Measurement of Residual Dipolar Couplings using Magnetically Aligned and Flipped Nanodiscs

Abstract

Recent developments in lipid nanodiscs technology have successfully overcome the major challenges in the structural and functional studies of membrane proteins and drug delivery. Among the different types of nanodiscs, the use of synthetic amphiphilic polymers created new directions including the applications of solution and solid-state NMR spectroscopy. The ability to magnetically-align large size (>20 nm diameter) polymer nanodiscs and flip them using paramagnetic lanthanide ions have enabled high-resolution studies on membrane proteins using solid-state NMR techniques. The use of polymer-based macro-nanodiscs (>20 nm diameter) as an alignment medium to measure residual dipolar couplings (RDCs) and residual quadrupole couplings by NMR experiments has also been demonstrated. In this study, we demonstrate the use of magnetically aligned and 90°-flipped polymer nanodiscs as alignment media for structural studies on proteins by solution NMR spectroscopy. These macro-nanodiscs, composed of negatively-charged SMA-EA polymers and DMPC lipids, were used to measure residual ¹H-¹⁵N dipolar couplings (RDCs) from the water-soluble ~21-kDa uniformly-¹⁵N-labeled flavin mononucleotide binding domain (FBD) of cytochrome-P450-reductase. The experimentally measured ¹H-¹⁵N RDC values are compared with the values calculated from crystal structures of cytochrome-P450 reductase that lacks the transmembrane domain. The N-H RDCs measured using aligned and 90°-flipped nanodiscs show a modulation by the function (3cos²θ−1), where θ is the angle between the N-H bond vector and the applied magnetic field direction. This successful demonstration of the use of two orthogonally oriented alignment media should enable structural studies on a variety of systems including small molecules, DNA and RNA.

Graphical Abstract

Introduction

The need for atomic-resolution structures of membrane proteins has been well demonstrated by the recent studies.^1–3 While there are many challenges in obtaining near-native structures, the introduction of nanodiscs has opened new avenues for structural and functional studies of membrane proteins.^4–9 A nanodisc is a lipid bilayer disc surrounded by an amphipathic molecule such as membrane scaffold protein (MSP),⁴ DNA,¹⁰ short amphipathic peptides,^11–13 or synthetic amphipathic polymers.^14–16 While all of these nanodiscs have been demonstrated to be excellent membrane mimetics and quite valuable for membrane protein structural biology, the polymer based nanodiscs studies have expanded the flexibility and scope of the nanodiscs technology as the synthetic polymers can be tailored to the need.^{14, 17–30} The recent developments of different types of synthetic polymers have enhanced the applications of polymer based nanodiscs by making them amenable for investigation by a variety of biophysical techniques including solution and solid-state NMR spectroscopy and cryoEM.^{21, 31–35} One of the unique advantages of these polymer nanodiscs is that the polymers can be used to directly extract membrane proteins along with lipids from their cellular environment without the use of a detergent.^{14, 17} As a result, it is possible to functionally reconstitute a membrane protein in a native lipid environment for further structural and functional studies. Another advantage is that the size of polymer nanodiscs can be varied by simply changing the ratio between the polymer and lipids.^20–21 The small size nanodiscs (<20 nm diameter) are useful for the well-established solution NMR studies, while the large-size nanodiscs (>20 nm in diameter, also called as ‘macro-nanodiscs’) magnetically align and therefore useful for static solid-state NMR studies.^20–21 These magnetically-aligned ‘macro-nanodiscs’ have also been demonstrated to be useful in the measurement of anisotropic NMR parameters such as residual dipolar couplings (RDCs)³⁶ and residual quadrupolar couplings (RQCs).³⁷ Using the polymer macro-nanodiscs as an alignment medium, we have previously reported the feasibility of measuring residual ¹H-¹⁵N dipolar couplings from water-soluble uniformly-¹⁵N-labeled cytochrome c for high-throughput structural studies by solution NMR spectroscopy. In this study, we demonstrate the feasibility of measuring RDCs using two different types of macro-nanodiscs alignment media whose alignment directions are orthogonal.

There has been considerable interest in the development of membrane mimetics and other media that can spontaneously align in the presence of an external magnetic field.^38–44 Studies have reported the magnetic-alignment of bicelles and macro-nanodiscs with the bilayer normal perpendicular to the magnetic field axis.^{21, 38–39, 45} The alignment direction of nanodiscs can be changed by varying the magnetic susceptibility with the addition of paramagnetic metal ions (such as lanthanide ions including Yb³⁺) as reported previously.^{21, 46–48} The addition of paramagnetic lanthanide ions has been shown to 90°-flip bicelles or macro-nanodiscs to result in the parallel orientation of the lipid bilayer normal with the magnetic field axis.^47–49 Although the magnetically-aligned media are commonly used to measure RDCs, this study demonstrates the feasibility of measuring RDCs using two different media that have orthogonal alignment directions. We used a negatively-charged SMA-EA polymer nanodiscs as an alignment medium to measure ¹H-¹⁵N RDCs from the ~21-kDa flavin mononucleotide binding domain (FBD) of cytochrome P450 reductase (CPR). The experimentally measured RDCs were compared with the values calculated from different crystal structures of the CPR, lacking the transmembrane domain, reported in the literature (Table S1). We then used the 90°-flipped nanodiscs to modulate the experimentally measured RDCs. The comparison of RDCs measured from the normally aligned and the 90°-flipped nanodiscs media show the dependence of RDC values on the second-order polynomial function, (3cos²θ−1); where θ is the angle between the N-H bond and the external magnetic field direction.

Materials and Methods

Poly(Styrene-co-Maleic Anhydride) cumene terminated (SMA), with a ~1.3:1 molar ratio of styrene:maleic anhydride and an average molecular weight of M_n~1600 g/mol, N-methyl-2-pyrrolidone (NMP), 2-aminoethanol (EA), triethylamine (Et₃N), HEPES, potassium phosphate, acetic acid, ytterbium(III) chloride, hydrochloric acid (HCl), and sodium hydroxide (NaOH) were purchased from Sigma-Aldrich®. 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine-N-diethylenetriaminepentaacetic acid (ammonium salt) (DMPE-DTPA) were purchased from Avanti Polar Lipids, Inc®. Uniformly ¹⁵N-labeled truncated-FBD (trFBD) lacking the transmembrane domain of cytochrome-P450-reducatse was expressed and purified as reported earlier.⁵⁰

Preparation of nanodiscs

An anionic SMA-EA polymer was used to prepare nanodiscs containing synthetic lipids. SMA-EA was synthesized and characterized as reported previously.²¹ SMA-EA polymer stock solutions were prepared by dissolving 100 mg of SMA-EA in 5 mL of 0.5 M NaOH, adjusted the pH with 0.5 M HCl to pH 7.4, and added water to adjust the volume to make 100 mg/mL solution. 10 mg/mL DMPC stock solutions were prepared by adding 100 mg of DMPC powder to 10 mL of 10 mM HEPES (and 100 mM NaCl at pH 7.4) and followed by three freeze-thaw cycles. DMPC:DMPE-DTPA lipid stock solution was prepared by dissolving DMPC and DMAPE-DTPA (95:5 molar ratio) in 80:20 v/v chloroform:methanol, and removing the solvent by evaporation under a stream of N₂ gas and followed by high vacuum drying for 4 hrs. The resulting DMPC:DMPE-DTPA lipid mixture was dispersed in buffer containing 10 mM HEPES (and 100 mM NaCl at pH 7.4) to give a final lipid concertation of 10 mg/mL. Nanodiscs were prepared by the addition of the polymer stock solution to the lipid stock solution with 1:1 v/v to give a 1:1 w/w ratio of lipid:polymer. The resulting transparent solution was subjected to three freeze-thaw cycles and incubated for overnight at 30 °C. The resulting transparent nanodiscs solutions were purified by removing free polymers (or polymer aggregates) using size exclusion chromatography (SEC). The purified nanodiscs fractions were collected and concentrated using a 50-kDa cut-off Amicon® filter to produce the required final concentration. In all the reported experiments, the lipid concertation was estimated based on the starting lipid concentration used in the sample preparation. The size of nanodiscs was measured from TEM images. A paramagnetic salt was added to the nanodiscs to flip the orientation of the magnetically-aligned nanodiscs in the presence of an external magnetic field. These “flipped-nanodiscs” were prepared by the adding the required amount YbCl₃ to DMPC:DMPE-DTPA nanodiscs from a 100 mM YbCl₃ stock solutions.

³¹P NMR experiments:

Bruker NMR spectrometer operating at a resonance frequency of 400.11 MHz for proton and 161.97 MHz for ³¹P nuclei was used to acquire ³¹P NMR spectra. A 5 mm double-resonance MAS NMR probe was used under static condition. ³¹P NMR spectra were acquired using a 5 μs 90° pulse followed by a 25 kHz TPPM (two pulse phase modulation) proton decoupling. 512 scans were acquired for each sample with a relaxation/recycle delay of 2.0 s. ³¹P chemical shift was externally referenced by setting the chemical shift of ³¹P resonance from H₃PO₄ to 0 ppm.

²H-NMR spectroscopy:

40 mg/mL of nanodiscs in 10 mM HEPES (and 100 mM NaCl at pH 7.4 and 10% D₂O) with and without YbCl₃ were taken in a 5 mm NMR tube. ²H NMR spectra were acquired using a 500 MHz Bruker NMR spectrometer.

RDC measurements using In-Phase, Anti-Phase Heteronuclear Single-Quantum Coherence (IPAP-HSQC)

Samples for the measurement of RDCs through NMR experiments were prepared by the addition of ¹⁵N-trFBD to a stock solution of nanodiscs to give a final concentration of 150 μM protein and 40 mg/mL lipid concertation. 10% D₂O was added to the NMR sample for locking. Deuterium NMR spectra were used to check the magnetic-alignment of nanodiscs. Two-dimensional ¹⁵N/¹H IPAP-HSQC NMR spectra were acquired using a Bruker 800 MHz NMR spectrometer equipped with a TCI cryoprobe. All IPAP spectra were acquired using the following parameters: 8 scans, 2048 t₂*512 t₁ points (for each AP and IP), 1 s recycle delay, 15 ppm spectral width for ¹H, and 40 ppm spectral width for ¹⁵N. After the completion of experiments, the acquired data was split into two HSQC data using the split ipap2 AU macro using the default setting. The data were then processed using Topspin by zero-filling up to 4028*4028 points. The spectra were then analyzed using the NMRFAM-SPARKY software⁵¹. NMR resonances were assigned as reported elsewhere⁵⁰. Peak position and line widths were measured using the integration module in Sparky and ¹H-¹⁵N RDCs were calculated using ¹J_HN(isotropic)-¹J_HN (anisotropic) in Excel. The lower limit for the accuracy in the measurement of a peak position in the spectrum was calculated by the ratio of LW/(S/N) as reported previously.⁵² The structural coordinates for trFBD were extracted from the X-ray crystal structures of CPR downloaded from RCSB protein data bank.⁵³ Hydrogen atoms were added to the structures using the PDB server⁵⁴. Alignment tensors were obtained using PALES software⁵⁵. PBD coordinates were loaded into the PALES software along with the measured RDCs. The alignment tensor and back calculated RDCs were obtained using singular value decomposition (SVD) method using the “bestFit” module with default setting in PLAES software. Correlations between the measured and calculated RDCs are represented by the correlation coefficient (R) obtained from the PALES software.

Results and Discussion

CPR is a ~78 kDa protein comprised of four domains: NADPH biding domain, flavin adenine dinucleotide (FAD) binding domain, flavin mononucleotide (FMN) binding domain (FBD), and the transmembrane (TM) domain. Several studies have utilized the water-soluble trFBD domain lacking the transmembrane region to study its interaction with cytP450.^{50, 56} Truncated-FBD is negatively charged at neutral pH (net charge is −19 at pH 7.4, and the isoelectric point (pI) is 4.4). In order to avoid any interaction between the polymer belt of the nanodisc and trFBD, we used a negatively charged polymer (called SMA-EA) to prepare nanodiscs (Figure 1A).²¹ We used DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine) and DMPE-DTPA (1,2-dimyristoyl-sn-glycero-3-phosphoethanolamine-N-diethylenetriaminepentaacetic acid) lipids to prepare the nanodiscs. DMPC is a zwitterionic lipid and DMPE-DTPA is a negatively charged lipid with a metal ion chelator as the head group. SMA-EA was synthesized as reported previously.²¹

Figure 1. Characterization of SMA-EA nanodiscs.

(A) Chemical structure of SMA-EA polymer. (B) Size exclusion chromatogram of nanodisc sample prepared from 1:1 w/w DMPC:SMA-EA. (C) size distribution of DMPC-SMA-EA nanodiscs. Gaussian fitting of the size distribution shown in (C) was calculated from the TEM images shown in (D-F). Nanodiscs were selected manually using the ImageJ software with the ROI module. The diameter of the nanodisc measured from TEM images is 35± 10 nm.

Magnetic-alignment and flipping of SMA-EA macro-nanodiscs

The SMA-EA nanodiscs were prepared and purified as explained above in the materials and methods section. The size distribution of SMA-EA macro-nanodiscs was characterized using transmission electron microscopy (TEM) images (Figure 1). Static ³¹P (from the lipid head group) and ²H (from D₂O) NMR experiments were carried out to evaluate the magnetic-alignment of nanodiscs as shown in Figure 2. 5 mol % DMPE-DTPA lipid, that can chelate the added paramagnetic metal ions and can avoid the metal binding to SMA-EA, was used to DMPC lipids to change the orientation of the nanodiscs. Nanodiscs prepared from the 95:5 molar ration of DMPC:DMPE-DTPA showed an aligned ³¹P NMR peak at −13 ppm (Figure 2A, bottom spectrum) suggesting that the nanodiscs are aligned in the presence of magnetic field with the lipid bilayer normal oriented perpendicular to the direction of the external magnetic field. The addition of YbCl₃ salt showed a ³¹P peak around +22 ppm (Figure 2A, top spectrum) suggesting the 90°-flipping of the nanodiscs where the lipid bilayer normal is oriented parallel to the magnetic field direction (Figure 2A).⁴⁸ The observed difference in the ³¹P line widths between the normally aligned (Fig. 2A, bottom) and the 90°-flipped (Fig. 2 A, top) nanodiscs is mainly due to the paramagnetic relaxation effect from the added Yb³⁺ ions that shorten the spin-spin (T₂) relaxation of ³¹P nuclei in the sample used to obtain the 90°-flipped spectrum (Fig. 2A, top). In addition, the orthogonal orientation of the motional axis of lipids (i.e. the lipid bilayer normal) to the magnetic field direction (B_o) for Fig. 2A (bottom) can effectively suppress the line-broadening contributions from any non-uniaxial alignment of nanodiscs and the mosaic spread of lipids within the nanodiscs. These observed ³¹P NMR spectra confirm the orthogonal orientations of nanodiscs in the aligned (Fig. 2A, bottom) and 90°-flipped (Fig. 2A, top) samples.

Figure 2. Characterization of magnetic alignment of nanodiscs.

³¹P (A) and ²H (B) NMR spectra of magnetically-aligned SMA-EA nanodiscs (1: 1 w/w lipid:polymer), containing 95:5 molar ratio of DMPC:DMPE-DTPA, recorded at 35 °C with the bilayer normal perpendicular (bottom) and parallel (top) to the direction of the external magnetic field. The phosphate head groups of the DMPC phospholipids contribute to the observed ³¹P signals (A), whereas the motionally-averaged water molecules contribute to the observed ²H quadrupole splittings (B). The concentration of lipids was 100 mg/mL for (A) and 40 mg/mL for (B). 1 mM YbCl₃ was added to flip the nanodiscs as explained in the supporting information. DMPE-DTPA lipid was used to chelate the paramagnetic Yb³⁺ metal ion to the DTPA group.

We used these nanodiscs to record deuterium NMR spectra which is typically used method to check the alignment of the medium used in solution NMR experiments.⁵⁷ The deuterium NMR spectra showed a motionally-averaged quadrupole coupling doublet (~1.6 Hz) further confirming the magnetic alignment of nanodiscs (Figure 2B). It should be noted that water molecules interacting with the lipid bilayer align with a smaller order parameter as compared to that of nanodiscs. Additionally, the measured ²H RQC (residual quadrupolar coupling) values are the average of the isotropic values from bulk (“free”) water molecules and the anisotropic values from the lipid-bilayer-bound water molecules. After the addition of YbCl₃, the ²H RQC (residual quadrupolar coupling) values increased by a factor of 2 (~3.4 Hz) suggesting the flipping of nanodiscs in complete agreement with the results observed from ³¹P NMR experiments.⁴⁸ These results suggest that the nanodiscs can be used as an alignment medium to measure RDCs from water-soluble molecules such as protein, RNA, DNA, small molecules, etc.

Measurement of residual dipolar couplings from trFBD using aligned nanodiscs

After establishing the alignment medium conditions, a uniformly labeled ¹⁵N-trFBD was added to the nanodiscs sample. ³¹P and ²H NMR experiments on the nanodiscs sample containing trFBD confirmed the alignment of nanodiscs and no observable disruption by the added trFBD protein. Then, 2D ¹H/¹⁵N-InPhase-AntiPhase(IPAP)-Hetero nuclear Single Quantum Coherence (HSQC) NMR spectra were recorded on the nanodiscs samples containing trFBD (Figures S1–S3). We used three types of nanodiscs to measure the RDCs values: 1) DMPC-SMA-EA, 2) DMPC-DMPE-DTPA-SMA-EA, and 3) DMPC-DMPE-DTPA-Yb³⁺-SMA-EA. Selected regions of IPAP-HSQC spectra are shown in Figure 3. The measured J (or scalar) couplings are modulated by the N-H RDCs in the 2D spectrum. These RDCs values were extracted from the spectra by subtracting the isotropic J couplings that were measured from trFBD in the absence of nanodiscs; additional details can be found in the materials and methods section. The measured RDC values are used for the analysis of the structure of trFBD. First, we analyzed the RDCs measured using DMPC-SMA-EA nanodiscs, where nanodiscs are aligned with their bilayer normal perpendicular to the magnetic field direction. The several crystal structures available in the PDB database for CPR lacking the transmembrane domain (Table S1) were used to extract the coordinates for the investigated trFBD domain and used to calculate the N-H RDC values. The calculated RDC values were then compared with the experimentally measured RDCs using the PALES software. The correlation plots are shown in Figure 4 and the correlation coefficient (R²) is shown in Figure 5C. Overall, the calculated RDCs using all the reported crystal structures of CPR showed a good correlation (with R²>0.9) with a few exceptions. An overlap of different crystal structures of trFBD used in the analysis of RDC values are shown in Figure 5B. Overall, the secondary structure of the trFBD domain in CPRs is conserved among all the different structures while the loop regions show a variation. There are four functionally important and highly conserved loops in the structure of trFBD: 85–90, 138–147, 174–180, 207–212. The difference between the calculated and experimental RDCs are shown in Figure S5 and in Table S2 for all the crystal structures used for the analysis. While the difference in the RDC values is within 3 Hz for most amino acid residues of truncated-FBD, the residues in the loop regions and a few residues in other regions of the protein showed larger deviation as shown in the plots in Figure S5 and the values reported in Table S2. While the variation in the structure of the loop regions is reflected as the difference between the calculated and experimental RDCs, the reason for the deviation observed for other residues is not clear. The trFBD protein structures deposited with PDB-ID 4Y9U and 5URE showed the best correlation with the experimental RDCs. The correlation plot of experimental and calculated RDCs is shown in Figure 5A for 4Y9U which shows an R² value of 0.948. These results demonstrate the feasibility of using an anionic polymer (SMA-EA) to measure RDCS from an anionic water-soluble protein (trFBD). While an excellent agreement between the calculated and experimental RDCs is observed, the deviations are mainly attributed to the low-resolution and variation of the structure of the loop regions of trFBD due to the large mobility of the residues in the loop. Further studies using this approach on other proteins could be valuable in developing an optimized protocol that can be used for a variety of systems.

Figure 3. RDCs measured from trFBD using nanodiscs.

A) 2D HSQC NMR spectrum of ¹⁵N-trFBD under isotropic conditions. B) 2D IPAP-HSQC NMR spectra of 150 μM ¹⁵N-trFBD in the presence of 1:1 w/w DMPC:SMAEA nanodiscs with 40 mg/mL lipid concentration, 10% D₂O, 10 mM Kpi, 100 mM NaCl, pH 7.4, and at 35 °C. The nanodiscs were magnetically-aligned with the lipid bilayer-normal oriented perpendicular to the external magnetic field direction. (C) Selected regions of the 2D IPAP-HSQC NMR spectra of 150 μM ¹⁵N-trFBD in the presence of DMPC, 95:5 molar ratio of DMPC:DMPE-DTPA with the bilayer normal perpendicular to the magnetic field axis, and 95:5 molar ratio of DMPC:DMPE-DTPA-Yb³⁺ with the bilayer normal parallel to the magnetic field axis as indicated. The combined residual N-H dipolar coupling and isotropic scalar (or J) coupling values are shown, and the scalar couplings are given in parenthesis. 2D ¹H/¹⁵N IPAP-HSQC NMR spectra are given in Figures S1–S3. Histogram plots showing the distribution of RDCs measured from NMR spectra (Figures S2 and S3) of ¹⁵N-trFBD in aligned (Figure S2) and flipped (Figure S3) nanodiscs are shown in Figure S4. The difference between the calculated (using crystal structures summarized in Table S1) and experimental RDCs is shown in Figure S5 and Table S2. As shown in Figure S6, no significant chemical shift perturbation due to the addition of nanodiscs, lipids or Yb³⁺ metal ions was observed.

Figure 4. Analysis of RDCs measured using aligned nanodiscs:

Correlation of experimentally measured and calculated RDCs for ¹⁵N-trFBD in DMPC-SMA-EA nanodiscs. The calculated RDC values were obtained using the X-ray crystal structures of CPR (cytochrome-P450 reductase) lacking the transmembrane domain (indicated by the pdb number) and PALES software.

Figure 5. Analysis of RDCs measured from FBD.

(A) Correlation of experimentally measured RDCs with the calculated values for truncated-FBD. Experimental RDCs were measured from NMR spectra as described in Figure 2, while the calculated RDCs were obtained from the crystal structure of truncated-CPR (pdb # 4Y9U). (B) Overlap of structures of truncated FBD obtained from different crystal structures used in (C). (C) The R² values obtained for different crystal structures of trFBD used in the calculation of RDCs. The correlation plots for all the crystal structures are shown in Figure 4.

Measurement of residual dipolar couplings from FBD using flipped nanodiscs

RDCs measured using a single set of alignment medium are useful for correlation of the known structures. However, we need a set of five independent orthogonal alignment tensors to completely describe a bond vector orientation, independent of the other structural information.⁵⁸ This is due to the degeneracy of RDCs, as a single RDC value can have multiple solutions spanning a two faced cone around the sphere.⁵⁹ Several methods were used to obtain the different alignment tensors such as modulating the charge of the alignment medium by doping⁵⁹, changing the charge on the protein by mutations,⁶⁰ composite alignment medium⁶¹, using a different alignment medium such as stretched gels,⁶² DNA⁶³, and filamentous phage⁶⁴. Here we used DMPE-DTPA as a negatively charged lipid to change the charge of the lipid bilayer in the nanodiscs to see whether we can obtain an orthogonal tensor. The experimentally measured RDCs using DMPC-SMA-EA nanodiscs with and without DMPE-DTPA lipids are compared in Figure 6A. The RDCs obtained by doping with DMPE-DTPA showed a negligible change when compared to that obtained from DMPC alone, and showed a linear correlation (Figure 6C). These results indicate that the alignment tensor is not altered upon the inclusion of negatively charged DMPE-DTPA lipids unlike the case with other alignment medium. The partial alignment of the protein in the presence of the alignment medium is due to the steric hindrance and electrostatic interactions.⁶⁵ Changing the charge of the alignment medium would change the interaction between the alignment medium and the protein due to the non-spherical distribution of charges on the surface of the protein. This change could lead to a different alignment tensor as previously shown using bicelles.^59–60 But, it is remarkable that this is not the case in the polymer nanodiscs used in this study as the high negative charge density of the SMA-EA polymers constituting the belt of the nanodisc overwhelms the minor negative charge from the 5 mol % DMPE-DTPA lipids used in the sample.

Figure 6. Effect of flipping the alignment axis of nanodiscs on RDCs.

Comparison of ¹H-¹⁵N RDCs measured from SMA-EA nanodiscs containing ¹⁵N-labeled truncated-FBD and DMPC (black) or DMPC:DMPE-DTPA (without (green) and with 1 mM YbCl₃ (red)) with the bilayer normal perpendicular (A and C) and parallel (B and D) to the magnetic field axis.

Our efforts in getting the orthogonal tensor using negatively doped nanodiscs did not give the results as observed for other types of alignment media. Therefore, we utilized this unique property of the nanodiscs samples used in this study to measure RDCs with 90°-filliped nanodiscs which do not change the alignment tensor in the molecular frame. Flipping of the nanodiscs was accomplished by adding Yb³⁺ ions to DMPC-DMPE-DTPA-SMAEA nanodiscs. Then, NMR experiments were carried out to measure RDCs using the flipped nanodiscs containing ¹⁵N-labeled trFBD. No significant chemical shift perturbation (CSP) was observed upon the addition of nanodiscs and Yb³⁺ ions, suggesting that there are no significant structural changes in the protein present in the aligned and 90°-flipped nanodiscs samples (Figure S6). The RDCs measured using aligned (that is without paramagnetic doping) and flipped (with Yb³⁺ ions) nanodiscs are different as compared to aligned nanodiscs (shown in Figures 6B), while the correlation between the calculated and measured RDCs are in good agreement (Figure S7). The RDCs are modulated by {3cos²(θ+90)-1} as shown in Figures 6D, S8 and S89 These results suggest that the entire matrix of alignment medium (that is nanodiscs) and the embedded trFBD are rotated by 90° upon 90°-flipping of the alignment direction of nanodiscs, while the alignment tensor in the molecular frame is unaltered (Figure S10). Any small deviation from their expected value (i.e., 3cos²(θ+90)-1) may be attributed to the differential averaging of RDCs between the two different (i.e., aligned and flipped) orientations of the nanodiscs as shown for the ¹⁷O residual quadrupole couplings (RQCs) of water.³⁷ It is worth mentioning that this type of experiment can only be possible with polymer nanodiscs, whereas bicelles tend to give different alignment tensors when the charge of the bilayer is changed⁵⁹ and the introduction of metal ions to flip bicelles would change the charge of bicelles.

Conclusions

In conclusion, we demonstrated the use of anionic SMA-EA nanodiscs with different lipid composition as alignment medium to measure the RDC values for the water-soluble ¹⁵N-trFBD. The experimentally measured RDCs were compared with the calculated RDCs from the known crystal structures to find the best correlated structure for trFBD. Our experimental results showed that due to the high polymer change density, it is possible to change the charge of the lipids within the nanodiscs without altering the alignment tensor in the molecular frame. This property enabled the measurement of RDCs under two different alignment conditions, with either the bilayer normal parallel or perpendicular to the magnetic field, but without altering the alignment tensor in the molecular frame. The RDCs measured under aligned and 90°-flipped orientation of nanodiscs showed a correlation defined by (3cos²θ−1). The successful demonstration of the use of nanodiscs to measure two different sets of RDCs will be useful in solution NMR studies and further expand the application of nanodiscs, and can also be used to determine the dynamics information of protein. Studies utilizing the reported approach to study other water-soluble biomolecules and optimizing the approach to investigate positively-charged molecules would further broaden the scope of the use of two orthogonally oriented nanodiscs alignment media.