Study of Molecular Mechanisms of α-Synuclein Assembly: Insight into a Cross-β Structure in the N-Termini of New α-Synuclein Fibrils.

Parkinson's disease is characterized by the self-assembly of α-synuclein (AS), in which its aggregates accumulate in the substantia nigra. The molecular mechanisms of the self-assembly of AS are challenging because AS is a relatively large intrinsically disordered protein, consisting of 140 residues. It is known that the N-termini of AS contribute to the toxicity of the proteins; therefore, it is important to investigate the self-assembly structure of the N-termini on AS as well. There have been extensive efforts to investigate the structural fibrils of AS(1-140), which have shown that the N-termini are disordered and do not participate in the fibrillary structure. This study illustrates for the first time that the N-termini of AS play a crucial role in the self-assembly of AS. This study reveals a new structure of AS(1-140) fibrils, in which the N-termini are essential parts of the cross-β structure of the fibrillary structure. This study suggests that there are polymorphic states of the self-assembled AS(1-140). While the polymorphic states of the N-termini do not participate in the fibrillary structure and fluctuate, our predicted new fibrillary structure of the N-termini not only participates in the fibrillary structure but also stabilizes the fibrillary structure.

Introduction

Parkinson’s disease is characterized by the formation of intracellular deposits of α-synuclein (AS) in the neuropathological inclusions “Lewy bodies” and “neurites” that accumulate in the substantia nigra.[1] AS is a 140-amino acid intrinsically disordered protein (IDP) and has been shown to play a role in neurotransmitter release, as studied by neuronal cell lines expressing AS.[2] The N-terminal region of AS is a positively charged region and includes seven imperfect repeats of 11 residues containing the highly conserved KTKEGV consensus sequence motif, whereas the C-terminus contains many acidic residues and is, thus, negatively charged. Residues 61–95, which are referred to the nonamyloid β component (NAC), encompass many hydrophobic residues.

Upon binding negatively charged vesicles, AS adopts a conformation that has a high α-helical propensity.[3,4] A structure of the full-length, membrane-bound form of AS reveals a conformation in which two-thirds of the N-terminal protein form a broken, amphipathic α-helix.[5,6] This structured region of the protein is responsible for membrane binding, and residues at the N-terminus are essential for this process.[7] Moreover, it was suggested that the N-terminus contributes to the toxicity of the protein. In the nuclear magnetic resonance (NMR) structure of AS, the C-terminal tail remains flexible and is structurally a random coil because of its low hydrophobicity and high net negative charge.[7]

In solution, the AS proteins are self-assembled into fibrils, forming cross-β structures with a considerable morphological heterogenicity.[8−10] Morphologically distinct AS fibrils lead to differences not only in the dimensions of the fibril but also in the mechanical and physical properties.[11] Therefore, it is important to investigate various morphologies of the self-assembled AS fibrils.

The molecular structure of the fibrillar NAC, that is, AS(61–95), was first predicted by Atsmon-Raz and Miller, illustrating three β-strands connected by two turns.[12] A further molecular structure of fibrillar AS(30–110) has been proposed by Xu et al.[13] based on a previous solid-state NMR (ssNMR) model[14] with five β-strands packed in the conventional β-strand-loop-β-strand fold (fivefold). The structure of the fibrillar NAC that had been predicted by Xu et al.[13] also consists of three β-strands connected by two turns, but their locations along the sequence differ from those proposed by the model of Atsmon-Raz and Miller.[12] Recently, the molecular structure of the full-length fibrillar structure of AS(1–140) has been solved using ssNMR, illustrating in-register β-sheets with a Greek key (G-key) topology, in which NAC is a part of this topology.[15] The NAC domain in the model of the Rienstra group consists of six β-strands connected by five turns. Therefore, obviously, when focusing only on the NAC domain of the fibrillar molecular structure, these three groups suggest three different folding states (Figure ). The molecular structure of the Rienstra group provided a well-organized molecular structure of only residues 30–110, while the N- and the C-termini have disordered regions.

Figure 1

Polymorphic structures of the self-assembled NAC domain (residues 61–95) in AS obtained from (A) Rienstra group,[15] (B) Xu et al.,[13] and (C) Atsmon-Raz and Miller.[12] Initial constructed models of self-assembled AS(30–95) octamers. Model C1 is an ssNMR structure observed by Rienstra group,[15] model C2 is predicted from the computational study of Xu et al.,[13] and model C3 is predicted in this study.

The aim of this study is to investigate how the extensions of NAC fibrils in the N- and C-termini in these three different models affect the stability of the full-length AS(1–140) fibrils. The experimental G-key model was extended in the N- and C-termini, but its full-length stability has not yet been investigated. Recently, the stability of AS(20–110) fibrils of the G-key model and the fivefold model has been investigated by using computational tools.[13,16] Yet, the full-length AS(1–140) fibrils have not been investigated. Moreover, herein, we propose two new fibrillar structures: one is of AS(30–95), which is an extension of NAC in the N-termini, and the other is of the full-length AS(1–140), which is an extension of NAC in both N- and C-termini. While the N-termini and the C-termini of the G-key model and the fivefold model are disordered, the new model that is presented in this study demonstrates stably folded N-termini with the formation of a cross-β structure.

Results and Discussion

Extensions of NAC Fibrils in the N-Termini Yield to a New Fibrillary Cross-β Structure in a Unique AS(30–95) Fibrillary Structure

While the NAC domain is indispensable for the aggregation of AS,[17−19] there is still a great interest to investigate the aggregation of the full-length AS(1–140). So far, a wide range of experimental studies proposed that AS(30–95) consists of β-strands along this sequence, whereas residues 1–29 and 96–140 lack β-strand structures.[14,20−23] We first investigated the extension of the fibrillary structure of NAC domains in the N-termini to form the fibrillary structure of AS(30–95).

Three various fibrillary structures were investigated in this study: C1–C3. The constructed models of these three fibrillary structures are detailed in the Material and Methods section and are seen in Figure . All of these three simulated models have shown stable fibrillary structures (Figure ); according to the root-mean-square deviation (RMSD), all models were converged (Figure S1). Energetically, model C1 is the most stable and populated model than the two other models, C2 and C3 (Figure S2, Table S1). Yet, one cannot neglect that all of these three structures are applicable and populated (Figure S2, Table S1). The polymorphism in various amyloids is well-known and reviewed elsewhere.[24] Herein, we suggest that there are ensembles of polymorphic states of the fibrillary structure of AS(30–95).

Figure 2

Simulated models of the self-assembled AS(30–95) octamers. Model C1 is an ssNMR structure observed by the Rienstra group,[15] model C2 is predicted from the computational study of Xu et al.,[13] and model C3 is predicted in this study.

The RMSD (Figure S1) and the hydrogen analysis (Figure S3) illustrate that all three models are converged and stable. Furthermore, the inner core distances show stable fibrillar cross-β structures for all three models (Figures S4–S6). Yet, although these models are well-organized fibrillar structures, they show fluctuations in the N-termini of each model, as seen in the root-mean-square fluctuation (RMSF) analysis (Figure ). The fluctuations in the N-termini of models C1 and C2 are relatively high in comparison with that in model C3. This is not surprising because the N-termini in model C3 are a part of the fibrillary structure of AS, whereas the N-termini in models C1 and C2 do not participate in interactions with other domains in the fibrillary structures. Interestingly, one can see that the N-termini in all three models are highly solvated and, particularly, that the N-termini show relatively more fluctuations in models C1 and C2 than that in model C3 (Figure S7). In fact, models C1 and C2 lack cross-β structures in the N-termini domain, whereas model C3 demonstrates a cross-β structure with an elongated sequence of residues (Figures S8–S10). Obviously, each model illustrates different disordered domains and different β-strand domains along the N-termini, according to the Define Secondary Structure of Proteins (DSSP) analysis (Figures S8–S10). While model C3 exhibits a relatively high propensity of β-strand domains along the sequence of A30-T44, model C2 shows a low propensity and model C1 does not present any β-strand propensity along this sequence.

Figure 3

RMSF analysis of all residues in models C1, C2, and C3.

The dihedral angles Φ and Ψ of the residues in these three models were computed and compared with the experimental values (Tables S2 and S3 and Figures S11–S13). The averaged deviation of the computed dihedral angles from the experimental values is in the range of 27–43%. Interestingly, the averaged deviation is relatively small while also considering the N-terminal residues in AS(30–95) compared with the values of residues of only NAC. Finally, the computed order parameter (OP) values of all three models have relatively small deviation compared with the experimental OP values (Table S4 and Figure S14); yet, the computed OP values of model C3 have the smallest deviation compared with the experimental values. The relatively high deviations of the OP values of models C1 and C2 do not indicate that these structural models are not feasible. The differences in the OP values between these three models indicate the polymorphic states of AS(30–95). Obviously, the polymorphic states of the self-assembled amyloids that were observed by the experiment are due to different conditions of the growth of amyloids.

Previously, the group of Riek revealed similar diameter values for the full-length AS(1–140) and the nonfull-length AS(30–110),[14] thus providing support for the premise that the central domain of AS plays a role in fibrillization. Therefore, it is reasonable to compare the diameters of our three models with those observed in the experimental studies. The group of Riek suggested a fibril diameter of 5.5 ± 0.5 nm based on two protofilaments of ∼2 nm.[14] The group of Carter showed protofilament diameters of 3.8 ± 0.6 nm,[25] and the group of Anderson observed protofilaments with a diameter of 4.5–6 nm.[26] Recently, the group of Melki has suggested that the diameter values within the same fibrillary structure vary from the narrow value of 8 ± 1 nm to the wider value of 18 ± 2 nm along the fibril axis.[8]Figure S15 shows the various heterogeneous diameter values of the simulated models. Interestingly, all simulated models are in good agreement with the various experimental diameter values, thus indicating the polymorphic states of the self-assembled AS(30–95).

Extensions of NAC Fibrils in the N- and C-Termini Domain Yield to Well-Organized Cross-β Structure in These Domains in a New AS(1–140) Fibrillary Structure

The study of the self-assembly of the full-length AS(1–140) is more challenging because of the relatively long sequence in comparison with that of amylin and Aβ amyloid. Previous ssNMR studies have struggled to solve the three-dimensional (3D) structure of the self-assembled AS(1–140) with no success.[14,20−23] Recently, the Rienstra group has succeeded to solve the self-assembled 3D structure of AS(1–140).[15] Herein, we applied the structure of the Rienstra group (model C5, Figure ), and we constructed a new structural model of AS(1–140)—model C4, which differs from the structure of the Rienstra group (Figure ). Molecular dynamics (MD) simulations were carried out for these two models, which are shown in Figure . Both models have shown a convergence along the time of simulations (Figure S16). Estimation of the conformational energies of these two models has shown that model C5 is relatively more stable than model C4 (Figure , Table S5). Yet, one cannot neglect the overlap between the distribution of energies of these two models. In fact, similar results have been shown previously for other amyloids in our group,[24,27−29] which indicate some fibrillary amyloid structures that are more preferred than others but still present polymorphic states.

Figure 4

Initial (left) and simulated (right) self-assembled structural models of AS(1–140) octamers. Model C4 is predicted in this study and model C5 is the ssNMR structure by Tuttle et al.[15]

Figure 5

(A) Scatter charts of the 500 conformations obtained from the GBMV energy values extracted from the last 5 ns of each model. The scatter charts represent the “histograms” of the number of conformations in the energy ranges. The averaged energy values are shown in the “boxes”. (B) RMSF analysis of all residues in models C4 and C5.

Although the conformational energy of C5 is lower than that of C4, the new model C4 is structurally more stable than C5. Interestingly, one can see that the hydrophobic and electrostatic interactions along the N-termini stabilize the fibrillary structure of model C4 (Figure ). After the convergence of these two models, the percentage of hydrogen bonds (Figure S17) in model C4 is higher than that in C5 because of the relatively low fluctuations at the N- and C-termini of AS(1–140) of C4 when compared with that of C5 (Figure ). Furthermore, model C4 exhibits more β-strands along the N-termini (residues 14–29) and C-termini (residues 96–105) than model C5 (Figures S18–S21). The various inner cores of each model have been computed and illustrated in Figures S22 and S23. These inner cores led us to conclude that the well-organized self-assembled fibrillary structure of model C4 is located along AS(14–105), whereas in model C5 it is located along AS(30–95).

Figure 6

Illustration of interactions in the N-terminal of a monomer in the fibrillary structure of the simulated model C4: hydrophobic (green) and electrostatic (red) interactions stabilize the fibrillary structure in the N-terminal.

Finally, the dihedral angles Φ and Ψ of the residues in these two models were computed and compared with the experimental values (Tables S6 and S7 and Figures S24 and S25). The averaged deviation of the computed dihedral angles from the experimental values is in the range of 32–55%. Interestingly, the deviation from the experiment is relatively small while considering the full-length AS(1–140) when compared with the NAC domain only. Obviously, these small deviations are due to the fact that the experimental values were measured for the full-length AS(1–140).

The fibril diameter of model C4 is ∼8.6 nm, which is in agreement with the experimental diameter value of Melki group,[8] and that of model C5 is ∼4.4 nm (Figure S26), which is in agreement with the experimental value of Anderson group.[26] Interestingly, these fibrillar diameter values of the full-length AS(1–140)—models C5 and C4 are similar to those of AS(30–95)—models C1 and C3, respectively. This indicates that the full-length models conserve the fibrillary diameter dimension, whereas model C4 has the well-ordered fibrillar structure of AS(14–105) and model C5 exhibits the fibrillary structure of AS(30–95). The other domains in the N- and C-termini show fluctuation and thus do not participate in the formation of the fibrillary structures.

Extensions of N-Termini and C-Termini of AS(30–95) Affect the Structural Stability of the Folded Self-Assembled State

The self-assembly of AS(30–95) presents a well-organized structure of both models C4 and C5, but the extensions of the N- and C-termini to the full-length AS(1–140) may affect the structural stability. Obviously, the self-assembly of both models of AS(30–95)—models C1 and C3 and that of both models of AS(1–140)—models C4 and C5 were converged during the MD simulations (Figures S1 and S16). Interestingly, the convergence of the structures of AS(1–140) yields lower values of RMSD when compared with the structures of AS(30–95). Moreover, our predicted models C3 and C4 illustrate lower RMSD values than models C1 and C5 because of the relatively large number of hydrophobic and electrostatic interactions between β-strands that form more inner cores than those of models C1 and C5.

Extensions of the N- and C-termini of C1 to C5 do not change the central inner cores (distances R2, R3, and R4 in Figures S4 and S22), but the inner cores in the ends are increased (distances R1, R5, and R6 in Figure S22) because of the relatively high fluctuations in the termini (Figure S27). Yet, the inner cores still present stable cores: the distances between two β-strands are less than 15 Å. Extensions of the N- and C-termini of our predicted structures of C3 to C4 and those of Rienstra’s models yield an increase in the inner cores in the ends (i.e., distances R1 and R2 in Figures S6 and S23). However, new inner cores were constructed at R3–R9 in model C4 (Figure S23), and the distance between the inner cores R4 and R6 illustrated stable cores along the MD simulations. The distances between two β-strands in these inner cores are less than 14 Å.

In fact, our predicted structural model of AS(1–140) illustrates a well-organized cross-β structure along the sequence of AS(14–109), whereas the full-length model of the Rienstra group demonstrates a cross-β structure along the shorter sequence of AS(30–95). The DSSP analyses show that our predicted structure, model C4, has more ordered β-strands at the N- and C-termini than those of the structural model C5 of the Rienstra group (Figures S18–S21). It is not surprising that the termini in the model of the Rienstra group have less ordered structure because the termini show more fluctuations than our predicted model (Figure S27). These N- and C-termini in model C5 are more exposed to water than that in model C4 because of the fluctuations and the disordered domains (Figure S28). Moreover, the extensions in the model of the Rienstra group destabilize the N-termini of AS(35–50), whereas the extensions in our predicted model stabilize this domain (Figure S27). This domain is stabilized in our predicted model because of the formation of more inner cores and formation of more cross-β structures along the sequence; therefore, the production of multiple cross-β structures stabilizes the termini of AS(1–140).

Finally, the diameter values of AS(30–95) and AS(1–140) were computed along the MD simulations (Figure S26). The diameter values of the fibrillary structure of our predicted models AS(30–95)—C3 and AS(1–140)—C4 are similar: 8.5 nm, which is in agreement with the experimental values of Melki group.[8] A further diameter value has been measured in C4: 4.5 nm, which is in agreement with the experimental values of Anderson group.[26] The diameter values of the fibrillary structure of the models AS(30–95), model C1, and AS(1–140), model C5 of the Rienstra group, are similar: 4.5 nm, which are in agreement with the experimental values of Anderson group.[26] The additional diameter value of C5 is ∼3.8 nm, which is in agreement with the group of Carter.[25] These various diameter values demonstrate polymorphic states of the fibrillary structure of AS(1–140).

Conclusions

AS is a 140-amino acid IDP, and it is self-assembled into oligomers and fibrils. The molecular mechanisms through which AS is self-assembled are elusive. There have been extensive efforts to solve the 3D structure of the fibrillary AS(1–140) using ssNMR with no success.[14,21−23] Recently, the group of Rienstra has solved for the first time the 3D structure of the full-length AS fibrils.[15] This study proposes a further new 3D structure of AS(1–140) fibrils, which differs from the ssNMR model of the Rienstra group. It is well-known that the self-assembled amyloids are polymorphic;[24,30−34] therefore, it is also expected that AS may demonstrate the polymorphic states of AS fibrils.

The novelty of this study is the elongated sequence of AS that forms a cross-β structure in the new proposed 3D structure. While the ssNMR model of the Rienstra group illustrates a well-organized cross-β structure along residues 30–95, the 3D model that is proposed in this study demonstrates a stable cross-β structure along residues 14–109 in AS. Although, energetically, the new proposed model is relatively less stable than the model of the Rienstra group, structurally the new model shows a stable cross-β structure with less fluctuations along the N-termini of the fibrillary structure.

This study provides for the first time the knowledge of polymorphism in AS fibrils. Obviously, the polymorphic states of AS fibrils are produced because of the different experimental conditions of the growth of these fibrils. There may also be several structures that may be produced during aggregation; however, only one will be more dominant than others. Our study has shown that at the molecular level so far there are two potential fibrillary structures of AS. It is expected that future studies will show further polymorphic states of AS fibrils that could be found by further studies, as has been found previously in Aβ amyloid[35−37] and amylin.[27,38] The observation of the polymorphic states of AS will assist in understanding the various molecular mechanisms of the self-assembly of AS and, consequently, will provide an important knowledge for the design drugs to inhibit the aggregations of AS.

Materials and Methods

Construction of AS(30–95) Octamer Fibril-Like Models

The first structural AS(30–95) fibrillar model C1 (Figure ) has been constructed from the G-key 3D structure of the self-assembled AS(1–140).[15] The residues 1–29 and 96–140 were removed to construct the self-assembled structures of AS(30–95), that is, examining only the effect of the N-termini extension of the NAC domain. We further examined the self-assembled structures of AS(30–95) based on the fivefold model that consists of residues 30–110.[13] In C2 model (Figure ), the residues 96–110 in the original fivefold model were removed.

In this study, we predicted a new self-assembled AS(30–95) fibril-like structure—model C3 (Figure ). Our predicted self-assembled AS(30–95), model C3, is based on an experimental ssNMR experiment that proposed the secondary structure (i.e., β-strands) for AS fibrils, but with a lack of 3D structures.[14] We applied the self-assembled NAC(61–95) fibril-like structure that has been predicted in our group[12] and extended the N-termini domain (residues 30–60) that considers the location of the β-strands along the sequence, as suggested by the experiment (see details in the Supporting Information).[14] We further examined various predicted models for AS(30–95), which are based on various available experimental models that lack the 3D structures. Scheme S1 illustrates the available experimental predicted models of AS(30–95). The prediction of the various 3D self-assembled AS(30–95), based on these available experimental models, that had been examined and shown in unstable fibrillar structures are detailed in the Supporting Information. The successfully predicted self-assembled structure, model C3, illustrated a converged and stable cross-β structure along all time scale of the simulations. It should be noted that the previous self-assembled NAC, that is, AS(61–95) fibril-like structure that had been predicted in our group was also based on the same ssNMR experimental model that was applied for model C3.

Construction of AS(1–140) Octamer Fibril-Like Models

We further investigated the structural stability of the full-length AS(1–140) fibrils to study the effect of extension of the self-assembled NAC fibrils to the N- and C-termini. We applied C3 of AS(30–95) and extended the C- and N-termini to construct AS(1–140) fibrillar structures. To extend the termini to form a 3D structure is a challenging issue because there is a lack of structural properties in these domains. We, therefore, extended the termini while forming maximum hydrophobic and electrostatic interactions between the residues along the folded structure, particularly in the inner cores (model C4, Figure ). We further investigated the ssNMR full-length AS(1–140) fibrils that have been recently solved by Rienstra[15] (model C5, Figure ). We investigated this model because the N- and C-termini are parallel-oriented; thus, it is expected that interactions between the residues in the N- and C-termini will be produced during the simulations to form stable cross-β structures. On the other hand, in the fivefold model, the N-termini and the C-termini are oppositely oriented. Therefore, it is expected that the interactions between the residues in the N- and C-termini will not be produced during the simulations; thus, the lack of interactions may lead to the unstable structure in these domains, that is, these termini will be disordered. Indeed, simulations of these termini in the fivefold model have shown disordered domains in the full-length AS(1–140).[16]

MD Simulation Protocol

We constructed the fibril-like AS models by using the Accelrys Discovery Studio software (http://accelrys.com/products/discovery-studio/), as detailed in the previous sections. MD simulations of the solvated octamers were performed in the NPT (N−number of particles; P−pressue; T−temperature) ensemble using nanoscale molecular dynamics (NAMD)[39] with the CHARMM27 force field.[40,41] The octamers were energy-minimized and explicitly solvated in a TIP3P[42,43] water box with a minimal distance of 15 Å from each edge of the box. All water molecules within 2.5 Å of the octamers were removed. Counterions were added at random locations to neutralize the charge on the octamers. The Langevin piston method[39,44,45] was applied with a decay period of 100 fs, and a damping time of 50 fs was used to maintain a constant pressure of 1 atm. The temperature was controlled at 330 K by a Langevin thermostat with a damping coefficient of 10 ps.[39] Short-range van der Waals interactions were calculated using a 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 cutoff of 12.0 Å.[46,47] The equations of motion were integrated using the leapfrog integrator with a step of 1 fs. The solvated systems were energy-minimized for 2000-conjugated gradient steps, where the hydrogen-bonding distance between the β-sheets in each octamer was fixed in the range of 2.2–2.5 Å.

The counterions and the water molecules were allowed to move. The hydrogen atoms were constrained to the equilibrium bond by using the SHAKE algorithm.[48] The minimized solvated systems were energy-minimized for 2000 additional conjugate gradient steps and 20 000 heating steps at 250 K, with all atoms being allowed to move. Then, the system was heated from 250 to 330 K for 300 ps and equilibrated at 330 K for 300 ps. Simulations were performed at a temperature higher than the physiological temperature (310 K), with the aim of investigating the stability of the constructed models. Obviously, structures that are stable at 330 K will also be stable at lower temperatures. All simulations were run for 80 ns. These conditions were applied to test the stabilities of all constructed models.

To further examine whether the time scale of 80 ns is a reasonable choice, RMSD was computed for models C1–C3 of AS(30–95) (Figure S1) and models C4 and C5 of AS(1–140) (Figure S16) along the MD simulations. One can see that all of these simulated and constructed models were converged after 20–40 ns of the simulations, therefore indicating that the time scale of 80 ns is a reasonable choice. Moreover, the DSSP analysis was performed for each simulated model for all frames of 80 ns and for only to the last 500 frames, that is, the last 5 ns of the simulations (Figures S8–S10,S17–S20). Interestingly, the DSSP results were similar to these two time scales for each model, thus indicating that all simulated models were converged. Furthermore, to validate the convergence of the simulated models, we computed the conformational energies using the generalized Born method and molecular volume (GBMV) method and population analysis of all simulated models after 60 and 80 ns of the simulations. Interestingly, one can see that the relative conformational energies and the populations yielded a similar trend as obtained for 60 ns (Tables S1 and S5), thus indicating that 80 ns is definitely a satisfactory time scale.

GBMV Method

To obtain the relative stability and the populations of the variant models of the self-assembled AS(30–95) octamer models and the full-length AS(1–140) octamer models, the trajectories of the models for the last 5 ns were first extracted from the explicit MD simulation, excluding water molecules. The solvation energies of all systems were calculated using GBMV.[49,50] In the GBMV calculations, the dielectric constant of water was set to 80.0. The hydrophobic solvent-accessible surface area term factor was set to 0.00592 kcal mol–1 Å–2. Each variant was minimized by 1000 cycles, and the conformational energy was evaluated by a grid-based GBMV. The minimization did not change the conformations of each model but merely relaxed the local geometries caused by the thermal fluctuations that occurred during the MD simulations.

A total of 1500 conformations of AS(30–95) (500 conformations for each of the three examined models: C1–C3) and 1000 conformations of the full-length AS(1–140) (500 conformations for each of the two examined models: C4 and C5) were used to construct the free-energy landscapes of the conformers and to evaluate the conformer probabilities by using Monte Carlo (MC) simulations. In the first step, one conformation of conformer i and one conformation of conformer j were randomly selected. Then, the Boltzmann factor was computed as e–(, where E and E are the conformational energies evaluated by GBMV calculations for the respective conformations i and j, K is the Boltzmann constant, and T is the absolute temperature (298 K used here). If the Boltzmann value is larger than a random number, the change from conformation i to conformation j is allowed. After one million steps, the conformations visited for each conformer were counted. Finally, the relative probability of a conformer n was evaluated to be P = N/Ntotal, where P is the population of conformer n, N is the total number of conformations visited for the conformer n, and Ntotal is the total number of steps. The advantages of using MC simulations to estimate the conformer probability rely on its good numerical stability and the control that they allow in the transition probabilities among several conformers.

For the complex kinetics of amyloid formation, a group of three conformers of AS(30–95) and two conformers of the full-length AS(1–140) likely represent only a very small percentage of the ensemble. Nevertheless, the carefully selected models cover the most likely structures. This includes the two models that were constructed directly from the experimental results that were reported by the Rienstra group[15,20] and the models that were examined by presenting maximum interactions to stabilize the structures.

Structural Analysis Details

We examined the structural stability of the studied octamer models by following the changes in the average number of hydrogen bonds between β-strands, with the hydrogen bond cutoff being set to 2.5 Å. This examination was performed by following RMSDs and RMSFs and by monitoring the change in the intersheet distances (Cα backbone–backbone distances) in the core domains of all of the examined structures. We calculated the average distance while excluding the values obtained from the monomers at the ends of each oligomer, therefore sampling six monomers in each model. For each model, different pairs of atoms were chosen to allow the most accurate evaluation of the distance within the inner cores of the cross-β structural models. Schemes S2 and S3 illustrate the various intersheet distances in the various core domains for each of the examined models C1–C5. Finally, we investigated the average number of water molecules around each side-chain Cβ atom within 4 Å for all simulated models.

Secondary Structure Analysis

In addition to the DSSP analysis, the secondary structures of the simulated octamers, models C1–C5, were determined by computing and averaging the backbone dihedral angles Ψ and Φ of the last 500 frames from the MD simulations, for each residue. The Ψ ranges of (−60)°–(−120)° and 90°–180° for Φ were defined as the values of a β-strand structure. The average computed dihedral angles for each residue that had been extracted from the MD simulations were compared with the experimental dihedral angles.[20,23]

Calculations of OPs from MD Simulations

OPs for various 13C–1H and 15N–1H bonds were calculated from the last 5 ns of the MD trajectories (500 frames/snapshots) for each model, as detailed by Vogel et al.[51] For the 15N–1H dipole–dipole interactions, DNH was calculated according to the bond length of 1.04 Å[20] and for 13C–1H, we used a value for DCH that was computed according to the bond length of 1.1 Å.[52] In short, OPs were computed for each residue from the tensor of a dipolar interaction averaged over all MD simulation frames. We extracted the vector coordinates of the bonds that were detailed by Comellas et al.;[20] thus, we compared the computed OPs with those of Comellas et al.[20] To avoid anomalies from the peripheral monomers, we calculated the average of the OP values of 13C–1H and 15N–1H while excluding the monomers that are in the ends of the fibrillary structures. Therefore, we sampled only six monomers in each model.

Estimation of Diameter Dimensions

To estimate the diameter dimensions, we chose each of the final simulated structural models (and not the initial structural models) because all of these final structural models have been converged structurally. We measured the diameters/distances for each model, as shown in Schemes S4 and S5.