Article pubs.acs.org/JPCB

Dimerization Process of Amyloid-β(29−42) Studied by the Hamiltonian Replica-Permutation Molecular Dynamics Simulations Satoru G. Itoh†,‡ and Hisashi Okumura*,†,‡ †

Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki, Aichi 444-8585, Japan Department of Structural Molecular Science, The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585, Japan

‡

S Supporting Information *

ABSTRACT: The amyloid-β peptides form amyloid fibrils which are associated with Alzheimer’s disease. Amyloid-β(29−42) is its C-terminal fragment and a critical determinant of the amyloid formation rate. This fragment forms the amyloid fibril by itself. However, the fragment conformation in the fibril has yet to be determined. The oligomerization process including the dimerization process is also still unknown. The dimerization process corresponds to an early process of the amyloidogenesis. In order to investigate the dimerization process and conformations, we applied the Hamiltonian replica-permutation method, which is a better alternative to the Hamiltonian replica-exchange method, to two amyloidβ(29−42) molecules in explicit water solvent. At the first step of the dimerization process, two amyloid-β(29−42) molecules came close to each other and had intermolecular side chain contacts. When two molecules had the intermolecular side chain contacts, the amyloid-β(29−42) tended to have intramolecular secondary structures, especially β-hairpin structures. The two molecules had intermolecular β-bridge structures by coming much closer at the second step of the dimerization process. Formation of these intermolecular β-bridge structures was induced by the β-hairpin structures. The intermolecular β-sheet structures elongated at the final step. Structures of the amyloid-β(29−42) in the monomer and dimer states are also shown with the free-energy landscapes, which were obtained by performing efficient sampling in the conformational space in our simulations.

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study their structures and amyloidogenesis mechanism.8−11 The fragment of the transmembrane domain Aβ(29−42), which consists of residues 29−42, forms amyloid fibrils by itself.8,9 It is suggested in experiments that Aβ(29−42) also has intermolecular β-sheet structures in the amyloid fibril.8,9 However, the structure and the amyloidogenesis process including the oligomerization process have yet to be clarified. The oligomerization process corresponds to the early stage of the amyloidogenesis process. In recent years, it has been reported that the Aβ oligomer is a better candidate for synaptic dysfunction than the amyloid fibril.12 It was also reported that the dimer is the smallest synaptotoxic species.13 However, it is difficult to investigate the oligomer structure and the oligomerization process by experiments because of their diverse morphologies and rapid conformational fluctuations.14 Therefore, it is useful to utilize computer simulations to study the structures and oligomerization process of Aβ. There are many works by computer simulations with all-atom models with respect to the dimerization and oligomerization of the Aβ fragments, for example, Aβ(10−35),15 Aβ(16−22),14,16−19 Aβ(21−30),20 and Aβ(25−35).21,22 As for dimerization of Aβ(29−42), several works were reported, which employed a coarse-grained model23 or an all-

INTRODUCTION Amyloid fibrils are associated with various human diseases. These fibrils are formed by aggregation of proteins or peptides, and a different aggregating protein is related to a different disease. For instance, Parkinson’s disease is characterized by the amyloid fibrils of α-synuclein, and hemodialysis-related amyloidosis is associated with β2-microglobulin.1 Alzheimer’s disease is one of the most well-known amyloidosis. This disease is related to aggregation of the amyloid-β peptide (Aβ).1,2 Aβ is comprised of 39−43 amino-acid residues and produced by proteolytic cleavage of the amyloid precursor protein (APP).3 It is necessary to clarify its structure in the amyloid fibril and the mechanism of amyloidogenesis in order to find a remedy for Alzheimer’s disease. The structure of Aβ in the amyloid fibril has been proposed in experiments.4−6 The dominant secondary structure of the amyloid fibril is a cross-β-sheet structure,4 and each Aβ forms two intermolecular β-sheet structures.5,6 These two β-sheets consist of residues 18−26 (β1) and residues 31−42 (β2), respectively.6 The C-terminal part after residue 29 including β2 corresponds to a transmembrane domain of APP,3 and the length of Aβ after residue 29 is a critical determinant of the amyloid formation rate. In fact, Aβ42 which is comprised of 42 residues readily forms the amyloid fibril in comparison with Aβ40 which consists of 40 residues.7 There are many experiments not only for the full-length Aβ (Aβ40 or Aβ42) but also for fragments including β1 or β2 to © 2014 American Chemical Society

Received: June 16, 2014 Revised: September 5, 2014 Published: September 5, 2014 11428

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atom model with an implicit solvent model.24 However, there had been no computational studies with all-atom models in explicit solvent for dimerization of Aβ(29−42). In our previous work, we therefore employed an all-atom model for two Aβ(29−42) peptides in explicit water and showed possible dimerization pathways from the monomer state.25 One of the generalized-ensemble algorithms,26,27 called the Coulomb replica-permutation method (CRPM),25 was applied to obtain efficient sampling. The CRPM is one of the realizations of the Hamiltonian replica-permutation method (HRPM).25 The HRPM combines the advantages of the replica-permutation method (RPM)28 and the multidimensional replica-exchange method (MREM).29 The MREM is also referred to as the Hamiltonian replicaexchange method (HREM).30 The RPM is a better alternative to the replica-exchange method (REM).31,32 In the RPM, not only temperature exchanges between two replicas but also temperature permutations among more than two replicas are performed. Furthermore, instead of the Metropolis algorithm,33 the Suwa−Todo algorithm 34 is employed for replicapermutation trials to minimize its rejection ratio. In the HREM, by exchanging the parameters that are related only to limited degrees of freedom, the number of required replicas can be greatly decreased in comparison with the REM.35−37 The HRPM realizes efficient sampling more than the HREM and is able to reduce the number of required replicas in comparison with the RPM.25 In this article, we investigate the dimerization process of Aβ(29−42) in more detail. We show the Aβ(29−42) structures in the monomer and dimer states as well. The sampling efficiency of CRPM is compared with that of the Coulomb replica-exchange method (CREM),36 which is one of the realizations of the HREM. Formulation of the HRPM and discussion on the sampling efficiency of CRPM and CREM is presented in the Supporting Information. The following sections are as follows: In the Methods section, we briefly introduce the CRPM. We present the details of our simulations in this section as well. The results are shown in the Results and Discussion section. The last section is devoted to conclusions.

λ Velec (qp) =

k ∈ M1 S ∈ M2

(λQ k)(λQ S) 4πϵ0rk S

2

+

∑∑ ∑ i = 1 k ∈ Mi S> k S∈ Mi

Q kQ S 4πϵ0rk S (2)

where rkl is the distance between atoms k and l in the solute molecules and ϵ0 is the dielectric constant in a vacuum. An appropriate number of noninteracting copies (or replicas) of the original system are prepared in the CRPM. Each replica is assigned to a different parameter value of λ. For each replica, a canonical molecular dynamics (MD) or Monte Carlo (MC) simulation at the assigned parameter is carried out simultaneously and independently. During these simulations, the parameter values are permuted among replicas with the Suwa− Todo algorithm (formulation of the Suwa−Todo algorithm is given in the Supporting Information). By changing the values of λ, the intermolecular electrostatic repulsive and attractive forces can be handled. Note that the original potential energy is recovered when λ = 1. Simulations. We performed Coulomb replica-permutation MD (CRPMD) simulations and Coulomb replica-exchange MD (CREMD) simulations for the two Aβ(29−42) molecules in explicit water solvent. The termini of Aβ(29−42) were blocked by the acetyl group and the N-methyl group to remove effects from the terminal charges. The amino-acid sequence was Ace-GAIIGLMVGGVVIA-Nme. Note that monomer and dimer structures of the zwitterionic form of these fragments were studied with a coarse-grained model.23 The number of water molecules was 6734. The AMBER parm99SB38 was used for the Aβ(29−42) molecules. The model for the water molecules was the TIP3P rigid-body model.39 Temperature was controlled by the Nosé−Hoover thermostat.40−43 The SHAKE algorithm was employed to constrain bond lengths with the hydrogen atoms of Aβ(29−42) and to fix the water molecule structures during our simulations. The system was put in a cubic unit cell with a side length of 60.5 Å with the periodic boundary conditions. The cutoff distance for the Lennard-Jones potential energy was 12.0 Å. The electrostatic potential energy was calculated by the particle mesh Ewald method.44 The multiple-time-step method was employed in our MD simulations. The time steps were taken to be 4.0 fs for interactions between the water molecules and 1.0 fs for other interactions. Three different initial conditions (IC1−IC3) were employed for the CRPMD and CREMD simulations. Initial velocities were different among ICs, but the initial conformations were the same. This common initial conformation was prepared as follows: Two extended Aβ(29−42) molecules were put so that the distance between two molecules would be 20.0 Å. The angle between the axes along each backbone was set to be 90°, as shown in Figure 1a. A canonical MD simulation was then performed for 4.0 ns at 600 K. In the final conformation, one of the two Aβ(29−42) molecules formed a 310-helix structure in residues 38−40, and the other molecule had a random-coil structure. Because there were no intramolecular and intermolecular β-strand structures, we employed this conformation as the initial conformation for the following CRPMD and CREMD simulations. The initial conformation is presented in Figure 1b. Note that the water molecules are omitted in Figure 1. The number of replicas in the CRPMD and CREMD was eight, and the values of λ were 0.85, 0.93, 1.00, 1.04, 1.07, 1.10, 1.12, and 1.14. These replicas in the CRPMD were divided into

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METHODS Coulomb Replica-Permutation Method. Let us consider a system consisting of solute molecules in explicit solvent, in which the number of atoms is N. The total potential energy is written as E λ(q) = Ep(qp) + Eps(qp , qs) + Es(qs)

∑ ∑

(1)

where Ep, Eps, and Es are the potential energy among the solute molecules, that between the solute and solvent molecules, and that among the solvent molecules, respectively. Here, q = {qp, qs}, where qp and qs are the coordinate vectors of the solute atoms and the solvent atoms, respectively, and denoted as qp ≡ {q1, ..., qNp} and qs ≡ {qNp+1, ..., qN} (Np is the total number of solute atoms). In the CRPM, a parameter λ is introduced to the Coulomb potential energy term in Ep. In order to enhance sampling between aggregation and disaggregation states for two Aβ(29−42) molecules, here, we employ λ only for the intermolecular electrostatic interactions. For the Aβ(29−42) molecules M1 and M2, the Coulomb potential energy is given by 11429

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Figure 1. (a) The extended structure to prepare the initial conformation. (b) The initial conformation for the CRRM and CREM simulations.

two subsets. Each subset had four replicas and four parameter values (see the Supporting Information and also ref 28 for more details). The simulation from each IC was performed for 200.0 ns at 300 K per replica including an equilibration run for 10.0 ns. Namely, the production run from each IC was carried out for 1.52 μs in total. The total time length of the CRPM and CREM production runs was 9.12 μs. In the CREM, the parameter λ was used only for the intermolecular electrostatic interactions between two Aβ(29−42) molecules in the same way as the CRPM. The trajectory data were stored every 400 fs. Trials of replica permutations or replica exchanges were performed every 4.0 ps. All simulations were performed with our own program. The DSSP (define secondary structure of proteins) criteria45 were utilized to determine the hydrogen bonds and the secondary structures of Aβ(29−42).

Figure 2. (a) Free energy at 300 K. The black, red, and blue lines represent those at λ = 0.85, λ = 1.00, and λ = 1.14, respectively. The abscissa is the smallest intermolecular distances between the Cα atoms. (b) Probability of at least one intermolecular side chain contact (red) and that of at least one intermolecular hydrogen bond (black) as functions of the smallest intermolecular distances between the Cα atoms.

one intermolecular side chain contact and at least one intermolecular hydrogen bond were obtained as functions of dαα in Figure 2b. Here, when the shortest distance between a pair of side chain atoms except hydrogen atoms was less than 5.0 Å, it was regarded as a side chain contact.51 The intermolecular side chain contact probability increases clearly when the intermolecular distance is less than 10 Å, and the slope of the free energy is also changed at 10 Å. This means that the free energy decreases by the intermolecular side chain contacts because Aβ(29−42) does not have a polar residue. The intermolecular hydrogen-bond probability increases at less than 6 Å. The free energy decreases more by the intermolecular hydrogen bonds, and this is the origin of the shoulder at 6 Å. The structure of the full-length Aβ in the amyloid fibril is expected to have the cross-β-sheet structure.4 In this case, each Aβ forms intermolecular β-sheet structures. However, it is not clear that Aβ has intermolecular β-sheet structures in the oligomer state as well. As for Aβ(29−42), intermolecular βsheet structures in the dimer state were observed in our simulations. Such intermolecular β-sheet structures were also observed in the previous simulations that used a coarse-grained model23 and an all-atom model with an implicit solvent model.24 Figure 3 shows the probability distributions of the number of residues that have intermolecular β-strand structures at T0 = 300 K and λ = 1.00. The distributions for the intermolecular parallel and antiparallel β-strand structures were evaluated individually. Namely, the summation of each distribution is equal to 1. In the dimer state, Aβ(29−42) has not only the parallel β-strand but also the antiparallel β-strand. A long antiparallel β-sheet is readily formed in comparison with a long parallel β-sheet. The probability of antiparallel β-sheet

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RESULTS AND DISCUSSION Dimerization of Aβ(29−42). We first discuss the tendency of aggregation for Aβ(29−42). Figure 2a shows the free energies at T0 = 300 K and λ = 0.85, 1.00, and 1.14 as functions of the smallest intermolecular distances between the Cα atoms, dαα. The free energy at parameter λ is given by F λ(dαα) = −kBT0 ln

λ Pave (dαα) 2 4πdαα

(3)

Pλave

where is the averaged probability distribution over the three CRPMD and three CREMD simulations, and each probability distribution was calculated by the reweighting techniques46,47 (the reweighting techniques for the CRPM are presented in the Supporting Information). The denominator is the Jacobian determinant of the coordinate transformation from Cartesian to polar coordinates. The errors were estimated by the jackknife method48−50 from the six CRPMD and CREMD simulations. The free energy at λ = 1.00 in Figure 2a has the global-minimum state at 4 Å. The free-energy difference between the aggregation and disaggregation states is large, and there is no local-minimum state in the disaggregation states. This is consistent with the experimental results that showed that Aβ(29−42) is hardly soluble.8 This free energy has a shoulder at 6 Å. To see the origin of the shoulder, the probabilities that the two Aβ(29−42) molecules have at least 11430

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Figure 3. Probability distributions of the number of residues that have intermolecular β-strand structures. The green bars and the red bars represent parallel β-strand structures and antiparallel β-strand structures, respectively.

formation is higher than that of parallel β-sheet formation regardless of the sheet length. It was reported by an infraredspectroscopy experiment for Aβ(29−42) that antiparallel βsheet structures exist in aqueous solution.8 Our simulation results are consistent with this experiment. In other simulation works for different Aβ fragments and different peptides that form amyloid fibrils in experiments, intermolecular antiparallel β-strand structures had also been observed in the oligomer states.14,16,18−22,52−54 In order to investigate intramolecular secondary structure changes in the dimerization process, the probability distributions of the numbers of residues forming intramolecular secondary structures were calculated with respect to each dαα value. The probability distributions are presented in Figure 4a. This probability was normalized for each dαα value. Here, the bin size of dαα was 1.0 Å and only α-helix and β-strand structures were employed as the secondary structures, because these structures are representative secondary structures in proteins. When the two molecules are away from each other (that is, Aβ(29−42) is in the monomer state), Aβ(29−42) tends to have a random-coil structure. When dαα takes a value between 5 and 9 Å, Aβ(29−42) tends to form the intramolecular secondary structures. When the two molecules get close, such as dαα < 5 Å, the probability of forming intramolecular secondary structures decreases. Figure 4b shows the ensemble-average values of the numbers of residues forming specific intermolecular and intramolecular secondary structures as functions of dαα. Increase of intramolecular secondary structures at dαα = 5−9 Å mainly comes from increase of intramolecular antiparallel β-strand structures, while α-helix structures also increase slightly. When the two molecules come sufficiently close, intermolecular parallel and antiparallel β-sheet structures increase with decrease of the intramolecular β-strand structures. As for increase and decrease of the secondary structures with respect to dαα, those of the αhelix, intramolecular parallel β-strand, and intermolecular parallel β-strand structures are less than those of the intramolecular antiparallel β-strand and intermolecular antiparallel β-strand structures. Let us see the reason why the intramolecular antiparallel βstrand structures increase at dαα = 5−9 Å. We also investigate which intramolecular antiparallel β-strand structures increase because several secondary structures such as a β-hairpin structure and a β-sheet structure with three antiparallel βstrands can be considered as the intramolecular antiparallel β-

Figure 4. (a) Probability distributions of the numbers of residues which have intramolecular secondary structures at the corresponding dαα values. The black bold line is roughly fitted to the largest probability at each distance. (b) Ensemble-average values of the numbers of residues that have secondary structures at the corresponding dαα values. Intermolecular-parallel β, intermolecularantiparallel β, intramolecular-parallel β, intramolecular-antiparallel β, and α-helix are shown by the open black triangles, the open red circles, the filled green triangles, the filled blue circles, and the filled purple squares, respectively.

strand structures. Here, we focus on a state at dαα = 8 Å as a representative state among intermediate states at dαα = 5−9 Å. Figure 5a shows the probability difference between the intramolecular Cα contact probability in the intermediate state at dαα = 8 Å and that in the monomer state. Here, when the distance between a pair of Cα atoms was less than 6.5 Å, it was regarded as a Cα contact.51 The probability of intramolecular Cα contacts in the monomer state was obtained from the trajectory with dαα > 12 Å. The contact pattern in the figure shows an increase of the β-hairpin structures at dαα = 8 Å. Increase of the intramolecular antiparallel β-strand structures at dαα = 5−9 Å in Figure 4b thus comes from increase of the βhairpin structures. It is expected that this increase of the βhairpin structures is related to the intermolecular side chain contacts. This is because the intermolecular side chain contact probability increases when the two molecules come close to each other, as seen in Figure 2b. For dαα < 9.0 Å, especially, this probability is higher than 50%. To see the relation of the βhairpin to the intermolecular side chain contacts, we show the intermolecular side chain contact map in Figure 5b. This intermolecular side chain contact map was calculated from the conformations at dαα = 8 Å in which at least one molecule had the intramolecular Cα contact between residues 34 and 40. The reason why we focused on this intramolecular Cα contact is that this contact has the highest probability in Figure 5a. The abscissa in Figure 5b is the residue number of the molecule that has the intramolecular Cα contact between residues 34 and 40. The ordinate is the residue number of the other molecule. Higher probabilities are seen in the contacts between the residues around residue 34 in the abscissa and the N-terminal residues in the ordinate and those between the residues around 11431

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chain contacts among Leu34, Met35, and Val40 with the intermolecular side chain contacts between these residues and residue Ile31. As seen in this representative conformation, stabilization of the β-hairpin structure by the intermolecular side chain contacts causes increase of the β-hairpin structures at dαα = 5−9 Å. Increase of the intramolecular β-strand structures may play an important role in forming intermolecular β-strand structures. Figure 6 shows the probability distributions with respect to the numbers of intramolecular and intermolecular β-bridges at some dαα values. When the two Aβ(29−42) molecules are in the monomer state, these molecules have random-coil structures, as shown in Figure 6a. When these molecules have intermolecular side chain contacts, either or both of the molecules forms the β-hairpin structure, such as the conformation in Figure 6b, as already discussed in Figures 4 and 5. The two molecules can form intermolecular β-bridges for dαα ≤ 5 Å, as shown in Figure 4b. The intermolecular βbridges at dαα = 5 Å are readily formed when there are intramolecular β-bridges. For example, the probability of forming one intermolecular β-bridge without an intramolecular β-bridge is lower than that with two intramolecular β-bridges. This implies that the intramolecular β-bridges induce the intermolecular β-bridges at d αα = 5 Å. In fact, the intermolecular β-bridges have a tendency to be formed between residues, either of which has the intramolecular β-strand structure as the conformation in Figure 6c. Moreover, a longer intermolecular β-bridge is created easily with longer intramolecular β-bridges at dαα = 5 Å. We confirmed this tendency up to three intramolecular β-bridges, while more than four intramolecular β-bridges were hardly observed due to the number of residues in the Aβ(29−42) molecule (14 residues). When the two molecules get sufficiently close such as dαα = 4 Å in Figure 6d, longer intermolecular β-strand structures with more than three intermolecular β-bridges are created more easily than at dαα = 5 Å. Such long intermolecular β-strand structures are observed even without the intramolecular βbridges. This is because, if a molecule has a bent structure, such as the β-hairpin structure, it is difficult to increase the number of intermolecular β-bridges with the bent molecule in the dimer state. A more extended structure is suitable to form a long intermolecular β-strand structure. Structures of Aβ(29−42) in the Monomer State. We show the Aβ(29−42) structures in the monomer state in this section. Here, if dαα > 12 Å, the two molecules are regarded as in the monomer state. To obtain the monomer structures, we utilized the principal component analysis (PCA)56 with respect to the Cα atoms. The details of PCA are presented in the Supporting Information. In Figure 7, we show the free-energy landscape for the monomer state at T0 = 300 K and λ = 1.00 with respect to the first and second principal components. We found nine localminimum states (state A-I) in this free-energy landscape. The representative structures in the local minima are also presented in the figure. Each structure has the following characteristics: (State A) The β-hairpin structure is formed in the C-terminal region. Met35 and Val36 form the antiparallel β-bridges with Val40 and Val39, respectively. Gly37 and Gly38 correspond to the turn region of the β-hairpin. (State B) Two kinds of structures are seen in this state. One is the same structure as in state A. The other is the β-helix structure, as shown in the figure. In this structure, Ile32 and Val36 form the parallel βbridge. (State C) The C-terminal residues form the β-helix

Figure 5. (a) Probability difference of intramolecular Cα contacts in the intermediate state at dαα = 8 Å and in the monomer state. (b) Intermolecular side chain contact map at dαα = 8 Å. The abscissa is the residue number of the molecule that forms intramolecular Cα contacts between residue 34 and residue 40. The ordinate is the residue number of the other molecule. Note that the glycine residues (G29, G33, G37, and G38) have no side chain and there is no side chain contact with other residues. (c) The snapshot of a representative conformation at dαα = 8 Å. The β-hairpin structure (yellow) in the gray molecule is stabilized by the intermolecular side chain contacts with the green molecule.

residue 40 in the abscissa and the N-terminal residues in the ordinate. This means that residues 34 and 40 that form the intramolecular Cα contact have stable intermolecular side chain contacts with the N-terminal residues in the other molecule. In Figure 5b, the peaks of the probability are less clear than those in Figure 5a. This is because, if a residue (R1) has an intermolecular side chain contact with another residue (R2), residues next to R1 also get close to R2 and residues next to R2. Figure 5c shows a representative conformation at dαα = 8 Å which has intermolecular side chain contacts between residues in a β-hairpin molecule and an N-terminal residue in the other molecule. This conformation corresponds to a class 2 tworesidue β-hairpin structure55 because hydrogen bonds are formed between CO of Val36 and NH of Val39, between CO of Val39 and NH of Val36, and between CO of Leu34 and NH of Ile41. Here, the hydrogen bonds were determined with the DSSP criteria,45 again. In this conformation, the β-hairpin structure is stabilized by reinforcing the intramolecular side 11432

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Figure 6. Probability distribution with respect to the number of intramolecular β-bridges and the number of intermolecular β-bridges at the corresponding dαα value. Representative structures are also presented.

structure with the intramolecular antiparallel β-bridges between Met35-Val36 and Val39-Val40 and between Leu34 and Ala42. Leu34 and Met35 in M1 form the intermolecular parallel βbridges with Val40 and Ile41 in M2, respectively. Ile31-Gly33 of both molecules forms the intermolecular antiparallel β-sheet structure. (State B) The antiparallel intermolecular β-sheet structure is formed between Val39-Ala42 in M1 and Gly38Ile41 in M2. The N-terminal parts of both molecules have random-coil structures. (State C) M1 has the β-hairpin with the intramolecular antiparallel β-bridges between Ala30-Ile31 and Leu34-Met35. M2 also forms the β-hairpin with the β-bridge between Val36 and Val40. This M2 has the 310-helix structure consisting of Val36-Gly38. Leu34 in M1 has the intermolecular antiparallel β-bridge with Ala30 in M2. (State D) In M2, the intramolecular antiparallel β-bridges are formed between Met35-Val36 and Val39-Val40 and between Leu34 and Ala42. Leu34 and Met35 in M1 form intermolecular parallel β-bridges with Val39 and Val40 in M2, respectively. Gly33-Leu34 in M1 and Ala30-Ile31 in M2 have the intermolecular antiparallel βbridges. (State E) M1 forms the β-hairpin with the intramolecular antiparallel β-bridge between Ile31 and Leu34. M2 also has the β-hairpin with the β-bridges between Met35-Val36 and Val40-Ile41. Gly37 in M1 forms the intermolecular antiparallel β-bridge with Ala30 in M2. (State F) Most of the conformations in this state have random-coil structures. About 30% of the conformations have the intermolecular antiparallel β-bridge between Val40 in M1 and Val40 in M2. Val40 in M2 forms the intramolecular parallel β-bridge with Leu34. (State G) M1 has the β-helix consisting of Ile32-Val36. M2 forms the β-hairpin. This β-hairpin has the intramolecular antiparallel βbridges between Gly29-Ala30 and Val40-Ile41 and between Gly33 and Val36. There is no intermolecular β-bridge in this

structure. The parallel β-bridge is formed between Gly37 and Ile41. (State D) Most conformations do not have any secondary structures. Random-coil structures are observed in this state, as shown in the figure. (State E) The N-terminus and C-terminus are close to each other, and Ala30 and Ile41 have the antiparallel β-bridge structure. (State F) The N-terminus and C-terminus are close also in this state. However, Ala30 and Ile41 form the parallel β-bridge. This conformation has a circular structure. (State G) The N-terminus and C-terminus have antiparallel β-bridges. These β-bridges are formed between Ile31 and Ile41 and between Ile32 and VAl40. (State H) The βhairpin structure is formed as shown in the figure. The β-strand of the N-terminus consists of Ala30 to Ile32, and that of the Cterminus consists of Val39 to Ile41. Leu34 to Val36 form the 310-helix structure which locates the turn region of the β-hairpin structure. (State I) Aβ(29−42) has the β-sheet structure with three β-strands. In this structure, Gly37 and Val40 form the antiparallel β-bridge. The parallel β-bridges are formed between Ile31 and Val40 and between Ile32 and Ile41. We remark that these monomer structures are coincident with our previous work,36 in which the simulations were performed with one Aβ(29−42) molecule in explicit water. Structures of Aβ(29−42) in the Dimer State. We discuss the dimer structures of Aβ(29−42) in this section. The dimer state is defined as dαα < 6.5 Å. PCA was utilized again to analyze the dimer structures, as shown in the Supporting Information. Figure 8 shows the free-energy landscape for the dimer state at T0 = 300 K and λ = 1.00 with respect to the first and second principal components. Ten local-minimum states (state A-I) are observed in the figure, and the corresponding structures are as follows: (State A) The Aβ(29−42) molecule M1 has the 310helix structure consisting of Gly38-Val40. M2 has the β-hairpin 11433

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Figure 7. Free-energy landscape for the monomer states at 300 K and the parameter value of 1.00. The abscissa and the ordinate are the first principle component axis and the second principle component axis, respectively. The unit of the free-energy landscape is kcal/mol. The free-energy local-minimum states are labeled as state A to state I. The corresponding representative structures are also presented.

Figure 8. Free-energy landscape for the dimer states at 300 K and the parameter value of 1.00. The abscissa and the ordinate are the first principle component axis and the second principle component axis, respectively. The unit of the free-energy landscape is kcal/mol. The free-energy local-minimum states are labeled as state A to state J. The corresponding representative structures are also presented.

state. (State H) M1 has the intramolecular antiparallel β-bridge between Ala30 and Val39. In M2, the intramolecular antiparallel β-bridge is formed between Met35 and Ile41. Val39-Ile41 in M1 and Gly33-Met35 in M2 form the intermolecular parallel βsheet. (State I) M1 has the β-helix consisting of Ile32-Val36. M2 forms the intramolecular β-bridge between Gly29 and Leu34. The intermolecular antiparallel β-bridge is formed between Val36 in M1 and Val39 in M2. The intermolecular parallel βbridge is also observed between Val40 in M1 and Leu34 in M2. (State J) M1 has the β-hairpin with the β-bridges between Gly33 and Ile41 and between Val36 and Val39. The 310-helix structure is formed at the turn region of the β-hairpin from Val36 to Gly38. Gly33-Leu34 in M1 have the intermolecular antiparallel β-sheet with Met35-Val36 in M2. There are various structures in the dimer state. When a short intermolecular β-sheet structure is formed, one of the two Aβ(29−42) molecules usually has the intramolecular β-bridges. Longer intermolecular β-sheet molecules have the extended structures at least partially. To form a much longer intermolecular β-sheet, both molecules must have fully extended structures. However, such a fully extended structure is hardly observed because this is entropically disfavored.

of the HRPM to two Aβ(29−42) molecules in explicit water. CREMD simulations were also applied to this system. CRPM realized more efficient sampling between the monomer and dimer states of Aβ(29−42) than CREM, as shown in the Supporting Information. As seen in the free energy at T0 = 300 K and λ = 1.00 as a function of dαα, Aβ(29−42) had a tendency to have the aggregation state. This was consistent with the experimental results that showed that Aβ(29−42) is hardly soluble. In our simulations, the intermolecular β-sheet structures were observed in the dimer state. Aβ(29−42) had not only the parallel β-strand structure but also the antiparallel β-strand structure. This result was also consistent with the infraredspectroscopy experiment for Aβ(29−42) in aqueous solution. The probability of the antiparallel β-sheet formation was higher than that of the parallel β-sheet formation. In the dimerization process of Aβ(29−42), when the two molecules came close to each other and had side chain contacts, the amount of intramolecular secondary structure increased. This increasing secondary structure was mainly the β-hairpin structure. The β-hairpin structure was stabilized by the intermolecular side chain contacts. In the presence of the intramolecular β-bridges, the intermolecular β-bridges were readily formed in comparison with the absence of the intramolecular β-bridges. This fact implied that such intramolecular β-strand structures play an important role in the early

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CONCLUSIONS In order to investigate the dimerization process of Aβ(29−42) in detail, we applied the CRPM which is one of the realizations 11434

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stage of forming intermolecular β-bridges. When the two molecules got close sufficiently, longer intermolecular β-strand structures were created. Because the molecules had extended structures to form a long intermolecular β-sheet, the intramolecular β-bridges were broken. We then showed the monomer and dimer structures. These structures were classified by utilizing PCA. The obtained monomer structures were coincident with our previous work in which the simulations had been performed with one Aβ(29− 42) molecule in explicit water. As for the dimer structures, the short intermolecular β-sheet structures were formed between the two molecules, either of which usually had the intramolecular β-bridges. The long intermolecular β-sheet structures were also observed as stable structures. Aβ(29−42) had various structures in the monomer and dimer states. However, most of these structures included β-strand structures in common, while a minor detail of each structure and that of the free-energy landscape may be changed with longer simulations. In fact, it was suggested in an experiment9 that Aβ(29−42) has a βstrand structure before forming an amyloid fibril. We showed the dimerization process of Aβ(29−42) in detail. The mechanism of inducing the intermolecular β-bridges by the intramolecular β-bridges would be applied to the oligomerization process by replacing the intramolecular β-bridges to the intermolecular β-bridges. That is, if there are stable intermolecular β-bridges in an oligomer, Aβ(29−42) in the monomer state readily forms intermolecular β-bridges with the oligomer via the stable intermolecular β-bridges. This corresponds to the rapid growth of amyloid fibrils with seed fibrils. It is necessary to employ more Aβ(29−42) molecules to understand the oligomerization process accurately. It is also important to investigate not only the oligomerization process but also the characteristics of Aβ molecules57 to overcome Alzheimer’s disease. To study such Aβ systems, the CRPM would be a powerful tool, as is the case for the two Aβ(29−42) molecules.

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ASSOCIATED CONTENT

S Supporting Information *

Detailed description of methods and discussion on sampling efficiency. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81 (0)564 557277. Fax: +81 (0)564 557025. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The computations were performed on the computers at the Research Center for Computational Science, Okazaki Research Facilities, National Institutes of Natural Sciences. This work was supported by JSPS KAKENHI (24740296 and 26102550) and the Okazaki Orion Project.

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