Accurate Backbone ¹³C and ¹⁵N Chemical Shift Tensors in Galectin-3 by MAS NMR and QM/MM: Details of Structure and Environment Matter

Abstract

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate ¹³C and ¹⁵N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for ¹⁵N atoms. Here we compare experimentally determined backbone ¹³C^α and ¹⁵N^H chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed ¹⁵N^H chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.

INTRODUCTION

Magic angle spinning (MAS) solid-state NMR spectroscopy is a powerful tool for the characterization of structure and dynamics of biological assemblies at atomic resolution.^[1] The most widely used NMR observable is the chemical shift since it is intricately dependent on the surrounding environment of the nucleus, influenced by conformation, motions, hydrogen bonding and electrostatic interactions.^[2–4] In solution, only isotropic chemical shifts can be extracted from the NMR spectrum, while in the solid state the anisotropic components of the chemical shift tensor (CST) can also be obtained. Importantly, chemical shift anisotropy (CSA) parameters can be used during the refinement stages of a protein structure determination to improve the accuracy of solid-state NMR structures.^[5]

Assessment of protein chemical shifts with respect to structure either relies on empirical formulae derived from databases of experimental chemical shifts or quantum mechanical (QM) methods, with the latter, in principle, permitting accurate calculations of CSTs.^[6–8] QM calculations for different levels of theory and molecular models have enjoyed varying degrees of success, although they remain particularly challenging for amide protons, carbonyl, and amide nitrogen atoms.^[9–12] Commonly, Density Functional Theory (DFT) is employed; however, DFT scales as N⁴ with the number of atoms, rendering it computationally too expensive for all but small systems. For chemical shift calculations of proteins, most frequently the protein is partitioned into smaller fragments that capture the local environment around the atoms under consideration. Fragments (clusters) are either selected based on simple distance criteria, or can be judiciously constructed to capture interactions that are important for the system of interest.^[13–15] Naturally, truncation of the protein into smaller fragments inevitably results in loss of accuracy.^{[16, 17]} Another approach uses hybrid quantum mechanics/molecular mechanics (QM/MM), which permits balancing the computational demands and the attainable accuracy. In essence, this method entails treating the region of interest quantum mechanically and a larger region around it with molecular mechanics. This approach can be implemented in an automated manner, (AF-QM/MM),^[18] where the individual calculations are parallelizable. Therefore, AF-QM/MM has unique advantages and can be easily implemented into protein structure refinement algorithms.

We previously investigated the accuracy of chemical shifts calculated by various quantum mechanical methods, exploring the dependence on the level of theory (functional and basis set), the nature and the size of the molecular fragment, and the inclusion of crystallographic water molecules.^[10–12] We found that prediction of accurate backbone ¹⁵N^H chemical shifts is still challenging, given their complex relationship with a variety of different factors, most notably hydrogen bonding. Here, we expanded our earlier studies and systematically investigated the accuracy of ¹⁵N^H and ¹³C^α chemical shift predictions for the carbohydrate recognition domain of galectin-3 (termed “galectin-3C” in the remainder of this text), a β-sheet 15.7 kDa protein, containing 10 anti-parallel β-strands, a small, 5-residue helix and several loops.^[19] Galectin-3C is ideally suited as a benchmark protein since it has been extensively characterized by solution NMR,^{[20, 21]} ~40 high-resolution crystal structures are available ^{[19, 22–27]} as well as a neutron diffraction structure at 1.7 Å resolution that permitted placing hydrogen atoms.^[27] Furthermore and importantly, we acquired extensive solid-state NMR experimental data for the crystal form that was used for both the X-ray and neutron diffraction studies. We measured ¹³C^α and ¹⁵N^H CSTs for microcrystalline galectin-3C in MAS NMR experiments and compared the measured values with CSTs calculated based on the high-resolution X-ray and neutron diffraction structures. We systematically examined geometry optimization protocols in both the QM and MM regions of the AF-QM/MM calculations as well as tested the influence of solvent dynamics for arriving at the best agreement between the computed and experimentally measured chemical shift tensor values. A high level of agreement between computed and experimentally determined ¹³C^α CSA values was found, similar to our previous results for isotropic ¹³C^α shifts in the same system.^[11] For ¹⁵N^H CSAs, the agreement is not as satisfying, but can be significantly improved by i) using the most up to date force fields (for example, Amber ff15ipq) and ii) taking solvent dynamics into account. As a result, we achieved the best to date agreement between experimental and calculated ¹⁵N^H CSTs. Therefore, we are confident that implementation of quantum mechanical CST calculations into protein structure refinement algorithms will yield improved MAS-derived protein structures in the future.

RESULTS AND DISCUSSION

Experimental ¹³C^α and ¹⁵N^H CSA Tensors

We obtained very high resolution 2D and 3D MAS NMR spectra for galectin-3C, which permitted complete resonance assignments for 136 out of 138 residues,^[11] and the determination of 73 ¹³C^α and 77 ¹⁵N^H site-specific chemical shift tensors was achieved using 3D RNCSA experiments.^[28] Representative CSA lineshapes are shown in Figure 1. The values for both ¹³C^α and ¹⁵N^H CSTs are consistent with those in other rigid microcrystalline proteins such as the B1 domain of protein G (GB1),^[29] E. coli thioredoxin,^[30] dynein light chain 8 LC8,^[30] CAP-Gly domain of the mammalian dynactin,^[31] and Oscillatoria agardhii agglutinin (OAA).^[12] Since galectin-3C is a primarily β-sheet protein, the ¹³C^α CSTs are all associated with residues in β-strands or loops/turns regions, and the values are indicative for this local geometry. In contrast to ¹³C^α, ¹⁵N^H CSTs are significantly influenced by hydrogen bonding, long-range electrostatics and the solvent environment, as reported recently for microcrystalline E. coli thioredoxin reassemblies, LC8, and CAP-Gly. Similar findings emerged for galectin-3C, for which an average ¹⁵N^H isotropic chemical shift for non-hydrogen bonded residues of 118.6 ppm is observed, while for hydrogen-bonded residues this value is 121.6 ppm. The same trend is seen for the principal components of the tensor (Table S1 of Supporting Information). The systematic effect of hydrogen bonding on experimental ¹⁵N^H CSTs is an important effect to consider when assessing the tensors calculated by QM/MM and attention has to be paid that distinct structural features have to be implemented for reliably using calculated CSTs in structure refinement protocols.

Figure 1.

a) Structure of galectin-3C (PDB ID: 3ZSJ), indicating one representative region of 3.5 Å sphere. The central residue (ball and stick representation) and a boundary region (wireframe representation) is depicted. The remainder of the protein is represented by point charges, illustrated by the mesh around the ribbon structure. b) The NCA 2D spectrum (left) and representative experimental (black) and simulated (magenta) ¹³C^α and ¹⁵N^H CSA lineshapes (right) for residues I240 and S244. Experimental CSA lineshapes were extracted from the corresponding peaks in the 2D NCA spectrum.

Backbone ¹³C^α Chemical Shift Tensors from QM/MM

Comparing the ¹³C^α experimental CSA values to those calculated by QM/MM for the 0.86 Å resolution X-ray crystal structure (PDB ID: 3ZSJ) of lactose-bound galectin-3C,^[19] excellent agreement was observed (Figure 2). The average relative error (i.e. the absolute error compared to the experimental ¹³C^α CSA magnitude) is only 0.1, suggesting that the region treated at the quantum level in the AF-NMR fragments faithfully reproduces the ¹³C^α CSA. Since the ¹³C^α CST is predominantly influenced by local geometry, the 3.5 Å cutoff distance is sufficient to represent the core of each fragment. Figure 2a shows the differences between calculated and measured ¹³C^α reduced anisotropy, Δδ_σ (δ_σ = δ₁₁ − δ_iso), plotted versus residue number. The accuracy of the calculated ¹³C^α CSTs appears similar throughout the entire chain. The significant outliers are residues with Δδ_σ > 2 ppm, which represents the approximate maximum error in the experimental measurement. Such error is typically no greater than 10% of the δ_σ value for CSTs measured using these RNCSA-based pulse sequences. For fifteen residues with Δδ_σ > 2 ppm, the largest differences come from glycine residues. This may be related to dynamics.^{[32, 33]} If residues undergo motions on nano- to microsecond timescales, the tensors are dynamically averaged, and accurate calculations require an integrated MD-QM/MM approach. This was previously noted for HIV-1 CA capsid protein assemblies.^[32] However, galectin-3C does not exhibit dynamics on these timescales, apart from terminal residues, since the dipolar order parameters for both ¹H-¹³C and ¹H-¹⁵N never fall below 0.9.^[11] The differences between calculated and observed principal components for δ₂₂ and δ₃₃ are very similar, while those for δ₁₁ are smaller. Specifically, the root-mean-square errors (RMSEs) are 3.9, 4.7, and 4.8 ppm for δ₁₁, δ₂₂, and δ₃₃, respectively, and are summarized in Table S2 of the Supporting Information. Naturally, the exact tensor orientations in the molecular frame vary depending on residue type and local backbone conformation. In addition, the position of the hydrogen atoms will also affect the tensor orientation. Here, the H^α atoms were positioned using Amber ff99sb force field libraries and this will affect the QM/MM calculations, i.e., may contribute to the noted differences between the experimental and QM/MM ¹³C^α chemical shift tensor orientations.

Figure 2.

¹³C^α chemical shift tensors for galectin-3C from MAS NMR experiments and QM/MM calculations using the X-ray structure (PDB ID: 3ZSJ) as input coordinates. a) Absolute difference between QM/MM calculated and MAS NMR ¹³C^α reduced anisotropy parameters, plotted versus residue number. β-sheet secondary structure is indicated with grey bars, and loop regions are shown in white. bars, and loop regions are shown in white. Residues exhibiting differences larger than 6 ppm between experimental and calculated ¹⁵N^H δ_σ are labeled in magenta. N^H atoms that are involved in H-bonds within the protein are labeled with a magenta asterisk and those that hydrogen bond to a crystallographic water molecule are labeled with a black asterisk. b) Linear correlation between the experimental and QM/MM calculated ¹⁵N^H CST principal components. For comparison, a trend line representing perfect agreement between theory and experiment is shown as the black solid line c) Residues (in magenta stick representation) with differences >6 ppm between experimental and calculated ¹⁵N^H CST principal component values mapped on the galectin-3C structure (grey ribbon representation).

Backbone ¹⁵N^H Chemical Shift Tensors from QM/MM

The role of input coordinates

The comparison between the experimental backbone ¹⁵N^H CSTs and those calculated by QM/MM using the X-ray structure (PDB ID: 3ZSJ) as input coordinates is shown in Figure 3. Here, large differences are noted and 17 out of the 21 outliers exhibit errors Δδ_σ > 6 ppm. The corresponding RMSEs for all tensor components are listed in Table S2 of the Supporting Information. Interestingly, all of these outliers are associated with β-strands. 15 out of the 21 are involved in hydrogen bonding, donating a H-bond to a backbone CO in the anti-parallel β-sheet. Two other ¹⁵N^H CSTs which exhibit large differences are N119 and Y247. Both of these amide protons hydrogen-bond to a crystallographic water molecule. These data suggest that the effect of hydrogen-bonding is not correctly taken into account in the QM/MM calculations based on modeled hydrogen positions. In addition, it may be the case that the overall effect of the hydrogen bond network in β-sheets, in which each hydrogen bonding unit affects its neighbors, cannot be accurately accounted for by including only those individual hydrogen-bond partners that are contained in the 3.5 Å sphere fragment. Thus, it seems insufficient to treat a single hydrogen bond in isolation in CSA calculations for deriving accurate ¹⁵N^H CSTs. Indeed, a previous computational study by Viswanathan et al. showed that hydrogen bonding enthalpy is more favorable when extended β-strands self-associate to form β-sheets,^[34] suggesting that the fragments for AF-QM/MM calculations do not correctly capture the effects imparted by extended β-sheets.

Figure 3.

¹⁵N^H chemical shift tensors for galectin-3C from MAS NMR experiments and QM/MM calculations using the X-ray structure (PDB ID: 3ZSJ) as input coordinates. a) Absolute difference between QM/MM calculated and MAS NMR ¹⁵N^Hreduced anisotropy parameter, plotted versus residue number. β-sheet secondary structure is indicated with grey bars, and loop regions are shown in white. Residues exhibiting differences larger than 6 ppm between experimental and calculated ¹⁵N^H δ_σ are labeled in magenta. N^H atoms that are involved in H-bonds within the protein are labeled with a magenta asterisk and those that hydrogen bond to a crystallographic water molecule are labeled with a black asterisk. b) Linear correlation between the experimental and QM/MM calculated ¹⁵N^HCST principal components. For comparison, a trend line representing perfect agreement between theory and experiment is shown by the black solid line c) Residues (in magenta stick representation) with differences >6 ppm between experimental and calculated ¹⁵N^H CST principal component values mapped on the galectin-3C structure (grey ribbon representation).

To test whether the accuracy of the calculated ¹⁵N^H CSTs can be improved by including the experimentally determined hydrogen atom positions, we used the coordinates of the 1.7 Å resolution neutron structure of galectin-3C (PDB ID: 6EYM). Following the generation of fragments for each residue, geometry optimization by DFT was carried out to optimize the ¹H^N position. The optimization protocols were systematically tested for a set of 20 residues (representing residues with both the best and worst agreement), and the results were compared to the equivalent calculations using the Amber-minimized X-ray crystal structure. As can be noted, optimization of hydrogen atom positions in the neutron structure fragments by DFT only resulted in a marginal improvement of the calculated ¹⁵N^H CSTs (Figure 4f and Table 1). The average difference between the N- H bond length in the Amber-minimized X-ray crystal structure and the DFT optimized neutron structure is 0.01–0.02 Å. The results of these calculations are in accord with our previous work,^[12] which found that such a difference in the N-H bond length will contribute <2 ppm towards the magnitude of the reduced ¹⁵N anisotropy.

Figure 4.

Summary of calculation strategies for ¹⁵N^H CSTs in galectin-3C. (a-d) Calculations for T133 as an example. QM/MM calculations were performed using two different force fields, Amber ff99sb (a) and ff15ipq (c). (b) Effect of DFT optimization of the hydrogen atom positions based on the neutron structure. (d) Solvent dynamics using solvated snapshots from a 40 ps MD simulation. (e-h) Linear correlation between experimental and calculated ¹⁵N^H δ_σ from QM/MM with ff99sb (e) and ff15ipq (g), DFT optimized ¹H^N positions from the neutron structure (f), and MD-QM/MM using ff15ipq and solvated snapshots (h). (i-l) Linear correlation between experimental and calculation ¹⁵N^H CST principal component values from QM/MM with ff99sb (i) and ff15ipq (k), DFT optimized ¹H^N positions from the neutron structure (j), and MD-QM/MM using ff15ipq and solvated snapshots (l). For comparison, a trend line representing perfect agreement between theory and experiment is shown as black solid lines.

TABLE 1.

Summary of ¹³C and ¹⁵N CSA tensors calculations for a selected set of 20 residues in galectin-3C for (representing the best and worst agreement with experiment).

		QM/MM (ff99sb)		QM/MM (ff15ipq)		DFT optimized		MD-QM/MM (with ff15ipq)
		m	R2	m	R2	m	R2	m	R2
Cα	δiso	0.99	0.93	0.95	0.88	1.02	0.97	0.99	0.96
	δσ	1.07	0.46	1.08	0.27	1.03	0.61	1.09	0.43
NH	δiso	1.10	0.82	0.97	0.74	1.12	0.56	0.55	0.26
	δσ	0.51	0.22	0.67	0.54	0.73	0.31	0.92	0.57

However, for some residues, the calculated ¹⁵N δ_σ values differ by >2 ppm between the two optimization methods, suggesting the presence of additional contributions. In these cases, inspection of individual fragments is instructive: For L131, the number and nature of atoms in the 3.5 Å sphere are identical for both structures, although we observe a reduction in Δδ_σ of 10.2 ppm when using DFT to optimize the geometry of the neutron structure fragment (Figure S1). Upon close inspection we find that the ¹⁵N^H and ¹H^N positions in the central residue are slightly different between the two fragments, which could affect the ¹⁵N CSA, however unlikely to such a large degree. In addition, the i-1 residue in the fragment, M130, exhibits a different sidechain conformation in the two structures. In the X-ray structure, two sidechain conformers (A and B) with different occupancies are modeled for M130. Conformer A has an occupancy of 0.7 and this conformer is present in the DFT optimized neutron structure fragment. In the Amber minimized X-ray fragment, the side chain of M130 is found in the low occupancy (0.3) conformer B. Since conformer A, the one in the DFT optimized neutron structure fragment, yields better agreement between experiment and calculation it may be likely that this side chain conformation is the predominant one in the microcrystalline sample used for MAS NMR. Similar detailed differences between the DFT optimized neutron and the Amber minimized structures apply to other fragments. For all fragments, the central core atom positions are very similar, while other atoms in the surrounding region can occupy different positions. Such differences may be due to the Amber minimization protocol, while the differences in hydrogen atom positions may result from the DFT optimization. As a result, we suggest that reliable ¹⁵N^H CSA calculations require not only accurate geometries for the core residue in the fragments, but also for the entire surrounding region.

The role of MM force field

In order to assess how the choice of the force field in the initial structure equilibration influences the input coordinates and the accuracy of the calculated ¹⁵N^H CSA, we applied the Amber force field ff15ipq^[35] to minimize the X-ray structure. Unlike other force fields, ff15ipq is re-parameterized to better capture the conformational propensities and preferences for each amino acid type. We hypothesized that the resulting energy-minimized structure would be a better starting structure for the AF-QM/MM calculations. Results obtained with the ff99sb and ff15ipq energy-minimized structures for the identical set of 20 residues are shown in Figure 4g and Table 1. The agreement between experimental and calculated ¹⁵N^H CSA is improved, with an increase in R² value from 0.22 (ff99sb) to 0.54 (ff15ipq). The improvement using a superior force field is more significant than using DFT to optimize ¹H^N positions in the neutron crystal structure. As pointed out above, manual inspection of the fragment geometries revealed the occasional difference in side chain orientation. In general, however, it is clear the details of the force field generating the input structure clearly influence the calculated CSA values.

For the calculations performed using ff99sb (Figure 4i), there is a systematic offset of the δ₁₁ component, which is approximately aligned with the N-H bond vector in the molecular frame. The systematic offset for the δ₁₁ component is eliminated in the calculations performed using ff15ipq (Figure 4k). Experimental and calculated δ₂₂ and δ₃₃ components show no significant differences for ff99sb versus ff15ipq minimized structures. As a result, inaccuracies in the δ₁₁ component will affect the ¹⁵N^H CSA. When comparing the minimized structures, the heavy atom RMSD between the minimized structures and the x-ray crystal structure is 0.06 and 0.03 Å for the calculations performed with ff99sb and ff15ipq respectively. Therefore, it is likely that ff15ipq is more reliable in capturing hydrogen bonding interactions (which directly affect δ₁₁), due to its implicitly polarized charge model. Taken together, it is clear that the ¹⁵N^H CST is influenced by multiple factors that must be carefully and accurately accounted for in order to achieve high levels of agreement between theory and experiment.

Inclusion of Solvent Dynamics from MD-QM/MM Increases Accuracy of ¹⁵N^H Chemical Shift Tensors

Finally, we also evaluated the effect of including solvent dynamics in the QM/MM calculations. Within a protein crystal, water molecules are dynamic on the picosecond timescale^[36] and it is not sufficient to include static crystallographic water molecules. We tested the role of solvent dynamics by performing a 40 picosecond molecular dynamics simulation in explicit solvent using the ff15ipq force field. Coordinate files were generated every 2 picoseconds, and a AF-QM/MM calculation was performed for each snapshot. After 40 picoseconds, the ¹⁵N^H CSA values were averaged to generate an “ensemble-averaged” value. The results of these calculations are summarized in Figure 4h and Table 1. As can be appreciated, this methodology yielded the most accurate results to date, with a correlation coefficient close to 1 (0.92) and an R² value equal to 0.57. Since galectin-3C does not exhibit large amplitude motions on the nano- to micro-second time scale, this improvement is due to the combination of using the most up-to-date force field as well as including solvent dynamics and short time scale conformational dynamics. The heavy atom RMSD between the structure snapshots throughout the MD trajectory varies from 0.5 Å to 0.8 Å, which is higher than for the static structures minimized from ff99sb and ff15ipq. However, throughout the trajectory, there is no correlation between RMSD and accuracy of the computed CSTs. Similar to the calculations based on the static ff15ipq refined structure, the δ₁₁ component does not exhibit a systematic offset. Additionally, the correlation between the experimental and calculated δ₃₃ component is also improved. Since the δ₃₃ component is also dependent on hydrogen bonding, it is important to represent these interactions correctly. For example, for residues located in loop regions, the simulation with explicit solvent indicates that the carbonyl group of the preceding residue forms a hydrogen bond with a water molecule. This interaction persists throughout the duration of the MD simulation, influencing the local environment in the peptide plane and modulating the δ₃₃ component of the CST. Thus, the modest improvement observed in the simulation with explicit solvent is readily accounted for. However, we also note that, while the agreements of Δδ_σ and the underlying principal components are all improved, the agreement of the isotropic chemical shift (δ_iso) becomes worse. Maybe the good agreement for δ_iso using the ff99sb-minimized X-ray structure is due to cancellation of errors in the principal components.

Taken together, our findings demonstrate that using improved force fields with the inclusion of solvent dynamics, significant improvements in accuracy of ¹⁵N^H CSA calculations are obtained. Importantly, our calculations were inexpensive with regard to computing power; the substitution of the ff99sb force field by ff15ipq added no additional computational time and 40 picoseconds molecular dynamics simulation are routinely accessible. Therefore, this approach is cheap and easy to implement into NMR structure refinement protocols.

While considerable improvements were seen using the above approach, we did not evaluate the effects of long-range electrostatics, currently modeled using point charges in the MM region. Since point charges directly affect the QM sub-system, their incorrect handling may contribute to errors in ¹⁵N^H CSA calculations. Using polarizable force fields allows for the MM and QM regions to be coupled to one another electrostatically, and the QM and MM regions are mutually polarized. Thus, instead of point charges, point multipoles are used to model electrostatic interactions. The use of polarizable force fields like AMOEBA^[37] may offer attractive alternatives to conventional additive QM/MM schemes and may further improve the accuracy of the calculated ¹⁵N^H CSA values.

CONCLUSIONS

Here we evaluated the agreement between MAS NMR-derived experimental and QM/MM calculated backbone CSA tensors for galectin-3C. ¹³C^α CSAs calculated from QM/MM generally agree well with the experimental values, indicating that fragmentation of the overall structure into 3.5 Å spheres treated by DFT represent an effective approach. For ¹⁵N^H CSAs, considerable variability in accuracy is observed, caused by details in a variety of factors, such as hydrogen bonding, electrostatics, and solvation. Significant improvement in the accuracy of calculated ¹⁵N^H CSAs was noted when using the Amber ff15ipq force field, combined with a 40-picosecond molecular dynamics simulation. Overall, our results illustrate the importance of accurate input coordinates for calculating CSA tensors, with further improvements via the inclusion of ensemble averages calculated over short dynamics trajectories. Correctly taking into account the multiple factors that contribute to the ¹⁵N^H CSA will allow to extract rich structural information in the future. Ongoing and further improvements in computational strategies will open the door for implementing CSA tensors into protein structure refinement.

MATERIALS AND METHODS

Protein expression, purification and crystallization of galectin-3C

Protein expression, purification and crystallization of galectin-3C were performed as described previously.^{[19, 38, 39]} The final protein purity was >95% as determined by SDS-PAGE and >98% by solution NMR. Microcrystals of galectin-3C were grown and 30 mg were packed into a 3.2 mm Bruker thin-walled rotor for MAS NMR experiments.

MAS NMR experiments

MAS NMR experiments were performed on a 14.1 T narrow bore Bruker AVIII spectrometer using a 3.2 mm HCN EFree MAS probe. ¹H, ¹³C, and ¹⁵N Larmor frequencies were 599.8 MHz, 150.8 MHz, and 60.8 MHz, respectively. 14 kHz MAS was used for all experiments and was maintained to within ± 5 kHz by a Bruker MAS III controller. The temperature of the sample in the MAS rotor was 4 ± 0.1 °C and kept using the Bruker BCU temperature controller. 90° pulse lengths were 2.9 μs (¹H), 3.7 μs (¹³C), and 4.8 μs (¹⁵N), with cross polarization contact times of 2.0 ms (¹H-¹⁵N) and 1.0 ms (¹H-¹³C). ¹H-¹⁵N and ¹H-¹³C CP used a 95–105% linear amplitude ramp on the ¹H channel. Band-selective ¹⁵N-¹³C^α transfer was achieved through the use of a 5.0 ms SPECIFIC-CP^[40] with a tangent amplitude ramp on the ¹⁵N channel and a constant rf field on the ¹³C channel. SPINAL-64 decoupling^[41] was used during direct and indirect acquisition periods. For ¹⁵N^H and ¹³C^α RNCSA 3D experiments,^[28] R14₂⁵ and R10₁³ recoupling sequences were used to selectively recouple the CSA interaction during t₁ evolution. The basic R element was a π pulse. The rf field strength (N/2nω_r) and phase (ν/N*180°) used for each symmetry sequence depended on the symmetry properties for each sequence. Heteronuclear interactions were decoupled during the RNCSA recoupling period by applying a π pulse on either the ¹³C or ¹⁵N channel at the center of each R cycle. A recycle delay of 2.0 seconds was used for all experiments.

NMR data processing

NMR data processing was performed using NMRPipe^[42] and all spectra were analyzed using Sparky. For the 3D datasets, 45° shifted sine bell apodization was used, followed by Lorentz-to-Gaussian transformation in the ¹³C and ¹⁵N dimensions. No apodization functions were applied to the ¹³C^α or ¹⁵N^H resonances during data processing. CSA lineshapes were extracted in a semi-automated process using home-written scripts.

Simulation of CSA lineshapes

Simulation of CSA lineshapes was performed using Simpson version 1.1.2.^[43] To produce a powder average, 320 pairs of (α,β) angles were generated using the REPULSION^[44] algorithm and 16 γ angles (5120 angle triplets) were used for all simulations.

QM/MM

QM/MM calculations of protein backbone ¹³C and ¹⁵N CSA tensors were performed using Gaussian 09^[45] at the OLYP^[46]/tzvp^[47] level of theory in the quantum mechanical region. Each input file was generated by AF-NMR. Initial coordinates for the calculations were derived from the X-ray crystal structure (PDB ID: 3ZSJ). The input coordinates of the X-ray structure were prepared for Amber minimization by removing any ligands, crystallographic water molecules and adding hydrogen atoms. This structure was then minimized using either the Amber FF99SB or the Amber FF15IPQ molecular mechanics force field. Calculated CSTs were referenced to ubiquitin (PDB ID: 1D3Z) calculated at the same level of theory (¹H=32.0 ppm, ¹³C=182.5 ppm, and ¹⁵N=237.8 ppm). Linear regression analysis was performed for each set of calculations to assess the agreement between experimental CSTs from MAS NMR and calculated CSTs from QM/MM. Perfect agreement between theory and experiment would be a slope and an R² value of unity, with no offset (intercept of 0).

DFT calculations

DFT calculations of protein backbone ¹³C and ¹⁵N CSA tensors were performed using Gaussian 09 at the OLYP/tzvp level of theory. Input files for 20 residues representing the best and worst agreement with experiment were generated by AF-NMR with no minimization or imbedded point charges. Initial coordinates were derived from the neutron crystal structure (PDB ID: 6EYM). The input coordinates of the neutron crystal structure were prepared by removing any ligands, crystallographic water molecules, directly replacing deuterium atoms with hydrogen atoms. For each fragment, heavy atoms were fixed and the hydrogen (deuterium) atom geometries were optimized using B3LYP/6–31g level of theory before calculating NMR CSA tensors.

Molecular dynamics simulations

Molecular dynamics simulations of galectin-3C (PDB ID: 3ZSJ) were performed using OpenMM^[48] with Amber ff15ipq and the SpcE water model. To prepare the simulation, a water box equal to the size of the crystal unit cell was constructed, and Cl⁻ counter ions were added to neutralize the charge. The structure was equilibrated and energy minimized for 1000 steps of 0.002 picoseconds. Following energy minimization, the molecular dynamics simulation was performed in explicit solvent with Langevin dynamics at 300 K for 20000 time steps, equivalent to 40 picoseconds. A snapshot was generated after every 2 picoseconds, and each snapshot was used directly as input into AF-NMR to calculate ¹³C and ¹⁵N CSA tensors.

Ensemble averaged CSA tensor calculations

Ensemble averaged CSA tensor calculations were prepared using snapshots from the MD simulations with QM/MM calculations. 20 solvated snapshots were extracted from the MD simulation. Each snapshot was used as input into AF-NMR without further manipulation, so the input files contained explicit water molecules. For the 20 residues of interest (which represented the best and worst agreement with experiment), a QM/MM calculation was performed for each snapshot, totaling 20 Gaussian 09 calculations per residue. The CSA tensors were then averaged for each residue, and referenced as described previously.