structural elements plus loops) within the family is 3.0 Å, and it reduces to 2.0 Å when only the secondary structural elements are considered, because less information is provided in loops by distance and dihedral angle restraints. When performing the same calculation by using only the diamagnetic restraints (distance and angle restraints only, and excluding pcs), the RMSD is sizably higher (5.8 Å for the whole backbone, and 4.1 Å for the secondary structural elements only), yielding a structure that is still largely undefined (Fig. 3B). The overall backbone RMSD (secondary structural elements plus loops) with respect to the X-ray structure is 3.1 Å, and it reduces to 2.1 Å when only the secondary structural elements are considered, whereas in the absence of paramagnetic restraints, the RMSD to the X-ray structure is 5.7 Å for the whole backbone and 4.1 Å for the secondary structural elements only. It is notable that the use of pcs increases both precision (RMSD within the family) and accuracy (RMSD from the X-ray structure) by approximately the same amount. Although the current precision is lower than that recently obtained for smaller systems (10, 15), the gap between precision and accuracy currently observed in their SSNMR structures (10, 15) is not observed here. This is probably because pcs are quantitative and accurate restraints that are not biased by relayed transfer effects like the other distance restraints (10).

Fig. 3.

Families of 15 structures obtained without paramagnetic restraints (B) and with paramagnetic restraints (C); the reference X-ray structure (PDB ID code 1RMZ) is shown in A. The overall backbone RMSD (secondary structural elements plus loops) is 5.8 Å for B and 3.1 Å for C; the overall heavy-atom RMSD is 6.4 Å for B and 3.9 Å for C; the backbone RMSD for secondary structural elements is 4.0 Å for B and 2.1 Å for C. The overall backbone RMSD with respect to the X-ray structure is 5.7 Å for B and 3.1 for C, whereas the backbone RMSD for secondary structural elements is 4.1 Å for B and 2.1 Å for C (PDB ID code 2K9C).

Not only is the use of pcs important in yielding a reasonably good structure with a modest number of distance restraints (<2 distance restraints per residue), but it was also helpful to obtain a rapid assignment of the spectra: After the assignment of the first 154 unambiguous cross-peaks (82 from PDSD and 72 from CHHC), a structural calculation including pcs was performed that generated a preliminary structure with backbone RMSD of 7.0 Å. Use of this poorly defined structure as a starting point was nevertheless sufficient to solve ambiguities, extending the assignment of the PDSD and CHHC spectra and generating a more refined structure. This procedure was manually iterated up to assignment of an additional 130 distance restraints (see SI Text for details).

The use of pcs in the protein structural calculations followed the well-described protocols for solution structure determinations (22, 46, 47), and average values reported in the literature for the paramagnetic tensor parameters Δχ_ax and Δχ_rh in cobalt(II) ions (Eq. 1) were used (47).^¶ Such calculations also show that some distance restraints are always needed, otherwise pcs alone hardly converge to a correct folding (22, 48).

Because pcs, as well as angle restraints, are more easily obtained from the NMR assignment than distance restraints, it appears that pcs may be valuable for structural determination in SSNMR, providing further structural restraints and helping in the assignment of distance restraints from PDSD and CHHC spectra.

In perspective, pcs can also be included into automated assignment software, which should reduce the problem of the high number of ambiguous restraints typical of the solid-state spectra (10, 15, 18). Because the positive effect of pcs in reducing the structure RMSD is already significant when relatively few distance restraints are used, it can be expected that the contribution of pcs may be even more important for samples whose spectra have a higher fraction of ambiguous distance restraints.

Use of the Intermolecular pcs for Structural Information on the Neighboring Molecules.

In this section, we address whether the intermolecular pcs are of good enough quality to actually allow one to obtain meaningful and quantitative information on the location and orientation of the neighboring protein molecules, given that the single protein structure is known. Because the pcs contributions from each metal ion to any nucleus are additive, the total pcs, observed in the fully labeled CoMMP-12 sample, can be described by Eq. 2:

where the sum runs over all of the n neighboring metals that give a nonnegligible contribution to pcs, r₁ and r_n are the distances of the observed nucleus from the internal and the nth metal, respectively, and θ₁,ϕ₁ and θ_n,ϕ_n are the polar and azimuthal angles describing the position of the observed nucleus with respect to the principal axes of the χ tensor relative to the internal and the nth metal, respectively. The paramagnetic tensor parameters Δχ_ax and Δχ_rh and the orientation of the principal axes of the χ tensor within the protein frame are the same for any metal. On these bases, starting from the structure of a single protein, one can optimize the position of the internal and external metals and the orientation of the principal axes of their χ tensors to minimize the RMSD among the experimental total pcs and the values calculated through Eq. 2. By doing so, the position and orientation of the neighboring molecules is also determined.

Whereas locating a single metal ion in a given structure and determining the parameters of its magnetic susceptibility anisotropy tensor requires an 8-parameter fit (i.e., Δχ_ax, Δχ_rh, the coordinates x, y, and z of the metal and the 3 Euler's angles defining the orientation of the principal axes of the χ tensor), increasing the number of metals beyond 1 requires 6 additional parameters each time (Δχ_ax and Δχ_rh being the same for all metals), i.e., 8 parameters for 1 metal, 14 for 2 metals, 20 for 3 metals, etc. In addition, although one can exploit hundreds of intramolecular pcs, with both positive and negative signs, to locate the internal metal ion, only a few tens of meaningful intermolecular pcs are available, most of which are of the same sign, to locate one of the neighboring metals. In fact, typically, only 1 edge of a protein molecule is exposed to the magnetic susceptibility of a neighboring protein.

The position and the tensor orientation parameters of each metal from the experimental pcs are obtained through a nonlinear least-square minimization that is repeated for many automatically generated initial guesses (see SI Text). As final optimized parameters, we chose those giving the minimal RMSD.

In the best-fitting of the intramolecular pcs (8-parameter fit) the internal metal could be placed in a position that is only 0.30 Å away from the crystallographic position, with an RMSD of 0.19 ppm. This is a remarkable result, because an indetermination of <0.5 Å is of the order of the average backbone RMSD for the best NMR structures in solution.

Once the position and the magnetic parameters of the internal metal are determined from the intramolecular pcs, we fitted the total pcs to establish the maximum number of external metals that can be safely determined. Thus the total pcs were fitted with Eq. 2 by using, first, only the internal metal and no external metals and, then, by adding 1, 2, and 3 external metals. The RMSD thus obtained were 0.87, 0.51, 0.19, and 0.17 ppm, respectively. By passing from none to 1 and from 1 to 2 external metals, the RMSD decreases significantly, whereas, when a third external metal is used, the effect is much less important. Finally, as already pointed out, RMSD <0.2 ppm are of the order of the experimental error in the pcs. The RMSD obtained in the fit with 2 or more external metals is comparable with the RMSD when the total pcs are calculated from the crystallographic positions; therefore, both values reach the limit posed by the pcs experimental error, and any further improvement is meaningless. It is concluded that, in this case, only 2 neighboring protein molecules can be safely placed. The best fit with 2 neighboring metals yielded the metal position of the neighboring proteins at 2.1 and 3.0 Å from the X-ray crystallographic positions for molecules 1 and 2, respectively, in Fig. 4.

Fig. 4.

Comparison of the orientations of the 2 nearest neighboring molecules of MMP-12 in the crystal as obtained from a best-fit of the total pcs (red) and from the X-ray crystal structure (blue). Small spheres indicate the position of the internal cobalt(II) ion and the orientation of the principal axes of the magnetic susceptibility anisotropy tensor as calculated by a best-fit program.

On the basis of the fitted orientation of the principal axes of χ, the orientation of the 2 neighboring protein molecules could also be determined. The determination of the orientation of the principal axes of the magnetic susceptibility tensor does not unequivocally fix the orientation of the protein: Indeed, the 4-fold symmetry of the pcs function allows for 4 possible protein orientations. This ambiguity was easily resolved by discarding the 3 solutions that give strong overlap with the internal protein (see details in SI Text). In Fig. 4, we compare the position of the neighbors determined by the SSNMR pcs (red) with the X-ray crystallographic positions (blue). As it can be seen, even the protein arrangements are in reasonably good agreement with the crystallographic positions. Further considerations on the robustness and the quality of the obtained solutions can be made with a Monte Carlo type of error analysis and are reported in SI Text.

Conclusions

In conclusion, we show that, in the investigation of paramagnetic proteins in the solid state, it is possible to experimentally separate the intramolecular pcs from the intermolecular contributions by using paramagnetic diluted samples. These pcs are helpful structural restraints: Intramolecular pcs can be used as restraints for protein structure determination in the solid state, whereas intermolecular pcs can be used to obtain spatial arrangements among different protein molecules. The calculations performed on the intermolecular contributions demonstrate that, in the present case, pcs alone are accurate enough to allow one to determine the position and the orientation of 2 neighboring protein molecules within a distance of a few angstroms from the values determined from X-ray crystallography. Of course, these results may not be taken to imply general validity, i.e., different molecules with different crystalline orders may prove either less or more suitable than the present example in providing information on neighboring molecules.

However, the approach based on the dilution of the paramagnetic species can, in principle, be extended to other systems without previous information about the crystallographic structure. Although in the present case, a 33% dilution is effective to separate intra- and intermolecular contributions, in other less favorable cases (e.g., peaks experiencing pcs from more than 2 paramagnetic centers), an increase in dilution might be required to have a clearer separation. In general, it could be possible to test more than 1 dilution ratio, by starting from the 33% dilution ratio, which is optimal to separate contributions from up to 2 paramagnetic centers, to find the optimal separation. Finally, intramolecular pcs can be used for structural determination even without an accurate determination of the paramagnetic tensor parameters Δχ_ax and Δχ_rh, because average typical values can be directly applied.

These results show that this method could be applicable to biomolecules in the solid phase that are not necessarily crystalline but are endowed with a 1-dimensional order such as fibrils, which cannot be structurally investigated by X-ray crystallography. It is worth recalling that paramagnetic metals, besides being incorporated in metalloproteins in the place of diamagnetic ones, can be also attached as tags to any protein (43, 44, 49), and this renders the approach quite general.

Materials and Methods

Preparation of the Microcrystalline Diluted Samples.

The ZnMMP-12 and the CoMMP-12 proteins complexed with the strong N-isobutyl-N-[4-methoxyphenylsulphonyl]glycyl hydroxamic acid (NNGH) inhibitor were prepared by following the published procedure (42). The diluted CoMMP-12 sample was obtained by mixing in solution 15 mg of ¹³C-¹⁵N-labeled CoMMP-12 with 30 mg of unlabeled ZnMMP-12 protein (45 mg overall). Analogously, for the diluted ZnMMP-12 sample, 15 mg of ¹³C-¹⁵N-labeled ZnMMP-12 and 30 mg of unlabeled CoMMP-12 (45 mg overall) were used. For each sample, the amount of protein was chosen to obtain ≈35–40 mg of microcrystalline material.

All of the samples were crystallized by following the reported procedure (38, 42), with minor changes: By using aliquots of 50 μl of 1.5 mM protein solution [10 mM Tris/5 mM CaCl₂/1 mM CoCl₂/300 mM NaCl/3 mM NNGH (pH 7.0)] mixed with 50 μl of reservoir buffer [0.1 M Tris·HCl/25% PEG 8000 (pH 8.3)] and all equilibrated against 250 ml of reservoir buffer. Crystals grew regularly up to 2.5–3 weeks and were then washed with 50 μl of a low-salt buffer [10 mM Tris·HCl/25% PEG 8000 (pH 8.3)] for 1 h and transferred in a 50-μl ZrO₂ HR MAS rotor.

Solid-State NMR Spectroscopy.

All of the NMR spectra were recorded on a Bruker Avance 700 wide-bore instrument operating at 16.4 T (700 MHz ¹H Larmor frequency, 176.0 MHz ¹³C Larmor frequency). A double/triple-channel 4-mm CP-MAS probe head was used. The spinning frequency of the ZrO₂ HR MAS rotor was stabilized to ±2 Hz. The probe temperature was kept at a nominal temperature of 270 K, which ensures a constant sample temperature ≈280 K.

Standard sequences were used for double-resonance CP, 2D PDSD (1, 10), and 2D CHHC (11) experiments and for triple-resonance 3D NCACX PDSD and 3D NCOCX PDSD experiments (3D experiments were acquired on the fully labeled CoMMP-12 sample only) by using standard sequences (6). The spectra were acquired at MAS frequency of 8.5 and 11.5 kHz in double-resonance and 11 kHz in triple-resonance experiments. Further details on the experimental condition are reported in SI Text. Details of the assignment procedure and analysis of the intermolecular pcs along with the calculation of the structure using intramolecular pcs are also reported in SI Text.