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.

Protein function in various cellular processes is mediated via protein motions, including translational or rotational motion of the whole molecule as well as internal dynamics of their constituent domains. Protein dynamics are typically represented as the superposition of several dynamical modes, each of them characterized by an order parameter describing the amplitude of motions and a correlation time representing the time scale of motions.[1] Most often proteins act as part of a system of biomolecules, where the concerted operation of the system relies on the fine-tuning of the extent and characteristic times of motions in the individual proteins. Consequently, alterations in protein dynamics caused by mutations or posttranslational modifications in an individual protein might lead to aberrant behavior of the whole system. A comprehensive knowledge of protein dynamics is thus an essential prerequisite for a mechanistic understanding of cellular processes.[2]

Intrinsically disordered proteins (IDPs) are a large class of proteins in eukaryotic proteomes, frequently involved in fundamental cellular processes, such as cell cycle control and signal transduction, and disease states, such as cancers and neurodegenerative diseases.[3] IDPs experience a vast range of motions occurring at multiple length and time scales, which can be accessed best through the combination of techniques. For example, proton relaxometry at low magnetic fields provides information on reorientational dynamics occurring at several nanoseconds;[4] NMR spin relaxation at high magnetic fields enables studying fast reorientational dynamics at single-residue resolution,[5] and nanosecond fluorescence correlation spectroscopy (nsFCS) combined with single-molecule Förster resonance energy-transfer spectroscopy gives access to distance dynamics at the length scale of several nanometers and the time scale of tens to hundreds of nanoseconds.[6] Indeed, several studies have combined molecular dynamics (MD) simulation with high-field NMR spectroscopy to describe protein dynamics in IDPs at single-residue resolution.[7−9] Recently, we demonstrated that it is particularly powerful to combine four different approaches (low-field proton relaxometry, high-field 15N spin relaxation, nsFCS, and microseconds-long MD) in order to obtain a comprehensive picture of the multiscale dynamics in the paradigmatic IDP α-synuclein.[10]

Amyloid-beta (Aβ) peptide is an intrinsically disordered peptide of 38–43 residues,[11] which assembles into β-sheet rich oligomeric and fibrillar aggregates in the brains of patients with Alzheimer’s disease (AD).[12] Several mutations and posttranslational modifications of Aβ alter the aggregation propensity of Aβ and potentially play a major role in the initiation and/or spreading of AD pathology.[13−15] Dynamic properties of Aβ, in both the wild-type peptide and the modified forms, have been extensively studied, largely through NMR 15N spin relaxation.[16−20] Here, we combine 15N NMR spin relaxation rates of Aβ at three magnetic fields with previously reported nsFCS,[21] a 30 μs long MD trajectory[22] and ensemble-based hydrodynamic calculations in order to dissect multiscale reorientational dynamics of the 40-residue Aβ peptide (Aβ40) at single-residue resolution. We discuss how the time scale information obtained through such dynamical studies may pave the way for a kinetic characterization of the key events in Aβ aggregation.

15N spin relaxation rates report on protein motions occurring on time scales faster than the rotational correlation time of a protein, which is normally shorter than several nanoseconds to a few tens of nanoseconds.[23] To investigate backbone dynamics in Aβ40, we measured 15N relaxation rates at three magnetic fields (Supporting Information, experimental details). The average 15N R1 rates were 1.99 ± 0.28, 1.70 ± 0.16, and 1.64 ± 0.14 s–1 at 400, 600, and 700 MHz proton Larmor frequency, respectively. The corresponding 15N R2 averages were 3.26 ± 0.80, 3.42 ± 0.93, and 3.60 ± 1.00 s–1, respectively. Residues His13, His14, and Gln15 exhibited larger R2 rates than the average at all three fields (Figure a). The larger R2 rates of these residues are probably caused by exchange-mediated relaxation due to protonation–deprotonation of histidine side chains. In addition, an overall sequence dependence of the 15N R2 was observed, with R2 rates decreasing from Val12 toward the N-terminus and from Lys16 toward the C-terminus. The average 15N,1H heteronuclear nuclear Overhauser effects (NOEs) were 0.06 ± 0.30 and 0.21 ± 0.24 at 600 and 700 MHz proton Larmor frequency, indicating that Aβ40 undergoes extensive dynamics on the picosecond time scale, especially at the N- and C-termini (Figure S1).

Figure 1

(a) Experimental 15N longitudinal (R1) and transverse (R2) relaxation rates of Aβ40 at proton Larmor frequencies of 400 (blue), 600 (green), and 700 MHz (red). (b) Spectral density mapping of experimental 15N relaxation rates, giving spectral densities at five frequencies: 0, ωN of 60 and 70, and ⟨ωH⟩ of 600 and 700 MHz. (c) Dependence of spectral densities at 15N Larmor frequencies, J(ωN), on the spectral densities at frequency 0, J(0), revealing a clear deviation from a single-Lorentzian profile expected for a rigid-body reorientational motion governed by a single correlation time (solid line). Most residues possess J(ωN) smaller than what would be expected for their J(0) values.

NMR relaxation rates carry information on the angular autocorrelation function (ACF) of NMR relaxation-active mechanisms, or equivalently, the spectral density terms relevant for the corresponding spin relaxation rates.[24] Through reduced spectral density mapping, the three 15N relaxation rates measured at each field were transformed to spectral densities at three frequencies, J(0), J(ωN), and J(⟨ωH⟩), where J(⟨ωH⟩) represents the average between J(ωH + ωN), J(ωH), and J(ωH – ωN) (Supporting Information).[25] As a result, the spectral density functions corresponding to reorientational dynamics of individual backbone amides were evaluated at five frequencies (Figure b). The spectral densities decreased at higher frequencies, while the J(0) dependence of J(ωN) and J(⟨ωH⟩) deviated from single-Lorentzian behavior, which would be expected for the rotational diffusion of a rigid molecule under a single rotational correlation time (Figures c and S2). Indeed, J(ωN) values were smaller and J(⟨ωH⟩) were larger than the theoretically expected values, indicating that Aβ40 experiences vast dynamics at time scales faster than 1/ωN of ∼2.3 ns/rad.

To evaluate the extent of exchange-mediated relaxation at time scales slower than the rotational correlation time of the peptide, the J(0) values calculated from 15N relaxation rates at 600 and 700 MHz were compared. The exchange-mediated transverse relaxation depends quadratically on the chemical shift difference between exchanging states (in hertz); therefore, it is expected to exhibit magnetic field dependence.[26] As shown in Figure S3a, the J(0) values obtained at the two magnetic fields were almost identical, suggesting that conformational exchange contributions can be largely excluded. Indeed, if field-dependent exchange-mediated contributions to the R2 rates were 15% or higher, the J(0) values obtained at 700 MHz would be more than 5% larger than the J(0) values at 600 MHz, a difference that is not observed (Figure S3a). In line with this finding, the exchange-free R2 rates (R20) calculated from the previously reported transverse cross-correlated relaxation (CCR) rates[19] showed good agreement with the R2 rates (Figure S3b).

Spectral density analysis of spin relaxation rates provides general insight on protein dynamics; however, interpretation of the obtained spectral density terms is not straightforward as they are determined by both the time scale and amplitude of protein motions.[24] On the other hand, the model-free analysis of 15N relaxation rates in IDPs is complicated by the fact that these proteins undergo multiple modes of internal motions, which may be coupled to each other and to the Brownian rotational diffusion of the protein. As a consequence, the motional parameters obtained through model-free analysis could be regarded only as “effective” parameters with limited physical implications.[27] To overcome these limitations, we combined the analysis of 15N relaxation rates with microseconds-long MD trajectories of Aβ40, which provide detailed atomistic information at various length and time scales. We started with a 30 μs MD trajectory of Aβ40, which was previously calculated at 300 K using a modified version of the a99SB-ILDN force field (a99SB-disp) developed for both folded and intrinsically disordered proteins (Supporting Information).[22] To our knowledge, this is one of the longest MD trajectories reported for Aβ40, which has been validated using a broad range of small-angle X-ray scattering (radius of gyration) and NMR (chemical shifts, scalar and residual dipolar couplings) data.[22]

First, we evaluated how accurately the MD trajectory reproduces some characteristic times of Aβ40 dynamics. For this purpose, the end-to-end distance dynamics of Aβ40 was calculated from the MD trajectory and compared with previously reported experimental nsFCS data.[21] The average end-to-end distance from the MD trajectory was 2.70 ± 0.79 nm, with the histogram of the end-to-end distances showing a small shoulder ∼1.2 nm (Figure a, inset). The calculated distance ACF was first fitted to a single-exponential decaying function, providing a relaxation time of ∼40 ns. However, the autocorrelation function was better described by a two-exponential decaying function (p-value < 0.0001), yielding two relaxation components with 2.5 ns (72%) and 136.2 ns (28%) (Figure a). This results in an MD-predicted weighted-average reconfiguration time of 40 ± 1 ns, which exceeds the experimental value of 30 ± 2 ns as reported in ref (21). The ratio of experimental to MD-based reconfiguration time of Aβ40 is thus 0.75 ± 0.05.

Figure 2

Distance and angular dynamics in the MD trajectory of Aβ40. (a) The end-to-end distance ACF derived from the MD trajectory, showing a good fit with a two-exponential fit (solid line). The inset shows the histogram of the end-to-end distances from the MD trajectory. (b) The angular ACF averaged over 39 backbone amides of Aβ40. The solid line shows an excellent fit to a three-exponential decaying function. The correlation time obtained for the slowest component was ∼3.9 ns, close to the correlation time of the 10–14-residue long segments of Aβ40 (inset, the dashed line).

Next, second-order ACFs were calculated for the 39 individual backbone N–H vectors of Aβ40 from the MD trajectory (Supporting Information). The ACFs showed an excellent fit with three exponential components, which was significantly better than the fit with one and two exponential components (p-value < 0.001). When the fastest correlation time (τfast) was fixed at different values in the range between 50 and 200 ps, the quality of fit remained excellent and the effect on the other fitting parameters was negligible. After the τfast was fixed at 100 ps, the individual ACFs were fitted to three-exponential decaying functions, providing correlation times of 1.2 ± 0.6 and 3.9 ± 1.2 ns for the intermediate (τint) and slow (τslow) motions, respectively. The τslow coincides with the reorientational correlation time calculated for the CA, CA vectors with n = 6 ± 1 (Figure b, inset), suggesting that the origin of the slowest component in N–H reorientations is related to segmental motions in Aβ40. Notably, the obtained value of n is similar to the persistence length reported for disordered polypeptide chains[28] and suggests the statistical (Kuhn’s) segments of 10–14 residues in length.

To further explore the origin of slow reorientations of Aβ40 backbone amides, we utilized the ensemble-based hydrodynamic calculation tool HYCUD.[29] It was previously shown that HYCUD can predict rotational correlation times for several flexible multidomain proteins and macromolecular complexes,[29−33] as well as a series of IDPs in agreement with experimental data from proton relaxometry.[34] Using HYCUD, we calculated the rotational correlation time of Aβ40 segments for an ensemble of 5000 random Aβ40 structures (Supporting Information). The HYCUD-predicted translational diffusion coefficient for Aβ40 at 278 K was 7.54 × 10–7 cm2·.s–1, which corresponds to a hydrodynamic radius of 1.8 ± 0.1 nm, in excellent agreement with experiment[20,35] and the predicted value for disordered peptides of the same size.[36] The HYCUD-predicted correlation time for Aβ40 at 300 K was 3.0 ± 0.1 ns. The ratio of HYCUD-predicted to the MD-predicted correlation time was 0.78 ± 0.23, in close agreement with the ratio of 0.75 ± 0.05 from the nsFCS data (see above). Taken together, we conclude that the MD trajectory requires a time axis scaling factor of ∼0.75 to reproduce the time scale of Aβ40 motions in the range from several to a few tens of nanoseconds.

Next, we used the experimental 15N relaxation rates to rescale the correlation time of the intermediate motions. Because of Aβ40 aggregation at higher temperatures, the 15N relaxation rates were measured at 278 K, which is different from the temperature of the MD trajectory (300 K) and therefore needs to be taken into account before further analysis. The slow segmental motions arise from the chain-like nature of the protein and involve displacement of the surrounding solvent layers; therefore, the temperature dependence of their correlation times is expected to be largely determined by the temperature dependence of solvent viscosity, as shown in ref (37). On the other hand, fast librational motions at the ∼100 ps time scale do not exhibit appreciable temperature dependence of their correlation times.[37] Unlike fast and slow motions, for which their temperature dependence can be fairly simply accounted for, the temperature dependence of the conformational fluctuations at intermediate correlation times is governed by local activation energies and requires further quantification. To estimate the scaling factors for the correlation times of intermediate motions, we followed the IASMIN approach, as introduced in ref (10). Briefly, we started with four 15N relaxation rates, R1 and R2 at the two magnetic fields of 600 and 700 MHz, and minimized a target function representing the deviation between the MD-predicted and experimental relaxation rates through optimization of the scaling factor for τint combined with the optimization of order parameters (Supporting Information). After optimization of the order parameters on the basis of 15N R1 and R2 measured at 600 and 700 MHz proton Larmor frequencies, we used 15N R1 and R2 measured at 400 MHz and the previously reported CCR rates[19] for cross-validation. As shown in Figure S4a, the best fits were obtained with a scaling factor of 1.15 ± 0.10 for the intermediate correlation times, consistent with an activation energy of ∼5 kJ mol–1 for the underlying backbone motions. Notably, the estimated average activation energy is in close agreement with the activation energy of intermediate motions in a disordered protein studied over a large temperature range (268–298 K).[37] The close agreement between the predicted and experimental relaxation rates supports the validity of the optimized order parameters (Figure S4b).

Using the optimized order parameters, we then evaluated τfast, the parameter to which hetNOEs are highly sensitive but R1 and R2 are relatively insensitive. Best agreement of MD-predicted with experimental hetNOEs measured at the two fields (root-mean-square deviation (rmsd) of 0.01) could be achieved by τfast of 125 ± 45 ps, without a significant worsening of the R1 and R2 fits (rmsd less than 4%).

The combined use of microseconds-long MD simulation and 15N relaxation rates at multiple fields thus allowed obtaining the time scales and amplitudes of Aβ40 backbone motions at single-residue resolution. Figure shows that the backbone reorientational dynamics of Aβ40 at 278 K can be satisfactorily described as motions effectively clustered within three distinct time scale regions: fast motions around 100–200 ps (26 ± 13%), intermediate motions around 1.4 ± 0.7 ns (53 ± 14%), and slow motions around 5.2 ± 1.6 ns (21 ± 12%). Notably, the extensive local dynamics of Aβ40 on fast and intermediate time scales is not sufficient to entirely remove the orientational memory of this IDP, in line with the generic presence of long-range correlated dynamics in IDPs as suggested in ref (34).

Figure 3

Residue-specific dynamical parameters of Aβ40, obtained after rescaling of the 30 μs long MD-trajectory of Aβ40 on the basis of the experimental nsFCS and NMR spin relaxation data. (a) Correlation times for the intermediate (τint) and slow (τslow) reorientational motions of backbone amide groups. Residues like S8, Y10, and E11; A21, V24, and G25; and A30 and I31 (highlighted with gray circles) possess τslow values longer than the adjacent residues. Error bars represent fitting errors, rescaled using the proper scaling factors for slow and intermediate motions. (b) Squared order parameters, corresponding to intermediate (S2int) and slow (S2slow) motions. The stretch of residues K16–F20 show consistently large S2slow values around 0.3 (shaded area). Error bars represent variation in the optimized order parameters, when the time-axis scaling factor ranged between 1.05 and 1.25 (see Figure S4a).

The high-resolution picture of Aβ40 dynamics obtained here reveals some interesting features in the regions of Aβ40, which are potentially important for the pathological aggregation of this peptide in Alzheimer’s disease. For instance, residues Ser8 and Tyr10, the sites of posttranslational modifications such as phosphorylation[38] and nitration[39] in the N-terminal region of Aβ, show long correlation times τslow of ∼8 and ∼10 ns, respectively. In the same region of Aβ40 a clear alternation in S2slow values with 1-periodicity is observed, suggesting a propensity of monomeric Aβ40 for structures formed along the aggregation pathway.[40] In addition, residues Ala21, Val24-Gly25, and Ala30-Ile31 possess long correlation times compared to their adjacent residues (Figure ). These residues are located approximately in the beginning, middle, and end of the hairpin conformation, a common structural motif observed along the aggregation pathway of Aβ (Figure a).[41] We speculate that the slow reorientational dynamics of these residues enables their potential roles as hinges during the formation and rearrangement of the hairpin structure.

Figure 4

(a) Cartoon representation of the hairpin structure of Aβ peptide, adapted from the PDB structure of Aβ40 fibrils 2LMO. Residues Y10, A21, V24-G25, A30-I31, and V40 are highlighted. (b) Schematic representation of the role of intra- and intermolecular diffusion and reorientational dynamics in Aβ aggregation, with their characteristic times at 300 K.

Another intriguing feature is that the stretch of hydrophobic residues Leu17-Phe20, known as the central hydrophobic cluster, shows large S2slow values, while their S2int values are relatively small (Figure b). The consistently large S2slow values of Leu17-Phe20 combined with small S2int values indicate that the central hydrophobic cluster in Aβ40 is less mobile already in the monomeric state, as previously suggested on the basis of NMR RDC data.[18] It was previously shown that residues Lys16-Glu22 of monomeric Aβ40 are in direct contact with the protofibril surface.[42] The higher rigidity of these residues in the monomeric Aβ40 reduces the entropic cost of the monomer–protofibril interaction and therefore potentially promotes the secondary nucleation of Aβ40 aggregation on the surface of protofibrils. It should however be noted that Aβ aggregation is a complex multistep process involving initial nucleation of Aβ monomers into oligomers, polymerization–depolymerization, secondary nucleation catalyzed by the protofibril/fibril surface, and fibrillar fragmentation.[43,44] The reorientational dynamics of monomeric Aβ at the residue level is therefore expected to have various impacts on the different steps of Aβ aggregation.

The importance of Aβ reorientational dynamics for aggregation has been extensively studied.[18,45,46] For instance, the higher aggregation propensity of Aβ42 than Aβ40 was suggested to have its origin in the higher rigidity of the C-terminus.[17] In addition, the reduction in the internal dynamics of Aβ40 upon phosphorylation was suggested to contribute to the inability of Aβ40 phosphorylated at Ser26 to aggregate into amyloid fibrils.[20] MD studies on wild-type and mutated forms of the peptide have also suggested an important role of internal flexibility in promoting or hampering fibril formation.[46] On the other hand, it has been suggested that the rate of intramolecular diffusion modulates aggregation propensity, with slow diffusion rates promoting protein aggregation.[47] For Aβ40, the reconfiguration time of ∼30 ns and the average end-to-end distance of 2.7 nm implies an end-to-end intramolecular diffusion coefficient of approximately 4.1 × 10–7 cm2·s–1, close to the values reported for the aggregation-prone disordered proteins.[47] After proper rescaling of the MD trajectory using the experimental nsFCS and NMR relaxation data as detailed above, the intramolecular diffusion coefficient can be determined for any pair of Aβ40 residues. For instance, the pair of residues Tyr10 and Val40 which lie adjacent to each other in several structural models of Aβ40 aggregates[41,48] exhibit a diffusion coefficient of ∼1.3 × 10–7 cm2·s–1, meaning that it would take around 13 ns for these two residues of Aβ40 to diffuse 1 nm away from each other. Because the average correlation times for the slow reorientation of residues Val12-Phe20 and Ser26-Val36 are significantly shorter (∼4 and 3 ns at 300 K, respectively), these two strands of Aβ40 seem to be able to frequently sample the relative orientation suitable for the formation and stabilization of the hairpin-like conformation. It is however important to note that the predicted (intermolecular) translational diffusion of Aβ40 is rather fast (∼1.4 × 10–6 cm2·s–1 at 300 K), meaning that two adjacent Aβ40 molecules can rapidly diffuse away before any stable intermolecular association is formed. Overall, a subtle balance between the intra- and intermolecular distance and reorientational dynamics seems to be important for the kinetic control of the key events during Aβ40 aggregation (Figure b). Support for this hypothesis can be provided through detailed studies of dynamics, where reorientational and distance dynamics are quantified simultaneously through integrative approaches in variants of Aβ with different aggregation properties.

A key feature of the integrative approach followed here is that the characteristic times of motions occurring at different time scales are accessed separately through different techniques. In our previous analysis of α-synuclein dynamics we used proton relaxometry at low fields to probe slow motions at the time scale of several nanoseconds.[10] Because of its low sensitivity, proton relaxometry is feasible only for protein samples at relatively high concentrations in the millimolar range, a condition hard to obtain with an aggregation-prone IDP such as Aβ. Because slow reorientational dynamics in IDPs is largely governed by the hydrodynamic coupling of their statistical segments,[34] we here utilized an ensemble-based hydrodynamic tool (HYCUD) in order to predict the rotational correlation time of Aβ40 segments. The time axis scaling factors derived from HYCUD and nsFCS data are in close agreement, a finding that supports the use of HYCUD-based correlation times for the rescaling of MD trajectories, especially when the protein of interest cannot be studied through proton relaxometry at low fields.

Recent developments in force fields and water models have led to a significant improvement in the accuracy of MD simulations in reproducing structural properties of disordered protein ensembles.[22,49−53] Nevertheless, our results with Aβ, as well as α-synuclein,[10] indicate that despite remarkable progress, the state-of-the-art MD force fields cannot yet accurately capture the time scale and the entire extent of reorientational dynamics in IDPs. The integrative approach presented here can thus be used to quantify the temporal and conformational mobility limitations of different force fields and serve as a benchmark to compare their performance in representing protein dynamics in IDPs.

In summary, we have combined NMR 15N spin relaxation rates at three magnetic fields with microseconds-long MD simulation and single-molecule nanosecond fluorescence correlation spectroscopy and obtained a high-resolution picture of the reorientational dynamics of Aβ40. A mechanistic picture emerges in which the aggregation behavior of Aβ is controlled through a subtle balance between the characteristic times of intra- and intermolecular diffusion and reorientational dynamics of this peptide. We suggest that a comprehensive investigation of Aβ dynamics through integration of different techniques paves the way for a mechanistic understanding of how disease-related mutations and modifications modulate misfolding and aggregation of Aβ in Alzheimer’s disease.