Protein fold determined by paramagnetic magic-angle spinning solid-state NMR spectroscopy

Abstract

Biomacromolecules that are challenging for the usual structural techniques can be studied with atomic resolution by solid-state nuclear magnetic resonance. However, the paucity of >5 Å distance restraints, traditionally derived from measurements of magnetic dipole-dipole couplings between protein nuclei, is a major bottleneck that hampers such structure elucidation efforts. Here we describe a general approach that enables the rapid determination of global protein fold in the solid phase via measurements of nuclear paramagnetic relaxation enhancements (PREs) in several analogs of the protein of interest containing covalently-attached paramagnetic tags, without the use of conventional internuclear distance restraints. The method is demonstrated using six cysteine-EDTA-Cu²⁺ mutants of the 56-residue B1 immunoglobulin-binding domain of protein G, for which ~230 longitudinal backbone ¹⁵N PREs corresponding to ~10-20 Å distances were obtained. The mean protein fold determined in this manner agrees with the X-ray structure with a backbone atom root-mean-square deviation of 1.8 Å.

The determination of three-dimensional (3D) structures of biological macromolecules is critical to understanding their physiological function and is also the primary focus of structural genomics initiatives.¹ Magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) provides a set of spectroscopic tools for structural studies of biological systems that cannot be induced to form sufficiently diffracting crystals and are also not amenable to solution NMR due to size limitations, such as certain membrane-bound polypeptides^2,3 and amyloids.^4,5 However, in spite of the remarkable recent progress in determining relatively high-resolution structural models for proteins with molecular weights up to ~20 kDa by MAS solid-state NMR,^5-19 the routine generation of such structures continues to present considerable challenges.

Even for small to medium-size uniformly ¹³C,¹⁵N or uniformly ¹⁵N and extensively ¹³C labeled proteins—the latter generally prepared by using complementary [1,3-¹³C] and [2-¹³C]glycerol based expression media⁶ in order to achieve improved spectral resolution and magnetization transfer efficiencies^6,15 by suppressing many one-bond ¹³C–¹³C dipolar and J-couplings—the 2D ¹³C-¹³C and ¹⁵N-¹³C chemical shift correlation spectra, which form the basis for the vast majority of the current solid-state NMR structure determination protocols, are typically highly congested and contain many tens to hundreds (or even thousands) of resonances. These spectra rely on magnetization transfers using radiofrequency pulse schemes such as transferred echo double resonance (TEDOR),^20,21 proton driven spin diffusion (PDSD) or dipolar assisted rotational resonance (DARR),²² CHHC, NHHC or NHHN,²³ or proton assisted recoupling (PAR),¹² and report on the magnitudes of through-space ¹³C-¹³C, ¹⁵N-¹³C and ¹H-¹H magnetic dipole-dipole couplings, and thereby distances, among the protein nuclei. Though the use of ultrahigh-field (≥ ~20 Tesla) NMR spectrometers, additional spectral dimensions and tailored isotope labeling schemes (e.g., perdeuterated proteins containing sparsely distributed proton nuclei at a limited number of amide and methyl sites),^18-20 as well as structure calculation algorithms that are able to deal with ambiguous distance restraints^8,9 has certainly helped to alleviate some of the problems related to NMR signal overlap, the fundamental limitation in most solid-state NMR structure determination endeavors has been the relative scarceness of unambiguous long-range interatomic distance restraints. This is primarily because dipolar couplings between ¹H, ¹³C and ¹⁵N spins, which scale with the inverse third power of the internuclear distance, become vanishingly small for distances in the ~5-10 Å regime and beyond (typical coupling magnitudes are on the order of a few Hertz to tens of Hertz). The detection and reliable quantification of these couplings is often further complicated by the fact that they are part of tightly coupled multiple spin networks. Consequently, correlations that encode information about the most structurally-relevant inter-residue dipolar couplings typically comprise only a small fraction of the observable resonances in multidimensional solid-state NMR datasets, and are also usually associated with some of the weakest cross-peak intensities.

In this article, we describe a general approach that has the potential to substantially accelerate the solid-state NMR protein structure determination process. In broad terms, this methodology involves the measurement of nuclear paramagnetic relaxation enhancements (PREs)^24,25 in several point mutants of the protein of interest modified with covalently-attached paramagnetic tags, followed by the application of these PREs as structural restraints to establish the global protein backbone fold. The PRE phenomenon is well-known in magnetic resonance—the magnitude of the effect scales with the inverse sixth power of the electron-nucleus distance^24,25 and it can be non-negligible for distances up to ~20-25 Å or longer depending on the observed nucleus and paramagnetic center (i.e., distances that are at least a factor of ~3-4 larger than those obtained by using traditional dipolar coupling based solid-state NMR techniques). Indeed, PRE-based methods of this kind, employing nitroxide spin labels and measurements of longitudinal or transverse amide ¹H relaxation enhancements, have previously been successfully used to define the fold of soluble proteins with limited nuclear Overhauser effect (NOE) data.^26-28

The latest advances in MAS NMR spectroscopy of paramagnetic proteins^29-36 have laid the foundation for application of the PRE-based approach to the structural analysis of biological macromolecules in the solid phase. Using several ¹³C,¹⁵N-labeled analogs of a model 56-residue protein, B1 immunoglobulin binding domain of protein G (GB1), containing EDTA-Cu²⁺ tags attached to cysteine residues introduced into the protein especially for this purpose,^37,38 we have recently demonstrated that residue-specific longitudinal PREs can be rapidly determined for most backbone amide ¹⁵N nuclei by multidimensional solid-state NMR methods.^34,35 These ¹⁵N PREs, which correspond to ~10-20 Å ¹⁵N-Cu²⁺ distances, were found to be in good quantitative agreement with those predicted for protein structural models based on the wild-type (WT) GB1 fold. Here we show that a set of ~230 such PREs recorded for six Cys-EDTA-Cu²⁺ mutants of GB1 (i.e., ~4-5 restraints per residue), supplemented only by standard chemical shift based restraints on secondary structure and, importantly, in the absence of any dipolar coupling based internuclear distance restraints, is sufficient to derive the correct global fold for GB1 in a de novo fashion. Notably, since PRE restraints can be easily extracted with high-sensitivity from routine 2D or 3D solid-state NMR chemical shift correlation spectra, this methodology is expected to become widely applicable to larger proteins available in limited quantities.

Results

Determination of ¹⁵N paramagnetic relaxation enhancements in GB1 mutants by solid-state NMR spectroscopy

Residue-specific backbone amide ¹⁵N longitudinal PREs, Γ ^N₁, were determined from measurements of longitudinal ¹⁵N relaxation rate constants using series of 2D ¹⁵N-¹³CO (NCO) spectra recorded with different values of the relaxation delay, τ_relax (see Fig. 1a and Supplementary Fig. S1), as described in the Methods section. Relaxation data were collected for six pairs of GB1 mutants containing non-native Cys-EDTA-Cu²⁺ or Zn²⁺ sidechains incorporated at solvent exposed sites corresponding to residues N8, E19, K28, E42, D46 or T53 in the WT protein (Fig. 1b); all of these GB1 analogs exhibit the WT fold as judged by the similarity of solution and solid-state NMR backbone chemical shifts to those of WT GB1.^33-35 For brevity, the GB1 mutants used in this study are labeled as 8EDTA-Cu²⁺/Zn²⁺, 19EDTA-Cu²⁺/Zn²⁺, 28EDTA-Cu²⁺/Zn²⁺, 42EDTA-Cu²⁺/Zn²⁺, 46EDTA-Cu²⁺/Zn²⁺ and 53EDTA-Cu²⁺/Zn²⁺, according to location of the Cys-EDTA-Cu²⁺/Zn²⁺ tag.

Figure 1. Determination of longitudinal backbone amide ¹⁵N paramagnetic relaxation enhancements in Cys-EDTA-Cu²⁺ GB1 mutants by solid-state NMR spectroscopy.

a, Pulse scheme used to determine residue-specific longitudinal ¹⁵N rate constants, R₁, from a series of 2D ¹⁵N-¹³CO correlation spectra recorded with different values of the relaxation delay, τ_relax. See Supplementary Fig. S1 for the complete pulse scheme description. b, Ribbon diagram of GB1 (PDB entry 2GI9) with the locations of the non-native Cys-EDTA-Cu²⁺/Zn²⁺ tags in point mutants investigated in this study (residues 8, 19, 28, 42, 46 or 53) indicated by blue spheres. c, Small regions of 2D ¹⁵N-¹³CO spectra recorded for ¹³C,¹⁵N-labeled 8EDTA-Zn²⁺ (green contours) and 8EDTA-Cu²⁺ (magenta contours) mutants with longitudinal ¹⁵N relaxation delays of 100 μs and 4 s, as indicated in the bottom left corner of each spectrum. The resonance assignments have been established previously,³⁵ and cross-peaks are labeled according to the amide ¹⁵N frequency of the residue involved. d, Representative site-resolved ¹⁵N longitudinal relaxation trajectories for residues T51 and T53 in 8EDTA-Cu²⁺ and Zn²⁺. Experimental trajectories for 8EDTA-Zn²⁺ (green circles) and 8EDTA-Cu²⁺ (magenta circles) correspond to integrated cross-peak intensities in a series of 2D NCO spectra recorded as a function of the relaxation delay. Simulated best-fit trajectories to decaying single exponentials used to extract the longitudinal ¹⁵N relaxation rate constants are shown as solid lines of the corresponding color. The ¹⁵N PREs are calculated by taking the difference between the ¹⁵N R₁ values obtained for the EDTA-Cu²⁺ and EDTA-Zn²⁺ proteins. e, Same as panel c for 28EDTA-Zn²⁺ (blue contours) and 28EDTA-Cu²⁺ (red contours). f, Same as panel d for residues Q32 and A48 in 28EDTA-Zn²⁺ (blue circles/lines) and 28EDTA-Cu²⁺ (red circles/lines).

In Fig. 1c and 1e we show representative small regions of 2D NCO spectra for 8EDTA-Cu²⁺/Zn²⁺ and 28EDTA-Cu²⁺/Zn²⁺ recorded with τ_relax values of 100 μs (reference spectra) and 4 s. While the reference spectra for the corresponding EDTA-Cu²⁺ and Zn²⁺ proteins are effectively indistinguishable from one another and contain all of the expected intense one-bond ¹⁵N-¹³CO correlations, a number of cross-peaks are severely attenuated or altogether missing in spectra recorded for the EDTA-Cu²⁺ proteins with longer relaxation delays (τ_relax ≈ 2-4 s). The most attenuated resonances (for example G9, G14 and T53 in 8EDTA-Cu²⁺ and T25, C28 and Q32 in 28EDTA-Cu²⁺) are invariably associated with residues located in the spatial proximity of the paramagnetic tag.^34,35 This is to be expected based on the Solomon dipolar relaxation mechanism,^24,25 and previously we have demonstrated that most experimental solid-state NMR ¹⁵N PREs and ¹⁵N-Cu²⁺ distances determined in this fashion are in quantitative agreement with the corresponding values predicted using protein structural models based on the WT GB1 fold.^34,35 Fig. 1d and 1f show the complete experimental relaxation trajectories and best fits to decaying single exponentials (i.e., I = A·exp{–R₁ × τ_relax}, where I is the instantaneous cross-peak intensity, A is the peak intensity at τ_relax = 0, and R₁ the ¹⁵N longitudinal relaxation rate constant; the two fit parameters are A and R₁) for representative residues in 8EDTA-Cu²⁺/Zn²⁺ and 28EDTA-Cu²⁺/Zn²⁺, respectively.

Collectively, these experiments yield 231 amide ¹⁵N longitudinal PRE restraints (Supplementary Table S1) for the six paramagnetic GB1 mutants (i.e., an average of ~38 out of 55 possible restraints per mutant or ~4-5 restraints per residue; the remaining PREs could not be determined reliably due to peak overlap in 2D NCO spectra). Approximately half of the PRE restraints (110 of 231) correspond to Γ₁^N values greater than 0.1 s^-1, and were used as is in the course of the protein structure calculations discussed below. The remaining 121 restraints were converted to purely repulsive ‘NOE-type’ distance restraints preventing the associated atoms from approaching closer than 15.1 Å. This was done in order to avoid potential complications with the convergence of the calculated structures, associated with small but detectable effects on the extracted Γ₁^N values stemming from the presence of intermolecular ¹⁵N-Cu²⁺ couplings and secondary protein Cu²⁺ binding sites.³⁶

Validation of the utility of solid-state NMR ¹⁵N PRE restraints for protein structure determination

In order to evaluate the ability of the longitudinal solid-state NMR ¹⁵N PREs to determine the correct protein fold in the absence of traditional dipolar coupling based distance restraints, we performed a set of preliminary, ‘ideal case’ scenario calculations for GB1 in Xplor-NIH³⁹ using protocols where all native sidechains as well as the backbone atoms for regular secondary structure elements were frozen in rigid bodies corresponding to their conformations in the 1.14 Å GB1 X-ray structure^40,41 (PDB entry 2GI9), and the Cys-EDTA-Cu²⁺ sidechain conformations (initially optimized using PRE data and 2GI9 atomic coordinates) were also fixed. The regular secondary structure elements included the α-helix (residues 22-37) and the four β-strands, β1 to β4, spanning amino acids (aa) 2-8, 13-19, 42-46 and 51-55, respectively. The backbone torsion angles for the remaining residues were randomized. Moreover, to enable the simultaneous use of all PRE restraints within the same structure calculation protocol, the Cys-EDTA-Cu²⁺ tags were placed on all six modified residues (even though separate NMR experiments were used to record PRE data for each of the GB1 mutants) with the concurrent disabling of interactions between atoms associated with the different tags.

In Fig. 2a and 2b we show representative sets of 10 lowest energy structures (out of a total of 1000 structures) calculated without and with the use of solid-state NMR longitudinal ¹⁵N PRE restraints, respectively, in addition to the more conventional potential energy terms described in the Methods section. Not surprisingly, when no experimental NMR data were incorporated into the calculations, the lowest energy protein structures obtained in Xplor-NIH are effectively random and show little resemblance to one another or to the GB1 X-ray structure (Fig. 2a). Within this set of 10 lowest energy structures, no structure, including the one displaying the smallest backbone atom (C′, Cα, N and O) coordinate root-mean-square deviation (RMSD) of 3.4 Å relative to 2GI9, correctly predicts the protein fold. Though occasionally (3 times out of 1000 for this dataset) the calculations with no experimental restraints included were able to yield protein structures with the correct GB1 fold (backbone RMSDs versus 2GI9 of ~1.5-2 Å), these ‘correct’ structures were associated with energies that were considerably higher than those obtained for numerous ‘incorrect’ structures having backbone atom RMSDs in the ~3-9 Å range. In stark contrast, analogous calculations which also include the 231 experimental ¹⁵N PRE restraints yield lowest energy protein structures that cluster tightly together, and, most importantly, correspond to the correct GB1 fold with backbone RMSDs of 0.9-1.8 Å relative to 2GI9 (Fig. 2b).

Figure 2. Results of idealized preliminary structure calculations for GB1 in the absence and presence of solid-state NMR longitudinal ¹⁵N paramagnetic relaxation enhancement restraints.

a, Backbone traces (blue) for the 10 lowest energy GB1 structures (out of 1000 total structures), calculated using Xplor-NIH³⁹ in the absence of experimental ¹⁵N PRE restraints. Shown for comparison is the backbone trace (red) corresponding to the 1.14 Å GB1 X-ray structure^40,41 (PDB entry 2GI9). Native sidechain torsion angles and backbone torsion angles for residues in regular secondary structure elements (β1: aa 2-8; β2: aa 13-19; α: aa 22-37; β3: aa 42-46; β4: aa 51-55) were fixed to their X-ray structure values during the calculations, and the remaining backbone torsion angles were randomized (a detailed description of the structure calculations is provided in the Methods section). The backbone coordinates of the 10 lowest energy structures show RMSDs ranging from 3.4 to 9.1 Å relative to the X-ray structure. b, Same as panel a except that 231 ¹⁵N PRE restraints recorded for the six paramagnetic GB1 mutants were additionally included in the structure calculations. The backbone coordinates of the 10 lowest energy structures show RMSDs relative to 2GI9 ranging from 0.9 to 1.8 Å. c,d, Plots of total energy vs. backbone atom coordinate RMSD from the 2GI9 reference X-ray structure for each of the 1000 structures calculated without (c) and with (d) the use of the ¹⁵N PRE restraints. In each plot, the 10 lowest energy structures are indicated by red circles.

The complete results for both sets of calculations employing large ensembles of 1000 random starting protein structures are summarized in Fig. 2c and 2d. These data clearly illustrate that in the absence of ¹⁵N PRE restraints there is effectively no correlation between the total energy of a particular protein structure obtained in Xplor-NIH and that structure displaying the correct GB1 fold (Fig. 2c). Indeed, nearly all structures obtained in this manner bear little resemblance to the reference GB1 X-ray structure. On the other hand, the addition of ¹⁵N PRE restraints to the structure calculation protocol leads to a funnel-like effect where a relatively strong correlation emerges between the total energy of a calculated structure and its RMSD relative to the 2GI9 backbone atom coordinates (Fig. 2d). While the convergence properties of these calculations may not be ideal and the calculation procedure generates multiple incorrect protein structures, it is important to note that all of these incorrect structures have high energies and can be readily identified. Most significantly, however, the lowest energy structures (associated with total energies of ~3000 kcal/mol or less in this case; the 10 lowest energy structures are indicated by red circles in Fig. 2c and 2d) all possess similar backbone folds that also closely match the GB1 X-ray structure (Fig. 2b).

De novo determination of the GB1 backbone fold

Having established the utility of solid-state NMR ¹⁵N PRE restraints for protein structure calculations, we proceeded to investigate whether the fold of GB1 could be determined in a de novo manner by using only ¹⁵N PRE data (Supplementary Table S1) and standard solid-state NMR chemical shift based backbone dihedral angle restraints for WT GB1 (Supplementary Table S2) to define local secondary structure. As described in detail in the Methods section, these realistic de novo calculations consisted of a two stage protocol. In the initial stage, backbone atoms for residues comprising regular secondary structure elements (identified within the torsion angle likelihood obtained from shifts and sequence similarity, TALOS+, software⁴² as having α or β conformation with greater than 85% confidence) were frozen in rigid bodies with their dihedral angles fixed to the ideal TALOS+ predicted values, while all other backbone and sidechain torsion angles (including the Cys-EDTA-Cu²⁺ tags) were randomized. We found that fixing the TALOS+ identified secondary structure regions during this initial stage resulted in significantly improved convergence relative to the standard protocols which allow more degrees of freedom, as well as improved accuracy of the final calculated structures. The initial calculation stage was followed by a second stage, in which the 10 lowest energy structures from the initial calculations (indicated by red circles in Fig. 3a) were further refined using 10 different sets of randomized velocities in a protocol that allowed all sidechains to move as well as all backbone dihedral degrees of freedom constrained only by the TALOS+ dihedral angle potential with minimum dihedral angle uncertainties of ±20°, to yield a final set of 100 structures. From this set, the 20 lowest energy structures, shown in Fig. 3b and indicated by yellow circles in Fig. 3a, were used to obtain a regularized mean structure.

Figure 3. De novo calculation of the GB1 fold using solid-state NMR longitudinal ¹⁵N paramagnetic relaxation enhancement restraints.

a, Plot of total energy vs. backbone atom RMSD from the reference X-ray structure obtained during the course of the de novo calculations. The 10 lowest energy structures from the initial calculations are indicated by red circles. These 10 structures were further refined as described in the text to yield a set of 100 structures. From this final set, the 20 lowest energy structures indicated by yellow circles were used to obtain the regularized mean structure (magenta circle). b, Backbone traces for the 20 lowest energy GB1 structures (blue), corresponding to the yellow circles in panel a, and the reference X-ray structure (red). c, Comparison of the GB1 X-ray structure with the regularized mean solid-state NMR backbone fold determined using the realistic, de novo calculations. The coordinates of the mean NMR structure (blue) show a backbone atom RMSD of 1.8 Å and an all heavy atom RMSD of 2.7 Å relative to the X-ray structure (red). The gray cloud is a reweighted atomic probability map⁵⁰ of the final ensemble of 20 lowest energy NMR structures shown in panel b plotted at 15% of maximum value, representing the conformational space occupied by the associated backbone atoms. Structure calculations were performed as described in the Methods section using 231 longitudinal ¹⁵N PRE restraints recorded for six paramagnetic GB1 analogs and solid-state NMR chemical shift-based dihedral angle restraints for WT GB1 obtained using TALOS+.⁴²

Remarkably, using these largely unrestricted de novo calculations, which did not utilize any conventional dipolar coupling based interatomic distance restraints or structural information derived from X-ray diffraction data, we were able to determine a backbone fold for GB1 that is in good agreement with the 1.14 Å X-ray structure (Fig. 3c; structure indicated by the magenta circle in Fig. 3a). The mean solid-state NMR structure obtained in this manner (blue) displays a backbone atom RMSD of 1.8 Å and an all heavy atom RMSD (excluding sidechains of residues 8, 19, 28, 42, 46 and 53) of 2.7 Å relative to the 2GI9 reference structure (red), and the backbone atoms for the vast majority of residues in the X-ray structure (with exception of several aa located in the loop regions or near the N-terminus) fall within the conformational space occupied by the ensemble of the 20 lowest energy conformers (gray cloud). Finally, in the course of these calculations we have also considered the possible influence of Cys-EDTA-Cu²⁺ sidechain disorder on the quality of the derived structures. The PRE refinement facilities within Xplor-NIH allow such structural heterogeneity to be modeled using ensembles of several sidechains, by either representing the PRE as a sum of contributions from each ensemble member (corresponding to slow interconversion between ensemble members) or 1/r⁶ averaging of the different ensemble members (for fast interconversion), and both approaches were attempted using ensembles of two and three Cys-EDTA-Cu²⁺ tags. We found that the use of such ensembles did not improve the results relative to using a single Cys-EDTA-Cu²⁺ conformer, presumably due to the presence of additional degrees of freedom for which there are insufficient data in this study.

Discussion

Notwithstanding the tremendous current progress,^5-19 the routine determination of protein structures by solid-state NMR remains a formidable task mainly due to challenges associated with the detection of large numbers of correlations that report on >5 Å internuclear distances. Measurements of such long-distance restraints in paramagnetic proteins, including PREs^33,34 and pseudocontact shifts (PCS),^30,31 have the potential to significantly accelerate and enhance solid-state NMR protein structure elucidation efforts. In fact, the utility of paramagnetic restraints of this type was recently illustrated by Bertini and co-workers for a 159-residue (~17.6 kDa) native metalloprotein, cobalt(II)-substituted matrix metalloproteinase 12,^31,32 where over 300 ¹³C PCS restraints were used in conjunction with ~300³¹ and ~800³² internuclear distances obtained from PDSD/DARR, CHHC and PAR experiments to arrive at 3D protein structures.

The approach toward global protein fold determination described here utilizes PRE restraints recorded for structural analogs of the protein of interest containing covalently-linked paramagnetic tags, and is readily applicable to a wide variety of protein molecules in the solid phase, including natively diamagnetic proteins. A major advantage of this approach, in addition to the fact that nuclear PREs yield almost exclusively structurally-relevant inter-residue restraints generally corresponding to >10 Å distances, is that these PRE restraints are very straightforward to extract by monitoring cross-peak intensities as a function of a relaxation delay in the simplest 2D or 3D solid-state NMR chemical shift correlation spectra that contain a minimum number of signals arising from adjacent, strongly dipolar coupled nuclei in the protein. As such, this methodology is pertinent to larger protein systems. While the implementation of this method requires the preparation of several point mutants of the protein under study, such biochemical manipulations are routine nowadays. It is also important to note that although the known 3D structure of GB1 was helpful in identifying suitable sites for introduction of the Cys-EDTA-Cu²⁺ tags in this study, the incorporation of such tags into proteins of unknown structure, with minimal influence on the backbone fold,³⁸ should be readily implementable using an approach discussed by Battiste and Wagner²⁷ that utilizes secondary structure information obtained from chemical shifts for the WT protein and the analysis of hydrophilicity patterns to identify the most probable solvent-accessible residues.⁴³

The current study demonstrates that ~4-5 longitudinal amide ¹⁵N PRE restraints per residue, collected using a condensed NMR data acquisition approach³⁵ for a set of six Cys-EDTA-Cu²⁺ mutants available in small quantities (~150-200 nanomoles of ¹³C,¹⁵N-labeled protein per sample), are sufficient to obtain a protein backbone fold for GB1 that is in close agreement with the X-ray structure without the use of any conventional internuclear distance restraints. Although the global protein fold determined in this manner does not correspond to the highest achievable resolution structure, it can be derived very rapidly and provides a reasonable structural model that is likely to be sufficient for many applications. Moreover, such a PRE-based model can serve as a major aid for resolving assignment ambiguities in conventional dipolar coupling based solid-state NMR spectra, and can readily be further refined to higher resolution, if desired, by incorporating additional interatomic distance restraints or by combining the PRE restraints with more advanced fragment-based chemical shift/molecular mechanics (CSMM) based structure calculation protocols such as CHESHIRE¹³ or CS-ROSETTA.¹⁴ It should be noted that the structure of GB1 has, in fact, been successfully solved (and to higher resolution) using the CHESHIRE approach with chemical shifts as the sole experimental input,¹³ whereas in this work we only extracted broad backbone torsion angle ranges from chemical shift data. While such CSMM methods, which utilize molecular mechanics force fields to obtain the proper protein fold, have chalked up an impressive record of correctly determined protein structures and we strongly advocate their use, they are also known to fail at times due to inadequacies of the MM force fields and the fact that chemical shift data contain essentially no long-distance information. In contrast, the PRE-based approach reported here uses direct distance restraints simply related to experimental observables, and thus serves as an independent means to solve or validate a protein fold.

Importantly, the number of paramagnetic-based structural restraints in these studies can be dramatically increased, by at least ~2-3-fold, with minimal effort by measuring other types of PREs, including longitudinal backbone and sidechain ¹³C PREs and transverse PREs for the different nuclei, in the same protein samples, as well as PCS restraints for ¹³C, ¹⁵N and potentially ¹H nuclei in analogous Cys-EDTA-Co²⁺ samples. This is expected to substantially enhance the resolution of the derived structures, and bodes well for the extension of this paramagnetic solid-state NMR methodology to larger proteins for which a significant fraction of resonances can be assigned. Indeed, such sequential resonance assignments in larger systems may be facilitated by using spectral editing approaches that take advantage of the presence of the paramagnetic tags.

Methods

Sample preparation

Plasmid cDNAs encoding for N8C, E19C, K28C, E42C, D46C or T53C mutants were constructed as described previously,³³ using T2Q-GB1 cDNA (referred to as GB1) and Stratagene QuikChange II site-directed mutagenesis protocol. Proteins were expressed in E. coli BL21(DE3) with Luria-Bertani medium or M9 minimal medium containing 1 g/L ¹⁵NH₄Cl and 3 g/L ¹³C-glucose (Cambridge Isotope Laboratories) and purified by gel filtration chromatography.^33,34 Cysteines were reacted with the sulfhydryl-specific reagent N-[S-(2-pyridylthio)cysteaminyl]EDTA³⁷ (Toronto Research Chemicals), pre-loaded with 1.1 equivalents of Cu²⁺ or Zn²⁺ (diamagnetic control). Protein microcrystals for solid-state NMR were prepared by co-precipitating the ¹³C,¹⁵N-EDTA-Cu²⁺/Zn²⁺ proteins with natural abundance GB1 in a 1:3 molar ratio using microdialysis at 4 °C and a 2:1:1 (v/v) 2-methylpentane-2,4-diol/isopropanol/deionized water precipitant solution.^34,36 Samples, each containing ~1.0-1.2 mg (~150-200 nanomoles) of ¹³C,¹⁵N-labeled protein, were packed into 1.6 mm zirconia rotors (Agilent Technologies) by centrifugation.

NMR spectroscopy

NMR spectra were recorded on a 500 MHz Varian spectrometer equipped with a 1.6 mm FastMAS™ probe. MAS rate and sample temperature were regulated at 40,000 ± 20 Hz and ~5 °C, respectively. Residue-specific amide ¹⁵N longitudinal relaxation rate constants, R₁, for the EDTA-Cu²⁺/Zn²⁺ GB1 mutants were determined from series of 2D NCO spectra recorded using the pulse scheme in Fig. 1a with relaxation delays, τ_relax, of 100 μs to 4 s. Spectra were collected with acquisition times of 25.6 ms (t₁) and 30 ms (t₂) and recycle delays of 0.4 s and 1.3 s for EDTA-Cu²⁺ and EDTA-Zn²⁺ proteins, respectively. The total experiment time required to record ¹⁵N R₁ data for all EDTA-Cu²⁺/Zn²⁺ GB1 mutants was ~18 days. Spectra were processed using NMRPipe⁴⁴ and analyzed with home-built software (available at http://code.google.com/p/nmrglue). ¹⁵N PREs, Γ₁^N, were calculated as Γ₁^N = R₁(Cu²⁺) – R₁(Zn²⁺), where ¹⁵N R₁ values for Cu²⁺ and Zn²⁺ proteins were obtained by fitting residue-specific relaxation trajectories to decaying single exponentials.

Structure calculations

Structure calculations were carried out in Xplor-NIH³⁹ with a protocol in which backbone atoms of regular secondary structure elements were frozen in rigid bodies corresponding to their X-ray (during initial calculations in Fig. 2) or ideal target conformations as predicted from TALOS+⁴² (during the realistic de novo calculations in Fig. 3). Regions of secondary structure were identified by inspection of the GB1 X-ray structure^40,41 (PDB entry 2GI9) for the initial calculations and from TALOS+ hits predicted with >85% confidence in the α or β Ramachandran regions for the realistic calculations. The remaining backbone torsion angles were randomized. Sidechain torsion angles were fixed in their X-ray conformation for the initial calculations and randomized for the realistic calculations. The EDTA-Cu²⁺ tags were present on all six residues which were modified, but inter-residue interactions of the associated atoms were disabled. In the initial calculations, conformations of the EDTA-Cu²⁺ sidechains were first optimized using PRE data and the 2GI9 coordinates and held fixed during structure calculations. For the realistic calculations, EDTA-Cu²⁺ sidechains were treated as other sidechains with torsion angles randomized.

PRE restraints consisted of explicit restraints using the PREPot term⁴⁵ with an electron correlation time of 3 ns²⁵ for Γ ^N₁ values above a cutoff of 0.1 s^-1 (Supplementary Table S1). Smaller PREs were included using a purely repulsive ‘NOE-type’ term restraining the associated ¹⁵N-Cu²⁺ distances to values >15.1 Å. TALOS+ was used to derive 102 (of 110 possible) backbone torsion angle restraints from GB1 ¹³C and ¹⁵N solid-state NMR chemical shifts (Supplementary Table S2). The radius of gyration term⁴⁶ was used to achieve appropriate protein packing density. Additional knowledge-based energy terms included the torsion angle potential of mean force,⁴⁷ the hydrogen bond potential of mean force,⁴⁸ and the low resolution residue contact term.⁴⁹ Standard bond, bond angle and improper torsion angle restraints were used to maintain proper covalent geometry, and a repulsive quartic van der Waals term used to prevent atomic overlap. During calculations in which EDTA-Cu²⁺ sidechains were allowed to move, the associated dihedral angles were restrained by a dihedral energy term.

The protocol consisted of initial conjugate gradient minimization without the PRE and repulsive distance terms, followed by minimization including all energy terms. This was followed by variable step-size dynamics for the smaller of 500 ps or 20,000 steps at 3000 K. Next, simulated annealing was performed from 3000 K to 25 K in 12.5 K increments, and at each temperature dynamics for the smaller of 1.6 ps or 400 steps was run. During simulated annealing the force constants of various energy terms were ramped to their final values as specified in Supplementary Table S3. For the realistic calculations, the initial structure calculation was followed by an additional calculation stage in which the 10 lowest energy structures from the initial calculation were refined using 10 different sets of randomized velocities (for a total of 100 structures) in a protocol which allowed all backbone dihedral degrees of freedom and omitted the initial minimization step. A regularized mean structure was calculated from the 20 lowest energy refined structures.