Solid-State NMR Provides Evidence for Small-Amplitude Slow Domain Motions in a Multispanning Transmembrane α-Helical Protein

Proteins are dynamic entities and populate ensembles of conformations. Transitions between states within a conformational ensemble occur over a broad spectrum of amplitude and time scales, and are often related to biological function. Whereas solid-state NMR (SSNMR) spectroscopy has recently been used to characterize conformational ensembles of proteins in the microcrystalline states, its applications to membrane proteins remain limited. Here we use SSNMR to study conformational dynamics of a seven-helical transmembrane (TM) protein, Anabaena Sensory Rhodopsin (ASR) reconstituted in lipids. We report on site-specific measurements of the 15N longitudinal R1 and rotating frame R1ρ relaxation rates at two fields of 600 and 800 MHz and at two temperatures of 7 and 30 °C. Quantitative analysis of the R1 and R1ρ values and of their field and temperature dependencies provides evidence of motions on at least two time scales. We modeled these motions as fast local motions and slower collective motions of TM helices and of structured loops, and used the simple model-free and extended model-free analyses to fit the data and estimate the amplitudes, time scales and activation energies. Faster picosecond (tens to hundreds of picoseconds) local motions occur throughout the protein and are dominant in the middle portions of the TM helices. In contrast, the amplitudes of the slower collective motions occurring on the nanosecond (tens to hundreds of nanoseconds) time scales, are smaller in the central parts of helices, but increase toward their cytoplasmic sides as well as in the interhelical loops. ASR interacts with a soluble transducer protein on its cytoplasmic surface, and its binding affinity is modulated by light. The larger amplitude of motions on the cytoplasmic side of the TM helices correlates with the ability of ASR to undergo large conformational changes in the process of binding/unbinding the transducer.


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. A comparison of 15 N spectra of ASR collected on a 600 MHz spectrometer at a spinning rate of 8 kHz, and at 7 °C and 30 °C. Spinning sideband intensities remain unchanged and match the theoretical simulation of a typical 15 N chemical shift anisotropy (CSA) tensor, overall indicating that the protein does not undergo rotational diffusion. Simulation was performed using the program SIMPSON 6 with the CSA parameters of !"# = -109 ppm, η=0.2. 7 Figure S3. Amino acid sequence and the topological model of ASR. Helices are shown as rectangles and are labelled A through G. Assigned residues at 7 °C are shown as blue and green circles; assigned residues at 30 °C are shown as green circles. The cytoplasmic side is on top. Figure S5. Bulk R 1ρ measurements at a spinning frequency of 14.3 kHz, at 7 °C and 30 °C for (A) 1 H, (B) 13 C and (C) 15 N. 15 N R 1ρ relaxation rates at fast MAS rates. R 1ρ relaxation rates measured in fully protonated samples may include coherent contributions from anisotropic interactions which are incompletely averaged by the fast (50-55 S6 kHz) magic angle spinning. To estimate an order of magnitude of the residual coherent effects, we measured 15 N R 1ρ relaxation rates in a model dipeptide N-Ac-[ 13 C, 15 N-labeled]-Val-Leu (NAVL) , under typical experimental conditions which were used to measure relaxation rates in ASR at 7 °C (ω r /2π=50 kHz, 15 N lock RF field ω 1 /2π=12 kHz). Previous multiple solid-state NMR measurements (e.g., internuclear distance measurements) on NAVL [9][10][11][12][13]  expect that R 1ρ rates to be governed by the residual anisotropic interactions. R 1ρ rates in NAVL were determined to be ~0.23±0.09 s -1 and 0.42±0.13 s -1 (Figure S6) for valine and leucine, respectively, with both values being less than the lowest R 1ρ rate of 0.60 s -1 measured in ASR for protonated amide nitrogen atoms.

Bulk order parameter measurements at 30 °C.
As explained in the main text, ASR samples were found to be unstable at 30 °C on the time scale of a full 3D DIPSHIFT experiment. To probe the amplitudes of motions, we performed the bulk order parameter measurements using 15 N-and 13 C-detected DIPSHIFT experiments with TMREV-4 recoupling (Figures S1A1, A2). 15 N and 1D NCA spectra are shown in Figure S7A, C, and representative dipolar dephasing curves are in Figure S7B, D. The observed small changes in the extracted dipolar order parameters are comparable to the small change in the order parameter of 15 N-labeled crystalline sample of N-Ac-Valine (Table S1).
Thus, small differences in the dipolar coupling at 7 °C and 30 °C are representative of the systematic effects from the equipment rather than from changes in the amplitudes of motions in ASR. Figure S7. TMREV-4 measurements of the 1 H-15 N bulk order parameter in the 1,3-ASR sample at 7 °C and 30 °C. (A) 1D NCA spectrum with some amino acid type-specific assignments indicated in the figure. (B) Representative TMREV 1 H-15 N dipolar dephasing from the bulk peak in the 13 Cα detected spectrum at 7 °C and 30 °C. (C) Nitrogen spectrum with amino acid assignment assignments. (D) Representative nitrogen-detected TMREV 1 H-15 N dipolar dephasing curves of the Thr/Ser/Gly peak at 7 °C and 30 °C.    Figure S9. Backbone 15 N R 1 (A) and R 1ρ (B) relaxation rates measured on a 800 MHz spectrometer at 7 °C (red squares) and 30 °C (black circles). This is the same as Figure 4 except only residues in the center and extracellular sides are shown. Relaxation rates of residues in the interhelical loops and on the cytoplasmic sides of TM helices (shown in grey) have been removed from clarity. Figure 4 represents the full version of this figure. Notes: * No residues detected in this region. ** Single residue detected in this region.

Simple Model Free Fit
For residues with at least 5 out of 6 experimentally measured 15  at 800 MHz and 30°C the best fit single motional order parameter !"" ! , timescale τ c,eff and activation energy E a were determined by minimizing the following χ 2 equation. (S2) We also calculate the Akaike's Information Criterion (AIC), 14 Bayesian Information Criterion (BIC) 15 and corrected Akaike's Information Criterion (AICc) 16 which are defined with respect to the number of fit parameters k and the number of experimental data points included in the fit n.
These values are calculated for each residue (see Table S5) and to allow comparison to EMF they are calculated for each molecular fragment (see Table S7).
Uncertainties in the best fit parameters !"" ! , τ c,eff and E a were determined by a Monte Carlo procedure. First, the best fit parameters were used to back calculate all experimental data.

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Gaussian distributed noise was then added to each of the back-calculated values for 5000 times, and the χ 2 minimization was done for each iteration to determine the distribution of the fit parameters.

Modified Extended Model Free Fit
In this modified EMF fit the spectral density function J(ω) is modelled assuming the presence of fast and slow motions where the fast motional parameters !,!"# ! , !,!"# , and !,!"# were defined locally for each residue and the slow motional parameters !,!"# ! , !,!"# and !,!"# were defined globally for all residues within the given molecular fragment (7 helices, BC and FG loops). The modified EMF approach was used for residues with all six experimental measurements available ( and R 1ρ at 800 MHz and 30 °C. The best fit parameters were determined by minimizing χ 2 for each of the nine fragments by using a grid search followed by steepest decent procedure: where relaxation rates are defined by Eqs 1-6 and 9 from the main text. The summation extends over all residues with all 6 experimentally measured values available within a molecular fragment (N 1 ). The reduced χ 2 and the degrees of freedom (d.f.) are defined as Uncertainties in the best fit parameters !,!"# ! , !,!"# ! , !,!"# , !,!"# , !,!"# and !,!"# were determined by the Monte Carlo procedure. First, the best fit parameters were used to back calculate experimental data. Gaussian distributed noise was then added to each of the backcalculated values for 1000 iterations, and the χ 2 minimization was done for each iteration to determine the distribution of the fit parameters. Helix E (D125-N148) 0 n/a n/a n/a n/a Helix G (Q195-L221) 0 n/a n/a n/a n/a   Helix E (D125-N148) n/a n/a n/a n/a n/a n/a Helix G (Q195-L221) n/a n/a n/a n/a n/a n/a S25 *NCO dipolar order parameters were used, where available 17 as additional experimental restraints in the fit compared to EMF results in Table S6.  Figure S15. Movie of a mode 7 from Normal Mode Analysis of ASR trimer performed using Nomad-Ref webserver 18 .