Solid-state NMR reveals a comprehensive view of the dynamics of the flexible, disordered N-terminal domain of amyloid-β fibrils

Amyloid fibril deposits observed in Alzheimer's disease comprise amyloid-β (Aβ) protein possessing a structured hydrophobic core and a disordered N-terminal domain (residues 1–16). The internal flexibility of the disordered domain is likely essential for Aβ aggregation. Here, we used 2H static solid-state NMR methods to probe the dynamics of selected side chains of the N-terminal domain of Aβ1–40 fibrils. Line shape and relaxation data suggested a two-state model in which the domain's free state undergoes a diffusive motion that is quenched in the bound state, likely because of transient interactions with the structured C-terminal domain. At 37 °C, we observed freezing of the dynamics progressively along the Aβ sequence, with the fraction of the bound state increasing and the rate of diffusion decreasing. We also found that without solvation, the diffusive motion is quenched. The solvent acted as a plasticizer reminiscent of its role in the onset of global dynamics in globular proteins. As the temperature was lowered, the fraction of the bound state exhibited sigmoidal behavior. The midpoint of the freezing curve coincided with the bulk solvent freezing for the N-terminal residues and increased further along the sequence. Using 2H R1ρ measurements, we determined the conformational exchange rate constant between the free and bound states under physiological conditions. Zinc-induced aggregation leads to the enhancement of the dynamics, manifested by the faster conformational exchange, faster diffusion, and lower freezing-curve midpoints.

Amyloid-␤ (A␤) 2 protein is one of the major components of neurotoxic amyloid plaques in the brains of patients with Alzheimer's disease. The deposits are made up of A␤ fibrils displaying distinct morphological features (1,2). A␤ is also present in vivo in oligomeric form, which is believed to be very toxic and capable of disrupting the cell membrane (3,4). Short fibrillary entities are also capable of membrane disruption, and, in general, cellular toxicity might be related to the dynamic properties of all A␤ species (5,6).
A␤  is most abundant in fibrils, although A␤ 1-42 is often considered to be more toxic (7). A␤ comprises a structured C-terminal domain spanning the well-characterized cross-␤ motif and a mostly unstructured N-terminal domain, corresponding to residues 1-16 of the full-length protein. Molecular dynamics simulations suggest that the N-terminal domain is not entirely disordered but can sample turns and ␤-sheet structures (8 -11).
The N-terminal domain has been found by several studies to be crucial in regulating the aggregation properties of A␤ (12)(13)(14)(15)(16)(17)(18). It contains the main binding and regulatory sites for interaction with metals (19 -25) as well as several regulatory sites that have recently been implicated to be controlled via posttranslational modifications (16, 17, 26 -29). For example, the H6R familial mutation associated with the early onset of Alzheimer's disease and isomerization of aspartate at position 7 to isoaspartate increase aggregation propensities and zinc-dependent oligomerization (26 -30). In vitro, this type of isomerization has also been suggested to lead to enhanced insolubility and resistance to enzymatic degradation (26,(31)(32)(33). Furthermore, molecular dynamics simulations revealed differences in the correlated dynamics between the C-terminal and N-terminal domains upon mutations at positions 6 and 7, which are important for defining polymorphic states and are likely to be involved in altering the aggregation properties between the WT and mutants (9). In general, Hori et al. (35) hypothesized that the region around positions His-6 and Asp-7 can be a "hot spot" that facilitates A␤ deposition and the development of Alzheimer's disease (34). Another important regulatory spot in the N-terminal domain is likely to be related to the post-translational phosphorylation of Ser-8, which has been shown to lead to a distinctly different fibril morphology and suggested to affect the initial nucleation of A␤ fibrillation (27,28) as well as promote and stabilize the formation of toxic aggregates (17,36,37). 3 Animal models show that Zn 2ϩ coordination can play a crucial role in the formation of plaques in vivo (20,40,41). At concentrations of the order of what is found at synapses, Zn 2ϩ specifically binds to A␤ and promotes aggregation (42,43). Noy et al. (44) proposed that Zn 2ϩ stabilizes transient (nonfibrillary) amyloid forms. The concentration of zinc ions in amyloid plaques reaches 1 mM (43). Miller et al. (46) suggested that the mechanism of Zn 2ϩ binding is due to a population shift of polymorphs, similar to other large zinc-binding proteins (47). In the NMR structure of Zn-bound A␤ [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] (48), His-6, Glu-11, His-13, and His-14 are coordinated with Zn. It has also been suggested that the aggregation may be governed by the conformational flexibility of His-6 (19).
The internal flexibility of the N-terminal domain is likely to be very important for its functionality of controlling the aggregation. Disordered protein regions are known for their control of multiple biological functions, including allosteric regulation and enzymatic catalysis (49 -51). Combined with the high number of existing post-translational modifications and mutations in the N-terminal region, which have the potential to modify structural ensembles, 3 studies of the dynamics of this region can reveal the underlying molecular basis of the aggregation control associated with these modifications.
The general flexibility of noncore regions in A␤ has been demonstrated by multiple techniques such as nuclear magnetic resonance (NMR) (52-57), EPR (58), hydrogen-deuterium exchange probed by MS (59 -61), X-ray crystallography (62), and fluorescence spectroscopy (63). However, experimental site-specific studies of the dynamics of the insoluble aggregates of A␤ in general and in the N-terminal domain in particular are relatively sparse due to challenges in obtaining the necessary resolution and sensitivity in the solid noncrystalline state (52, 64 -69). Of note are the works of Fawzi et al. (70,71), who utilized solution NMR saturation transfer approaches to probe the binding of monomeric A␤ to the surface of protofibrils.
In fact, the available structures of the WT A␤ 1-40 fibrils solved by solid-state NMR start at residue 9 (53,72), highlighting the enhanced dynamics of the N-terminal region. Furthermore, Hong and co-workers (69) identified several pools of water in the fibrils such as in the matrix, interfibrillar, peptidebound, and inside cavities. These different water pools are likely to be crucial in modulating the A␤ dynamics and transient interactions between the two domains. The structure of fibrils has been shown to be hydration-independent, at least in the structured region, based on chemical shift data (54). Thus, solvation likely has the largest effect on the properties of the dynamics rather than the overall structure. The motions in the N-terminal region in particular are expected to be highly sensitive to hydration.
The goal of this work was to characterize the site-specific dynamics of selected side chains in the flexible N-terminal domain in the context of hydrated A␤ 1-40 fibrils. We utilized deuterium static solid-state NMR techniques (73)(74)(75)(76) in combination with the selective labeling of the side chains to achieve a comprehensive view of the dynamics of this largely disordered domain. The results allowed us to obtain a quantitative picture of the motions of the domain, with the flexibility of the side chains gradually decreasing along the N-terminal chain in the hydrated fibrils. Using 2 H R 1 measurements, we also measured the rate of the conformational exchange of the N-terminal domain, which likely arises due to the transient interactions with the structured amyloid core. Finally, we compared the dynamics in the N-terminal domain of the mature A␤ 1-40 fibrils of the 3-fold symmetric polymorph with those of the amorphous aggregates formed in the presence of zinc, which demonstrate the enhancement of the dynamics.

"Singly" labeled samples for N-terminal domain side chains
Using A␤ 1-40 peptides with deuterium labels incorporated at a single residue along the N-terminal sequence, we generated a number of singly labeled samples of A␤ fibrils with morphologies corresponding mostly to the 3-folded symmetric/twisted polymorph (2,67,77). We employed previously developed protocols based on seeding procedures (2,54) and confirmed the resulting morphologies using transmission EM (TEM).
The positions of the labeled residues and typical TEM images are shown in Fig. 1, and the position of the label in each individual side chain is listed in Table 1. For the His-6 side chain, the labeling with the -His modification was employed, for which the deuteration site is in the methyl group. This modification did not affect the morphology of the resulting fibrils (Fig. S1).
The deuterium line shape and longitudinal relaxation measurements were used to probe the dynamics in these selectively labeled samples. We have previously investigated the effect of multiple labeling sites in valine to investigate side-chain dynamics. The conclusion is that the relaxation times of C ␤ deuteron are over an order of magnitude longer than for methyl groups and are effectively suppressed in static experiments with the use of short interscan delays (78).

Qualitative analysis of the data suggests a hypothesis of free and transiently bound states for the N-terminal domain
The high-temperature line shapes for the N-terminal residues in the hydrated fibrils are significantly narrowed beyond what is expected due to typical local fluctuations such as fast methyl rotations, rotameric jumps, and ring flips (Fig. 2) 79). As the temperature is lowered, a widening of the lines is observed with a sharp increase in the wide component appearing around the bulk freezing point of water (ϳ265 K) for the Ala-2, Phe-4, and His-6 residues. For the Gly-9 and Val-12 residues, a significant fraction of the wide component is already apparent at much higher temperatures. For Val-12, a typical relatively wide pattern corresponding to rotameric jumps is observed at 37°C, whereas for Gly-9 in addition to the wide component, there is still a narrowed region at the center of the spectrum. In addition, for the Phe-4, His-6, and Gly-9 side chains, the longitudinal relaxation data (Fig. 3) display a striking crossover curve (i.e. an abrupt sigmoidal-like change in T 1 with temperature), suggesting two different contributions to relaxation stemming from the dramatic differences in the local environments of the two components. At the same time, the relaxation curves remain single exponential even at the middle of the crossover (Figs. S2 and S3), pointing to the likelihood of exchange between the two components on the timescale faster than T 1 . As will be elaborated later, for Ala-2 and Val-12, relaxation is dominated by fast local methyl rotations and is not sensitive to hydration.

Flexibility of N-terminal domain of A␤ fibrils
The temperature-dependence behavior of both the line shapes and relaxation does not exhibit any hysteresis behavior; i.e. the same results are obtained independently of whether the experiments are performed by starting at the physiological conditions and freezing the samples or by starting at low temperatures and heating the samples. This points toward the fact that the system is in equilibrium with respect to freezing the bulk water surrounding the immediate hydration layer and cavities (69); in other words, we do not have a situation in which there are two states of bulk water.
Specific evidence on a dynamic exchange between the two fractions, detected by line shape and longitudinal measurements, is also seen from the rotating frame relaxation measurements, 2 H R 1 . These experiments are particularly sensitive to microsecond timescale conformational exchange processes (80 -92). The existence of the relaxation rate "dispersion curve," the dependence of the relaxation rate on the radio frequency field strength, serves as an indication of the presence of conformational exchange at the microsecond timescale. As elaborated below, we observed such a dispersion profile for the fibrils labeled at the Ala-2 methyl position. Interestingly, for all residues, the dry fibrils lack the features of the narrowing behavior in the line shapes and the crossover behavior in the relaxation data (Figs. 3 and 4), indicating that solvation is crucial in the onset of the global dynamical modes responsible for these features.
Based on all the available data, we propose a hypothesis that in the hydrated fibrils, the N-terminal domain exchanges between the free state in which large-scale concerted motions of the whole domain dominate the dynamics at high temperatures and the "bound" state in which these motions are quenched (Fig. 5). The nature of the bound state is likely due to transient interactions with the well-structured C-terminal Table 1 Residue-specific side-chain labeling patterns and main local motional modes at high temperatures for the free state of the N-terminal domain

Figure 2. Representative 2 H static solid-state NMR line shape data in the hydrated fibril samples of A␤ 1-40 in the 3-fold symmetric polymorph at several temperatures. Also shown (lowest right panel, in red)
is the line shape of the isolated N-terminal domain (residues 1-16) labeled at the F4-ring-d 5 position, for which the narrow peak around 0 kHz is attributed to the HOD signal. Note the intrinsic differences in the quadrupolar interactions for different residues, specified in Table 2.

Flexibility of N-terminal domain of A␤ fibrils
domain of A␤. Residues located closer to the N terminus (Ala-2, Phe-4, and His-6) have a significantly lower fraction of the bound state, probably due to weaker interactions with the C-terminal domain compared with the residues further along the chain. As the temperature is lowered, the large-scale motions of the N-terminal domain diminish, and they are very significantly quenched near the bulk freezing point of water when the frozen bulk solvent no longer acts as a plasticizer. This effect of water is reminiscent of the hydration effect on slow dynamics in globular proteins (i.e. solvent-driven glass transition) (78, 93-96). Bauer et al. (97) also reported the crucial effect of solvation on the s-ms-scale dynamics of the exposed residues of amyloid fibrils composed of HET-s 218 -289 protein using 13 C and 1 H solid-state NMR under magic-angle spinning conditions and over a broad temperature range. The role of solvent on amyloid structure formation has also been probed by explicit molecular dynamics simulations to illustrate how water controls the self-assembly of higher-order structures and plays a role in amyloid polymorphism (98). The rest of the quantitative data analysis proceeds according to the described hypothesis, and the R 1 measurements allow us to determine the chemical exchange rate constant between the free and bound states under physiological conditions. Note that the N-terminal domain in isolation (corresponding to residues 1-16 of the full-length A␤) in the hydrated state surprisingly does not show the line narrowing observed in the context of the fibrils. Fig. 2 (see the red line in the bottom panel) demonstrates the line shape of this isolated fragment labeled at the F4-ring-d 5 position. Thus, it appears that the packing of the fibrils renders enhanced flexibility to the N-terminal domain, which likely is functionally relevant. It is also important to note that the methyl-bearing side chains in the C-terminal core of the fibrils (Leu-17, Leu-34, and Val-36), when probed with the same technique of 2 H line shape analysis, did not show any dependence on solvation, unlike the side chain of Met-35 span-

Figure 5. Schematic representation of the model in which the disordered N-terminal domain (curved line) transiently interacts with the structured C-terminal domain (blue rectangle).
In the free state, the N-terminal domain is assumed to undergo isotropic diffusion, as represented by the gray sphere, whereas in the bound state, the interactions quench this mode. The parameters of the models are shown as the corresponding symbols.

Flexibility of N-terminal domain of A␤ fibrils
ning a water-accessible cavity (66,67,69). Thus, solvation in conjunction with the environment of the fibrils promotes the flexibility of the N-terminal domain. Without the environment of the fibrils in the lyophilized hydrated state, the side chains of the N-terminal fragment are free to stack against each other by forming nonnative intermolecular contacts, which are likely to lead to the partially aggregated state responsible for the observed restriction in the dynamics.

Determination of the fraction of free and bound states from the line shape data
The general strategy for the determination of the fractions of the free and bound states corresponds to the decomposition of the line shapes into a narrow component of the Lorentzian shape and the wide non-Lorentzian components (Fig. S4). The former component is assumed to correspond to the free state with motions governed by isotropic diffusion, and the latter component is assumed to correspond to the bound state. For the case of Gly-9, this analysis yielded an unreasonably high fraction of the bound state (75%) at 37°C, which contradicted the existence of the crossover in the relaxation data. Thus, for this residue, we assumed that a part of the non-Lorentzian line shape is due to deviations from isotropic diffusion. The deviation could arise because the probe is at the backbone. The fraction bound in this case was taken as a percentage of the rigid (full powder pattern) line shape. In this regard, it is important to note that for Val-12, located further along the backbone, all of the non-Lorentzian line shape can be attributed to the bound state, with some extent of rotameric motions of the valine side chains present in the bound state, as detailed under "Experimental procedures." To determine to what extent the location of the probe on the backbone rather than on the side chain affects the freezing of Gly-9 at a higher temperature, we also probed the Phe-4 site at the backbone position labeled as D ␣ only (Fig. S5). The spectrum remains almost entirely unfrozen at 280 K, at which Gly-9 is already over 70% in the bound state. At 263 K, there is still a significant fraction of the mobile phase for the F4-D ␣ site. Thus, it is clear that the backbone position alone does not cause a significantly higher freezing point. Due to the low sensitivity of this sample (only one deuterium per A␤ molecule), quantitative line shape decomposition was unreliable, and we were not able to assess deviations from the approximation of isotropic tumbling.
The resulting fractions at 37°C (Fig. 6A) show that the population of the bound state progressively increases along the N-terminal sequence. The temperature dependence of the populations (Fig. 6B) displays sigmoidal behavior. The data were fitted to the following function, in which T m is the midpoint of the freezing curve, is the characteristic width of the transition region, and a and b are the higher and lower temperature baselines, respectively. The midpoint of the transition is at 268 K for Ala-2, Phe-4, and His-6 and at 284 K for Gly-9 (supporting information SI5). Thus, the midpoint of the freezing of the first 6 -7 res-idues coincide with the freezing of the bulk point of water, whereas for the residues further along the chain, freezing is observed at higher temperatures. Additionally, the transition is significantly wider for Gly-9 (the value of is 3.5-4 times higher than that of Ala-2-His-6) Note that parameter a might yield a more accurate overall hightemperature fraction bound projection than just the estimation at a single temperature of ϩ37°C, and we thus display it in the same figure (Fig. 6A) for comparison purposes.

Determination of the timescale of the large-scale motions in the free state assuming an isotropic diffusion model
We invoke the simplest assumption for the large-scale motions of the N-terminal domain as isotropic diffusion. Obvi- Figure 6. A, fraction of the bound state (p bound ) derived from the 2 H line shape analysis, either determined directly from line shape data at 37°C (blue) or as the upper temperature baseline parameter from the fits to the sigmoidal curves of Equation 1 (black). Note that the fit to Equation 1 was not performed for Val-12. B, p bound as a function of the temperature. The solid lines represent the fits to the data according to Equation 1. C, diffusion coefficient D fitted based on the 2 H line shapes at 37°C according to the isotropic diffusion approximation.

Flexibility of N-terminal domain of A␤ fibrils
ously, this is an approximation, as the environment in the fibrils is not expected to be isotropic. However, this simple model allows us to obtain the relative timescales of the diffusive motions in the free state. The local motional modes were taken as typical modes for the given residues consistent with the temperature dependence of the line shapes (73,75,79,99,100) (Table 1). By modeling isotropic diffusion as discrete nearestneighbor jumps on the surface of a sphere, as described under "Experimental procedures," the diffusion coefficients D were obtained by matching the experimental and simulated line shapes. The resulting values of the diffusion coefficients at 37°C are shown in Fig. 6C, and they demonstrate a sizeable decrease along the N-terminal sequence. An alternative model with the sharp temperature dependence of the diffusion coefficient could not reproduce the line shapes at temperatures close to T m ; i.e. it is not possible to reproduce the existence of both the central sharp component and the wide powder pattern (supporting information SI7 and Fig. S6) with a single value of D.

The origin of the crossover in relaxation curves and determination of the timescale of chemical exchange between free and bound states at temperatures close to the midpoint transition
The relaxation behavior (Fig. 3) both below and above freezing is governed by mechanisms consistent with the topology of the side chain (73,79). Furthermore, the most effective mechanisms are closest in timescale to the Larmor precession frequencies: for the Ala-2 and Val-12 side chains, these are methyl three-site jumps; for Phe-4, the phenylalanine ring flips; and for Gly-9, these are two-site jumps of the CD 2 group. The situation is more complex for His-6 as in principle both fast methyl rotations and ring flips can contribute to relaxation. An interesting and important feature is that for the side chains for which there is a considerable hydration dependence of the relaxation (i.e. relaxation times become much smaller upon hydration), there is also a crossover in the relaxation curves. This is the case for the Phe-4, His-6, and Gly-9 side chains.
For the Phe-4 site, relaxation at high temperatures is consistent with ring flips, whereas at the low temperatures, the flipping motion slows significantly. Note that the diffusion around the ring rotation axis (i.e. around the 2 dihedral angle) is ruled out based on the line shape pattern (101,102). At low temperatures, one can observe strong relaxation anisotropy: at a frequency of 0 kHz, the contribution is primarily from the free state, whereas at Ϯ60 kHz, the contribution is primarily from the more rigid bound state. Around the midpoint of the crossover, when there is still a significant fraction of the free state even though the intrinsic relaxation rate of the bound state is not very effective, the relaxation of the wide component (Ϯ60 kHz) is actually governed by the exchange between the free and bound states, as elaborated at the end of this section.
For His-6, at low temperatures, the comparison with the dry sample in which methyl jumps dominate the relaxation as well as the analysis of the temperature dependence of the relaxation indicates that methyl three-site jumps are the main relaxation mechanism. The values of T 1 in the low temperature range of the relaxation curve show a decrease in temperature, indicating that the motions are in the fast regime with respect to the Larmor frequency. This behavior would not be expected for the ring-flipping motions of the imidazole ring. In contrast, at high temperatures, there is the onset of an additional ring-flipping motion of the imidazole ring, giving rise to a major contribution at a frequency of 0 kHz. The ring flipping of imidazole can be functionally relevant for the modulation of the metal coordination properties of the N-terminal domain. Similar to the case of Phe-4, at intermediate temperatures, the relaxation of the bound component is governed by the exchange between the free and bound states. However, unlike the case of Phe-4, the powder pattern spectrum of the bound state is motionally narrowed by 1 ⁄ 3 due to methyl rotations, and thus there is less of a spectral separation between the bound and free states, which complicates the determination of the exchange rates.
For the case of Gly-9, the two-site jumps of the CD 2 group are the major relaxation mechanism at both extremes of the temperature ranges, albeit with different efficiencies for the free and bound states. For the intermediate temperature range of 280 -260 K, if we assume that the relaxation is determined by the CD 2 jumps in the bound state, the resulting rate constants would yield a line shape pattern inconsistent with the experimental results (i.e. these simulations would show overpronounced horns for the wide component). Thus, the exchange between the bound and free states again dominates the relaxation in this temperature range.
The quantitative details of the modeling of the relaxation rates are elaborated under "Experimental procedures." The temperature dependence of the rate constants and high and low temperature limits yield values of activation energies for the local motions. They do not provide any major insights relevant to our global picture, and we list them in supporting information SI6.
Based on the simplified treatment using the McConnell equations (103,104), the relaxation of the bound state at intermediate temperatures for Gly-9, His-6, and Phe-4 is given by R 1 bound ϭ p free k ex . By taking p free from the line shape data, we calculate the k ex rate for temperatures close to the midpoint of the relaxation crossover. These temperatures are slightly below the T m values corresponding to the p bound freezing curves from the line shape analysis (Fig. 7). The resulting values of k ex are 21 Ϯ 3 s Ϫ1 for Phe-4 at 262 K, 9 Ϯ 2 s Ϫ1 for His-6 at 262 K, and 8 Ϯ 2 s Ϫ1 for Gly-9 at 280 K.

Determination of the conformational exchange rate constant between bound and free states at 37°C at the A2-CD 3 site using 2 H R 1 measurements
To determine the rate of conformational exchange between the free and bound states of the N-terminal domain of the fibrils, we utilize 2 H solid-state NMR rotating frame relaxation dispersion measurements under static conditions, which we have previously tested using a model compound (105). Rotating frame NMR relaxation has yielded a multitude of insights into protein dynamics in solution (106), and the momentum has picked up to enhance the development of these techniques for solid-state applications (81)(82)(83)(84)(85)(86)(87)(88)(89)(90)(91)(92). 2 H relaxation rates were measured as a function of the spinlocking field strengths, SL , between 5 and 35 kHz (Fig. 7) for

Flexibility of N-terminal domain of A␤ fibrils
the fibrils labeled at the A2-C ␤ D 3 position. Because of the significant narrowing of the line shapes due to the diffusive motion (Fig. 2), the analysis can be performed within the Redfield limit of NMR relaxation theory, given by the condition that the relaxation rate is much smaller than the rate constant of the underlying motional process (supporting information SI8) (107). Experimental relaxation decay curves are not exponential and can be approximated with a double-exponential decay (Fig.  7D), in which only the fast component (Fig. 7A) shows dependence on SL. The slow component, with a relative contribution to overall signal intensity of 30%, is defined with a much smaller extent of precision within which it does not exhibit any pronounced dependence on SL and is of the order of 6 -7 ms.
Based on the line shape analysis, the fraction of the bound state is 8% for A2 at 37°C (Fig. 6A) and the dynamics can be approximated by an isotropic diffusion model. In the bound state, the tensor is considered to be static with an effective quadrupolar coupling constant of 55 kHz after narrowing due to methyl rotations taken into account. The diffusion mode alone cannot explain the characteristic dependence of the fast component on SL (SI8 and Fig. S7). Thus, the mode of the conformational exchange between the free and bound states plays a central role in defining the dispersion curve. The main fitting parameter for this mode is rate constant k ex ϭ k 1 ϩ k Ϫ1 . The modeling procedure takes into account all possible relative tensor orientations in the free and bound states. Fitting the fast component (T 1 fast ϭ 1/R 1 fast ) of the double-exponential fit in this manner, one can thus extract the values of D and k ex . The best-fitted values are D ϭ 3.5⅐10 6 rad 2 /s and k ex ϭ 3⅐10 4 s Ϫ1 (Fig. S8). The diffusion coefficient is larger than that determined solely from the line shape analysis, 1.1⅐10 6 rad 2 /s. The line width is very sensitive to the presence of slight motional anisotropy, and thus this deviation allows us to estimate its extent (supporting information SI8, Fig. S9, and sup-porting information SI10). As elaborated on in supporting information SI8 (Figs. S7-S12), the presence of the additional slow component points to the need for a more involved motional model with a possibility of including an additional state. It is interesting that an intermediate state was found for the exchange between the monomeric A␤ and its oligomerbound form, even for the methyl group of Ala-2, based on darkstate exchange saturation transfer (DEST) solution NMR measurements (70,71).
To probe the temperature dependence of the conformational exchange process, we also performed the measurements at the lower temperature of 25°C (Fig. 7A). The fitted value of k ex is unchanged (3⅐10 4 s Ϫ1 ) within the precision of the data, whereas the diffusion coefficient is smaller, D ϭ 2.5⅐10 6 s Ϫ1 , and the fraction of the bound state is 9%. Thus, the results suggest a relatively low activation energy value for the conformational exchange process between the bound and free states.

Zinc-induced aggregation leads to the enhancement of the dynamics
To determine whether the dynamics are sensitive to different states of A␤, we investigated the aggregates formed in the presence of equimolar amounts of zinc chloride. These amorphous aggregates have a very wide range of sizes from 1,000 to 10,000 nm, as estimated from dynamic light scattering results. The observed distribution is in qualitative agreement with that found by Noy et al. (44) for zinc-containing aggregates based on analytical ultracentrifugation studies. In particular, they emphasized the existence of large-molecular-weight aggregates in a very broad range of sizes. The details of the dynamic light scattering and TEM data are shown in supporting information SI11 (Figs. S14 and S15). Thus, the sample morphology is different from the fibrillary form.
We analyzed these aggregates using the 2 H static line shapes and R 1 measurements employed for the fibrillary form (Fig. 8).

Flexibility of N-terminal domain of A␤ fibrils
At 37°C, there are minor changes in the spectra with an overall moderate extent of narrowing compared with the fibrillary form (Fig. 8A), with more pronounced changes toward the end of the N terminus (His-6, Gly-9, and Val-12). Upon freezing, it is evident that the midpoint of the freezing curves is shifted to lower temperatures (see Fig. S13 and the typical spectra close to the midpoint of freezing in Fig. 8a). Fitting the freezing curves to Equation 1 indicates a significant lowering of the midpoint temperatures (Fig. 8B, supporting information SI5, and Fig.  S13) by about 4 -5 K for Ala-2 and Phe-4 and 7-8 K for His-6 and Gly-9. Additionally, the value of for Gly-9 is about 40% smaller, reflecting the narrowing of the transition. It has previously been suggested that the aggregation may be partially controlled by the conformational flexibility of His-6 (19). Our results indicate that the changes in the dynamics in the presence of zinc are more pronounced for the side chain of His-6 and further residues along the backbone of the N-terminal domain, which correlates with the previous study of Istrate et al. (19). We note that the use of -His reduces the coordination efficiency of the histidine ring, and thus the actual changes in the dynamics upon zinc-induced aggregation may be even more pronounced.
The 2 H R 1 measurements (Fig. 8C) at the A2-CD 3 site display a steeper dispersion for the fast component of the relaxation curve T 1 fast . The fraction of the bound state based on the line shape analysis is 6% for this residue compared with 8% for the fibrils. The fitted values of the conformational exchange constant within the model of Fig. 5 is 4.5⅐10 4 s Ϫ1 , which is 1.5 times larger than that for the fibrillary form, and the fitted value of the diffusion coefficient D is 5⅐10 6 rad 2 /s compared with 3.5⅐10 6 rad 2 /s in the 3-fold symmetric fibrils. The combined results of the line shapes and R 1 relaxation analysis indicate the enhanced mobility of the aggregates.
As mentioned in the Introduction, the flexibility of the N-terminal domain of A␤ and its exposure to solvent has been known for some time (52, 54,56,57). In particular, the works of Olofsson et al. (56) and Whittemore et al. (57) have measured hydrogen-deuterium exchange rates for backbone amide hydrogen in solution using solution NMR spectroscopy. Compared with the structured regions, the N-terminal domain displayed low protection factors for several of the residues that could be detected. The current work expands these results to the fibrillary state of A␤ in the 3-fold polymorph and shows a clear progression for the freezing of the dynamics along the sequence in terms of both the fraction of the bound state and the kinetics of the motions approximated by the isotropic diffusion mode. Furthermore, instead of the backbone, the side chains were tackled, which is expected to be important in the inter-residue contacts (both intra-and intermolecular) that can hinder flexibility. Additionally, the 2 H R 1 experiments allowed us to identify the conformational exchange rate constant, likely due to the transient interactions between the unstructured N terminus and core of the fibrils.
As a first step toward assessing changes in the dynamics in different forms of A␤, we determined the differences between the 3-fold symmetric fibrillary form and Zn-induced aggregates. To obtain the full biological significance of the role of the dynamics in the potential control of aggregation, further studies will need to focus on discerning the changes in the dynamics between different polymorphs of A␤ (1, 2, 77, 108 -110) as well as in the variants of A␤ that include post-translational modifications in the N terminus and mutations mentioned in the

Flexibility of N-terminal domain of A␤ fibrils
Introduction. In particular, it will be important to test the 2-fold native polymorph as well as H6R and D7N mutants (11,35,111) and the Ser-8 -phosphorylated fibrils that were shown to lead to conformational changes in the N terminus and accelerate aggregation (17,27,28).

Conclusion
Our results demonstrate the quantitative features of the flexibility in the N-terminal domain of A␤ fibrils probed at several selectively deuterated side-chain sites along the N-terminal sequences. Based on deuterium static solid-state line shape and relaxation data, we proposed the two-state model in which the free state of the N-terminal domain undergoes a diffusive motion; however, in the bound state, this motion is quenched, likely due to transient interaction with the structured C-terminal subdomain. Local motions such as rotameric jumps, methyl rotations, and ring flips dominate the dynamics of the bound state, whereas they coexist with the diffusive motion in the free state.
The fraction of the bound state at the physiological temperature was determined to be 8% for the most extreme N-terminal residues (Ala-2, His-4, and Phe-6), and this increases significantly further along the sequence, with Gly-9 already at 36% and Val-12 at 87%. We also calculated the rate of the diffusive motion by using the isotropic diffusion approximation that, although an oversimplification, allows us to obtain the relative scale of the diffusive motion along the sequence. Thus, the diffusion coefficient of His-6 is 64% of that of Ala-2, but it drops to 30% for Gly-9 and to under 10% for Val-12.
The temperature dependence of the fractions exhibits sigmoidal behavior, with the midpoint of freezing at 267-268 K for Ala-2, Phe-4, and His-6 and at 284 K for Gly-9. Thus, the midpoint of the freezing of the first 6 -7 residues is close to the temperature of the freezing of the bulk water, whereas for residues further along the chain, freezing is observed at higher temperatures. The crossover in the longitudinal relaxation times is also evident for the residues that display strong solvation dependence of the relaxation: Phe-4, His-6, and Gly-9. For Ala-2 and Val-12, the relaxation is dominated by local methyl rotations. Around the midpoint of the crossover in the relaxation curves, relaxation in the bound state is governed primarily by the exchange process between the two states, and thus we can determine the exchange rate constant between the free and bound states at these conditions. The rate constant falls by about 21 s Ϫ1 for Phe-4 (at 262 K) and 9 s Ϫ1 for His-6 (at 262 K) and Gly-9 (at 280 K).
The newly developed 2 H R 1 methodology permitted the determination of the conformational exchange rate constant between the free and bound states at the physiological temperature. Probed at the A2-CD 3 site, the conformational exchange rate constant is 3⅐10 4 s Ϫ1 . The effect of zinc-induced aggregation on the dynamics manifests in the overall enhancement of the dynamics. The conformational exchange rate constant is increased by a factor of 1.5, and the line shapes are somewhat narrowed at room temperature, especially for the His-6, Gly-9, and Val-12 residues. Furthermore, the midpoint of the freezing curves is lowered by 4 -5 K for Ala-2 and Phe-4 and by 7-8 K for His-6 and Gly-9. Future studies of the differ-ent polymorphs of A␤ as well as mutants and post-translational modifications at the N-terminal region will be helpful for revealing the biological importance of the flexibility of this disordered domain.

Preparation of the A␤ 1-40 peptide
The peptide was prepared by using solid-state peptide synthesis (performed by Thermo Fisher Scientific, Rockford, IL). Fluorenylmethyloxycarbonyl (Fmoc)-phenylalanine-ring-d 5 , Fmoc-alanine-d 3 , Fmoc-glycine-d 2 , and Fmoc-histidine-ring-CD 3 were purchased from Cambridge Isotopes Laboratories (Andover, MA). The native sequence is DAEFRHDSGYEVH-HQKLVFFAEDVGSNKGAIIGLMVGGVV. The peptides were purified by reversed-phase HPLC, and their identity and purity were confirmed by MS and reversed-phase HPLC. The resulting peptides had isotopic labels in only one chosen residue. The details of the labeling patterns are shown in Table 1.

Preparation of the fibrils
Fibrils of the WT A␤ 1-40 in the "twisted/3-fold" polymorphs were produced by using established seeded growth protocols under quiescent conditions (2,54). For the preparation of the bulk samples, lyophilized peptides were initially dissolved at a 5 mM concentration in dimethyl sulfoxide (DMSO) and immediately transferred to a solution of 10 mM monosodium phosphate buffer at pH 7.4 also containing seeds in a 1:10 ratio by weight. The fibrils were allowed to grow for at least 4 days at room temperature with sonication performed at 24 h during the growth period: aliquots corresponding to 10% of the bulk volume were taken out of solution and sonicated for 2 min by using a probe sonicator, cooled for 15 min, and then added back into the bulk solution. The peptide concentration of the bulk samples was 0.5 mg/ml. The bulk fibrils were pelleted by centrifuging at 300,000 ϫ g for 12 h. Fibril pellets were resuspended in deionized water, rapidly frozen with liquid nitrogen, and lyophilized. The resulting morphologies were confirmed with TEM imaging (Fig. 1 and supporting information SI1).

Preparation of amorphous aggregates in the presence of zinc
Lyophilized peptides were dissolved at a 5 mM concentration in DMSO and immediately transferred to a solution of 10 mM monosodium phosphate buffer containing equimolar amounts of zinc chloride at pH 7.4 to a total concentration of peptide of 0.5 mg/ml. The aggregates were allowed to grow for at least 3 days at room temperature. The solution underwent dialysis in water using a membrane with a 3-kDa molecular-mass cutoff followed by lyophilization.

Transmission electron microscopy
Samples were stored at room temperature and diluted to about 0.1 mg/ml with Millipore filtered water. Samples were negatively stained by using the drop method (112) in the following manner. Four-microliter aliquots of the sample, Millipore filtered water, and 2% uranyl acetate aqueous stain were applied sequentially to a freshly glow-discharged (113) Formvar carbon-coated 300 mesh copper grid for the fol-

Flexibility of N-terminal domain of A␤ fibrils
lowing incubation times: 2 min, 10 s, and 1.5 min, respectively. Each 4-l droplet was removed by wicking with filter paper for 5 s. The filter paper was blotted prior to the addition of the next droplet. After staining, the grid was air-dried under a vacuum for 20 min. Images were collected under low-dose conditions of 120,000ϫ using an FEI Tecnai G2 Spirit Biotwin microscope operating at 80 kV.

Hydration and preparation of the NMR samples
A hydrated state with a water content of 200% by weight was achieved by exposing lyophilized powder to water vapor in a sealed chamber at 25°C until the water content reached saturation levels corresponding to about 40% by weight (24 -48 h was sufficient to achieve this) followed by pipetting the remaining water by using deuterium-depleted H 2 O. The samples were packed in 5-mm NMR tubes (cut to 21-mm length) using Teflon tape to center the sample volume in the coil of the NMR probe. The amount of material packed was 12-15 mg for Alaand Val-labeled peptides and 20 -28 mg for His-, Phe-, and Gly-labeled peptides.

Deuteron static solid-state NMR spectroscopy
Experiments were performed on 17.6-and 14.1-T spectrometers equipped with a static probe operating at temperatures between 160 and 380 K. Line shape experiments were performed with a quadrupole echo pulse sequence based on an eight-step phase cycle (73) with a delay of 31 s between 90°p ulses. A line broadening function of 0.5-2 kHz was chosen to enhance the signal. T 1 measurements under static conditions were performed at 17. 6 T by using the inversion recovery sequence for relaxation times below 80 ms and a saturation recovery sequence for longer times. For the relaxation measurements at low temperatures at which the full-width powder pattern was observed, we utilized the multiple echo acquisition detection scheme (QCPMG) for signal enhancement (114). Briefly, QCPMG detection breaks the powder pattern spectrum into a series of spikes that roughly follow the shape of the powder pattern. Unlike magic-angle spinning, QCPMG detection does not suppress relaxation anisotropy (115). The durations of 90°pulses were between 2.0 and 3.0 s. Ten to 15 QCPMG echoes were collected with 52-s pulse spacing, corresponding to QCPMG spikelets (side bands) spaced at 20-kHz intervals. The number of scans ranged from 128 to 2,048 depending on the signal-to-noise ratio in each sample. Five to seven relaxation delays were collected. Relaxation times T 1 were obtained by using single-exponential fits to the magnetization buildup curves.
The R 1 experiment was performed as described in previous work (105) with the pulse sequence (Fig. S12) and further details shown in supporting information SI8. A 600-MHz NMR spectrometer with a Bruker Neo console equipped with a wideline low-E probe (116) with a 5-mm-inner-diameter coil was employed. Spin-lock times varied between 200 s and 30 ms (12-17 relaxation delays), and powers varied from 5 to 35 kHz. Sixteen to 32 dummy scans were utilized.

Motional modeling
The isotropic diffusion of the free state was modeled as discrete nearest-neighbor jumps on the surface of a sphere, using 192 sites with the DistMesh program (38) for the discretization of the Smoluchowski equation. The jump rate was the same for all pairs of sites and was selected to match the second nonzero eigenvalue of the diffusion operator (corresponding to the second-order Legendre polynomial eigenfunction) to be 6D. Supporting information SI7 provides further details of line shape modeling. The parameters of the quadrupolar tensors, quadrupolar coupling constant C q , and tensor asymmetry (73) for each type or residue were taken from the low-temperature spectra. The effective values in the fast motional regime, given by the limit at which the rate constant is much greater than C q , were calculated for the free state by employing the motional models described under "Results." The values are listed in Table  2. For the case of Gly-9, the averaging of the tensor in the fast limit results in an asymmetry parameter of 1, which yields effective narrowing by itself without the diffusion mode. Diffusion causes further line shape narrowing. In the case of valine-d 3 , the additional local mode of rotameric jumps had to be added explicitly as the fast limit approximation was not valid. At 37°C, the rotameric exchange rate constant of 1 ϫ 10 5 s Ϫ1 and three rotamers, as well as the corresponding rotations around the 1 angle, with populations in the 5:1:1 ratio were used. The simulations utilized the EXPRESS program (39). For the simulated line shapes, an additional line broadening of 1-1.5 kHz was used to approximately account for the effect of inhomogeneous dipolar interactions (45).
To model the longitudinal relaxation rates, static quadrupolar tensor parameters were used (Table 2), and the motional modes listed in Table 1 under "Results and discussion" were assumed. The values of the rate constants were obtained by matching the experimental and simulated values of T 1 . The activation energies in the high and low temperature limits were determined by using the Arrhenius law for the rate constants.
To model the R 1 rates, in addition to the isotropic diffusion mode modeled as described for the line shapes, an additional mode of exchange between the free and bound states was included. This was accomplished by the introduction of one additional site with an arbitrary fixed angular position in the crystal-fixed frame. The exchange was modeled by jumps between every site describing the spherical diffusion and Table 2 Quadrupolar coupling tensor parameters: quadrupolar coupling constant C q and asymmetry for the N-terminal residues of A␤ 1-40

Flexibility of N-terminal domain of A␤ fibrils
bound-state site (supporting information SI8). These simulations were performed in the Redfield framework (107).