Atomic-resolution chemical characterization of (2x)72-kDa tryptophan synthase via four- and five-dimensional 1H-detected solid-state NMR

Significance The atomic-level understanding of protein function and enzyme catalysis requires site-specific information on chemical properties such as protonation and hybridization states and chemical exchange equilibria. This information is encoded in NMR chemical shifts, which serve as important complementary information to structural data from other experimental techniques or structure prediction algorithms. This study demonstrates that comprehensive chemical-shift assignments are achievable for large and highly complex proteins, offering insights into chemical structure and dynamics. The access to the active-site chemistry in the 144-kDa (72-kDa asymmetric unit) enzyme tryptophan synthase demonstrated here extends the elucidation of chemical properties to a member of an important class of enzymes of interest in pharmacology and biotechnology.


Contents:
1) General statistics on NMR studies S2 2) General trends for relative sensitivity of nD experiments for solids and solution S2 3) Assignment strategies involved S3 4) New pulse sequences and experimental parameters S4 5) Bulk sensitivities of 4D and 5D experiments S14 6) Practical implementation of 5D HNcoCANH and HNcaCONH pulse sequences S15 7) Implementation of 5D HNcoCANH and HNcaCONH pulse sequences and assignment strategy on SH3 S16 8) Additional considerations regarding overlap in assignment vs. relaxation experiments S18 9) SCS analysis S19 10) FLYA-aided assignment of TS S20 11) Protonation states of the TS internal aldimine state (blue), and >90% (green)) levels of backbone assignment as a function of molecular weight of the asymmetric unit, including both, solution and solid-state NMR. B) Comparison of molecular weight (individual polypeptide chains) of structures solved by NMR (green) and X-ray crystallography, demonstrating the importance to exceed the existing molecular-weight barriers of NMR spectroscopy.

Section 2: General trends for relative sensitivity of nD experiments for solids and solution
Estimation and plotting of general sensitivity tendencies for solids and solution (Main text Fig.  2C) was done in Mathematica based on the following (simplified and generic) assumptions for sake of generality: Solid-state NMR: Average CP transfer efficiency of 70%, starting with 2 transfers for a 2D and one additional transfer implemented with each additional dimension; antiproportionality between the copies of molecules in the rotor and molecular weight (constant rotor volume). Solution NMR: average 15 ms transverse magnetization per INEPT, one additional magnetization transfer added for each additional dimension; using a generic relaxation rate constant approximated to 1.4 s -1 /ns of tc, (2) and the empirical MW-to-tc regression of 0.6 ns/kDa. (3) For both aggregation states, reduction to 63 % of the signal due to frequency modulation and a further reduction to 65 % due to integral T2 losses up to t1max for each indirect dimension was assumed. All data was normalized to the sensitivity calculated for a 2D correlation of a 10 kDa protein in the respective aggregation state. Losses through pulses were not taken into account. The plot only returns general trends rather than specific scenarios. Naturally, precise numbers depend on the kind of experiment, spectrometer field strength, temperature, solvent, shape of the target molecule, choice of t1max evolution times in indirect dimensions, NUS density weighting, and many more. x,x C) 4D hCCNH pulse sequence with MOCCA mixing (Δ = 60 µs, n = 256) (5,6) and the COPORADE approach (7). Phase cycling: φ1 = -x,x; φ2 = x,-x; φ3 = x,x,-x-x; φ4 = x,x,x,x,-x,-x,-x,-x; φ5 = x,x,x,x,x,x,x,x,x,-x,-x,-x,-x,-x,-x,-x; φrec = x,-x,-x,x,-x,x,x,-x,-x,x,x,-x,x,-x,-x,x. D) 4D hCACBcacoNH pulse sequence. Phase cycling: φ1 = x,-x; φ2 = x,x,-x,-x; φ3 = x,x,x,x,-x,-x,-x,-x; φrec = x,-x,-x,x,-x,x,x,-x. The delay τ was set to 6 ms (<1/(4J)) to achieve maximal transfer to Cβ. Phases after evolution periods of indirect dimensions were changed to obtain phase-sensitive spectra by the States-TPPI method (marked by asterisks). In case of the 4D hCCNH a block of pulses was phase-cycled together (marked by small hashes). Filled and empty rectangles represent 90° and 180° pulses. The carrier changes on the carbon channel are denoted with arrows. Water suppression was achieved by MISSISSIPPI without gradients (8). A random, Gaussian weighted schedule was used for the 5D experiment and the 4D hCCNH, all other 4Ds were acquired with a sinusoidal weighted Poisson Gap sampling scheme (9).  All experiments were recorded with 13 C or 15 N decoupling during acquisition using WALTZ-16 at 10 kHz for both nuclei. Low-power 1 H decoupling was achieved through the XiX scheme (10) with an RF amplitude of approximately 13 kHz. All NUS schedules were random. All 4D spectra except the 4D hCCNH were recorded using a sine-bell-squared-weighted Poisson-Gap schedule, while the 4D hCCNH and all 5Ds were recorded using a Gaussian weighted, fully random schedule with sigma set to TimeIncr/2. Measurement times (note the squared time requirements for desired s/n increase) were chosen with respect to both, sensitivity ( thermal noise and potential reconstruction artifacts) ratio of greater than 50:1 or 20:1 was obtained within 7 or 1.5 d of measurement time, respectively, compare Fig. S7.) Note that all experiments were recorded at a moderate Larmor frequency of 700 MHz. 1 GHz or 1.2 GHz, increasingly available for future important targets, would strongly accelerate the measurements, theoretically by a factor of up to 3 or 5, respectively. Due to NUS, sampling requirements (reflecting the resolution-limited regime) can be fulfilled within a few days of measurement time even for 5D experiments. The acquisition was split into smaller fragments (usually two days), after which field drift (using a simple 1D experiment) and instrument stability (tuning/matching) could be adjusted/checked. Reconstruction by SSA turned out to be robust against smaller differences in chemical shift.

Section 4: New pulse sequences and experimental parameters
Magnetization transfers in backbone experiments were generally enabled by dipolar methods (CP and BSH-CP (11) for heteronuclear and homonuclear transfers, respectively), with settings similar to those described earlier (4). Cα/Cβ transfers were performed by INEPT transfers as described before (12) with a delay of ~1/(2J) to fully evolve the Cα/Cβ antiphase terms as out-and-back DREAM (13) turned out to yield a slightly lower signal-to-noise ratio for this sample (see Fig. S5A). Shown is a representative slice through the H/CB plane. The sign of the INEPT spectrum is inverted and the INEPT delay was optimized to 6 ms. (7.2 ms would correspond to full evolution of the anti-phase term.) Both spectra here were recorded with 32 scans. B) Relative bulk sensitivity of HNcoCANH and HNcaCONH. Given that the remainder of the transfer efficiencies are comparable, the differential sensitivities are directly representative for the differential transfer efficiencies of CACO vs. COCA BSH-CP/DREAM, which are in line with differential transfer efficiencies for the two directions reported in more detail previously (12).
Temperature-dependent 2D H/N correlations were recorded by placing a perdeuterated/backexchanged TS sample into a 0.7 mm rotor and spinning to only 55 kHz, using the same 700 MHz spectrometer. This -in contrast to 55 kHz in a 1.3 mm rotor or 110 kHz in a 0.7 mm rotor -allows to reach temperatures down to 5 °C. For each of the temperatures 5, 10, 15, 20, and 25 °C a 2D H/N spectrum was recorded. (Higher temperatures would require VT gas temperatures above 50 °C.) Due to the lower sensitivity in this setup, an experimental time of 2d per spectrum was used. Line shapes were characterized by peak deconvolution of extracted slices after apodization with 100 Hz exponential line broadening. Temperature calibration was performed based on the H2O chemical shift (2,14,15) with respect to the DSS methyl signal referenced to 0 ppm.

Section 5: Bulk sensitivities of 4D and 5D experiments
Measurement times for 72 kDa TS are necessarily excessively larger than for the SH3 domain (10x lower molecular weight) or any other small to mid-size proteins due to a fixed sample volume filled up in the rotors and necessarily remains a major effort. Importantly, however, in contrast to solution NMR, the relative intensities of the HN bulk signal, compared to the hNH intensity, remain essentially the same (Fig. S6A below). Indeed, the intensity of a single, well resolved and well-behaved residue is reduced by a factor of 12 ( Fig. S6B), as expected from the linear decrease of sensitivity with molecular weight and maintained transfer efficiencies.
It is interesting to note that the bulk sensitivity of the HNcoCANH is comparable with the solids pendant of the HNCACB, or 2-to-2.5 times more sensitive than that of an HN(CO)CACB, both being experiments established as standard backbone assignment experiments in protondetected solid-state NMR (12,16,17). Expansion of 4D HNCACONH-type experiments to NUS 5D experiments can be done without additional magnetization transfers and only causes an intensity drop due to chemical-shift evolution in the additional indirect dimension. As t1max, however, can be short compared to T2, and NUS increases the sensitivity by intensityweighted sampling (18), sensitivity loss effectively occurs only due to amplitude modulation upon additional incrementation, which is to a factor of 2/p or by ca. 36 %.

Section 6: Practical implementation of 5D HNcoCANH and HNcaCONH pulse sequences
As pointed out by work of Kosiński (19), a conventional reconstruction of 5D experiments is highly demanding in terms of computational time as well as computer memory and disk space and therefore should be avoided. In this work we therefore use the concept of Sparse Multidimensional Fourier Transform (SMFT) and Signal Separation Algorithm (SSA) as introduced by Koźmiński and co-workers (19)(20)(21)(22) and illustrated in main text Fig. 3C. For details about the incorporated processing we refer to comprehensive work on intrinsically disordered proteins by the Koźmiński group at University of Warsaw. To make 5D processing feasible, only two out of five dimensions are Fourier transformed, based, however, on an a-priori defined three-dimensional peak resulting in a stack of 2D planes for each 3D peak. A direct Fourier transformation (nuFT) of the (highly) sparse spectrum is accompanied not only by thermal noise but also sampling artifacts which, however, are not entirely random and therefore can be reduced in a previous step. As the signal-to-artifact ratio is only dependent on the total number of NUS points (22), a 5D experiment can be acquired within short experimental times if sensitivity is not the limiting factor.
The 3D peak list is obtained by acquiring and peak picking a 3D experiment that shares its three dimensions with the 5D. Non-picked signals will stay invisible in the processed 5D and therefore high resolution and good peak picking are crucial. This can usually be achieved by using NUS and long acquisition time also for the 3D experiment. Here, we used a 3D hCANH for the 5D HNcoCANH and a 3D hCONH for the 5D HNcaCONH experiment, due to their higher sensitivity compared the hCAcoNH or hCOcaNH as possible alternatives. 3D and 5D experiments were acquired with a Gaussian weighted, random schedule (for more details see Table S1-S3).
Processing of all spectra was performed by SSA in a two-step procedure, as implemented in cleaner3d/reconstructor3d (20), cleaner4d/reconstructor4d (23) and cleaner5d/reconstructor5d (19). 3D and 4D spectra were fully Fourier-transformed, while for the 5D only the two additional indirect dimensions were transformed at peak positions of 3D base experiments by sparse multidimensional Fourier transform (SMFT (24)). Peak picking was performed in a semi-automatic way using the peak-picker of CCPNMR V2 (25). For artifact removal the threshold for detecting intensive points was lowered to 5. Line broadening of 50 Hz or 100 Hz was used in the 15 N, 13 C, and 1 H indirect dimensions to increase signal intensity. (This ultimately will result in a mixed Gaussian / exponential weighting.)

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Section 7: Implementation of 5D HNcoCANH and HNcaCONH pulse sequences and assignment strategy using the SH3 domain as a model system Fig. S7 shows the implementation of the two alternative HNcoCANH and HNcaCONH 5D experiments for the SH3 domain of chicken a-spectrin. Both the originating amide group as well as the successive amide are encoded in addition to either a Ca or CO shift. The 5D experiment can be set up as a correlation with either the preceding or the successive amide group (see Fig. S7A). However, each of the individual experiments is sufficient for an assignment walk with match-making reliability on the basis of two shifts (H N and N H ) on its own. (No pair of experiments is necessary.) The high sensitivity of the straight-through pulse sequence, in combination with sparse non-uniform sampling, allows a representative singlepeak signal-to-noise/artifact ratio in the 5D of around 50:1 within 7 d of measurement time (using a simple read out from 1D cross sections, shown in Fig. S7E/F). (S/N in reconstructed NUS spectra is characterized by both, thermal noise and reconstruction artefacts.) The minimal phase cycle/NUS schedule used, however, also allows for around 1.5 d as a minimum experimental time or less, still according to a high signal-to-noise/artifact ratio of ~20:1 (S7C/D). Similar to the 3D/4D HNcocaNH, experiments with the same number of magnetization transfers, the 5D HNcoCANH and HNcaCONH yield a sensitivity of ~7% and ~5%, respectively, of the hNH sensitivity in the first FID (compare Fig. S7B). Whereas naively one would expect equal signal-to-noise for the two variations of the 5D experiment, the slight difference (also compare Fig. S6) is in line with our previous experience on BSH-CP regarding either CO to Ca or Ca to CO transfer and the literature (12). Fig. S7C-H show relevant sections of the processed 2D planes from the 5D experiments allowing for either forward or backward walk for two residues, superimposed on an H/N correlation spectrum and including crosssections through the peaks displayed. With no additional transfer steps compared to their lower-dimensionality versions, the 5Ds allow for acquisition with the same minimal phase cycle and result in highly intense and unprecedentedly dispersed cross peaks, allowing a facilitated sequential walk, particularly when manual assignments are pursued, when only a limited combinatorial space can be managed successfully. With the well-resolved H/N spectrum, backbone resonance assignment for 48 out of 52 potential correlations of the SH3 domain is straightforward based solely on a single 5D data set and an hCACBNH, either manually or alternatively by automated assignment via the FLYA routine (26) (not shown here). Missing peaks represent cases when prolines or flexible residues are involved in the magnetization pathways. Details on acquisition parameters are given above. 5D spectra were Fourier transformed only in F4 and F5 at actual F1-3 peak positions as defined by 3D source experiments (19,27) (vide supra). In congruency with the above, the 5Ds were again specifically implemented as HNcoCANH and HNcaCONH, instead of HNCAcoNH and HNCOcaNH to make use of the higher sensitivity of the hCANH and hCONH, respectively, as source experiments compared to hCAcoNH/hCOcaNH.  S7. Backbone walk for three residues of the SH3 domain based on two alternative 5D experiments allowing for either a forward (blue) or a backward walk (green). A) Coherence transfer pathways for the 5D HNcoCANH (left) and HNcaCONH (right). The shaded portion denotes the respective source experiment needed for processing 2D slices out. The HNcoCANH correlates two amide groups with additional signal dispersion of Ca. As the provided 3D peaks are obtained from an hCANH source experiment characterizing residue i, the processed 2D plane will show the i+1 amide correlation. By using a reversed transfer pathway and exploiting dispersion in the CO dimension, amide H/N shifts of residue i are obtained based on the basis of H/N/CO coordinates of residue i+1. B) Comparison of bulk signal intensities in the first scans of HNcoCANH (blue) and HNcaCONH (green) with the H/N correlation (yellow) in the SH3 domain. C-F) Exemplary backbone walk for E22 to T24 using the HNcoCANH. (Spectra in C/D ("short") were recorded with the minimal phase cycle of 8 scans (instead of 24 scans for the other spectra shown) and fewer NUS points (0.4 % density instead of 2 %) in only 36 h.) G) and H) The same walk but reversed using the HNcaCONH. Source coordinates, as given in the text field, are marked with a cross without sections in the 5Ds. Due to the possibility of back transfer during CPs, the redundant amide signal of the diagonal peak appears weakly in addition for some cases (as in panels C and E). Line widths are estimated by fitting a Lorentzian peak shape in two indirect dimensions using NMRFAM-Sparky (28) and subtracting 100 Hz and 50 Hz of line broadening applied for 1 H and 15 N during the processing. Given that the spectra represent reconstructed NUS data, the S/N (obtained via the according Sparky routine from 1D cross sections) corresponds to a mixture of thermal noise and artifacts.

Section 8: Additional considerations regarding overlap in assignment vs. relaxation experiments
Assignment experiments need to characterize two residues in each peak, residues i and i + 1. In conventional approaches (CO-based backbone walk in hCONH/hCOcaNH experiments, Ca-based backbone walk in hCANH/hCAcoNH experiments, Ca or Ca/Cb-based backbone walk in hcaCBcaNH/hcaCBcacoNH experiments, Ca/CO-based backbone walk in 4D hCACONH/hCOCANH experiments, H/N-based backbone walk in HNcacoNH experiments etc.) two dimensions are used for characterizing residue i identity, whereas one or two dimensions are used for match making. Fig. S8 depicts some 4D excerpts from TS from which it becomes clear that for a given Ca/CO shift combination for match making, multiple H/N correlations come into question (Fig. S8A, commensurate with the probability of overlap in a Ca/CO spectrum). Accordingly, for a given H/N shift combination, multiple Ca/CO peaks are obtained (Fig. S8B)  By contrast, for relaxation experiments, each of three dimensions in a pseudo-4D experiment is used to characterize the peak of interest. Hence ambiguity is commensurate with the resolution in the underlying 3D experiment. Fig. S9 shows exemplary slices from the pseudo-4D experiment used for R1r measurements. Still, for a small set of residues, exact overlap in three dimensions is obtained, for which relaxation rates could not be extracted.  S9: Demonstration of overlap in pseudo-4D relaxation data. Two exemplary slices from highly crowded regions are shown. A problem for relaxation data only occurs whenever one peak exactly overlaps with another one in all three dimensions (This is not the case for any of the peaks shown.), meaning that ambiguity is negligible for most peaks even in (only) pseudo-4D relaxation data.

Section 9: SCS analysis
Prediction of secondary structure elements were performed by TALOS-N (29) and secondary chemical shifts (30,31). For TALOS all unassigned residues were removed and automatic offset correction for carbons as well as deuteration was performed. In case of glycine residues only Ca atoms were considered for the SCS.  (26) is an established automated assignment tool that is increasingly used for facilitation of assignment in complex proteins, including in solids (32, 33), when a multitude of different spectra and an extremely high combinatorial workload would bear on the quality assessment in an unassisted manual process. Although FLYA can yield high correct assignment rates even with fully automatically generated peak lists (34,35), peak picking was carefully done in multiple iterations in a semi-automated and validated fashion in CCPNmr (25) (as done before (32, 36)) and a curated peak list input provided to minimize false-positive or false-negative results. With FLYA, the combinatorial space of assignment is assessed and quantitatively evaluated in each step on a single-residue level, converging into peak lists and assignments of superior reliability than from manual-only assignments. Defining the formal magnetization pathways for the experiments was done as: Manual treatment of the data and FLYA runs (always using 100 independent repetitions) were iteratively consolidated into a consensus assignment. Optimal results (see Fig. S11) were found with tolerances for chemical shift matching set to 0.1 ppm, 0.8 ppm and 0.5 ppm for 1 H, 13 C and 15 N, respectively. A priori chemical shift distributions were determined by SPARTA+ (37) on the basis of the crystal structure (pdb 4ht3), instead of general BMRB statistics. To warrant a high confidence of resonances marked as "strong", we further restricted the standard definition of a "strong" assignment to be not only i) occurring in 80% of the independent runs but also to have ii) at least two strong assignment present in one residue, iii) to have at least four strong assignments present in the directly adjacent residues and iv) to have the amide H and N assigned as strong. 5Ds are useful for FLYA as they lead to higher redundancy with intrinsically perfect referencing between different kinds of data, which is particularly challenging for ssNMR (32), as well as to the direct experimental connection of two residues, including one Ca.
To be included in the most rigorous category, the assignment certainty for all of H N , N, Cα, CO, and Cβ resonances within these residues had to be marked "strong" (green tones in main text Fig. 4A). Under this criterion, 369 residues could be assigned, which corresponds to 59 % of the 630 non-proline residues. An additional 121 residues (19 %, gray tones in Main text Fig.  4A) were determined to most probably be correct also, but with not all of the five listed shifts obtained with a classification as "strong" (referring again to the definition of "strong" modified to more conservative preconditions).  S11: Result of automated FLYA resonance assignment of TS using 4D hCACONH, 4D hCOCANH, 4D hCACBcaNH, 4D hCACBcacoNH, and 5D HNCAcoNH experiments. Dark colors indicate only strong assignments according to the modified (conservative) definition (see SI text). Note that the final assignments are not a simple FLYA output but were carefully curated through numerous iterations using all available information, also including the side-chain to backbone correlations, which yield residue type information and can allow to unambiguously map even short stretches.

Section 11: Protonation states of the TS internal aldimine state from NMR-assisted crystallography
The active-site experimental chemical shifts were used as restraints to evaluate computational models of structure and dynamics using "NMR-assisted crystallography," the synergistic combination of solid-state NMR spectroscopy, X-ray crystallography, and first-principles computational chemistry (38)(39)(40)(41)(42)(43)(44)(45)(46)(47). In this approach, models of the active site are built on the framework of an X-ray crystal structure, and these models are quantitatively screened and ranked based on the agreement between their first-principles predicted chemical shifts and the results of solid-state NMR experiments.
Our approach follows that outlined by Caulkins et al. (43). To begin, a cluster model of the enzyme active site was constructed starting with the crystal structure of the resting, internal aldimine form of TS (PDB ID: 4HT3) by selecting all residues that contained atoms within 7 Å of the cofactor. This selection was expanded to include complete residues and was modified as follows: (1) Residues that were not part of continuous backbone segments and with only two atoms within the initial 7 Å cut were deleted; (2) residues with two backbone atoms and no side chain residues within 7 Å were converted to glycine (βL349); (3) residues having two side chain atoms and no backbone atoms within 7 Å were truncated by removing the backbone atoms and replacing Cα with a methyl group (βH313, βD383); (4) N-terminal nitrogen atoms were replaced with a hydrogen atom and C-terminal carbonyls were capped with an -NH2 group (amidated); (5) the Cs + cation was replaced with Na + ; and (6) hydrogen atoms were added. The final clusters contained 577-578 atoms depending in the protonation state of the cofactor.
Next, the active-site cluster was used as a framework for building first-principles computational models. Five candidate structures (Scheme S1) were generated by systematically varying the protonation states of the following ionizable sites: the pyridine ring nitrogen; the pyridoxal phenolic oxygen; and the Schiff base nitrogen (Nz of βLys87). A binary code for the protonation states of the active site was used to label the models, where 1 indicated that the site was protonated and 0 indicated no protonation. The code refers to the following 3 positions in order: (pyridine nitrogen)(phenolic oxygen)(Schiff base nitrogen). Based on its 31 P CSA tensor (48), the phosphate was fixed as di-anionic for all calculations. The fully deprotonated (000) and triply protonated (111) models were not considered, nor was the state in which both the phenolic oxygen and Schiff base were protonated (011).
Scheme S1: Candidate chemical structures for the internal aldimine state Models were geometry optimized in Gaussian09 at the DFT B3LYP level of theory using the Grimme D3 empirical dispersion correction and a two-tier, locally dense basis set with S 23 6-31G(d,p) for the cofactor and 6-31G for the remaining atoms. Atoms within 4 Å of the cofactor and all hydrogens were allowed to adjust while remaining atoms were fixed at their crystallographic coordinates.
For each optimized structure, NMR shieldings were calculated using Gauge Independent Atomic Orbital (GIAO) method at the DFT B3LYP level of theory using a three-tier, locally dense basis set assignment with the PLP/Lys87 atoms at 6-311+G(2d,p), atoms within 4 Å of the PLP/Lys87 at 6-311G(d,p), and all remaining atoms at 6-31G. NMR shielding values were converted to chemical shifts using the following linear rescaling Finally, models were ranked based on the agreement between their first-principles predicted chemical shifts and the experimental NMR parameters using the reduced-χ 2 statistic, after application of isotope shift correction (51,52) to the set of synthetic shifts. Here, N is the number of measured NMR shifts, f is the number of adjustable model parameters (0 for static models, 1 for fast-exchange models), δi exp is the experimental chemical, δi model is the predicted chemical shift from first-principles calculations, and si 2 is the nuclide-specific weighting derived by setting si to the respective RMSE from benchmark studies (1.5 and 4.3 for 13 C and 15 N, respectively). The reduced-χ 2 should approach 1 for a large number of measured chemical shifts, provided the weights have been properly assigned. For a finite number of experimental values, the reduced-χ 2 varies due to sampling statistics in a manner consistent with the χ 2 probability distribution.
Experimental chemical shifts for βK87 were obtained via a combination of the 4D hCCNH, the H/N, and a long-range H/C correlation as described in the main text. Experimental shifts for the PLP ring were reported previously at -10 o C, but were measured again at 30 o C for consistency ( Fig. S12 and Table S6).  Table S6: Experimental and first-principles predicted chemical shifts (ppm) for cluster models of the internal aldimine with varying protonation. Table S6 summarizes the first-principles chemical shifts for the 5 cluster models of the active site with varying protonation and quantifies their agreement with the experimental chemical shifts. None of the single, static models shows acceptable agreement with the experimental shifts, with the Schiff-base nitrogen (βLys87 Nζ) an outlier for all models.

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Of the candidate structures, none was found to show acceptable agreement between the predicted and experimental chemical shifts, with the lowest reduced-χ 2 = 28.1 (Table S6). Based on the temperature dependence of the Schiff-base nitrogen, we next considered fastexchange equilibrium models in which all models, regardless of protonation state, were paired and their populations optimized for best agreement with the experimental chemical shifts. These models were again ranked, and the results are summarized in Table S7. The best-fit, with a reduced-χ 2 of 1.7, is for the exchange between the protonated Schiff-base (61%) and the protonated phenolic oxygen (39%) forms (shifts summarized in Main Text Table 1). In this dynamic fast-exchange equilibrium, the proton merely changes position between the nitrogen and oxygen atoms in the internal hydrogen bond (main text Fig. 5B). The next-best exchange model has an unlikely proton exchange between the Schiff base and pyridine ring nitrogens and with a reduced-χ 2 of 5.1 does not conform to the experimental chemical shifts within the expected error range.

Bayesian Probability Analysis
Following the approach of Engel et al., a Bayesian probability analysis was used to quantify the overall confidence in the identification of the experimental structure (53). In this approach, the posterior probability, , that M is the experimental structure given the measured set of chemical shifts y * is given as where is the probability of observing chemical shifts y * for a given structure M, and is the prior probability of structure M matching the experimental structure. The The p-value was then converted into a relative probability for model M according to using a fixed relative probability . Reduced-χ 2 for the 7 best exchange models are given in Table S7, along with their relative probabilities, .
The prior probability was used to introduce consistency with the observed temperature dependence of the Schiff base nitrogen. Temperature dependence at this site requires exchange models that include tautomeric exchange at the Schiff base nitrogen. These models were assigned relative probabilities while all other models were assigned Taking into account both the isotropic chemical shift data on the βLys87 and the PLP cofactor, along with the observed temperature dependence of the Schiff base nitrogen, the proposed exchange model is found to be the most probable experimental structure with 85% confidence.

Section 12: External contributions to Proton Exchange
The free-energy difference between the exchanging PSB and phenolic tautomers was determined by fitting the experimental chemical shift to a fast-exchange average shift for the phenolic and PSB states where the populations were used to define an equilibrium constant, K, and a change in enthalpy and entropy for the exchange In this fit, νPhen and νPSB were set to their theoretical values of 319.3 ppm and 166.8 ppm, respectively. The best fit to the data gives ΔH = 9.6 ± 1 kJ/mol and ΔS = 28.6±3 J/(mol K) (Main Text Fig. 6C).
To estimate the activation energy for the proton exchange, the linewidth of the Schiff-base nitrogen was fit to the two-site exchange model developed by Tian et al. (54) for the residual linewidth (in Hz) in the fast-exchange limit: . (1 ) f K T K k p n n n p -D = + +

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In this expression, 1/T2 is the spin-spin relaxation rate, νPSB and νPhen are the limiting chemical shifts (in Hz) of the Schiff-base nitrogen in the PSB and phenolic tautomeric forms, K is the equilibrium constant for the exchange given above, and kf is the forward exchange rate (PSB to Phen). A limiting linewidth in the fast-exchange limit of 20 Hz (T2=16 ms) was assumed. Any contribution due to direct spin-spin interaction and anisotropic bulk magnetic susceptibility, adding to the observed linewidth, are unknown and were ignored for simplicity. To fit the data, νPhen and νPSB were again set to their theoretical values of 319.3 ppm and 166.8 ppm (and converted to Hz) and K calculated at each temperature based on the free energy difference determined above. The best fit to the data gives a forward rate of 2.4 x 10 6 /s and a free energy of activation of 36.8 kJ/mol (Fig. S13).

Fig. S13
. Temperature dependence of the βK87 Nζ linewidth. Opposed to the 1.3 mm rotor used in the remainder of the study, temperatures down to 5 °C could be achieved using a perdeuterated sample in a 0.7 mm rotor spun at only 55 kHz, half the speed usually employed and needed for fully protonated samples but also used for the 1.3 mm measurements. This procedure comes at the cost of a 50% sensitivity drop due to the smaller volume, which -in conjunction with the exchange-broadened lines -results in relatively poor signal-to-noise ratio for the assessment, prohibiting a more detailed assessment of enthalpic and entropic contributions to the free energy of activation. The general linewidth, however, unambiguously points to an exchange on the 1 µs timescale, which number is hardly affected by assuming a limiting linewidth of 20, 40, or 100 Hz. The data was fit to a two-site exchange model between the PSB and phenolic forms to extract an activation barrier ΔG ‡ = 36.8 ± 0.5 kJ mol -1 for an assumed limiting linewidth of 20 Hz. 15 N R1r measurements were performed as a uniformly sampled pseudo-4D experiment using an hCONH 3D spectrum as a basis with a 5 kHz on-resonance continuous wave spin lock. Six spectra were recorded with increasing spin-lock duration: 5 ms, 10 ms, 20 ms, 40 ms, 60 ms, and 100 ms. The coherence decays were fit to a mono-exponential decay function. To account for a potential temperature increase due to longer spin-locks, a heat-compensatory spin-lock block was included during the recycle delay period with a length of Tmax -Tsl, where Tmax = 100 ms. The decay curves (see below) can be unambiguously fit for part of the active site to slightly enhanced rates such as 5.4 for βG84 and 8.9 s -1 for βD381, front left in Fig. S15. Such values are often found in mobile residues of otherwise rigid proteins (55)(56)(57) and deviate from rates of only around ~1 -1.5 s -1 that are generally observed for immobile/inconspicuous residues in this preparation. The likely presence of plasticity in the gate at room temperature is an interesting feature also becoming generally accessible for more in-depth studies. Actual relaxation dispersion studies on TS, which would be admirable to specifically quantify possible exchange contributions to the R1r rates, are associated, however, with extensive measurement time requirements at 700 MHz given the multiple pseudo-4D relaxation experiments (i. e., a pseudo-5D).

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Fig. S15. Assigned residues in the active site of the β-subunit, with 15 N R1r rates annotated and colorcoded on the X-ray structure (PDB 4HT3). The color code is shown on the top. Residues in gray sticks are assigned but not sufficiently resolved in the pseudo-4D relaxation experiments. Residues b113 -b118 (helix in the front) are also assigned but shown as cartoon for better viewing apart from bQ114 as the connecting residue (transparent sticks). The PLP cofactor is shown in black, with its phosphate group in orange. H-bonds (yellow dashes) are shown with their inter-heteronuclear distances (in Å).

Section 13: Sensitivity of fully protonated samples in 0.7 mm rotors
As (like for TS) unfolding/refolding protocols may be unsuccessful, H/D exchange problems may be overcome by avoiding deuteration in the first place. One such option is using a fully protonated sample in a 0.7 mm rotor and higher MAS speeds. To investigate this alternative, we acquired and compared H/N correlations and a 4D hCOCANH spectrum on fully protonated TS with focus on sensitivity, sample homogeneity and line width.
The fully protonated sample shows line widths in the expected range of 50-100 Hz for protons and is in congruency with the deuterated sample used in the study. Due to the lower rotor volume as well as reduced transfer efficiencies, it expectedly proves to be less sensitive, however, especially in the higher-dimensional experiments. Fig. S16 shows the comparison of deuterated and protonated samples in 1.3 mm and 0.7 mm rotors, recorded at 700 MHz and 800 MHz proton Larmor frequency upon 55 and 111 kHz MAS, respectively, with the same number of scans and identical apodization, under conditions as similar as possible otherwise. Slight changes in the H/N correlation spectrum might be due to slight inconsistencies of the temperature, which is difficult to compare between probe types. Scaling the noise to the same level, an intensity difference of around 3x is apparent. Taking into account that with full protonation all residues should contribute to the bulk signal with maximum intensity, the average single-peak S/N will be slightly lower than derived from Fig.  S16A. Fig. S16B shows an overlay of 2D H/N correlations and respective cross sections for appreciation of the line widths obtained. Fig. S16C shows the Fourier transform of the first FID from an hCOCANH experiment. Here, lower transfer efficiencies for each of the multiple transfer steps due to a higher degree of protonation apparently add additional reduction of the signal-to-noise ratio.

Section 14: Sample preparation
TS was expressed and purified as described before (58)(59)(60). Triply labeled protein was expressed in E. coli CB149 with a pEBA-10 plasmid using minimal media containing 13 C6, 2 H7glucose (2 g/L), 15 NH4Cl (2 g/L), D2O and supplemented with 20 mL/L of 10X BioExpress rich media. The protein was purified via cell lyses and clearance by centrifugation, crystallization and re-crystallization during dialysis induced by spermine and PEG-8000 in the presence of Cs + with an excess of the high-affinity α-site ligand N-(4'-trifluoro-methoxybenzenesulfonyl)-2amino-ethyl phosphate (F9). Doping with 40 mM Cu-edta (61) was achieved by step-wise soaking of crystallites with dopant-containing mother liquor. As for TS, unfolding/refolding protocols unfortunately turned out to be unsuccessful, amide back exchange was given a time of around two weeks before and several weeks after crystallization before the spectra shown were recorded. Even though we find most peaks to be generally present on the basis of 3D hCONH and 4D hCACONH spectra, back-exchange certainly remains only partial at some sites as suspected from very different individual peak intensities. Even though faster probes allow proton detection without deuteration (Sect. 13), back-exchanged, uniformly deuterated samples spun at around 60 kHz MAS currently provide the highest signal to noise, which arguably renders this approach the best compromise for the unprecedented molecular weight of the target.