U-¹⁵N,¹³C-labeled KirBac1.1 was expressed and purified as described previously (Amani et al., 2020; Borcik et al., 2020). Briefly, the protein was expressed from E. coli in M9 minimum media enriched with ¹⁵NH₄Cl, ¹³C-glucose, and a 10 ml aliquot of 10X concentrated BioExpress (Cambridge Isotopes Laboratories, Tewksbury, MA 01876) (Bhate et al., 2013; Amani et al., 2020; Borcik et al., 2020). Protein overexpression was induced at an OD₆₀₀ of 0.8 by adding isopropyl β-D-1-thiogalactopyronoside (IPTG) to a concentration of 1 mM. After 16 h of induction at 18°C, cells were harvested via centrifugation. Cells were lysed via homogenization at 10–15 kpsi. The protein was extracted by adding decyl-β-D-maltopyranoside (DM) to a 30 mM concentration and leaving the lysate on an orbital shaker for 4 h in the presence of Pierce^TM Protease inhibitors tablets, EDTA-Free (Thermo Scientific). After extraction, supernatant was spun in an ultracentrifuge, sterile filtered, and loaded onto a 5 ml HisTrap (GE Healthcare Life Sciences) column. The sample was subsequently passed through a HiPrep 26/10 desalting column (GE Healthcare Life Sciences), followed by a HiLoad 16/600 Superdex 200 size exclusion column (GE Healthcare Life Sciences). Purified protein was mixed with CHAPS solubilized POPC at a 1:1 ratio (w/w). The sample was then stepwise reconstituted via the slow addition of BioBeads-SM2 (Bio-Rad, Hercules, CA). BioBeads were then removed and the sample pelleted via centrifugation and packed into a 3.2 mm limited speed PENCIL rotor (Revolution NMR, Ft. Collins, CO).

All SSNMR spectra were acquired at field strengths of either 17.6 T (750 MHz ¹H frequency) or 14.1 T (600 MHz ¹H frequency) on SSNMR spectrometers located at National Magnetic Resonance Facility at Madison (NMRFAM, University of Wisconsin, Madison, WI). The CCC 3D DARR spectrum (Zhou et al., 2006) was acquired with 50 and 500 ms of DARR mixing in the first and second mixing periods, respectively, at 750 MHz with a Varian (Fort Collins, CO) 3.2 mm Balun probe in double resonance mode ¹H-¹³C mode. Magic-angle spinning (MAS) (Andrew et al., 1958; Lowe, 1959) was performed at 12.5 kHz with a variable temperature (VT) set point of −30°C and a flow rate of 40 lpm (calibrated to −15 ± 3°C). This temperature was chosen because it provided the greatest overall signal for this 3D experiment. 83 kHz of SPINAL-64 (Fung et al., 2000) ¹H decoupling was applied during all chemical shift evolution periods, and hard 90° pulses were 2.4 μs for ¹H and 3.05 μs ¹³C. Polarization transfer was facilitated via adiabatic cross polarization (CP) (Pines et al., 1972) with a 1 ms contact time. During CP 1H power was set to 78 kHz and ¹³C power set to 65 kHz. The recycle delay was set to 1.5 s. The three-dimensional (3D) data was acquired with non-uniform sampling of the indirect dimensions, with a 256 × 256 grid of acquired points with 12.5% points acquired corresponding to 35.4% sampled points in each dimension.

The water accessibility experiments were performed at a magnetic field strength of 14.1 T (600 MHz ¹H frequency). The rotor was placed in a 3.2 mm Varian (Fort Collins, CO) T3 HXY probe in double resonance mode, and spun at the magic angle at a spinning rate of 12.5 kHz. To ensure all water surrounding the protein was liquid, the VT was set to 10 C (sample temperature of 25 ± 3°C) for all water edited experiments with a flow rate of 40 lpm. The cross-peaks in these spectra were matched to similar 2D spectra acquired at −5°C and −15°C to confirm no major chemical shift differences. In our past work, KirBac1.1 was assigned over this temperature range to facilitate this process. Pulse widths of 2.7 and 2.55−μs were applied to 1H and 13C, respectively. A 1.5 s recycle delay was implemented for all water edited experiments. Water-edited spectra were acquired using an initial 1H T₂ filter of 1.5 ms, to eliminate ¹H polarization arising from protein and lipid signals. 1H to 13C transfer was mediated via cross polarization with spin lock fields of 65 and 84 kHz on ¹H and ¹³C, respectively, for a contact duration of 1 ms. Additional parameters for the water edited spectra include a 50 ms DARR mixing followed by 70 kHz of ¹H SPINAL-64 decoupling. We assessed the water accessibility with ¹H-¹H spin diffusion times of 4 and 16 ms.

Throughout all calculations, strict C4 symmetry was maintained using the symSimulation facility (Schwieters et al., 2018), and subunit backbone geometry of residues 36–301 was restrained to that of 1p7b using a non-crystallographic term allowing up to 1 Å of deviation with zero energy penalty. An additional NCS term was employed between the centroids of opposite subunits to prevent overall expansion. Energy terms employed during structure calculations included ¹³C-¹³C intra- and inter-subunit distances (NOE potential), TALOSN derived dihedral angles (CDIH) (Bermejo and Schwieters, 2018), the hydrogen bond potential of mean force (HBPot) (Schwieters et al., 2020), and either the EEFx (Tian et al., 2014; Tian et al., 2015) or EEFx with IMMx (Tian et al., 2017) terms which both model realistic non-bonded interactions within implicit solvent. In their current implementation the IMMx potential builds upon the EEFx potential by including terms explicitly defining the hydrophobic thickness of the bilayer and its dielectric properties. The bilayer dielectric is adjustable and can be scaled differently during initial structural solution and the final refinement. In each calculation, the backbone dihedral angles of residues 1–35 and 302–333 were randomized then relaxed into non-clashing conformations employing the repulsion-only RepelPot term (Schwieters et al., 2018) using gradient minimization, followed by 40 ps of high-temperature (3500 K) molecular dynamics. During this initial repulsion-only phase, EEFx and IMMx not enabled, as they are not stable in the presence of initial close-contacts. The nonbonded representation was then switched over to the implicit model and 30 ps of molecular dynamics was run. This was followed by annealing to 25 K using EEFx or EEFx with IMMx. Following initial calculations, refinement was performed including the PSolPot term (Wang Y. et al., 2012; Gong et al., 2018; Kooshapur et al., 2018) representing site-specific protein-water interactions along the other restraints in a procedure identical to that above with the exception that there is no torsion angle randomization. We performed three PSolPot calculations. In the first we only used completely unambiguously assigned solvent-accessible residues. This generated an ensemble of structures with improved overall structural resolution. These structures were then used to aid in assigning ambiguous water-proximal resonances. The complete set of water-accessible restraints were then used to refine the ensemble of structures. At the end we ran another simulated annealing structural refinement with several Ramachandran outliers deleted from the PSolPot table. The result of last set of PSolPot calculation showed small improvement in some cases. Structure quality was assessed by MolProbity (Williams et al., 2018). All RMSDs were measured via VMD-XPLOR (Schwieters and Clore, 2001).

NMR structures are solved by including distance measurements and other structural restraints as pseudopotentials into simulated annealing calculations. However, as proteins grow larger, spectral crowding will occur. This is compounded when the protein structure is dominated by a single type of secondary structure, as often occurs in α-helical membrane proteins. Thus, as more distances are measured more peaks appear leading to greater information at the cost of reduced site-specific resolution. However, following observations reported by several groups and within our own laboratory, we found that large domain motions may be mapped by the observable solvent accessible surface (Borcik et al., 2020).

Water-edited SSNMR . We measured the solvent-accessible surface of the closed state of the I131C mutant of KirBac1.1 in POPC bilayers using water-edited SSNMR. These water-edited spectra of U-¹⁵N,¹³C-KirBac1.1 are similar to spectra described previously, but they probe the native closed state rather than the closed state of the R49/151/153/Q mutant (Borcik et al., 2020). This technique capitalizes on the great disparity in ¹H transverse relaxation times (T₂) between water and protons within the protein, where ¹H signal persists for a much longer time within the water bath. Thus, using a T₂ filter we can actively select the ¹H signal originating from the surrounding water. This signal is transferred to the protein via spin diffusion. This polarization transfer follows a characteristic buildup curve obeying a rate equation we adapted previously (Borcik et al., 2020; Luo and Hong, 2010; Najbauer et al., 2019). Representative buildup curves are depicted in Figure 1A. These buildup curves exhibit a good overall fit to our derived rate equation (Eq. 1) (Borcik et al., 2020). As depicted in Figure 1B in red, 4 ms of ¹H_water-¹H_protein mixing is a good representation of solvent-exposed residues. To better understand the water accessible surface, we also acquired a spectrum with 16 ms of ¹H-¹H spin diffusion. The contoured difference in these spectra is depicted in Figure 1C. At 16 ms of ¹H_water-¹H_protein spin-diffusion more embedded parts of protein appear in the spectra, consistent with fit buildup curves presented in Figure 1A. With 16 ms of ¹H_water-¹H_protein mixing we observe most resonances in a standard DARR spectrum without a T₂ filter, further indicating large spin-diffusion coverage (Supplementary Figure S1). M p ( t m ) = M w ( 2 R p R 1 p + 2 R p − R 1 w ) ( e − R 1 w t m − e − ( R 1 p + 2 R p ) t m ) (1) In Eq. 1 the p index specifies protein and w specifies water. M is magnetization on the specified chemical species at mixing time t_m, and R is the rate of longitudinal cross relaxation for the specified species.

In KirBac1.1, we consistently found the best ¹H_water-¹H_protein mixing time for surface residues to be 4 ms. We were able to assign many sites in these spectra (Figure 2). Initially, 51 unambiguous water-edited peaks were assigned based upon our chemical shift assignments for this state of the protein. After multiple iterations of structure refinement, the initial structures helped us to assign an additional 187 ambiguous peaks for a total of 238 solvent-accessibility restraints (Supplementary Figure S2) as described below. However, many solvent accessible peaks, especially methyl groups, remained too degenerate for reasonable assignment. However, three- and four-dimensional versions of these pulse sequences may resolve this ambiguity in even more challenging membrane protein systems.

¹³ C- ¹³ C- ¹³ C 3D spectrum. We obtained sparse distance restraints for tertiary and quaternary structure from a CCC 3D spectrum with 50 and 500 ms of DARR mixing during the first and second mixing periods. The 3D cross peaks were assigned based upon our reported 3D chemical shift assignments. Only completely unambiguous cross peaks were assigned, providing 54 intra subunit distances and 3 inter subunit distances. Given that the sample was uniformly ¹³C enriched, this limited number of distances was expected. More extensive distance assignments would require significantly less isotopic enrichment to provide the needed resolution.

Initial structural calculations. We started our structure refinement process by generating structures using dihedral angles and distance information in Xplor-NIH. The protocol described above in which the PSolPot term was not used in the initial phase was necessitated by difficulties the term has in representing the very extended structures obtained during initial randomization. Using our previously reported ¹³C chemical shift assignments, we determined backbone dihedral angles in TALOSN. The prediction resulted in 502 dihedral angle restraints (φ, ψ). In the first step of structural refinement, 100 structures were generated using Xplor-NIH version 3.2.9 with 502 SSNMR dihedral angles, 54 intra- and 3 inter-subunit SSNMR unambiguous distances, the hydrogen bond potential of mean force (HBPot), and the EEFx potential adapted from CHARMM22 (MacKerell et al., 1998; Tian et al., 2015). The ensemble of the 10 lowest energy structures is presented in Figure 3A. An additional 100 structures were generated with identical restraints, but with the addition of the IMMx function to the EEFx potential with membrane parameters of 27.0 for POPC membrane thickness, profileN set to 2, and the delectric screening value or A parameter to 0.85 (calculations that lack the IMMx function are simply called EEFx and the calculations with IMMx added to EEFx potential function are called IMMx). This ensemble is presented in Figure 3D. As shown in Tables 1, 2, the calculated pairwise RMSD (pwRMSD) via VMD-Xplor for the first step of this structure calculation without water-edited restraints, are 2.4 ± 1 Å and 2.2 ± 0.5 Å for backbone residues 1 to 301 of the EEFx and IMMx calculations respectively. The pwRMSD for the backbone of the well-ordered regions of the protein (residues 40–282) improves to 2.2 ± 1 and 2 ± 0.5 for the EEFx and IMMx calculations respectively. Although these pwRMSD are acceptable for this level of experimental dihedral angle and distance restraints, there is significant room for improvement. This improvement in the quality of the calculated structures shows the importance of water-edited restraint usage for the structure calculation.

Water-accessibility restraints. Previous applications of solvent accessibility as a structure refinement tool utilized solution based paramagnetic relaxation enhancement (sPRE). Generally, paramagnetic relaxation enhancement (PRE) results from the coupling between a magnetically active nucleus and an unpaired electron. The electron may be a stable radical or metal. This unpaired electronic spin may be bound to the protein or free in solution. This interaction has r⁻⁶ range dependence. Recently, soluble paramagnetic probes gained popularity. When these moieties contact the surface of the protein, they introduce the sPRE which can thus be tied to solvent accessible surface (S_Acc). Surface accessibility restraints were initially incorporated in Xplor-NIH using an empirical expression involving distances to neighboring nuclei, and it was shown to qualitatively represent water-protein interactions in solution and solvent PRE data (Wang et al., 2012). Wang et al. found that S_Acc can be calculated with a linear equation, where the slope and intercept is a unique function of a specific protein’s topology. More recently (Gong et al., 2018; Kooshapur et al., 2018), a more quantitative representation of solvent PRE data has been developed, where the observable is represented by Eq. 2. For sPREs this expression is approximate, with the quantitative relationship between Eq. 2 and solvent PRE being somewhat more complicated (Okuno et al., 2020), and yet this formulation has been employed with some success. In this vein, our residue-based water-edited SSNMR-derived surface area data are fit to values computed from molecular structure using Eq. 2. In keeping with the qualitative nature of the representation, the corresponding Xplor-NIH energy term depends only on the correlation between the two quantities (Gong et al., 2018). Gong et al. and Kooshapur et al proposed a grid search algorithm to determine the accessible surface. This included a protein surface integral that can be written in form of a tessellation composed of triangular patches (Eq. 2). In Eq. 2, k' is a constant prefactor, n is the outward-facing distance normal surface, and r is the distance from this surface to a nucleus: Γ s P R E = − k ′ 9 ∑ i a i n i . r i | r i | 6 (2)

They incorporated these concepts into sPRE module and energy potential (PSolPot) to include sPRE data in Xplor-NIH simulated annealing calculations. This potential was shown to be quite effective in direct structure refinement (Gong et al., 2018; Kooshapur et al., 2018).

We now present a new application of the PSolPot potential function to refine protein structures using water-edited SSNMR spectroscopy derived restraints. Water-edited SSNMR identifies the accessible surface of the protein with a similar r⁻⁶ distance dependence. As described above, previous studies found that the overall surface area of the water-protein interface can be expressed by Eq. 3 S A c c = V P π D e f f t m s (3) Where S_Acc is the surface area of the water-protein interface, t m s is the time of mixing until saturation, V_P is the volume of the protein, and D_eff is the effective diffusion parameter. This equation provides a global picture rather than a site-specific view of the water-protein interface. Following Andreas et al. (Najbauer et al., 2019), we previously found the water-to-protein polarization transfer could be defined by a longitudinal cross relaxation-dependent rate equation stated above (Eq. 1).

It has been long known (Bloembergen et al., 1948) that the relaxation term for longitudinal cross relaxation depends on the ¹H-¹H dipolar coupling that has the form of equation 4 from dipolar alphabet. 〈 H l o c 2 〉 A v =   1 3   γ 2 ℏ 2 I ( I + 1 ) ∑ j ( 1 − 3 ⁡ cos 2 θ i j ) 2 r i j − 6 (4) Thus, because of the similar r⁻⁶ dependence, we found the PSolPot potential could accommodate our restraints after modification.

As shown in Figure 2, our extensive chemical shift assignments of water-edited spectra provide restraints for nearly half the protein (full assignments of the aliphatic region are shown in Supplementary Figure S2). Because PSolPot is a correlation function that fits the water accessible surface, the relative signal intensity of each peak can be used as the data input for structural refinement. The chemical shift assignments of the water-edit spectra were performed in two rounds. In the first round, the integrated intensity of resolved unambiguous peaks were used for structure refinement. These 51 assignments were used to refine two sets of 100 structures starting from the 10 lowest energy structures of the EEFx (Figure 3B) and IMMx (Figure 3E) calculations respectively. In the second round, we included the integrated intensity of all possible assignments, corresponding to 238 total PSolPot restraints. This provided two additional sets of 100 structures starting from the same PSolPot-free EEFx (Figure 3C) and IMXx (Figure 3F) ensembles. We then determined the bbRMSD and judged the quality in MolProbity. This indicated the overall structural quality slightly diminished relative to the PSolPot ensemble with only unambiguous restraints (Table 3 and Figure 4). We then deleted 6 Ramachandran outliers and their neighboring residues and repeated the calculations with only 223 PSolPot restraints. This slightly improved the overall structural quality.

We judged the internal consistency of all four final structural ensembles using heavy-atom RMSD, and backbone RMSD. We also judged their objective quality via rotameric, Ramachandran, and Z-score analysis in MolProbity. The statistical summary of all four stages of simulated annealing with EEFx are provided in Table 1. These calculations include the ensemble with only EEFx, the addition of 51 unambiguous assignments, 238 assignments (ambiguous and unambiguous), and finally 223 assignments (ambiguous and unambiguous without Ramachandran outliers). In Table 2 the same statistics are listed after IMMx is included in the calculation. As mentioned above, the addition of the unambiguous water-edited restraints in structure calculation improved the structural quality dramatically. Using the EEFx forcefield and the 51 unambiguous restraints, the pwRMSD for the protein backbone improved from 2.4 ± 1 Å to 0.9 ± 0.2 Å (Table 1) for residues 1 to 301. In the well-ordered regions, residues 40 to 282, the pwRMSD improved from 2.2 ± 1 Å to 0.7 ± 0.3 Å. When the IMMx membrane potential is added to the calculation the pwRMSD improved from 2.2 ± 0.5 Å to 0.9 ± 0.2 Å for the first 301 residues, and from 2.0 ± 0.5 Å to 0.7 ± 0.1 Å for the well-ordered regions (Table2). In most cases the utilization of IMMx produces improvements relative to EEFx within the hydrophobic region of the protein. The addition of unambiguous water-edited restraints did not result in a significant improvement in the structure, where the pwRMSD slightly diminished. Deleting identified Ramachandran violators only improved the pwRMSD slightly.

Overall, the objective structural quality improved with the addition of EEFx, IMMx, and PSolPot restraints as judged by MolProbity. As stated above, the 1p7b crystal structure lacks 75 residues (22.5% of the residues in WT-KirBac1.1 sequence). Our initial Rosetta model includes all 75 residues missing from 1p7b. Out of the 75 residues missing in the X-ray crystal structure, we have experimental SSNMR restraints for 51 residues. The final 24 residues of the protein remain unrestrained. Despite the incomplete information on end of the C-terminus of protein, the best structural ensembles possess up to 92.6% favored rotameric scores and up to 87.6% of residues occupy most favored regions of Ramachandran space. Ramachandran plots and the location of Ramachandran outliers is depicted in Figure 4. As shown in Table 3, the inclusion of EEFx and the 51 unambiguous PSolPot restraints dramatically improved the structural quality compared to both the 1p7b X-ray structure and the starting Rosetta model. The population of residues in favored Ramachandran and rotameric space increases from 66.5 to 74.3% to 85.2 and 82.9% when EEFx terms are included. The addition of 51 PSolPot restraints further improves these statistics to 87.6 and 88.1% favored occupancy. As further depicted in Table 3 and Figure 4, the inclusion of all possible PSolPot restraints does improve upon structural ensembles without these restraints, but slightly deteriorates, indicating that PSolPot is very capable of improving structures with a set of high-quality but relatively sparse restraints, compared to a much longer list of lower-quality information. However, after fully analyzing the structures solved with 238 restraints, and comparing Ramachandran violators to overlapped regions of solvent accessible spectra, we deleted several Ramachandran space violators. This improved the favored rotamer percentage and favored Ramachandran percentage to 91.5 and 87.6%. This further indicates that PSolPot is best implemented with high-quality rather than high-quantity restraints. After significant data quality control, only marginal improvement over the unambiguous structure is observed.