Molecular dynamics simulations of amyloid-β peptides in heterogeneous environments

Alzheimer’s disease is thought to be caused by the aggregation of amyloid-β (Aβ) peptides. Their aggregation is accelerated at hydrophilic/hydrophobic interfaces such as the air–water interface and the surface of monosialotetrahexosylganglioside (GM1) clusters on neuronal cell membranes. In this review, we present recent studies of full-length Aβ (Aβ40) peptides and Aβ(16–22) fragments in such heterogeneous environments by molecular dynamics (MD) simulations. These peptides have both hydrophilic and hydrophobic amino-acid residues and tend to exist at the hydrophilic/hydrophobic interface. Therefore, the peptide concentration increases at the interface, which is one of the factors that promote aggregation. Furthermore, it was found that Aβ40 forms an α-helix structure and then a β-hairpin structure at the interface. The β-hairpin promotes the formation of oligomers with intermolecular β-sheets. It means that not only the high concentration of Aβ40 at the interface but also the structure of Aβ40 itself promotes aggregation. In addition, MD simulations of Aβ40 on recently-developed GM1-glycan clusters showed that the HHQ (13–15) segment of Aβ40 is important for the recognition of GM1-glycan clusters. It was also elucidated that Aβ40 forms a helix structure in the C-terminal region on the GM1-glycan cluster. This result suggests that the helix formation, which is the first step in the conformational changes toward pathological aggregation, is initiated at the GM1-glycan moieties rather than at the lipid-ceramide moieties. These studies will enhance the physicochemical understanding of the structural changes of Aβ at the heterogeneous interfaces and the mechanism of Alzheimer’s disease pathogenesis.


Introduction
Proteins are normally folded correctly and maintain their functions in the body. However, at high concentrations, many proteins aggregate to form oligomers, spherical aggregates, or amyloid fibrils, needle-like aggregates. These protein aggregates are associated with about 40 human neurodegenerative diseases [1][2][3][4][5]. For example, Alzheimer's disease is associated with amyloid-β (Aβ) peptides, Huntington's disease with polyglutamine tracts, and Parkinson's disease with α-synuclein.
Deposition of Aβ peptides is observed in the brains of Alzheimer's disease patients [19,20], and Aβ oligomers and amyloid fibrils show toxicity to neurons [21][22][23][24]. To develop therapeutic and preventive agents for Alzheimer's disease, it is important to understand the aggregation process of Aβ at the atomic level. However, the mechanisms by which oligomers and amyloid fibrils are formed are still not fully understood.
Next, we introduce MD simulations of a single Aβ40 peptide at the air-water interface to reveal the structure of a fulllength Aβ peptide in a heterogeneous environment [27]. To understand the effect of the interface, it is essential to clarify the difference between an Aβ peptide at the air-water interface and that in bulk water. We therefore also compare Aβ40 with and without an interface (i.e., bulk water).
Finally, we describe MD simulations of Aβ40 on the surface of GM1-glycan clusters as a heterogeneous environment that is more similar to the neuronal membrane surface [32,34]. Recently, GM1-glycan clusters, in which GM1 glycans are transplanted on supramolecular metal complexes, have been developed [97]. Several experimental [97] and computational [34,98] studies have been performed using this GM1-glycan cluster as a model system to elucidate the binding process of Aβ to the GM1 cluster. As the last topic of this review, the structural change of Aβ upon binding to the GM1-glycan cluster is discussed.

Aβ40 Peptide at the Air-Water Interface
In this section, we explain the structure of the full-length Aβ peptide, Aβ40, at the air-water interface [27]. The aminoacid sequence of Aβ40 is DAEFRHDSGYEVHHQKLVFFAEDVGSNKGAIIGLMVGGVV. The N-and C-termini are uncapped. MD simulations of an Aβ40 peptide were performed in a system with air-water interfaces. The air-water interface was again prepared by removing half the water molecules in a cubic simulation box with the side length of 108.0 Å. Nine different initial conditions (three coordinates × three velocities) were employed for statistical analysis. The initial   (16)(17)(18)(19)(20)(21)(22) at the airwater interface. Reproduced with permission from Ref. [33].
Tachi et al.: Aβ peptides in heterogeneous environments e190010_5 structure of Aβ40 was fully-extended with all dihedral angles φ and ψ of 180° for all the three initial coordinates. An MD simulation was performed from each initial condition for 230 ns after an equilibration run for 10 ns. Temperature was controlled at 350 K by the Nosé-Hoover thermostat [99][100][101]. In the Aβ (16)(17)(18)(19)(20)(21)(22) system in the previous section, the temperature was set at 310 K. The reason for setting the temperature at 350 K here is to make it easier to obtain various conformations of Aβ40 because it is longer than Aβ (16)(17)(18)(19)(20)(21)(22). For comparison, MD simulations of the Aβ40 peptide in bulk water were also performed. The initial structure of Aβ40 in bulk water was also the fully-extended structure. Nine different initial conditions were prepared as well, with nine different initial velocities. The side length of the cubic unit cell was 91.1 Å. An MD simulation was performed from each initial condition for 230 ns after an equilibration run for 10 ns, again. For other simulation details, please refer to Ref. [27].
Aβ40, like Aβ (16)(17)(18)(19)(20)(21)(22) peptide, was observed to exist at the air-water interface. To investigate the structure of Aβ40 at the interface, the average distance from the interface to the Cα atom of each residue was calculated, as shown in Fig. 6(a). The positive value of this distance means that the Cα atom exists in the water, and the negative value means that it exists in the air. We can see that Aβ40 has an up-and-down shape at the interface. The up-and-down shape was observed in all MD simulations starting from the nine initial conditions. Our simulations, therefore, can be regarded as sufficiently sampling the conformational space. This result is in good agreement with the NMR experiments for the structure of Aβ40 on lyso-GM1 micelles [135], in which Val12-Gly25, Ile31-Val36, and Val39-Val40 of Aβ40 (red lines in Fig. 6(a)) were found to bind to lyso-GM1 micelles. Note that Val12-Gly25 almost coincides with the β1 region, and Ile31-Val36 and Val39-Val40 are included in the β2 region. We remark that the structure of Aβ40 at the air-water interface has not yet been revealed experimentally. Here, we showed that the MD simulation results of Aβ40 at the air-water interface are consistent with the experimental results on lyso-GM1 micelles. In addition, these results agree with the experimental results on GM1 micelles, too [136]. Therefore, we can think that the result that Aβ40 takes the up-and-down shape may hold for other hydrophilic/hydrophobic interfaces in general.   Figure 6(b) shows a typical structure at the interface obtained from the simulations. The β1 and β2 regions are bound at the interface, and the N-terminal region and the linker region between β1 and β2 are in the aqueous solution. Like the Aβ (16)(17)(18)(19)(20)(21)(22) peptide, Aβ40 can be regarded as an amphiphilic molecule and tends to exist at a hydrophilic/hydrophobic interface.
Although the pH condition at the air-water interface has been discussed, it is still controversial whether the interface is acidic or basic [137][138][139]. In our simulation study, the pH of the interface was considered to be the same as that in bulk. However, since it is the hydrophobic residues that are exposed to the air at the interface, the effect of pH on the up-anddown shape obtained in the MD simulations is considered to be small. Tahara and coworkers have measured the state of cytochrome c at the air-water interface using electronic sum frequency generation spectroscopy [140]. Their results show that the hydrophobic residues are exposed and denatured in the air at the interface. They also concluded that the effect of pH on the interfacial denaturation of cytochrome c was small because the effect of the interfacial perturbation was predominant.
To investigate the effect of the air-water interface on the structure of Aβ40, the contact probabilities of Cα atoms were also calculated from the MD simulations. Figures 7(a) and 7(b) show the contact probabilities for the system with the interface and in bulk water, respectively. The β1 and β2 regions form helix structures at the interface, which is consistent with the experimental results on the lyso-GM1 micelles [135]. In addition, a β-hairpin structure is formed when the β1 and β2 regions have contact with each other. On the other hand, in bulk water, as shown in Fig. 7(b), both the β1 and β2 regions have helix structures, but the β-hairpin structure is hardly formed. The difference between the β-hairpin formation probability at the interface and that in bulk water leads to a difference in the oligomer formation ability. It was reported by the MD simulations of several Aβ fragments that the β-hairpin structure promotes the formation of intermolecular βsheet structures with other Aβ fragments [48,62]. The importance of the β-hairpin structure in the formation of oligomers with intermolecular β-sheet structures has also been shown in experimental studies [141,142]. As we explained in the previous section, since Aβ40 has both hydrophilic and hydrophobic residues, the Aβ40 concentration increases at the hydrophilic/hydrophobic interface, and the aggregation is enhanced there. However, it is not only the high concentration of Aβ40 but also the structure of Aβ40 itself that promotes the aggregation.
Next, we explain why the β-hairpin structure is stabilized at the interface. As shown in Fig. 6, the β1 and β2 regions tend to be trapped at the interface, and these regions only move at the interface. Therefore, the motion of the β1 and β2 regions is restricted to two dimensions (Fig. 8). In bulk water, on the other hand, the β1 and β2 regions can move in three dimensions. Entropy increases as they take different conformations in bulk water. However, at the interface, the entropy increase is suppressed due to the two-dimensional motion. To reduce the enthalpy under this restriction, hydrogen bonds are formed between the β1 and β2 regions. Thus, the β-hairpin structure is formed more at the interface.

Figure 8
Schematic illustration of Aβ40 at the air-water interface and in bulk water. Reproduced with permission from Ref. [27].
To illustrate the β-hairpin formation process in detail, the time series of snapshots are shown in Fig. 9. The initial conformation of Aβ40 was fully extended ( Fig. 9(a)). The β1 and β2 regions first formed helix structures, as shown in Fig. 9(b). These regions were stably bound to the interface and moved only at the interface. Then, the helix structure of the β1 region was destroyed, as shown in Fig. 9(c), and the extended β1 region approached the β2 region, forming a βbridge ( Fig. 9(d)). The helix structure in the β2 region was then destroyed, as shown in Fig. 9(e). The β-hairpin structure with more β-bridges was finally formed, as shown in Fig. 9(f). In this way, the hydrogen bonds between the β1 and β2 regions were formed step by step, and the structure changed from the helix structure to the extended structure.
In this simulation study, Aβ40 took various conformations at the interface. To classify these conformations, principal component analysis (PCA) was performed. Figure 10(a) shows the free energy landscape for the first and second principal components of the system with the interface. Five local minimum states (States A-E) were observed. The typical structures of these states are shown in Fig. 11(a), where the N-terminal region D1-E11 was omitted for clarity because this region is flexible and has various conformations. The representative structure of each state is as follows. (State A) The β1 and β2 regions are close to each other. The β1 region has an extended structure, and the β2 region has a helix structure. A β-bridge is formed between these regions. (State B) The β1 and β2 regions are closer to each other than the structure at State A. Both regions have an extended structure, forming a stable β-hairpin structure. (State C) The β1 region forms a helix structure while the β2 region forms a β-bridge. Another β-bridge was formed near the linker region between the β1 and β2 regions. (State D) The β1 region forms a β-hairpin structure, while the β2 region forms a helix structure. No β-bridge is formed between the two regions. (State E) Aβ40 takes a random coil structure and does not form a specific secondary structure. Figure 10(b) shows the free energy landscapes for the first and second principal components obtained from the simulations in bulk water. Again, five local minimum states (States A'-E') are observed. Figure 11    The free energy and fractional population of each state are listed in Table 1. The most stable state at the interface is State B, and the next stable state is State A. As shown in Fig. 11(a), both states form a β-hairpin structure between the β1 and β2 regions. On the other hand, the most stable state in bulk water is State D', in which a β-bridge is formed in the β2 region, but no β-hairpin structure is formed between the β1 and β2 regions. The state E', in which the β-hairpin structure is formed between the β1 and β2 regions, is the fourth-lowest local-minimum free-energy state. These results indicate that Aβ40 rarely forms the β-hairpin structure with the β1 and β2 regions in bulk water and that the probability of the βhairpin structure at the interface is higher than in bulk water.

Aβ40 Peptide on the GM1-Glycan Cluster
The last topic of this review is the conformational change of an Aβ peptide upon binding to a GM1-glycan cluster [34], which consists of a self-assembled supramolecule and GM1 glycans transplanted on it. The conformational change of Aβ upon interaction with the GM1 glycans is a subject of interest.
To prepare the initial conformations for the MD simulations, the GM1-glycan cluster and Aβ40 were placed with a distance of 55 Å between their centers of mass in explicit water, as shown in Fig. 12. Nine different initial conditions were prepared like Fig. 12. After energy minimization, equilibration MD simulations were performed for 2 ns in the isothermal-isobaric ensemble at 300 K and 1 atm. Temperature and pressure were controlled by using the Langevin thermostat [143] and the Berendsen barostat [144], respectively. The production run was then performed for 1.5 μs in the canonical ensemble from each initial condition. The temperature was set at 300 K so that it is the same as that in the experimental condition [97]. For comparison, MD simulations of an Aβ40 monomer only were also performed in explicit water. Here, nine different initial conditions were prepared again. The canonical MD simulations were performed for 1.5 μs from each initial condition. For more details of the simulations, please refer to Ref. [34].
As a result of the simulations, the spontaneous binding of Aβ to the GM1-glycan cluster was observed. It is also found that the HHQ region, which corresponds to residues 13-15, binds well to the GM1-glycan cluster. This fact is almost consistent with the results for the air-water interface, as we mentioned in the previous section that the β1 region (residues 10-22) is present at the air-water interface. Furthermore, the HHQ region, unlike the other residues, was found to be attached to any of all sugar residues of the GM1-glycan cluster. Detailed structural analysis revealed that the fivemembered rings of the histidine side chains in the HHQ region were stacked on the six-membered rings of the sugar residues, as shown in Fig. 13. These results suggest that the binding of Aβ to the GM1-glycan cluster is mainly stabilized by the stacking of the histidine side chains in the HHQ region with any sugar residues of the GM1-glycan moiety.
To clarify the structural characteristics of Aβ on the GM1-glycan cluster, the secondary structures of Aβ on the GM1-glycan cluster were compared with that of an Aβ monomer in bulk water with Define Secondary Structure of Proteins (DSSP) analysis. As shown in Fig. 14, an αhelix structure at residues 31-37 in the C-terminal region increases when Aβ is bound to the GM1-glycan cluster. This result is in good agreement with previous experimental studies, in which Aβ formed an α-helix structure at residues 31-36 on GM1 micelles [27].
It has been shown that on the GM1 clusters on the neuronal cell membranes, Aβ undergoes a conformational change to pathological aggregates after an increase in the α-helix structure [145]. Therefore, the α-helix formation can be considered as the first process of this structural change. Since the GM1-glycan moiety is the headgroup that exists above the lipid ceramide moiety (Fig. 2), this result suggests that the pathological conformational change of Aβ has already started in the GM1-glycan moiety and that Aβ then moves to the lipid interface. It was proposed that this α-helix formation of Aβ occurs in two steps as follows.

Figure 12
An initial structure used in the MD simulations of the Aβ40 peptide and GM1-glycan cluster. Reproduced with permission from Ref. [34].
Biophysics and Physicobiology Vol. 19 e190010_10 Step 1: In the monomeric state in water, the C-terminus of Aβ and Lys28 form a salt bridge. At this time, the C-terminal region forms a turn, bend, or β-sheet structure. Such conformations correspond to State D' in Fig. 11(b), which is the most stable state of Aβ in bulk water.
Step 2: When Aβ binds to the GM1-glycan cluster, Lys28 also forms a salt bridge with Neu in the GM1-glycan moiety, preventing the formation of a salt bridge with the C-terminus. Therefore, the C-terminal region is hydrated, and then the α-helix increases. A schematic illustration of these two steps is shown in Fig. 15. The above results show that the α-helix formation is the first step in the structural change that leads to the pathological aggregation. Preventing this structural change may be a strategy for developing a preventive drug for Alzheimer's disease.

Figure 15
Schematic illustration of the mechanism of conformational change of Aβ40 upon binding to the GM1-glycan cluster.
Step 1 and Step 2 represent before and after binding, respectively. Reproduced with permission from Ref. [34].

Figure 13
Stacking of the HHQ (13-15) region to the GM1-glycan moiety. The sugar and amino-acid residues that are stacked are shown in red. Reproduced with permission from Ref. [34]. As described in the previous section, at the air-water interface, Aβ first formed the α-helix structure in the C-terminal region and then formed the β-hairpin structure between the β1 and β2 regions (Fig. 9). However, on the GM1-glycan cluster, Aβ formed the α-helix structure in the C-terminal region, but did not form the β-hairpin structure between the β1 and β2 regions. In other words, we can regard that Aβ on the GM1-glycan cluster reached only a conformation that corresponds to Fig. 9(c) at the air-water interface. The reason for this difference can be considered as follows. Unlike the GM1 clusters on the neuronal cell membrane, the GM1-glycan moiety on the self-assembled supramolecule has low fluidity. Aβ can reach only the GM1-glycan moiety that corresponds to the headgroup of the GM1 cluster on the membrane because the low fluidity makes Aβ trapped at the GM1-glycan moiety. The GM1-glycan moiety is relatively hydrophilic, and the difference between hydrophobicity and hydrophilicity at the interface between the GM1-glycan region and the aqueous solution is smaller than that at the air-water interface. The reason for the formation of the βhairpin structure is that the β1 and β2 regions are constrained at the interface, as shown in Fig. 8. However, the GM1glycan moieties of the GM1-glycan cluster do not constrain the β1 and β2 regions as much as the air-water interface. Therefore, it is considered that the β-hairpin structure was not formed on the GM1-glycan cluster. By performing MD simulations for Aβ with the GM1 clusters on the neuronal cell membrane in the future, it is expected that Aβ peptides can reach the interface between the GM1-glycan moiety and the lipid-ceramide moiety and form the β-hairpin structure. Further research progress is awaited.

Conclusions
In this review, we described the recent MD simulations of the Aβ peptides in the heterogeneous environments. The Aβ (16)(17)(18)(19)(20)(21)(22) fragments and Aβ40 peptides tend to exist at hydrophilic/hydrophobic interfaces, such as the neuronal cell membrane surface and air-water interface because these peptides have both hydrophilic and hydrophobic residues. Therefore, the concentration of the Aβ peptides is high at the interface. This is one of the factors that promote the aggregation at the interface. In addition, after Aβ40 forms the α-helix structure, the β1 and β2 regions approach each other to form the β-hairpin structure. This β-hairpin structure is rarely formed in bulk water. It is known in previous studies that the β-hairpin structure plays an important role in oligomer formation because the β-hairpin structure enhances the oligomer formation with intermolecular β-sheet structures. Thus, not only because the concentration of the Aβ peptides is higher at the interface, but also because the β-hairpin structure is formed more, Aβ oligomers are formed more at the interface than in bulk water. The reason of the β-hairpin formation is as follows. The β1 and β2 regions can only move in two dimensions, and the entropy of Aβ at the interface is smaller than in bulk water. To reduce the free energy, the enthalpy must be reduced. The enthalpy is reduced by the formation of hydrogen bonds between the β1 and β2 regions. The β-hairpin structure is thus formed.
In addition to the air-water interface, we reviewed the conformational changes of the Aβ40 peptide on the GM1-glycan cluster, which is composed of a self-assembled supramolecule and GM1-glycan moieties transplanted on it. When Aβ40 binds to the GM1-glycan cluster, the13th-15th residues (HHQ region) stack against any glycan residue. This interaction contributes to the stabilization of Aβ40 on the GM1-glycan cluster. The binding to the GM1-glycan cluster stabilizes the α-helix structure in the C-terminal region of Aβ. The helix structure is formed in the following two steps. (1) In the monomeric state in water, the C-terminus of Aβ and Lys28 form a salt bridge while the C-terminal region forms a turn, bend, or β-sheet structure. (2) When Aβ binds to the GM1-glycan cluster, Lys28 forms a salt bridge with Neu in the GM1glycan moiety, preventing the formation of a salt bridge with the C-terminus. Therefore, the C-terminal region is hydrated, and then the α-helix structure increases. These results suggest that the α-helix formation, the first pathological structural change of Aβ, has already started when Aβ binds to the GM1-glycan moiety.
In this way, the MD simulations have revealed the conformational change process of the Aβ peptides in the heterogeneous environments. Furthermore, it has been elucidated which atom or amino-acid residue plays an important role. These studies will enhance our physicochemical understanding of the structural changes of Aβ at the interface and the mechanism of Alzheimer's disease pathogenesis. We hope that MD simulation will be a tool for developing treatments for neurodegenerative diseases such as Alzheimer's disease in the future.

Conflict of Interest
The authors declare no conflict of interests.

Author Contributions
Y. T., S. G. I., and H. O. wrote the manuscript.