Distinct Binding Dynamics, Sites and Interactions of Fullerene and Fullerenols with Amyloid-β Peptides Revealed by Molecular Dynamics Simulations

The pathology Alzheimer’s disease (AD) is associated with the self-assembly of amyloid-β (Aβ) peptides into β-sheet enriched fibrillar aggregates. A promising treatment strategy is focused on the inhibition of amyloid fibrillization of Aβ peptide. Fullerene C60 is proved to effectively inhibit Aβ fibrillation while the poor water-solubility restricts its use as a biomedicine agent. In this work, we examined the interaction of fullerene C60 and water-soluble fullerenol C60(OH)6/C60(OH)12 (C60 carrying 6/12 hydroxyl groups) with preformed Aβ40/42 protofibrils by multiple molecular dynamics simulations. We found that when binding to the Aβ42 protofibril, C60, C60(OH)6 and C60(OH)12 exhibit distinct binding dynamics, binding sites and peptide interaction. The increased number of hydroxyl groups C60 carries leads to slower binding dynamics and weaker binding strength. Binding free energy analysis demonstrates that the C60/C60(OH)6 molecule primarily binds to the C-terminal residues 31–41, whereas C60(OH)12 favors to bind to N-terminal residues 4–14. The hydrophobic interaction plays a critical role in the interplay between Aβ and all the three nanoparticles, and the π-stacking interaction gets weakened as C60 carries more hydroxyls. In addition, the C60(OH)6 molecule has high affinity to form hydrogen bonds with protein backbones. The binding behaviors of C60/C60(OH)6/C60(OH)12 to the Aβ40 protofibril resemble with those to Aβ42. Our work provides a detailed picture of fullerene/fullerenols binding to Aβ protofibril, and is helpful to understand the underlying inhibitory mechanism.


Introduction
Amyloids are involved in a broad range of neurodegenerative diseases, including Alzheimer's, Huntington's and Parkinson's diseases [1][2][3]. The major constituents of amyloid plaques are associated with fibrils formed by amyloid-β (Aβ) protein that display a cross-β structure characterized by β-strands perpendicular to and inter-strand hydrogen bonds parallel to the fibril axis [4,5]. The fibrillation occurs through a complex multistep process, involving the formation of soluble oligomers, protofibrils and insoluble mature fibrils [6,7]. Small aggregates (soluble oligomers and protofibrils) in the early stage of aggregation are suggested as primary neurotoxic agents [8][9][10][11]. Therefore, a promising strategy to reduce the small toxic oligomer species is to inhibit Aβ peptide aggregation.

Dynamics of the Fullerene/Fullerenol Molecule Binding to Aβ42-Trimer
To investigate the binding process of the fullerene/fullerenol molecule to Aβ42-trimer, we first monitored the time evolution of their minimum distance dmin (Figure 2a-c). As for the Aβ42-trimer-C60 system, the C60 molecule was initially placed 2 nm away from the Aβ42-trimer. Once the MD simulations were initiated, dmin started to decrease or increase, depending on the initial velocity distributions. The minimum distances in Run 1, 2 and 4 were observed to decline to ~0.30 nm within the first 3 ns, while those in Run 3, 5 and 6 took ~10 ns to reach ~0.30 nm. Such fast and slow binding processes were also observed in Aβ42-trimer-C60(OH)6 and Aβ42-trimer-C60(OH)12 systems. Similar fast and slow processes were reported in a previous MD study of DMF binding to Aβ fibril [31]. Moreover, we found that the slow binding processes may last tens of nanoseconds for C60(OH)6 and C60(OH)12, much longer than that for C60. It takes over 25 ns for two MD runs of Aβ-C60(OH)6 system (Runs 3, 6) to reach a minimum distance of ~0.30 nm, and the situation was the same in Aβ-C60(OH)12 system (Runs 3, 4). Specially, in Run 3 of Aβ42-trimer-C60(OH)12 system, dmin increased sharply at 49.8 and 83.6 ns, and declined to ~0.30 nm in the next twenty nanoseconds. These indicate that the binding process of the C60(OH)6/C60(OH)12 molecule to Aβ42-trimer is slower than that of C60.
To further examine the binding status of the fullerene/fullerenol molecule after the initial adsorption to Aβ42-trimer, we monitored the time evolution of the number of contacts between individual residue and the nanoparticle in a representative MD run for each simulated system in Figure 2d-f. The C60 molecule was observed to stay at a relatively fixed location during the remaining simulation time once stable contacts are formed. The C60(OH)6 molecule also had a relatively fixed binding site, while it can shift to other location transiently. As for the C60(OH)12 molecule, its binding location kept changing when simulation time increased, corresponding to a slow move on the protein surface. C60(OH)12 also contacted with more residues at the same time, which indicated a lower specificity of binding sites. These results reflect that with the hydroxylation extent of C60 increased, the binding strength between Aβ42-trimer and the nanoparticle molecule gets weaker.  40 -trimer and C 60 /C 60 (OH) 6 /C 60 (OH) 12 . (d) The initial conformation of the Aβ 42 -trimer-C 60 system with the C 60 molecule placed at three different positions (I-III). Color codes: positively charged residues (blue), negatively charged residues (red), hydrophobic residues (white) and polar residues (green) in Aβ peptides; carbon atoms (cyan), oxygen atoms (red) and hydrogen atoms (white) in fullerene/fullerenol. For clarity, water molecules in the simulation box are not displayed; box vectors are shown, and z-axis is the fibrillar elongation direction.

Dynamics of the Fullerene/Fullerenol Molecule Binding to Aβ 42 -Trimer
To investigate the binding process of the fullerene/fullerenol molecule to Aβ 42 -trimer, we first monitored the time evolution of their minimum distance d min (Figure 2a-c). As for the Aβ 42 -trimer-C 60 system, the C 60 molecule was initially placed 2 nm away from the Aβ 42 -trimer. Once the MD simulations were initiated, d min started to decrease or increase, depending on the initial velocity distributions. The minimum distances in Run 1, 2 and 4 were observed to decline to~0.30 nm within the first 3 ns, while those in Run 3, 5 and 6 took~10 ns to reach~0.30 nm. Such fast and slow binding processes were also observed in Aβ 42 -trimer-C 60 (OH) 6 and Aβ 42 -trimer-C 60 (OH) 12 systems. Similar fast and slow processes were reported in a previous MD study of DMF binding to Aβ fibril [31]. Moreover, we found that the slow binding processes may last tens of nanoseconds for C 60 (OH) 6 and C 60 (OH) 12 , much longer than that for C 60 . It takes over 25 ns for two MD runs of Aβ-C 60 (OH) 6 system (Runs 3, 6) to reach a minimum distance of~0.30 nm, and the situation was the same in Aβ-C 60 (OH) 12 system (Runs 3, 4). Specially, in Run 3 of Aβ 42 -trimer-C 60 (OH) 12 system, d min increased sharply at 49.8 and 83.6 ns, and declined to~0.30 nm in the next twenty nanoseconds. These indicate that the binding process of the C 60 (OH) 6 /C 60 (OH) 12 molecule to Aβ 42 -trimer is slower than that of C 60 .
To further examine the binding status of the fullerene/fullerenol molecule after the initial adsorption to Aβ 42 -trimer, we monitored the time evolution of the number of contacts between individual residue and the nanoparticle in a representative MD run for each simulated system in Figure 2d-f. The C 60 molecule was observed to stay at a relatively fixed location during the remaining simulation time once stable contacts are formed. The C 60 (OH) 6 molecule also had a relatively fixed binding site, while it can shift to other location transiently. As for the C 60 (OH) 12 molecule, its binding location kept changing when simulation time increased, corresponding to a slow move on the protein surface. C 60 (OH) 12 also contacted with more residues at the same time, which indicated a lower specificity of binding sites. These results reflect that with the hydroxylation extent of C 60 increased, the binding strength between Aβ 42 -trimer and the nanoparticle molecule gets weaker. In order to quantify the binding strength, we calculated in Table 1 the binding free energy and its different components between Aβ42-trimer and the fullerene/fullerenol molecule using the MM/PBSA (molecular mechanics/linear Poisson−Boltzmann surface area) method. The binding energy was calculated over all six MD runs for each simulated system using the last 20 ns data of each MD trajectory. The binding energy components show that the van der Waals interaction (ΔEvdW) has a dominant contribution to the total binding energy (ΔGbind). It is shown that ΔEvdW is -24.02 ± 0.74 kcal/mol in the Aβ-C60 system, -24.02 ± 0.74 kcal/mol in the Aβ-C60(OH)6 system and -18.20 ± 1.02 kcal/mol in the Aβ-C60(OH)12 system. Interestingly, although C60(OH)6 carries six more hydroxyl groups than C60, their ΔEvdW is quite similar, and that of C60(OH)12 became ~6 kcal/mol larger. This reveals that the increment of ΔEvdW is not in proportion to the hydroxylation level of C60 surface. Due to the additional partial charges that hydroxyls bring, the electrostatic interaction (ΔEelec) is strengthened as the hydroxyl number increases. The nonpolar solvation component ΔGnonpolar contributes little to the free energy change. The enhanced hydrophilicity with the addition of hydroxyls results in a positive value of ΔGsolv (solvation effect), indicating that water is favorable for fullerenols and solvation effect goes against the binding of fullerenol to Aβ. Our results are consistent with a previous study on fullerenol C60(OH)16 interacting with Aβ40 [30]. They found that the electrostatics contribution is much increased in fullerenol with respect to that in fullerenes, yet hydroxyl groups contribute a positive amount to the binding free energy. Overall, our free energy calculation demonstrates that the total binding free energy rises with more hydroxyl groups attached to C60. This gives the explanation that higher hydroxylation level leads to slower binding dynamics and weaker binding strength. In order to quantify the binding strength, we calculated in Table 1 the binding free energy and its different components between Aβ 42 -trimer and the fullerene/fullerenol molecule using the MM/PBSA (molecular mechanics/linear Poisson−Boltzmann surface area) method. The binding energy was calculated over all six MD runs for each simulated system using the last 20 ns data of each MD trajectory. The binding energy components show that the van der Waals interaction (∆E vdW ) has a dominant contribution to the total binding energy (∆G bind ). It is shown that ∆E vdW is -24.02 ± 0.74 kcal/mol in the Aβ-C 60 system, -24.02 ± 0.74 kcal/mol in the Aβ-C 60 (OH) 6 system and -18.20 ± 1.02 kcal/mol in the Aβ-C 60 (OH) 12 system. Interestingly, although C 60 (OH) 6 carries six more hydroxyl groups than C 60 , their ∆E vdW is quite similar, and that of C 60 (OH) 12 became~6 kcal/mol larger. This reveals that the increment of ∆E vdW is not in proportion to the hydroxylation level of C 60 surface. Due to the additional partial charges that hydroxyls bring, the electrostatic interaction (∆E elec ) is strengthened as the hydroxyl number increases. The nonpolar solvation component ∆G nonpolar contributes little to the free energy change. The enhanced hydrophilicity with the addition of hydroxyls results in a positive value of ∆G solv (solvation effect), indicating that water is favorable for fullerenols and solvation effect goes against the binding of fullerenol to Aβ. Our results are consistent with a previous study on fullerenol C 60 (OH) 16 interacting with Aβ 40 [30]. They found that the electrostatics contribution is much increased in fullerenol with respect to that in fullerenes, yet hydroxyl groups contribute a positive amount to the binding free energy. Overall, our free energy calculation demonstrates that the total binding free energy rises with more hydroxyl groups attached to C 60 . This gives the explanation that higher hydroxylation level leads to slower binding dynamics and weaker binding strength.

Binding Sites of The Fullerene/Fullerenol Molecule to Aβ 42 -Trimer
Identifying the binding sites of the C 60 /C 60 (OH) 6 /C 60 (OH) 12 molecule to Aβ 42 -trimer is the first step to understand the underlying inhibition mechanism. To this aim, we calculated the residue-based binding free energy of the nanoparticles to Aβ 42 -trimer in Figure 3a-c using last 20 ns data of the simulations. As shown, C 60 has the lowest binding energy with aromatic residue F4, and hydrophobic residues V39 and A2, as well as G25 located in the turn region; C 60 (OH) 6 has the lowest binding energy with aromatic Y10 and F4, negatively charged E11, and hydrophobic L34, L17 and V39; C 60 (OH) 12 has the lowest binding energy with hydrophobic L34, negatively charged E22 and aromatic F4. This indicates the critical roles of aromatic stacking and hydrophobic interactions in the interplay between Aβ and all the three nanoparticles. As for fullerenols C 60 (OH) 6 and C 60 (OH) 12 , their hydrogen bonding interaction with negatively charged residues of Aβ is also important.

Binding Sites of The Fullerene/Fullerenol Molecule to Aβ42-Trimer
Identifying the binding sites of the C60/C60(OH)6/C60(OH)12 molecule to Aβ42-trimer is the first step to understand the underlying inhibition mechanism. To this aim, we calculated the residue-based binding free energy of the nanoparticles to Aβ42-trimer in Figure 3a-c using last 20 ns data of the simulations. As shown, C60 has the lowest binding energy with aromatic residue F4, and hydrophobic residues V39 and A2, as well as G25 located in the turn region; C60(OH)6 has the lowest binding energy with aromatic Y10 and F4, negatively charged E11, and hydrophobic L34, L17 and V39; C60(OH)12 has the lowest binding energy with hydrophobic L34, negatively charged E22 and aromatic F4. This indicates the critical roles of aromatic stacking and hydrophobic interactions in the interplay between Aβ and all the three nanoparticles. As for fullerenols C60(OH)6 and C60(OH)12, their hydrogen bonding interaction with negatively charged residues of Aβ is also important. Residue-based binding free energy. The binding energy was calculated over all six MD runs for each simulated system using the last 20 ns data of each MD trajectory. (d-f) Schematic diagrams for binding sites of the fullerene/fullerenol molecule to Aβ42-trimer. The positions where the fullerene/fullerenol molecule has high binding affinity are named with P1, P2, etc., from N-termini to C-termini, and z-axis is the fibrillar elongation direction. The color code is consistent with that in Figure 1. (d-f) Schematic diagrams for binding sites of the fullerene/fullerenol molecule to Aβ 42 -trimer. The positions where the fullerene/fullerenol molecule has high binding affinity are named with P 1 , P 2 , etc., from N-termini to C-termini, and z-axis is the fibrillar elongation direction. The color code is consistent with that in Figure 1.
According to the residue-based binding free energy, we found that C 60 preferentially interacts with Aβ 42 -trimer at three different sites: 2AEF4, 23DVG25 and C-terminal residues 31-41. Through the binding energy analysis at each site (Table 2), we found that C-terminal residues 31-41 and 2AEF4 have the lowest binding energy, indicating these two regions are the most favorable binding sites for C 60 . This finding is in agreement with the binding sites (aromatic residues F4 and C-terminal hydrophobic residues 31-40) identified in DMF interacting with Aβ dimer [34]. The C-terminal hydrophobic region of residues 31-41 was also reported to be the dominant binding site in DMF interacting with Aβ fibrillar hexamer [31]. As for C 60 (OH) 6 , it prefers to bind to Aβ 42 -trimer at four sites: 2AEF4, 9GYE11, 17LVF19 and C-terminal residues 31-41, among which C-terminal residues 31-41 and 9GYE11 have the lowest binding energy. As for C 60 (OH) 12 , it has three preferential sites: N-terminal residues 4-14, 22ED23 and 34LM35, among which N-terminal residues 4-14 are the most favorable. The hydrophobic clusters A2-F4-L34-V36, L17-F19-I31 and A30-I32-M35-V40 play critical roles in the structural stability of Aβ 42 fibril [5]. The strong binding of C 60 /C 60 (OH) 6 to these clusters is expected to interfere with the hydrophobic packing of Aβ side chains, and as a result goes against further fibrillization. To exhibit the relation between binding dynamics and binding sites clearly, we presented the schematic diagrams for binding sites of C 60 /C 60 (OH) 6 /C 60 (OH) 12 to Aβ 42 -trimer. The positions where the fullerene/fullerenol molecule has high binding affinity are named with P 1 , P 2 , etc., from N-termini to C-termini. As shown in Figure 3d, there are three positions P 1 , P 2 and P 3 at which C 60 prefers to stay when binding to Aβ 42 -trimer, mainly corresponding to the binding sties 2AEF4, 23DVG25 and C-terminal residues 31-41, respectively. Note that C 60 staying at P 1 can interact with the region 2AEF4 and the C-terminal residues 31-41 at the same time. Trajectory tracing shows that C 60 binds mostly at P 1 and P 3 with a respective probability of 22.7% and 29.8%, in agreement with the free energy calculation, and the location of C 60 is relatively fixed. Moreover, the C 60 molecule is able to wander on the surface groove along z-axis of Aβ 42 -trimer at P 1 position. These preferential positions are near two hydrophobic clusters A2-F4-L34-V36 and A30-I32-M35-V40, indicating that the binding of C 60 to Aβ 42 -trimer is dominantly driven by the hydrophobic interaction. The importance of hydrophobic interaction was reported in other studies on the binding processes of fullerene and other small molecules to Aβ [29,37,38]. With respect to P 1 and P 3 , C 60 has a relatively lower binding affinity to P 2 . This binding site is facilitated by the groove of a proper size in the 23DVGS26 region, where the side chains of D23 and S26 are in the outer side of Aβ 42 -trimer and G25 has no side chain. Similar concave-induced binding sites were observed in the study of fullerenes with Aβ and other proteins [31,39,40].
As for C 60 (OH) 6 , it has four preferential binding positions P 1 , P 2 , P 3 and P 4 (Figure 3e), mainly corresponding to the binding sties 2AEF4, 9GYE11, 17LVF19 and C-terminal residues 31-41, respectively. Interestingly, the C 60 (OH) 6 molecule is able to slip on the elongation surface (perpendicular to z-axis), wandering between P 1 and P 4 or between P 3 and P 4 with a low probability. The P 3 position is adjacent to another hydrophobic cluster L17-F19-I31 of Aβ 42 -trimer. Besides, C 60 (OH) 6 has high binding affinity to 9GYE11 (P 2 ), facilitated by the hydrogen bonds (H-bonds) formed in between. As for C 60 (OH) 12 , it prefers to bind to three positions P 1 , P 2 and P 3 (Figure 3f), corresponding to the binding sties N-terminal residues 4-14, 22ED23 and 34LM35, respectively. Different from the binding behaviors of C 60 and C 60 (OH) 6 , C 60 (OH) 12 is more likely to stay at the hydrophilic parts of protein surface. It is able to move between positions P 1 and P 3 , or slip along the N-terminal β-strand, forming H-bonds with main chain or side chain of amino acids. The C 60 (OH) 12 molecule may also contact with 22ED23 region. As the side chains of E22 and D23 are oriented to water solution, C 60 (OH) 12 is inclined to form H-bonds with them. Considering the important roles of C-terminal hydrophobic residues in Aβ aggregation and toxicity [41][42][43], it is conceivable that the binding of C 60 and C 60 (OH) 6 molecules to the C-terminal region can prevent Aβ fibrillization. In addition, the C 60 (OH) 6 molecule has higher affinity to bind to elongation surfaces than C 60 and C 60 (OH) 12 , which makes C 60 (OH) 6 a more effective inhibitor. As previous computational and experimental studies suggested that binding at fibril ends goes against fibrillar elongation [44][45][46], this binding would block the backbone amide sites for fibril growth and as a result, slows down or inhibits the elongation process. It is noted that the bindings of nanoparticles to protofibril and mature fibril are supposed to be distinct, because the relative area of the exposed ends compared to the entire fibril surface will be greatly decreased in mature fibrils.

Structural Influence of The Fullerene/Fullerenol Molecule on Aβ 42 -Trimer
In order to detect the influence of fullerene/fullerenol binding on the Aβ 42 -trimer structure, we first examined the secondary structural difference relative to the isolated Aβ 42 -trimer. The β-sheet contents of Aβ 42 -trimer, Aβ 42 -trimer-C 60 , Aβ 42 -trimer-C 60 (OH) 6 and Aβ 42 -trimer-C 60 (OH) 12 systems are 80.5%, 83.3%, 81.1% and 80.4%, respectively, showing little difference. Then, we calculated the average Cα-root-mean-square deviation (Cα-RMSD) with respect to the initial coordinates of Aβ 42 protofibrillar trimer using the last 20 ns data of each MD trajectory. As shown in Figure 4a, the values of Cα-RMSD in the absence and presence of the C 60 (OH) 12 molecule are 0.27 ± 0.03 nm and 0.27 ± 0.01 nm, showing no statistically significant difference. In the presence of C 60 /C 60 (OH) 6 , Aβ 42 -trimer has an increased Cα-RMSD of 0.32 ± 0.02 / 0.34 ± 0.05 nm, while the values are still within the error of estimate with respect to that of isolated Aβ. These indicate that the C 60 /C 60 (OH) 6 /C 60 (OH) 12 molecule has a negligible influence on the structural stability of Aβ 42 -trimer. Figure 4b,c display the time evolution of Cα-RMSD of the MD trajectory contributing most to the total Cα-RMSD in Aβ 42 -trimer-C 60 and Aβ 42 -trimer-C 60 (OH) 6 systems, respectively. With C 60 , the Cα-RMSD value of Aβ 42 -trimer keeps rising in the first 20 ns and finally fluctuates at around 0.55 nm. During this process, the C 60 molecule is observed to contact abundantly with side chains of V39 and I41, and lead to twisted C-termini. In the Aβ 42 -trimer-C 60 (OH) 6 system, the Cα-RMSD value of Aβ 42 -trimer keeps at~0.30 nm until t = 40.8 ns. After that, it rises sharply and increases to >1.0 nm. When Cα-RMSD begins its quick rise, the C 60 (OH) 6 molecule is observed to bind at the C-terminal residues 31-41, and the hydrophobic cluster A2-F4-L34-V36 starts to collapse. Then, the sidechains of A2 and F4 dissociate with those of L34 and V36 one by one, and finally the N-termini and C-termini get separated far away. Note that it is the only MD trajectory among all the simulations we performed in this study that N-and C-termini dissociation is observed. It needs further studying to connect this dissociation with Aβ-C 60 (OH) 6

interaction explicitly.
binding of C60 and C60(OH)6 molecules to the C-terminal region can prevent Aβ fibrillization. In addition, the C60(OH)6 molecule has higher affinity to bind to elongation surfaces than C60 and C60(OH)12, which makes C60(OH)6 a more effective inhibitor. As previous computational and experimental studies suggested that binding at fibril ends goes against fibrillar elongation [44][45][46], this binding would block the backbone amide sites for fibril growth and as a result, slows down or inhibits the elongation process. It is noted that the bindings of nanoparticles to protofibril and mature fibril are supposed to be distinct, because the relative area of the exposed ends compared to the entire fibril surface will be greatly decreased in mature fibrils.

Structural Influence of The Fullerene/Fullerenol Molecule on Aβ42-Trimer
In order to detect the influence of fullerene/fullerenol binding on the Aβ42-trimer structure, we first examined the secondary structural difference relative to the isolated Aβ42-trimer. The β-sheet contents of Aβ42-trimer, Aβ42-trimer-C60, Aβ42-trimer-C60(OH)6 and Aβ42-trimer-C60(OH)12 systems are 80.5%, 83.3%, 81.1% and 80.4%, respectively, showing little difference. Then, we calculated the average Cα-root-mean-square deviation (Cα-RMSD) with respect to the initial coordinates of Aβ42 protofibrillar trimer using the last 20 ns data of each MD trajectory. As shown in Figure 4a, the values of Cα-RMSD in the absence and presence of the C60(OH)12 molecule are 0.27 ± 0.03 nm and 0.27 ± 0.01 nm, showing no statistically significant difference. In the presence of C60/C60(OH)6, Aβ42-trimer has an increased Cα-RMSD of 0.32 ± 0.02 / 0.34 ± 0.05 nm, while the values are still within the error of estimate with respect to that of isolated Aβ. These indicate that the C60/C60(OH)6/C60(OH)12 molecule has a negligible influence on the structural stability of Aβ42-trimer. Figure 4b,c display the time evolution of Cα-RMSD of the MD trajectory contributing most to the total Cα-RMSD in Aβ42-trimer-C60 and Aβ42-trimer-C60(OH)6 systems, respectively. With C60, the Cα-RMSD value of Aβ42-trimer keeps rising in the first 20 ns and finally fluctuates at around 0.55 nm. During this process, the C60 molecule is observed to contact abundantly with side chains of V39 and I41, and lead to twisted C-termini. In the Aβ42-trimer-C60(OH)6 system, the Cα-RMSD value of Aβ42-trimer keeps at ~0.30 nm until t = 40.8 ns. After that, it rises sharply and increases to >1.0 nm. When Cα-RMSD begins its quick rise, the C60(OH)6 molecule is observed to bind at the C-terminal residues 31-41, and the hydrophobic cluster A2-F4-L34-V36 starts to collapse. Then, the sidechains of A2 and F4 dissociate with those of L34 and V36 one by one, and finally the N-termini and C-termini get separated far away. Note that it is the only MD trajectory among all the simulations we performed in this study that N-and C-termini dissociation is observed. It needs further studying to connect this dissociation with Aβ-C60(OH)6 interaction explicitly.  The detailed interactions between Aβ 42 -trimer and the fullerene/fullerenol molecule were also investigated. As a previous study suggested that the salt bridges between H6, E11 and H13 stabilize the kink in the N-terminal part of the β-sheets around Y10 [5], we examined the interplay of H6-E11-H13 and found that the interaction pairs stably stay together in all simulated systems except for one MD trajectory of Aβ 42 -trimer-C 60 (OH) 6 system. This trajectory corresponds to the MD run shown in Figure 4c, and its snapshot of the final state is presented in Figure 5a. Even if the Nand C-termini are dissociated, the interaction pairs of H6, E11 and H13 mostly stay together, and the interactions of side chains are weakened by excluding those of H6-3 (H6 in Chain 3) and E13-1 (E13 in Chain 1).
In Figure 5b,c, we calculated the number of H-bonds formed between individual residue and fullerenols. It shows that C 60 (OH) 6 favors H-bonding with main chains of Aβ 42 -trimer, and forms H-bonds mostly with residues I32 and D1. The C 60 (OH) 12 molecule forms almost the same amount of H-bonds with main chains and side chains, and it preferentially forms H-bonds with residues E11, H13, Q15, D23, E22 and V36. Previous Thioflavin T (ThT) fluorescence and atomic force microscopy experiments showed that fullerenol C 60 (OH) 16 can prevent Aβ 40 fbrillization [30]. The recent study using ThT assay and transmission electron microscope demonstrated that fullerenemalonate can inhibit Aβ 42 aggregation [47]. Their computational results showed that the inhibition is attributed to the hydrogen bonding of the fullerenemalonate carboxylate groups with Aβ. Here, the formation of H-bonds between main chains and fullerenols is supposed to block the backbone amide sites for further addition of peptides in β-sheet structure, which goes against the oligomerization or fibrillization of Aβ. The higher affinity of C 60 (OH) 6 bonding with main chains of Aβ peptides makes C 60 (OH) 6 a more efficient inhibitor than C 60 (OH) 12 .

Dynamics, Sites and Interactions of The Fullerene/Fullerenol Molecule Binding to Aβ40-Trimer
We also carried out multiple MD simulations to examine the binding dynamics, binding sites and interactions of the C60/C60(OH)6/C60(OH)12 molecule with Aβ40-trimer. Although the structure of Aβ40-trimer is different from that of Aβ42-trimer (see Figure 1), the binding behavior of nanoparticles to Aβ40-trimer was found to display a remarkable resemblance with that to Aβ42-trimer. As shown in Figure 6, with the hydroxylation extent increased, the C60 molecule displays slower binding dynamics, corresponding to weakened binding strength. The binding free energy analysis shows that the favorable residues of Aβ40-trimer with which the nanoparticle tend to interact are a little different from those of Aβ42-trimer. Still, these residues are mostly hydrophobic or aromatic, indicating the critical roles of hydrophobic and aromatic interactions in Aβ-nanoparticle interactions. Moreover, the preferential binding regions of the nanoparticles interplaying with Aβ40-trimer resemble with those of the nanoparticles binding to Aβ42-trimer. We also examined the stability of the D23-K28 salt bridge, which is important for the structural stability of Aβ40 [4]. The salt bridge would be interfered by the nanoparticle binding, whereas the connection between the salt bridge disruption and the hydroxylation extent of C60 is not explicit. The π-stacking interaction is important in the self-assembly of amyloid fibrils, with parallel, T-shaped and herringbone (~50 • ) orientations suggested for aromatic rings in proteins [48]. The binding energy analysis reveals the important role of F4 in the interaction between Aβ 42 -trimer and the fullerene/fullerenol molecule. To examine the aromatic stacking interaction between F4 and C 60 /C 60 (OH) 6 /C 60 (OH) 12 , we calculated the number of π-stacking structures between Aβ42-trimer and fullerene/fullerenol during the last 20 ns in Figure 5d-f. For the Aβ 42 -trimer-C 60 system, π-stacking structures were observed in three MD trajectories. Run 6 had the largest number of π-stacking structures, and the maximum number was three. This means that the C 60 molecule is able to have π-stacking interaction with all the aromatic rings of F4 in Aβ 42 -trimer at the same time. The inset snapshot displays the corresponding structure, and the aromatic rings of F4 are oriented in parallel or herringbone alignment relative to the C 60 surface. As for C 60 (OH) 6 , it forms less π-stacking structures with Aβ 42 -trimer, and the maximum number of π-stacking decreases to two. For the Aβ 42 -trimer-C 60 (OH) 12 system, π-stacking structures are observed in two trajectories and the total number of π-stacking structures is the least. Only one aromatic ring of F4 can have π-stacking interaction with the C 60 (OH) 12 molecule at one moment, and the ring is mostly oriented in herringbone alignment relative to the carbon surface of C 60 (OH) 12 . These results indicate that the more hydroxylated C 60 is, the fewer and weaker π-stacking interactions with Aβ 42 -trimer the nanoparticle has.

Dynamics, Sites and Interactions of The Fullerene/Fullerenol Molecule Binding to Aβ 40 -Trimer
We also carried out multiple MD simulations to examine the binding dynamics, binding sites and interactions of the C 60 /C 60 (OH) 6 /C 60 (OH) 12 molecule with Aβ 40 -trimer. Although the structure of Aβ 40 -trimer is different from that of Aβ 42 -trimer (see Figure 1), the binding behavior of nanoparticles to Aβ 40 -trimer was found to display a remarkable resemblance with that to Aβ 42 -trimer. As shown in Figure 6, with the hydroxylation extent increased, the C 60 molecule displays slower binding dynamics, corresponding to weakened binding strength. The binding free energy analysis shows that the favorable residues of Aβ 40 -trimer with which the nanoparticle tend to interact are a little different from those of Aβ 42 -trimer. Still, these residues are mostly hydrophobic or aromatic, indicating the critical roles of hydrophobic and aromatic interactions in Aβ-nanoparticle interactions. Moreover, the preferential binding regions of the nanoparticles interplaying with Aβ 40 -trimer resemble with those of the nanoparticles binding to Aβ 42 -trimer. We also examined the stability of the D23-K28 salt bridge, which is important for the structural stability of Aβ 40 [4]. The salt bridge would be interfered by the nanoparticle binding, whereas the connection between the salt bridge disruption and the hydroxylation extent of C 60 is not explicit.

Molecules
The Aβ peptide (39-43-amino acid) is derived from the amyloid precursor protein (APP) through proteolytic cleavage by βand γ-secretase, and the most abundant Aβ are Aβ 42 (sequence: DAEFRHDSGY 10 EVHHQKLVFF 20 AEDVGSNKGA 30 IIGLMVGGVV 40 IA) and Aβ 40 . The initial coordinate of the Aβ 42 protofibrillar trimer was taken from the Aβ 42 fibril structure [5] (PDB ID: 5OQV) determined by cryo-electron microscopy (cryo-EM). The coordinate of the Aβ 40 protofibrillar trimer was taken from the Aβ 40 fibril structure [4] (PDB ID: 2M4J) obtained from solid-state nuclear magnetic resonance (NMR) spectroscopic data. The protonation of the peptide was adjusted to the neutral pH. The Nand C-termini were respectively capped by NH 3 + and COO − in accordance with experiments.
The structure of C 60 /C 60 (OH) 6 /C 60 (OH) 12 molecules used in this study is displayed in Figure 1. The force field parameters were taken from a previous MD study on the interaction of Aβ and hydroxylated carbon nanotube [49]. To simplify the modeling, the hydroxyl groups in C 60 (OH) 6 /C 60 (OH) 12 molecules are distributed uniformly on the C 60 surface.
The Aβ 42 -trimer-C 60 simulation system consists of an Aβ 42 protofibrillar trimer and a C 60 molecule placed 2.0 nm (minimum distance) away from Aβ, as shown in Figure 1. To remove the bias of the initial position of C 60 on the binding site, the C 60 molecule was initially placed at three different locations (I, II, III). The other Aβ-fullerene/fullerenol systems were constructed similarly, and were immersed in SPC [50] water. Counterions Na + and Clwere added to neutralize the system and provide an additional 0.1 M salt concentration. Systems of isolated Aβ 42 -trimer and Aβ 40 -trimer in water were run as control groups.

Analysis Methods
Trajectory analysis was performed using the GROMACS-4.5.3 package toolkits and in-house developed codes. The secondary structure was calculated using the DSSP program [61]. Here, an atomic contact is defined when two non-hydrogen atoms come within 0.54 nm. The H-bond is determined using geometrical criteria: the distance between donor D and acceptor A is less than 0.35 nm and the D-H-A angle is larger than 150 • . The π-stacking structure is defined when the centroid of residue aromatic ring is within 0.45 nm from the spherical carbon surface of fullerene/fullerenol [62]. The binding energy between a ligand and a receptor was estimated by means of (MM/PBSA) [63,64]: ∆G bind = ∆E MM + ∆G solv − T∆S, ∆E MM = ∆E vdW + ∆E elec , ∆G solv = ∆G polar + ∆G nonpolar , ∆G nonpolar = γ· SASA + b. Here, E MM is the gas-phase energy, consisting of electrostatic (∆E elec ) and van der Waals (∆E vdw ) terms; ∆G solv is the sum of polar solvation energy ∆G polar and nonpolar solvation component ∆G nonpolar ; ∆G polar is estimated by solving the Poisson−Boltzmann equation; ∆G nonpolar is estimated by solvent accessible surface area (SASA). A water probe radius of 0.14 nm was used to calculate SASA, and γ (surface tension of the solvent) and b (fitting parameter) were set to 0.542 kcal/mol/nm 2 and 0.92 kcal/mol, respectively. As the binding free energy (∆G bind ) reported here is the relative binding free energy, the contribution of conformational entropy of peptides was ignored in accordance with a number of previous computational studies [33,34,65,66].

Conclusions
We investigated the dynamics, sites and interactions of the C 60 /C 60 (OH) 6 /C 60 (OH) 12 nanoparticle binding to Aβ 42/40 protofibrillar trimer by performing extensive atomistic MD simulations. To our knowledge, this is the first atomistic explicit-solvent simulation study to investigate the binding behavior of fullerenols to Aβ 42/40 protofibril. Our simulations demonstrate that the higher hydroxylation level of C 60 leads to slower binding dynamics and weaker binding strength. When binding to Aβ 42 -trimer, C 60 preferentially interacts with C-terminal residues 31-41 and 2AEF4; C 60 (OH) 6 prefers to bind to C-terminal residues 31-41 and 9GYE11; C 60 (OH) 12 favors to bind to N-terminal residues 4-14. In addition, the C 60 (OH) 6 molecule has higher affinity to bind to elongation surfaces than C 60 and C 60 (OH) 12 . The binding of these nanoparticles has a slight influence on the secondary structure and structural stability of Aβ 42 -trimer during the simulation time. The hydrophobic interaction plays a critical role in the interplay between Aβ 42 and all three nanoparticles; π-stacking interaction gets weakened as C 60 carries more hydroxyls. The situations are quite similar when the C 60 /C 60 (OH) 6 /C 60 (OH) 12 nanoparticle binds to Aβ 40 protofibrillar trimer. Overall, the proper binding strength and high affinity to form hydrogen bonds with protein backbones make the water-soluble C 60 (OH) 6 molecule an efficient inhibitor. This study provides a detailed picture of fullerene/fullerenols binding to Aβ protofibril and expands the understanding of the underlying inhibitory mechanism, which is helpful to the design of novel agents with anti-amyloid properties.