Reorientational Dynamics of Amyloid-β from NMR Spin Relaxation and Molecular Simulation

Amyloid-β (Aβ) aggregation is a hallmark of Alzheimer’s disease. As an intrinsically disordered protein, Aβ undergoes extensive dynamics on multiple length and time scales. Access to a comprehensive picture of the reorientational dynamics in Aβ requires therefore the combination of complementary techniques. Here, we integrate 15N spin relaxation rates at three magnetic fields with microseconds-long molecular dynamics simulation, ensemble-based hydrodynamic calculations, and previously published nanosecond fluorescence correlation spectroscopy to investigate the reorientational dynamics of Aβ1–40 (Aβ40) at single-residue resolution. The integrative analysis shows that librational and dihedral angle fluctuations occurring at fast and intermediate time scales are not sufficient to decorrelate orientational memory in Aβ40. Instead, slow segmental motions occurring at ∼5 ns are detected throughout the Aβ40 sequence and reach up to ∼10 ns for selected residues. We propose that the modulation of time scales of reorientational dynamics with respect to intra- and intermolecular diffusion plays an important role in disease-related Aβ aggregation.

15 N R 1 rates were measured using conventional pulse sequence schemes with eight relaxation delays spaced between 10 and 800 ms. A train of selective 180 degree 1 H pulses during the relaxation block was used to eliminate cross-correlated relaxation effects while minimally perturbing water magnetization 1 . 15 N R 2 rates were measured through a CPMG-based pulse sequence with τ cp of 1 ms (ν CPMG = 1000 Hz) and ten relaxation delays spaced between 4 and 240 ms 1 . Residue-specific R 1 and R 2 rates were determined through fitting to single exponential decay functions. The corresponding errors were estimated via 100 Monte Carlo (MC) simulation runs, for which the fit residuals served as random noise. 1 H, 15 N heteronuclear NOEs were obtained by comparison of peak intensities between saturated and reference spectra, using a saturation block of 7.5 s and a total recycle delay of 8 s. Because of the inherently low sensitivity, the heteronuclear NOE experiment was not measured at the 400.13 MHz spectrometer with a room-temperature probe. The exchange-free R 2 rates, R 2 0 , were estimated from previouslyreported CCR rates 2 , where the value of κ was evaluated with the magnitude (∆σ) and angle (θ) of the 15 N CSA tensor set to -170 ppm and 22.5°, respectively 3 . Data were processed using NMRPipe 4 and analyzed using Sparky 3 (T.D. Goddard and D.G. Kneller, http://www.cgl.ucsf.edu/home/sparky).

Spectral density analysis
Reduced spectral density mapping of 15 N relaxation rates 5 was achieved using an in-house MATLAB script. Briefly, the 15 N relaxation rates R 1 and R 2 and heteronuclear NOE measured at each magnetic field (i.e. 600 and 700 MHz proton Larmor frequency) were converted to three spectral density values, J(0), J(ω N ) and J(<ω H >), where J(<ω H >) represents the average between J(ω H +ω N ), J(ω H ) and J(ω H -ω N ). As a result, the spectral density function was evaluated at five different frequencies: 0, 60, 70, and (effective) 600 and 700 MHz.

MD simulation
The MD trajectory was taken from 6 . As described there: the MD simulation of Aβ40 was performed using the a99SB-disp force field with the optimized TIP4P-D water model. The simulation started from an extended conformation of Aβ40, solvated in a 60 × 60 × 60 Å 3 box containing 6661 water molecules and 50 mM NaCl. The system was initially equilibrated at 300 K and 1 bar for 1 ns, then 30,000-ns production run at 300 K and 1 bar was performed in the NPT ensemble with the Anton specialized hardware at 2.5 fs time step. Nonbonded interactions were truncated at 12 Å and the Gaussian split Ewald method with a 32 × 32 × 32 mesh was used for the electrostatic interactions. The MD frames were saved at 1 ns intervals.

MD-based analysis of 15 N relaxation rates
Second-order angular autocorrelation functions (ACFs) for the 39 individual backbone N-H vectors of Aβ40 (all residues except D1) were calculated from the MD trajectory. A Gaussian window function with a correlation time of 50 ns was applied to all ACFs to ensure their decay to zero without considerably affecting the initial part of the ACFs. The ACFs were then fitted to exponential decay functions, with i=1,2,3, S 2 and τ represent the squared order parameters and correlation times, respectively, and ∑ 2 = 1. Using the best-fit parameters obtained with a three-exponential decay function, which was generally better than one or two-exponential functions, the individual spectral density functions at angular frequency ω were then calculated as: Finally, 15 N longitudinal (R 1 ) and transverse (R 2 ) auto-relaxation rates, 15 N-1 H cross-relaxation rates (σ) and heteronuclear NOEs, and transverse cross-correlated relaxation rates (CCR, η xy ) were calculated as: . The effective NH bond length of 1.04 Å was used to account for zero-point vibrations 7 . The 15 N CSA tensor magnitude (Δσ) was set to -170 ppm. The angle θ between NH bond vectors and the main axis of the 15 N CSA tensors was set to 22.5° 3 .

MD-based analysis of segmental reorientations
Second-order angular ACFs were calculated for the C A i-1 ,C A i and C A i-n ,C A i+n vectors of Aβ40 from the MD trajectory with n=1,2,3,4,5 and 7. The obtained ACFs showed better fits to a threeexponential decay functions when compared to one-and two-exponentials (p-value <0.0001). Using the best-fit parameters obtained with a three-exponential decay function, the weightedaverage reorientational correlation times were calculated for the segments of various lengths (as shown in Fig. 2b, inset), with the uncertainties in the correlation times estimated on the basis of fitting errors.

MD-based analysis of intramolecular diffusion rates
To compare with the previously reported experimental sm-nsFCS data, where the N-and Ctermini of Aβ40 were labelled with Alexa488 and Alexa 647, 8 the end-to-end distance between the N-terminal nitrogen atom of Asp1 and the C-terminal oxygen atom of Val40 was evaluated along the MD trajectory. The end-to-end distance ACF was then calculated. After applying a Gaussian window function with a correlation time of 400 ns to ensure the decay of ACF to zero at very long times without significantly affecting its initial part, the distance ACF was fitted to one-or two-exponential decay functions and the reconfiguration time of the Aβ40 chain between its two termini was determined. The MD-based reconfiguration time required a scaling factor of 0.75±0.05 to match the experimental value. Assuming that the relative motion of the two termini of Aβ40 is best described as diffusion of a Gaussian chain in a square-well potential, the effective end-to-end diffusion coefficient (D) of Aβ40 was estimated through 9 : where <r 2 > is the mean square end-to-end distance from the MD trajectory and τ r is the MDbased reconfiguration time after scaling by 0.75 (see above). A similar procedure was followed for the analysis of intramolecular diffusion between Tyr10 and Val40.

HYCUD calculations
An ensemble of 5000 random Aβ40 structures was generated using the program Flexible-Meccano 10 , thereafter side-chain atoms were added by the program SSCOMP. HYCUD calculations were performed as described in [11][12] . Briefly, each member of the Aβ40 ensemble was split into three non-overlapping fragments (residues 1-13, 14-27, 28-40), and hydrodynamic calculation for the isolated fragments were made at 5 °C using the atomic effective radius (AER) of 2.9 Å 13 . The use of this AER value was validated by the comparison between the HYCUDpredicted translational diffusion coefficient and its corresponding hydrodynamic radius (R h ) with the experimental values. After correction for the hydrodynamic drag caused by nearby fragments, the ensemble-average rotational correlation time of each fragment was obtained. The uncertainty of the HYCUD-predicted correlation time was estimated from the standard deviation of the results obtained for 10 sub-ensembles each containing 500 conformers.  Figure S3. Contribution of conformational exchange to Aβ40 relaxation rates. a) The J(0) values obtained from the spectral density analysis of 15 N relaxation rates at two magnetic fields show close agreement, suggesting that the field-dependent exchange-mediated relaxation does not significantly contribute to R 2 . b) The exchange-free R 2 rates estimated using CCR rates are in close agreement with the R 2 rates measured at 600 MHz, further supporting the negligible contribution of conformational exchange to relaxation rates. The largest deviations were observed for residues Gln15 and Lys16, probably due to the protonation-deprotonation of their nearby Histidines 13 and 14. Figure S4. Temporal rescaling of the MD trajectory of Aβ40, on the basis of 15 N R 1 and R 2 rates measured at proton Larmor frequencies of 600 and 700 MHz. a) When combined with the order parameter optimization, the best agreement between the MD-predicted and experimental rates were achieved using a scaling factor of 1.15±0. 10