2767
2008, 112, 2767-2770 Published on Web 02/14/2008
Amyloid-β(29-42) Dimer Formations Studied by a Multicanonical-Multioverlap Molecular Dynamics Simulation Satoru G. Itoh* and Yuko Okamoto Department of Physics, School of Science, Nagoya UniVersity, Nagoya, Aichi 464-8602, Japan ReceiVed: December 31, 2007
Amyloid-β peptides are known to form amyloid fibrils and are considered to play an important role in Alzheimer’s disease. Amyloid-β(29-42) is a fragment of the amyloid-β peptide and also has a tendency to form amyloid fibrils. In order to study the mechanism of amyloidogenesis of this fragment, we applied one of the generalized-ensemble algorithms, the multicanonical-multioverlap algorithm, to amyloid-β(29-42) dimer in aqueous solution. We obtained a detailed free-energy landscape of the dimer system. From the detailed free-energy landscape, we examined monomer and dimer formations of amyloid-β(29-42) and deduced dimerization processes, which correspond to seeding processes in the amyloidogenesis of amyloid-β(2942).
Alzheimer’s amyloid-β (Aβ) peptide is comprised of 39 to 43 amino-acid residues and generated by cleavage from the amyloid precursor protein (APP).1 Aβ has a tendency to form amyloid fibrils,2-4 which are associated with Alzheimer’s disease.5,6 In order to establish a remedy for Alzheimer’s disease, the understanding of the structure of amyloid fibrils and the mechanism of amyloidogenesis with respect to Aβ peptides is of importance. Especially, it is necessary to obtain information about the formations and aggregation process of Aβ dimer to understand the early process of amyloidogenesis. It was reported experimentally that the structure of Aβ in amyloid fibrils has two intermolecular β-sheet regions by Petkova and co-workers.7 These two β-sheets are constructed by the residues 12-24 (β1) and the residues 30-40 (β2). For variousfragmentsofAβ,furthermore,therearemanyexperiments.2-4,8 For example, it was reported by Balbach and co-workers that Aβ16-22, which consists of the residues 16-22 of Aβ and is a part of β1, is the shortest fragment of Aβ that forms amyloid fibrils.8 The C-terminal residues after residue 29 of Aβ correspond to the transmembrane domain of APP,1 and the fragment length after residue 29 is a critical determinant of the rate of amyloid formation. Actually, Aβ42, which is composed of 42 aminoacid residues from the N-terminus, readily forms amyloid fibrils in comparison with Aβ40, which consists of 40 amino-acid residues from the N-terminus.9 Moreover, Aβ29-42, which consists of the residues 29-42 of Aβ and contains β2, also forms amyloid fibrils by itself.2,3 By experiments,2,3 it is suggested that Aβ29-42 peptides have intermolecular β-sheet structures in amyloid fibrils. However, the detailed conformations or aggregation processes of Aβ29-42 peptides have yet to be clarified. In order to elucidate these issues and understand the early process of amyloidogenesis, therefore, we applied the multicanonical-multioverlap molecular dynamics (MD) algorithm,10,11 which is a generalization of the multioverlap * Corresponding author. E-mail:
[email protected].
10.1021/jp712170h CCC: $40.75
algorithm,12-15 to an Aβ29-42 dimer. We remark that the shortest fragments, Aβ16-22, have also been simulated to study the oligomerization of β1.16,17 The present work is the first attempt to study the oligomerization of β2 by computer simulations. The multicanonical-multioverlap algorithm is one of the generalized-ensemble algorithms (for reviews, see, e.g., refs 15 and 18). This algorithm has combined the advantages of the multicanonical and multioverlap algorithms. The multicanonical algorithm is one of the most well-known generalized-ensemble algorithms and realizes effective samplings in the conformational space. The multioverlap algorithm also effectively samples the vicinity of specific conformations. The multicanonical-multioverlap algorithm realizes effective samplings in the conformational space more than these two algorithms.10,11 In the multicanonical-multioverlap algorithm, by employing the nonBoltzmann weight factor Wmco, which we refer to as the multicanonical-multioverlap weight factor, a uniform probability distribution with respect to the potential energy and a dihedral-angle distance is obtained:
Pmco(E,d) ) n(E,d)Wmco(E,d) ≡ const
(1)
where E is the potential energy, and d is the dihedral-angle distance. The dihedral-angle distance is defined by
d)
1
n
d(Vi,V0i ) ∑ nπ i-1
(2)
where n is the total number of dihedral angles, Vi is the dihedral angle i, and V0i is the dihedral angle i of the reference conformation. The distance d(Vi,V0i ) between two dihedral angles is given by
d(Vi,V0i ) ) min(|Vi - V0i |, 2π - |Vi - V0i |) © 2008 American Chemical Society
(3)
2768 J. Phys. Chem. B, Vol. 112, No. 10, 2008
Letters TABLE 1: Dihedral Angles of the Reference Conformation in Figure 1 strand 1
strand 2
angle (°) φ1
30
Figure 1. Reference conformation in our multicanonical-multioverlap simulation. The figure was created with RASMOL.19
Figure 2. Typical conformations of the Aβ29-42 molecule at 300 K when two molecules are spatially separated. We consider that two Aβ29-42 molecules are spatially separated if the distance between the center of mass is more than 15 Å.
The multicanonical-multioverlap weight factor at a constant temperature T0 can be written as
Wmco(E,d) ) exp(-β0Emco(E,d))
(4)
where β0 is defined by β0 ) 1/kBT0 (kB is the Boltzmann constant), and Emco(E,d) is the multicanonical-multioverlap potential energy. Equation 1 implies that multicanonicalmultioverlap simulations realize a free random walk in the twodimensional potential-energy and dihedral-angle distance space and are able to effectively sample the conformational space. Accordingly, we can obtain accurate free-energy landscapes of protein systems and estimate folding pathways and the transition states among the specific conformations.10,11 In our simulation, the N-terminus of Aβ29-42 and the C-terminus of Aβ29-42 were blocked with the acetyl group and the N-methyl group, respectively. This is because we wanted the total charge of the Aβ29-42 system to be neutral. Consequently, the amino-acid sequence is Ace-GAIIGLMVGGVVIANme. In multicanonical-multioverlap simulations, we must have a reference conformation. We adopted the conformation in Figure 1 as the reference conformation in this article. This conformation was obtained by taking only the corresponding part from the conformation whose PDB ID code is 2BEG.20 We show dihedral angles of the reference conformation in Table 1, and these values were employed as the reference dihedral angles V0i of the dihedral-angle distance in eq 2. Here, we took into account only the backbone dihedral angles φ (the rotation angles around the N-CR bonds) and ψ (the rotation angles
ψ130 φ131 ψ131 φ132 ψ132 φ133 ψ133 φ134 ψ134 φ135 ψ135 φ136 ψ136 φ137 ψ137 φ138 ψ138 φ139 ψ139 φ140 ψ140 φ141 ψ141
54.7 -127.8 -111.4 102.2 -118.6 117.6 -109.3 104.2 -104.6 106.5 -110.5 125.2 -111.7 112.1 -93.9 121.9 -140.4 78.5 -119.0 128.7 -127.5 124.1 -121.9 114.2
angle (°) φ2
30
ψ230 φ231 ψ231 φ232 ψ232 φ233 ψ233 φ234 ψ234 φ235 ψ235 φ236 ψ236 φ237 ψ237 φ238 ψ238 φ239 ψ239 φ240 ψ240 φ241 ψ241
62.0 -134.3 -116.8 111.1 -134.8 142.2 -135.8 126.3 -115.5 123.8 -125.7 118.2 -97.4 115.2 -96.7 79.8 -103.5 70.1 -106.2 120.9 -115.5 110.5 -109.4 107.2
around the CR-C bonds) of the residues 30-41 of Aβ29-42 as the reference dihedral angles in our simulations. The force field that we adopted is the CHARMM 22 parameter set.21 We employed the GB/SA model22-24 as an implicit solvent model. We also introduced the harmonic constraint k(r-r0)2/2 when the distance between the center of mass of two Aβ29-42 molecules exceeded 20 Å in order to avoid the states in which two molecules are too much spatially separated. Here, r is the distance between the center of mass of two molecules, and k is a force constant whose value is 200 kcal/(mol Å2), and the value of r0 is set 20 Å. The multicanonical-multioverlap weight factor was first determined so that a free random walk was realized in the two-dimensional energy-overlap space. As for the potential-energy random-walk, this weight factor covered the temperature range from 300 to 600 K. We then performed a multicanonical-multioverlap production run, in which the time step was 0.5 fs, for 29.5 ns after equilibration of 0.5 ns. An initial conformation of Aβ29-42 dimer for the production run was a random-coil conformation. In Figure 2 we show conformations of Aβ29-42 monomer in the case when the distance between the center of mass of two peptides is more than 15 Å at 300 K. We identified three major metastable states. These states correspond to low concentrations of Aβ29-42 peptides or to their monomeric states. Conformation 1 in Figure 2 is a β-helix-like structure, Conformation 2 is an R-helix (or sometimes π-helix) structure, and Conformation 3 is an intramolecular antiparallel β-sheet (β-hairpin) structure. When the Aβ29-42 peptide is in a monomeric state, therefore, it seems that the conformations of Aβ29-42 peptides have the same structure as those in Figure 2. We show the free-energy landscape of the dimer system at 300 K in Figure 3a. The free-energy landscape was obtained from the results of the multicanonical-multioverlap MD simulation by the reweighting techniques.25,26 The abscissa is the number of backbone CR intermolecular contacts, and we regard a pair of CR atoms as being in contact if the distance between the two atoms is within 6.5 Å. dR and dβ in the label of the ordinate are dihedral-angle distances, which we introduced to set the reaction coordinates of the free-energy data analysis.
Letters
Figure 3. (a) Free-energy landscape of an Aβ29-42 dimer system at 300 K. The ordinate is an indicator of structure for helix and strand. When the value of the ordinate is close to 1, conformations of Aβ29-42 become helical. Conversely, if the value is close to 0, the conformations have extended forms. The abscissa is the number of backbone CR intermolecular contacts. Contour lines are drawn every 1 kcal/mol. (b) Typical structures in the corresponding local-minimum states in Figure 3a. The arrows indicate possible pathways of the early stages of amyloidogenesis.
Namely, we set the values of V0i so that (φ,ψ) ) (-π/3,-π/3) for dR and (φ,ψ) ) (-2π/3,2π/3) for dβ with respect to the backbone dihedral angles of the residues 34-38 in eq 2. When the value of dR (dβ) is close to 0, the structures of Aβ29-42 molecules are helical (extended strand). Accordingly, if the value of the ordinate is close to 0, the structures of Aβ29-42 molecules are straight strands. If the value of the ordinate is close to 1, on the other hand, the structures are helical. From the free-energy landscape in Figure 3a, we identified seven local-minimum states. In Figure 3b we show typical conformations of the
J. Phys. Chem. B, Vol. 112, No. 10, 2008 2769 Aβ29-42 dimer in each local-minimum state. In the localminimum state “A,” the Aβ29-42 dimer has helical structures. Namely, Conformation 1 has β-helix-like structure, and Conformation 2 has R-helix (or sometimes π-helix) structures. In “B”, the structures of the two molecules are helices. In “C” the molecules have helix conformations with extended parts, and the extended parts form intermolecular β-ladders in “D”. The Aβ29-42 dimer forms intermolecular β-sheet structures frequently with intramolecular β-sheet conformations in “E”. In “F”, a short intermolecular β-sheet conformation is realized. In the localminimum state “G,” Aβ29-42 dimer has intermolecular extended parallel or antiparallel β-sheet structure. In the amyloid fibrils, as mentioned above, Aβ29-42 peptides have intermolecular β-sheet structures. From Figure 3b, therefore, conformations of the Aβ29-42 dimer, which can be seeds of amyloid fibrils, are intermolecular parallel or antiparallel β-sheet structures such as Conformations 1 and 2 in the local-minimum state “G”. From Figures 2 and 3 we deduce the dimerization (oligomerization) process, which corresponds to a seeding process in amyloidogenesis, for Aβ29-42 peptides as follows: Stage 1: When the Aβ29-42 peptides are in the monomeric state, the peptides are mainly in one of the three conformational states in Figure 2. Stage 2: Aβ29-42 peptides come close to each other and create dimers (or oligomers) as a result of hydrophobic effects. If the structures are intramolecular antiparallel β-sheet structures before dimerization, such as Conformation 3 in Figure 2, the conformation after dimerization will correspond to Conformation 2 in the local-minimum state “E” in Figure 3b. If the structures are like Conformation 1 or 2 in Figure 2, on the other hand, the Aβ29-42 dimer will have structures like those of the conformations in “A” or “B” in Figure 3b. Stage 3: If the conformations in Stage 2 are in states “A” or “B” in Figure 3b, then the peptides have helical conformations with extended parts like those in “C”. If the conformations in Stage 2 are already in “E” in Figure 3b, on the other hand, this corresponds to Stage 4 below. Stage 4: The extended parts will create intermolecular β-ladders such as those in “D” or “E”. Stage 5: The intramolecular secondary structures are broken, and the peptides will have a fully extended form such as those in “F”. Stage 6: The Aβ29-42 dimer has intermolecular parallel or antiparallel β-sheet structure like those in “G”. These pathways are summarized in Figure 3b (see the arrows). In the early process of amyloidogenesis, these intermolecular parallel or antiparallel β-sheet structure can be a seed of amyloid fibrils. In summary, we calculated the free-energy landscape at 300 K for a Aβ29-42 dimer in aqueous solution from the results of a multicanonical-multioverlap MD simulation. We identified some of the monomer and dimer states of Aβ29-42. From these results, we deduced a dimerization process of Aβ29-42 peptides and showed conformational changes from helical to strand structures step by step. These detailed conformational changes in the dimerization process for Aβ fragments are first clarified by computer simulations with the multicanonical-multioverlap algorithm. Although it is difficult to apply this algorithm to full Aβ peptides because of large computational cost, we believe that the present results together with those for Aβ16-22 clarify the dimerization of Aβ. Acknowledgment. The computations were performed on the computers at the Information Technology Center, Nagoya University. This work was supported, in part, by Grants-in-Aid for the Next Generation Super Computing Project, Nanoscience Program, and for Scientific Research in Priority Areas, “Water
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