Molecular dynamics simulations of amyloid-β(29–42) aggregation in bulk water and at the air–water interface

Abstract

Oligomers of amyloid-β (Aβ) peptides are related to Alzheimer’s disease, and their formation is accelerated at hydrophilic–hydrophobic interfaces. We performed all-atom molecular dynamics simulations of Aβ(29–42) peptides in bulk water and at an air–water interface. In bulk water, the fragments formed stable aggregates, and the secondary structures were hardly changed. At the interface, the peptides were more easily separated from each other due to the low free-energy barrier and changed their secondary structures more frequently. This conformational flexibility is likely to promote amyloid fibril growth, suggesting a key role of interfacial environments in early aggregation processes.

Significance

Understanding how amyloid-β (Aβ) peptides behave at hydrophobic–hydrophilic interfaces is crucial for elucidating the molecular mechanisms of Alzheimer’s disease. We revealed that the air–water interface enhances both the structural flexibility and dissociation dynamics of Aβ(29–42) peptides, which may accelerate amyloid fibril formation. These findings provide molecular-level insights into how biological interfaces such as membranes or lipid surfaces can promote pathogenic aggregation, offering a potential target for therapeutic intervention.

Introduction

Proteostasis is a process that, among other functions, regulates protein conformations for mammals. However, due to both internal and external factors, the proteostasis network, developed by mammalian cells, can be affected. Aging is one of the causes of the disruption of the proteostasis network, thus some neurodegenerative diseases involving protein aggregation, such as Parkinson’s and Alzheimer’s diseases, are often related to aging [1,2]. The said aggregates consist of oligomers and amyloid fibrils. Oligomers are spherical aggregates and amyloid fibrils are needle-like aggregates with a cross-β structure [3].

In the case of Alzheimer’s disease, the aggregates are composed of amyloid-β (Aβ) peptides [1,4]. Amyloid-β peptides can be composed of 40 to 43 amino-acid residues, but these isoforms are not all equally involved in Alzheimer’s disease. For instance, Aβ42 is believed to be far more predominant in senile plaques, especially in the early ones [5,6]. Moreover, Aβ42 aggregates much faster than Aβ40 [7], the reason of which has been revealed by molecular dynamics (MD) simulation [8]. These phenomena have been investigated not only by wet experiments but also by MD simulations, as summarized in some review papers [9–11].

The study of the fragment of Aβ42 specifically composed of amino-acid residues 29 to 42 is interesting for several reasons. Firstly, it has been shown that C-terminal fragments of different lengths, Aβ(x–42) with x in the range of 28 to 42, could reduce the neurotoxicity of Aβ42 oligomers [12]. Moreover, because this region mainly consists of hydrophobic residues, the Aβ(x–42) fragment aggregates spontaneously in aqueous solution while forming intermolecular β-sheet structures [3]. These experimental observations have been enriched by several MD simulations that were performed to study this particular fragment. For example, the monomer state and dimer formation of this fragment had been studied with an all-atom model in an implicit solvent with the multicanonical-multioverlap MD algorithm [13]. A coarse-grained model was also used to look into the formation rate of the amyloid fibril [14]. In 2014, the dimerization of the fragment with an all-atom model in an explicit solvent was investigated for the first time by the Hamiltonian replica-permutation method [15,16], in which the secondary structure was also highlighted [17]. Later, the investigation of this fragment’s oligomerization showed that the oligomer was formed by the sequential addition of a monomer through a condensation with the already-formed oligomer [18]. All these simulations confirmed the presence of the β-sheet structure observed in the experiments.

However, these simulations were performed in bulk water, while another experiment demonstrated that the Aβ peptide, and especially the Aβ(29–42) fragment, interacts with neuronal cell membranes [19]. It is known that aggregation of Aβ peptides is accelerated not only at the membrane surface [20,21] but also at the air–water interface [22,23]. To understand the effect of the interface on peptide aggregation, some MD simulation studies have been conducted at the air–water interface. All-atom MD simulations of 100 Aβ(16–22) fragments were performed at the air–water interface [24]. It was shown that the existence probability of the peptides at the interface is higher than in bulk water because the Aβ(16–22) fragment has both hydrophilic and hydrophobic amino-acid residues and tends to exist at hydrophilic–hydrophobic interfaces. This tendency is also true for full-length Aβ peptides [25]. On the other hand, the Aβ(29–42) peptide mainly consists of hydrophobic residues and contains no hydrophilic residue. Therefore, the Aβ(29–42) peptides may behave differently at the interface than the Aβ(16–22) peptides.

Building upon these previous advances, this study aims to address the following questions: Is there a difference in the aggregation behavior of Aβ(29–42) peptides between bulk water and the air–water interface? If so, what are the specific characteristics of this difference? Because no MD simulation has yet been carried out to provide further explanation on this aspect, we performed MD simulations of Aβ(29–42) peptides to compare their aggregation both in bulk water and at the air–water interface.

Computational details

Each Aβ(29–42) peptide in all the simulations in this paper has the following amino acid sequence: Ace-GAIIGLMVGGVVIA-Nme. The N- and C-termini were capped by respectively the acetyl and the N-methyl group, to prevent secondary interactions induced by the charged ends of the peptides. The initial conformation of the peptide was created with all the dihedral angles of ϕ=ψ=ω=180°. Aβ(29–42) peptide is known to adopt helical, β-sheet, and random coil structures [13,17,18]. To avoid potential bias toward a particular secondary structure, we selected such an extended conformation as the initial structure for our simulations. The initial simulation setup was constructed by placing four of these Aβ(29–42) peptides, as described below. This number was chosen because it was considered sufficient to observe the early stages of peptide aggregation. For the MD simulations in bulk water, we used a rectangular simulation box with side lengths of 99.431 Å, 99.431 Å, and 62.145 Å in the x-, y-, and z-axis, respectively. Four Aβ(29–42) peptides and 19,919 water molecules were included in this simulation box, as shown in Fig. 1(a). The peptides were displayed in the (x, y) plane, in the middle of the z-axis. The total number of atoms was 60,561. For the MD simulations at the interface, we used a rectangular simulation box with side lengths of 99.431 Å, 99.431 Å, and 124.289 Å in the x-, y-, and z-axis, respectively. The number of each atom is the same as that in the MD simulations in bulk water. Two initial conformations were prepared in the simulations at the interface. In one of them, four Aβ(29–42) peptides were initially located in the middle of the z-axis, as shown in Fig. 1(b). In the other conformation, they were initially displayed at the interface, as shown in Fig. 1(c). In both conformations, the upper and lower quarters in the simulation box along the z-axis were vacuum: no atom existed in these regions. Thus, to be accurate, the “air” in this paper is a vacuum in the initial conditions. After the simulations began, some water molecules evaporated, and the air phase became water vapor. This interface is actually a vapor–water interface. We prepared three different initial momenta for each initial conformation for the statistical analysis. That is, nine MD simulations were performed.

Figure 1.

(a) Initial conformation for the peptides in bulk water. (b) Initial conformation with the air–water interface, in which Aβ(29–42) peptides were placed at the center. (c) Initial conformation with the air–water interface, in which Aβ(29–42) peptides were placed at the interface.

The program used to perform the simulations is Generalized-Ensemble Molecular Biophysics (GEMB), which was developed by one of the authors (H. O.) and has been applied to several biomolecular systems [26–29]. The AMBER14SB force field was adopted for the Aβ(29–42) peptides. The TIP3P rigid body model [30] was used for water by adopting the symplectic [31] quaternion scheme [32,33]. The electrostatic potential was calculated using the particle mesh Ewald (PME) method [34]. The cut-off distance for both the Lennard-Jones (LJ) potential and the electrostatic potential was 10.0 Å. The temperature, controlled by the Nosé-Hoover thermostat [35–37], was set at 298 K.

The time step was taken to be Δt=0.5 fs for the bonding interactions of the peptide atoms, Δt=2.0 fs for the LJ interactions, the real part of the PME calculation of the peptide atoms, and those between the peptide atoms and solvent molecules, and Δt=4.0 fs for the LJ interaction, the real part of the PME calculation between the solvent molecules, and the reciprocal part of the PME calculation of all the atoms. Because the symplectic rigid body algorithm was used for the water molecules, Δt can be taken as long as 4.0 fs [33]. For each initial condition shown in Fig. 1(a) and Fig. 1(c), simulations were performed for 1.0 μs using three different initial velocities, yielding a total simulation time of 3.0 μs for each system. As will be discussed later, the binding free energy obtained from simulations of this length was calculated with sufficiently low uncertainty, indicating that the simulation time was adequate. In simulations initiated from the conformation shown in Fig. 1(b), all peptides separately migrated to one of the interfaces within 200 ns. Consequently, the MD simulations for this conformation were not extended beyond 200 ns.

Results and discussion

No external forces were needed to maintain the water–vapor interface. All simulations in this study were performed under constant-volume conditions. At temperatures below the critical temperature, when the average density of the system lies between the liquid and vapor coexistence densities, the system spontaneously undergoes phase separation into liquid and vapor because such a configuration is thermodynamically more stable [38–40]. The present simulations were conducted under these conditions; therefore, the interface formed naturally without any external forces. Some water molecules migrated into the vacuum region during the simulation. The density of water molecules in the vapor region increased slightly from 0.0 g/cm³ to 0.50×10^–4 g/cm³ after the simulations. In contrast, the density of water in the bulk region decreased from the initial value of 0.996 g/cm³ to 0.971 g/cm³.

The behavior of the Aβ(29–42) peptides is shown in Supplementary Movies S1 to S9. In bulk water, they aggregated within a short period of time (10 to 40 ns) and formed various secondary structures; namely intra- and intermolecular β-sheets and α-, 3₁₀-, and π-helix. The same structures were observed in the interface simulations. When the peptides were originally displayed in the middle of the simulation box, they moved to the air–water interface during the simulation. When they were originally displayed at the interface, they stayed near the interface.

The results below were obtained for the interface simulations in which all the Aβ(29–42) were placed at the center in the initial conformation. The mass density distribution of all the atoms in the system, along the z-axis, is shown in Fig. 2(a). Fig. 2(a) shows that the density distribution of all the atoms was slightly higher at the very beginning of the simulation, given that the four peptides were displayed at the center of the simulation box. This means that, after the simulation began, the peptides promptly left the center of the simulation box. However, there were not enough peptides in the system to make a significant difference in the mass density distribution at the interface during the simulation. The reason why this peptide is likely to be present at the interface is that this peptide, Aβ(29–42), is composed mainly of hydrophobic residues and contains no hydrophilic residues at all. Experimental [41] and simulation [25] studies of full-length Aβ have been performed at the interface. These studies have shown that amino-acid residues 29–42 are present in the hydrophobic region.

Figure 2.

Mass density distributions of (a) all the atoms of the system as a function of their z coordinate and (b) all the atoms of the Aβ(29–42) fragments as a function of the z coordinate.

Fig. 2(b) focuses only the Aβ(29–42) peptides. The density was initially the highest in the middle of the simulation box. It gradually decreased in bulk and increased near the air–water interfaces. It means that, given the hydrophobic nature of their residues, the Aβ(29–42) peptides moved to the interfaces. Because only one, two, or three peptides moved to one of the interfaces, and the other peptides moved to the other interface, we performed the second set of interface simulations with the peptides initially displayed at the interface, in order to better compare with the simulations in bulk water.

The mass distribution barely changed after 100 ns in the MD simulations that started from the center in the system with the interface. The following results deal with the bulk simulations and the interface simulations with peptides initially displayed at the interface. Based on the above observation, the averages of the physical quantities were calculated using the MD data from 100 ns to 1.0 μs, corresponding to a total of 900 ns per trajectory and 2.7 μs per system, based on three simulations with different initial velocities.

In order to study the aggregation of peptides, the minimum intermolecular C_α-C_α distance, d_Cα-Cα, was calculated for each peptide. The free-energy landscape of the peptides was then calculated as a function of d_Cα-Cα as follows:

$$\begin{array}{c}\hfill F\left(d_{C\alpha -C\alpha }\right)=-k_{B}T\ln P\left(d_{C\alpha -C\alpha }\right),\#(1)\end{array}$$

where P(d_Cα-Cα) is the probability distribution of d_Cα-Cα, at T=298 K, as shown in Fig. 3. For both simulations, the probability distribution of d_Cα-Cα graph narrows around 4.0 Å. However, at high values of d_Cα-Cα, P(d_Cα-Cα) is not null and is spread more widely in the interface simulations. Consequently, for bulk simulations, free energy diverges at low and high values of d_Cα-Cα, which means that d_Cα-Cα can only take values around 4.0 Å. On the contrary, free energy in interface simulations does not diverge for higher values of d_Cα-Cα. These results mean that peptides are forced to aggregate in bulk, whereas they can stay non-aggregated at the interface.

Figure 3.

Free-energy landscape of the Aβ(29–42) fragments, as a function of the intermolecular distance between two α carbons.

When the shortest distance between two C_α atoms was small, namely d_Cα-Cα<6.0 Å, peptides were considered aggregated. Between 6.0 Å and 10 Å (6.0 Å≤d_Cα-Cα<10.0 Å), it was considered as an intermediate state, and for d_Cα-Cα≥10.0 Å, peptides were considered dissociated. We thus calculated the binding free energy of the monomer from F(d_Cα-Cα) at d_Cα-Cα=10.0 Å. At the interface, the binding free energy was found to be –4.51±0.16 kcal/mol. In contrast, it could not be calculated precisely in bulk water because none of the monomers dissociated from the complex during the simulations. Based on Fig. 3, the binding free energy in bulk water is estimated to be less than –7.0 kcal/mol (i.e., its absolute value is estimated to be greater than 7.0 kcal/mol); however, an exact value could not be determined from our MD simulations. The reason why the peptide can be dissociated at the interface is again that this peptide is composed mainly of hydrophobic residues. When a peptide is separated from the aggregate at the interface, there is less free energy disadvantage than in bulk water because the new hydrophobic surface area is only exposed to an environment with fewer water molecules, i.e., almost surrounded by the air. This peptide thus can exist in a hydrophobic environment at the interface without aggregating with other peptides.

The secondary structure was determined using the DSSP (Define Secondary Structure of Proteins) criteria [42]. For each simulation, the average number of residues involved in the secondary structure and its standard deviation were calculated, as shown in Table 1. Though some differences could be observed by just considering the average number of residues involved in the different types of secondary structure, the standard deviation does not allow us to conclude a real difference between bulk and interface simulations. Indeed, considering the standard deviation, it is not possible to clearly discriminate between both simulations.

Table 1.

Average number of residues involved in the different types of secondary structure and the corresponding standard deviation (Ave.=average/St. dv.=standard deviation)

	Helix		Intra- and inter-molecular β-sheet		Intramolecular β-sheet		Intermolecular β-sheet
	Ave.	St. dv.	Ave.	St. dv.	Ave.	St. dv.	Ave.	St. dv.
Bulk	10.8	8.7	10.3	6.8	7.5	5.6	4.9	3.8
Interface	17.3	6.5	8.7	3.4	5.2	2.0	5.1	3.3

However, the standard deviations of all the structures are greater in bulk water than at the interface. The large standard deviation of the secondary structure in bulk water is due to the different secondary structures obtained for the different initial conditions of each simulation. Typical snapshots of the bulk and interface simulations are shown in Fig. 4. The snapshots in bulk water have different structures for the three initial conditions. Some simulations show a lot more helix structures (Fig. 4(a)), some show noticeably more β-sheet structures (Fig. 4(b)), and some show both helix and β-sheet structures on relatively comparable proportions (Fig. 4(c)). This result suggests that in bulk water, each simulation is stuck in a local minimum free-energy state. On the other hand, all simulations at the interface form all of the intra- and intermolecular β-sheet and helix structures (Fig. 4(d)–(f)), regardless of the initial conditions from which they were started. Although peptides aggregate, some peptides are sometimes prone to dissociation at the interface, as described earlier. If left aggregated, a peptide may not have enough space to change its structure because of the presence of other peptides around it. However, at the interface, even once aggregated, the peptide can dissociate, making it relatively easy for the peptide to change its structure. Therefore, no matter which initial conditions we start the simulation from at the interface, it is likely to reach the most stable state without being trapped in a local minimum free-energy state. On the other hand, in bulk water, each simulation easily gets trapped in a local minimum free-energy state, and the secondary structure obtained for each initial condition is different.

Figure 4.

Representation of the peptides with their secondary structure (a), (b), (c) in bulk water and (d), (e), (f) at the interface.

Our simulation results agree well with the experimental findings reported by Lin et al. [43] They investigated the surface effects on the aggregation of Aβ(12–28) peptides using atomic force microscopy. They found that the peptides could freely diffuse on mica surfaces, form self-assembled protofibrils, and grow much faster than in solution. The experimental observation that peptides diffuse freely at the interface corresponds to our simulation results, in which peptides readily associate and dissociate. This behavior reflects a decrease in the free energy barrier for dissociation at the interface, as shown in Figs. 3 and 4. In contrast, in bulk water, once peptides aggregate, they tend not to dissociate easily. As a result, if they aggregate into a form that is unfavorable for amyloid fibril formation—namely, a non-β-sheet structure—it becomes difficult for them to further grow into amyloid fibrils. On the other hand, at the interface, peptides can easily associate and dissociate, so even if they aggregate into a non-fibril-forming structure, they are likely to dissociate again. Through repeated association and dissociation, they may eventually form intermolecular β-sheet structures. Once such a β-sheet structure forms, it is likely to be stabilized, thereby facilitating the growth of amyloid fibrils.

Acceleration of peptide aggregation at interfaces has also been observed for other peptides experimentally, such as full-length Aβ (Aβ42), Aβ(14–23), α-synuclein [44], and model peptides [45]. Thus, our findings are likely not specific to the Aβ(29–42) peptide but may be generalizable to other amyloid-β peptides or aggregation-prone proteins.

Conclusion

It is known that Aβ peptides aggregate more readily at a hydrophilic–hydrophobic interface such as the cell membrane surface, rather than in bulk water. Aβ(29–42) is composed of hydrophobic amino-acid residues and aggregates spontaneously in aqueous solution. To investigate the behavior of this peptide at an air–water interface, we performed MD simulations of four Aβ(29–42) peptides in explicit water. Three simulations were performed in the absence of the air–water interface, and six simulations were performed in the presence of the interface.

We showed that peptides tended to exist at the air–water interface rather than staying in bulk water in the simulations with the interface, which is consistent with the hydrophobic nature of the residues. In bulk water, peptides got aggregated because of the hydrophilic environment. Once the aggregate is formed, because the free-energy barrier is high, peptides do not dissociate. On the other hand, the free energy barrier is lower and, consequently, can be overcome more easily at the interface. Thus, peptides sometimes dissociate at the interface.

Moreover, the difference in the free-energy barrier impacts the secondary structure of the peptides. In bulk water, because peptides get stuck in a local minimum free-energy state, they cannot easily change their conformation, while the secondary structure is more prone to change at the interface. As a result, at the interface, the secondary structures in the aggregates converged to similar fraction regardless of the initial conditions. Thus, it was found that the interface has the effect of accelerating structural change to a more stable structure for hydrophobic peptides. Such the interface effect may play a role in accelerating the aggregation even for full-length Aβ. That is, when a full-length Aβ is at the interface, it may accelerate amyloid fibril formation by facilitating structural changes for its hydrophobic region.

Studying peptides in the presence of a hydrophilic–hydrophobic interface is important because some experiments show that Aβ peptides interact with the cell membrane surface [19,46]. Our simulation study gives useful information to understand the behavior of hydrophobic peptides at the air–water interface. Here, we employed Aβ(29–42) for our simulations. In the future, simulations at the interface on other hydrophobic peptides could help understand the behavior of such peptides more accurately, and notably determine whether the conformation change is also observed or not.

Conflict of interest

A.-I. F., S. G. I., and H. O. declare that they have no conflict of interest.

Author contributions

S. G. I. and H. O. designed the research. A.-I. F. performed the simulations, analyzed the results, and wrote the paper. All authors discussed the results and revised the paper.

Data availability

The evidence data generated and/or analyzed during the current study are available from the corresponding author on reasonable request.