The unique Alzheimer's β-amyloid triangular fibril has a cavity along the fibril axis under physiological conditions

Abstract

Elucidating the structure of Aβ_1–40 fibrils is of interest in Alzheimer's disease research because it is required for designing therapeutics that target Aβ_1–40 fibril formation at an early stage of the disease. M35 is a crucial residue because of its potential oxidation and its strong interactions across β-strands and across β-sheets in Aβ fibrils. Experimentally, data for the three-fold symmetry structure of the Aβ_9–40 fibril suggest formation of tight hydrophobic core through M35 interactions across the fibril axis and strong I31-V39 interactions between different cross-β units. Herein, based on experimental data, we probe conformers with three-fold symmetry of the full-length Aβ_1–40. Our all-atom molecular dynamics simulations in explicit solvent of conformers based on the ssNMR data reproduced experimental observations of M35-M35 and I31-V39 distances. Our interpretation of the experimental data suggests that the observed ~5–7Å M35-M35 distance in the fibril three-fold symmetry structure is likely to relate to M35 interactions along the fibril axis, rather than across the fibril axis, since our measured M35-M35 distances across the fibril axis are consistently above 15Å. Consequently, we revealed that the unique Aβ_1–40 triangular structure has a large cavity along the fibril axis and that the N-termini can assist in the stabilization of the fibril by interacting with the U-turn domains or with the C-termini domains. Our findings, together with the recent cyroEM characterization of the hollow core in Aβ_1–42 fibrils, point to the relevance of a cavity in Aβ_{1–40/1–42} oligomers which should be considered when targeting oligomer toxicity.

I. Introduction

Alzheimer's disease (AD) is the most common cause of dementia. Biochemical analysis revealed that the main constituent is a small polypeptide Aβ_1–40 or Aβ_1–42, which is derived from endoproteolytic cleavage of the transmembrane amyloid precursor protein (APP).¹ While Aβ₄₂ increases significantly in the brain,² Aβ₄₀ is the most abundant Aβ isoform.³ Peptide assembly from soluble oligomers into insoluble fibrils was suggested to occur via a multi-step process;^4–5 however, this suggestion has been controversial. Full Aβ₄₀ molecular structures are of interest in drug discovery which targets fibril formation at an early disease stage. ssNMR studies of Aβ₄₀ fibrils led to two models: two-fold-symmetric⁶ and three-fold-symmetric.⁷ These reflect high population conformers under different experimental synthesis conditions. Both models exhibit in-register parallel twisted β-sheets constructed from nearly the same β-strand segments. In both models, the C-termini face the internal fibril surface and the N-termini are exposed to the exterior bulk solvent. They differ in non-β-strand segments (the U-turn and the flexible N-terminal domain) and in the quaternary structure (contacts between cross-β units). Based on ssNMR data of the full-length Aβ_1– fibril,⁷ the N terminal is less ordered and a molecular model for the three-fold symmetry is only available for Aβ_9–40.

In the two-fold symmetric Aβ₄₀, M35 interactions along and across the fibril axis stabilize it. In the three-fold symmetric Aβ₄₀,⁷ M35 residues also interact. If the interactions involve M35 from different β-sheets, it can be expected that no cavity will be formed in the core. We construct models that satisfy three-fold symmetry and compare them with ssNMR constraints.⁷ We focus on two M35-M35 interaction types: along the fibril axis and across the cavity. While all interactions exhibit agreement with the experimental constraints, the M35-M35 interactions across a cavity disagree. Consequently, we suggest that the observed M35-M35 constraints are more likely to result from interactions along the fibril axis in the same sheet than across the fibril cavity.

II. Material and Methods

1. Experiment-based Aβ_1–40 fibril models construction

Herein, based on Tycko's three-fold symmetry model,⁷ we constructed three conformers of Aβ_1–40, (Figures 1A–1C) where each conformer consists of 24 monomers: three parallel octamers arranged in a triangular shape. For each monomer, we linked the G9 to the N-terminal fragment peptide (D1-S8). All three conformers exhibit contacts between different cross-β units that are related by the three-fold symmetry (I31-V39 interactions). The three conformers differ in the N-termini (D1-S8) orientations: in conformer 1, the N-termini are flexible and do not interact with any domain of the peptides. (Figure 1A) Conformer 2 presents a contact between F4 in the N-terminal and V12 in the C-terminal of each monomer (Figure 1B) and conformer 3 was constructed by forming interactions between F4 in the N-termini of one octamer and G25 in the loops region of a nearby octamer. (Figure 1C) To study the polymorphism due to the U-turn shape of the three-fold symmetry model, we constructed one conformer of Aβ_1–40 (conformer 4, Figure 1D) based on Lührs' model for the Aβ_17–42 coordinates (PDB: 2BEG).⁸ We note that Lührs model has coordinates for one layer of Aβ_17–42. We used the third monomer conformation of the Aβ_17–42 peptide from the Aβ pentamer in the PDB coordinate file, and generated three parallel octamers arranged in a triangular shape. Residues I41 and A42 were removed from each monomer and the L17 of each monomer were linked to the N-terminal fragment peptide (D1-K16). This conformer was also constructed by forming interactions between F4 in the N-termini of one octamer and G25 in the loops region of a nearby octamer, as in conformer 3. However, while all three conformers based on Tycko's model demonstrate I31-V39 interactions between cross-β units in the three-fold symmetry structure, these interactions are not present in the conformer based on Lührs' model. We note that we tested a conformer based on Lührs' model with I31-V39 interactions; however this conformer exhibits an unstable structure. (Figure S1).

Figure 1.

Experiment-based three-fold symmetry conformers before (I) and after (II) simulations of 60ns. In all four conformers the M35 residues (color: gray) form hydrophobic core. Conformers 1, 2 and 3 are based on Tycko's model. The N-termini (residues D1-S8) were linked to the C-termini (residues G9-V40). Conformer 4 is based on Lührs' model. The N-termini (residues D1-L16) were linked to C-termini (residues L17-V40). Residues I41 and A42 were removed from the PDB: 2BEG file. In conformers based on Tycko's model the I31 (color: orange) and V39 (color: purple) form contacts between different cross-β units, while in the conformer based on Lührs' model, the M35 and V39 form contacts between the different cross-β units. (A) Conformer 1: The N-termini are flexible and do not interact with any domain in the peptides. (B) Conformer 2: F4 (color: red) in the N-termini form hydrophobic interactions with V12 (color: green) in the C-termini. (C) Conformer 3: F4 (color: red) in the N-termini form hydrophobic interactions with G25 (color: blue) in the loop regions. (C) Conformer 4: F4 (color: red) in the N-termini form hydrophobic interactions with G25 (color: blue) in the loop regions.

Conformer 1 was constructed using directly the six-mer (i.e., six layers) coordinates provided by Tycko's lab, with 2 additional layers. For conformer 4, we used the third monomer conformation of the Aβ_17–42 peptide from the Aβ pentamer in the 2BEG PDB coordinate file, and generated three 8-mer oligomers in a parallel arrangement in the three-fold symmetry structure.

To study the effect of the pH on the structural stability and the populations, we used different protonation states of titratable side-chains to simulate the constructed models at different pH values. For pH=7, only the positively charged residues (Lys and Arg) were protonated.

2. Molecular Dynamics (MD) Simulations procedure

Molecular dynamics simulations of solvated Aβ_1–40 oligomers were performed in the NPT ensemble using the NAMD program⁹ with the CHARMM27 force-field.^10–11 The oligomers were explicitly solvated with TIP3P water molecules.^12–13 The Langevin piston method^14–16 with a decay period of 100 fs, and a damping time of 50 fs was used to maintain a constant pressure of 1 atm (1 atm = 101.3 kPa). The temperature (300 K) was controlled by Langevin thermostat with a damping coefficient of 10 ps⁻¹.¹⁴ The short-range van der Waals (VDW) interactions were calculated using the switching function, with a twin range cutoff of 10.0 and 12.0 Å. Long-range electrostatic interactions were calculated using the particle mesh Ewald method with a cut-off of 12.0 Å for all simulations.^17–18 The equations of motion were integrated using the leapfrog integrator with a step of 2 fs.

All initial Aβ_1–40 oligomers were energy minimized and then solvated in a TIP3P water box with a minimum distance of 10 Å from any edge of the box to any Aβ atom. Any water molecule within 2.5 Å of the Aβ was removed. Counterions (Na⁺) were added at random locations to neutralize the Aβ_1–40 charge.

The solvated systems were energy minimized for 2000 conjugated gradient steps, where the hydrogen bond distances between the β-sheets in Aβ_1–40 is fixed in the range 2.2 – 2.5 Å. The counterions and water molecules were allowed to move. The hydrogen atoms were constrained to the equilibrium bond using the SHAKE algorithm.¹⁹ The minimized solvated systems were heated for additional 5000 conjugate gradient steps at 250 K, where all atoms were allowed to move. Then, the systems were heated from 250 K to 300 K for 300 ps and equilibrated at 300 K for 300 ps. All simulations ran for 60 ns and structures were saved every 10 ps for analysis. These conditions (300 K and 60 ns of timescales) are applied to test the stabilities of all Aβ_1–40 oligomers.

For each conformer a single molecular dynamics (MD) simulation was performed where the systems were heated from 250 K to 300 K for 300 ps and equilibrated at 300 K for 300 ps. To test the results obtained from these MD simulations, we ran simulations with different initial conditions for each conformer: the systems were heated from 100 K to 200 K for 300 ps and equilibrated at 250 K for 300 ps. Those different initial conditions still lead to the same simulation results. M35-M35 distance values demonstrate similar distributions (Figure S2) and the conformational energies (Table 1) illustrate that the stabilities of the four conformers follow the same trend.

Table 1.

Conformational energy of the four constructed conformers

Aβ1–40 Conformer	Experiment-based model	Interactions	Conformational energy (kcal/mol)*	Conformational energy (kcal/mol)*
1	Tycko,Ref. 6	None	−24977.7 (433.1)	−25069.1 (387.7)
2	Tycko,Ref. 6	F4-V12	−25340.5 (390.5)	−25576.3 (310.1)
3	Tycko,Ref. 6	F4-G25	−25156.8 (390.7)	−25378.3 (415.5)
4	Lührs, Ref. 7	F4-G25	−25176.1 (385.4)	−25320.2 (397.6)

^*Conformational energies were computed using the GBMV calculations. The standard deviation values are presented in parenthesis. The conformational energies in the fourth and the fifth column are computed for different initial states of conformers.

3. Generalized Born Method with Molecular Volume (GBMV)

In the GBMV calculations,^20–21 the dielectric constant of water was set to 80. The hydrophobic solvent-accessible surface area (SASA) term factor was set to 0.00592 kcal/mol·Å². Each conformer is minimized using 1000 cycles and the conformational energy is evaluated by grid-based GBMV. The minimization does not change the conformations of each conformer; it only relaxes the local geometries due to thermal fluctuation which occurred during the MD simulations.

4. Analysis details

The core cavity is defined by the three averaged values of Cε of M35- Cε of M35 distances along the fibril cavity. The relative conformational stabilities of the oligomers were measured by root mean-squared deviation (RMSD) of the C-terminal region (residues L17-V40), the N-terminal region (residues A2-Q15) and the U-turn region (residues E22-G29) with respect to the initial minimized structure throughout the simulations. We followed the change in the D23-K28 distance: the averaged distance between Cγ of D23 and N sidechain of K28 in the same peptide, and the averaged distance of the two C=O bonds of D23 to the N atom in K28 in the same peptide.

The structural stability of the constructed conformers was tested by following the change in the distances: M35-G37 and L34-M35 distances between the methyl carbon of M35 and the backbone nitrogen sites of G37 and L34; Cε of M35- Cε of M35 along the fibril axis, Cε of M35-amine group of G37 within the same peptide, amine group of L34- Cε of M35 also within the same peptide and Cβ of I31- Cβ of V39 between cross-β units in the three-fold symmetry structure. All distances were calculated for each of the 8 layers separately and then averaged. Finally, the probabilities of the distances F4-V12, M35-M35 along the fibril cavity and I31-V39 between cross-β units in the three-fold symmetry structure were computed from average distances of all atoms.

III. Results

1. Conformational stability of Aβ_1–40 oligomers: Polymorphic N-terminal arrangements

In order to compare potential oligomers, we constructed four conformers of the three-fold symmetry model and generated 500 conformations for each arrangement by MD simulations. Our simulations indicated that all four conformers are structurally stable, suggesting that they could exist under physiological conditions: both the C-termini and U-turn root-mean-square deviations (RMSDs) are low. (Figure 2)

Figure 2.

The figure shows the RMSDs of conformers based on Tycko's and Lührs models. The RMSD are computed separately for the two parts of each of the four conformers: C-terminal (residues 17–40) and U-turn (residues 22–29).

Focusing on stability and populations, we test various distances and compared the constraints observed from ssNMR⁷ for the experiment-based model with the averaged distances in our conformers. The reported constraints are the intra-peptide M35-G37 and L34-M35 and the salt-bridge D23-K28 distances. All the averaged distances in the constructed conformers exhibit a good agreement with the reported experimental constraints. (Figures 3 and Figure S3) The methyl carbon of M35 fluctuates along the simulations, therefore when the methyl carbon points to G37 the M35-G37 distance decreases and when it points to L34 the L34-M35 decreases. For example, as seen in Figure 3, the M35-G37 distance for conformer 3 at around 10 ns increases to ~ 8.5 Å, while around this timescale the L34-M35 distance is ~ 6.5 Å. At 17 ns, the M35-G37 distance decreases to ~ 6.5 Å, whereas the L34-M35 distance is ~ 8.5 Å. Finally, the I31-V39 contacts between cross-β units that are related by the three-fold symmetry illustrate a ~ 6–7 Å distance for all conformers based on Tycko's model (in agreement with experiment) and of ~ 13 Å for Lührs' model. (Figure 4) In Lührs model the loop region shape differs from that in Tycko's, leading to the larger distances between the I31-V39 contacts. The proximity of the V39-I31 residues may contribute to the stabilization of the cavity along the fibril axis, as illustrated in the next section.

Figure 3.

(A) The averaged M35-G37 distances within the peptide for all four conformers. (B) The averaged L34-M35 distances within the peptide for all four conformers. (C) The averaged distance between Cγ of Asp23 and N side-chain of Lys for all four conformers.

Figure 4.

The distribution of the I31-V39 distance for all four conformers.

2. The triangular fibril has a stable cavity along the fibril axis

From a top view along the fibril axis of the experiment-based model (Figure 4 in ref. 7), the interactions between the three M35 in each layer exhibit a hydrophobic cluster in the interior cross section without a cavity. However, all four constructed conformers reveal a stable cavity along the fibril axis. Figure 5A illustrates that the averaged M35-M35 distances along the simulations increased and stabilized for each conformer. The M35-M35 distance distribution across the fibril cavity shows high cavity probability with ~16 Å, ~20 Å, ~21 Å and ~23 Å respectively for conformers 1, 2, 3 and 4. (Figure 5B) In addition, conformer 3 presents a smaller (~7Å) cavity for a short duration, due to the initial conformation used in simulation. The averaged M35-M35 distances for a cavity across the fibril axis in our conformers exhibit distances much larger than 7Å. However, in our conformers the averaged M35-M35 distances along the fibril axis are in the range of 5–7Å. (Figure 5C) Therefore, our interpretation of the ssNMR observation suggests that the 5–7Å averaged M35-M35 distances are due to M35-M35 distances along the fibril axis and not across the cavity.

Figure 5.

(A) The averaged M35-M35 distances in the cavity region along the simulations for all four conformers. (B) The distribution of the M35-M35 distances for all four conformers indicates a cavity along the fibril axis. (C) The averaged M35-M35 distances along the fibril axis for all four conformers during the time of simulation.

It is of interest to examine whether water molecules exist in the hollow hydrophobic core in all four conformers studied here. Therefore, we computed the averaged solvation of the side-chains of all residues in each conformer. Figure 6 demonstrates that Met35 has higher solvation exposure than L34 and V36, indicating the presence of water in the hollow hydrophobic core. The methyl carbons of the M35 residues point into the hollow hydrophobic core; therefore, the side-chains of the M35 are relatively 4 times more solvated than the side-chains of L34 and V36. Other side-chains of residues in the hollow core domain (I31-L34 and V36-A40) do not point to the hollow core, thus do not exhibit large solvation.

Figure 6.

Average water molecules around each sidechain Cβ carbon within 4 Å. Glycines has no sidechain Cβ carbon, which results in zero value in the plots. In all conformers, Met35 has higher solvation exposure than L34 and V36, indicating the existence of water in the hollow hydrophobic core.

Tycko's group also presented paramagnetic relaxation enhancement data for the 3-fold-symmetric Aβ₄₀ structure, indicating that M35 is less influenced by Cu²⁺-EDTA than I32. In another paramagnetic relaxation enhancement study, Wickramasinghe et al²² found that I31 and I32 have similar relaxation rate enhancement for a two-fold symmetry fibril. Regardless of whether the paramagnetic relaxation enhancement can be explained by M35 being more buried than I31/I32, M35 side-chain methyl carbons may not be accessible to Cu²⁺-EDTA in solution. We examined if the cavity size allows free access of Cu²⁺-EDTA into the interior. As can be seen in Figure 7, entry of Cu²⁺-EDTA into the cavity clashes with the Connolly surface. Thus, Cu²⁺-EDTA needs complementary force to allow its binding with the fibril cavity. Such scenario rarely happens between Cu²⁺-EDTA and any protein, as there is no EDTA-protein complex in the entire protein structural database (PBD). Hence, our results indicated that the cavity size found in our study still does not allow close encounter of Cu²⁺-EDTA and M35, I31, and I32.

Figure 7.

The fibril cavity size is not large enough to allow free access of Cu²⁺-EDTA. M35 is represented by balls with the sulfur in yellow. The bottom right corner illustrates the overall Connolly surface of the three-fold symmetry conformer 2, with the Cu²⁺-EDTA as a ball sitting in the center. The enlarged figure shows the clash of the Connolly surfaces of Cu²⁺-EDTA and conformer 2. Cu²⁺-EDTA is represented by ball-and-stick, with oxygen in red, nitrogen in blue and Cu²⁺in magenta.

3. Polymorphic Aβ_1–40 oligomers: Hydrophobic interactions of the N-terminal with the C-terminal and U-turn

For the complex kinetics of amyloid formation, the four constructed conformers are likely to represent only a very small percentage of the ensemble. Nevertheless, the carefully selected conformers sample the most likely organizations. Based on Monte-Carlo simulations with the energy landscape computed with the Generalized Born Method with Molecular Volume (GBMV), we estimated the relative stabilities of all constructed conformers. Conformer 1 which is based on Tycko's model and exhibits nonhydrophobic interactions between the N-termini and other regions in the Aβ peptides is energetically less stable compared to the others. (Table 1) However, conformer 2 (also based on Tycko's) forms strong hydrophobic interactions between the C- and the N-termini (~7Å between F4 and V12) within each monomer (Figure 8) and is the most stable. So far, it was believed that the disordered N-terminal segment is not involved in fibril formation. However, here we show that the intramolecular interactions between the flexible N-terminal and the C-terminal within each peptide in the triangular fibril structure stabilize the conformer. In addition, as seen in conformer 3, intermolecular hydrophobic interactions (F4-G29) between the flexible N-terminal of one Aβ peptide and the loop region of another demonstrate increased stability compared with conformer 1. Consequently, we suggest that the N-terminal stabilizes the fibril and thus plays a role in fibril formation. Finally, loop flexibility allows slightly different loop types which contribute to polymorphic amyloid morphologies. Herein, we constructed the triangular Aβ with two experiment-based coordinates which differ in the loop region: conformer 3 based on Tycko's file and conformer 4 based on Lührs' PDB file. The similar energies of conformers 3 and 4 (Table 1) indicate that the triangular Aβ₄₀ structure based on the two different U-turn shapes have similar stabilities and consequently further confirm a likely polymorphic scenario in amyloid formation.²³

Figure 8.

The distribution of the F4-V12 distance for conformer 2.

IV. Discussion and Conclusions

The hydrophobic cavity in Aβ_1–40/ Aβ_1–42 amyloid structures was observed in previous studies.^6,24–27 Water molecules travel along the hydrophobic cavity of these structures to form hydrogen bond interactions with residues in the cavity domain. This stabilizes the cavity and allows optimization of the intermolecular sheet-sheet packing. The role of the hydrated hydrophobic cavity in amyloids is still controversial, because the mechanism of the amyloid toxicity is not yet clear. Herein, we demonstrate a stable cavity in the three-fold symmetry experiment-based model for Aβ_1–40 with dimensions in a range of 16–23 Å for the constructed models. Recently, Zheng et al²⁴ reported a cavity also in the three-fold symmetry experiment-based model for Aβ_9–40 with similar dimension in the interior cross section (~20.4 Å).

Our study leads to an important conclusion: the triangular structure studied here exhibits a cavity along the fibril axis, and is stabilized by I31-V39 contacts between cross-β units and N-terminal interactions with the U-turn region. Recently, a cryoEM density map of a two-fold Aβ_1–42 fibrils also led to a model which presented a hollow core and N-terminal-turn interactions.²⁵ Both the Aβ_1–42 two-fold and the triangular Aβ_1–40 three-fold symmetry conformers share these features and are stabilized by across the-fibril-axis N-terminal - U-turn interactions. However, while the C-terminal faces inside the core in the three-fold Aβ_1–40 fibril, in the Aβ_1–42 fibril the N-terminal is more likely to face inside the hollow core, as illustrated by Miller et al.²⁸ These common features argue for consideration in AD drug design.

Finally, it should be noted here that the N-terminal may and probably does play a role in aggregation. However, simulation²⁹ and experimental³⁰ studies suggest that even if the N-terminal participates in aggregation, it does not determine the aggregation interface.