Spontaneous self-assembly of amyloid β (1–40) into dimers

The self-assembly and fibrillation of amyloid β (Aβ) proteins is the neuropathological hallmark of Alzheimer's disease. However, the molecular mechanism of how disordered monomers assemble into aggregates remains largely unknown. In this work, we characterize the assembly of Aβ (1–40) monomers into dimers using long-time molecular dynamics simulations. Upon interaction, the monomers undergo conformational transitions, accompanied by change of the structure, leading to the formation of a stable dimer. The dimers are stabilized by interactions in the N-terminal region (residues 5–12), in the central hydrophobic region (residues 16–23), and in the C-terminal region (residues 30–40); with inter-peptide interactions focused around the N- and C-termini. The dimers do not contain long β-strands that are usually found in fibrils.


Introduction
The self-assembly of amyloidogenic proteins is related to several neurodegenerative diseases. [1][2][3] According to the amyloid cascade hypothesis, self-assembly of amyloid b (Ab) is the primary model for the development of Alzheimer's disease (AD). 1,4 The nal products of the amyloid self-assembly process are brillar structures that contain long b-strands, [5][6][7] whereas Ab monomers are largely unstructured, [8][9][10] which leads to the question of how the conformational transition occurs during self-assembly.
Recent compelling evidence show that amyloid oligomers rather than brils are the most neurotoxic species. [12][13][14][15][16] The neurotoxicity of Ab oligomeric species have been attributed to intracellular, membrane, and receptor-mediated mechanisms. [17][18][19][20][21][22][23][24][25][26][27][28] Various morphologies have been ascribed to oligomers, from spherical aggregates to lamentous. 29,30 It is proposed that oligomers form the critical entities, called nuclei, needed to transition to proto-bril states before nally brillating. 31 Spectroscopic characterization of Ab oligomers revealed that they are composed of random coil secondary structure, which is able to transition to b-structure as the aggregation progresses. [31][32][33][34] Sarkar et al. showed that the oligomer chemical shis are very different from brils, in particular in the N-terminal and the central segment (residues [22][23][24][25][26][27][28][29]. 33 These nding are in line with the data from Ahmed et al., which show that oligomers have disordered molecular conformations. 31 There are two principle alloforms of amyloid b proteins, Ab  and Ab , dened by the number of residues; with the former being the most abundant and the latter the most aggregation prone and neurotoxic. [35][36][37][38][39][40][41] Despite the small structural difference (two amino acids) between the Ab40 and Ab42 alloforms, they display distinct behavior, although the structural basis for this is unknown. [38][39][40][41][42] Hence, a detailed characterization of the oligomeric forms of these Ab species is important for understanding neurotoxicity and pathology in AD. Recent studies have demonstrated that single-molecule approaches are powerful methods to study oligomers. [43][44][45][46] Single-molecule techniques, such as AFM, 11,47-51 tethered approach for probing inter-molecular interactions (TAPIN), 52,53 and FRET, 33 have shown that the early-stage oligomers exhibit prolonged lifetimes and stabilities. Novel features of the interaction and self-assembly of Ab40 and Ab42 peptides were determined using single-molecule AFM-based force spectroscopy. 11 However, due to their transient nature and heterogeneity, many questions about the oligomer formation process and the structure and dynamics of Ab oligomers are le unanswered. 54,55 Computational simulations have been utilized to supplement the novel single-molecule techniques used to probe early stages of aggregation and, in some cases, elucidate the dynamics and mechanism of aggregation. 50,[56][57][58][59][60] Computational studies of the dynamics of Ab42 lead to the discovery that, in an aqueous environment, the protein mainly assumes a-helical structure. 61 However, the helices are not stable and transition between structured and unstructured conformations multiple times. Further studies showed that Ab42 is more structured compared to Ab40 and has a less exible C-terminal segment. 57 These ndings are in line with the comparison of Ab40 and Ab42 by Yang and Teplow, which showed that Ab42 forms more stable conformations that tend towards b-structure and stable C-terminus. 62 More recent simulations have revealed that the size and distribution of the early aggregates for Ab40 and Ab42 vary, the most common oligomer being dimers for the former and pentamers for the latter. 63,64 These results qualitatively reproduce the main features of oligomer size distributions measured experimentally. 42,65 Furthermore, Ab42 displayed turn and b-hairpin structures that are absent in Ab40.
Biased simulation strategies using a coarse-grained approach has also been employed to investigate the aggregation pathway. 66 Zheng et al. demonstrate that while pre-brillar oligomers typically consist of antiparallel b-structure they are distinct from brillar structures and very dynamic. These structural characteristics are also demonstrated for the Ab40 dimer in the ndings of Tarus et al., which show that dimers are compact conformations with inter-peptide antiparallel b-structures. 67 Similar observations were also reported by Watts et al. using a different force eld. 68 However, how the structures of oligomers contribute to neurotoxicity remain unclear. Leaving the fundamental questions related to the mechanism of oligomer self-assembly and dynamics unanswered. Which, in turn, has impeded the progress in the development of treatment for these diseases.
We recently characterized the conformational changes in monomers of Ab42 peptide upon dimer formation using long time-scale all-atom molecular dynamics (MD) simulations. 69 The simulations revealed that the dimer is very dynamic and resulted in a multitude of different conformations being iden-tied. By utilizing the recently developed Monte Carlo pulling (MCP) approach, 58 we were able to identify the most likely native conformations of the Ab42 dimer, which generated statistically similar dissociation forces and interaction proles as was observed in AFM experiments.
Here, we applied the developed MD simulation strategy to analyze the dimer formation of full-length Ab40 protein using the special purpose Anton supercomputer. 70,71 A variety of dimer conformations were identied, all with small segments of ordered structures and lacking the characteristic b-sheet structures found in amyloid brils. These dimers structures were then validated using MCP simulations and by comparing with stability and interaction data obtained from AFM-based force spectroscopy experiments. The validated dimer conformations were then used to compare Ab40 and Ab42 dimers and characterize the differences between the interaction of monomers in the resulting dimers.

Ab40 monomer simulation
To generate the initial structure of the monomer used for the dimer simulation, we conducted all-atom MD simulations using GROMACS ver. 4.5.5 (ref. 72) employing Amber ff99SB-ILDN force eld 73 and the TIP3P water model. 74 The initial monomer structure was adopted from NMR data 8 (PDB ID: 1AML) with an extra N-terminal Cys residue added to mimic experimental sequence. 69 The monomer was then solvated, neutralized with NaCl ions, and kept at 150 mM NaCl concentration. Following which energy minimization was performed, before 500 ns NPT (isothermal-isobaric ensemble) MD simulation, at 1 bar and 300 K, was carried out.

Spontaneous dimerization of Ab40
The initial Ab40 dimer conformations were prepared in the Maestro soware package (Schrödinger, New York, NY), using the same force eld and water model as for the monomer MD simulation. Dimer conformations were created by placing two copies of the representative monomer, cluster 1 in Fig. S1, † at 4 nm center of mass (CoM) distance. Two congurations were created, parallel and orthogonal (90 rotation between the two monomers with respect to the long peptide axes). The dimers were then solvated, neutralized, and NaCl concentration kept at 150 mM; aer which they underwent energy minimization and 50 ns NPT simulation to relax the systems. They were then submitted for 4 ms MD simulation on the special purpose supercomputer Anton.

Accelerated MD simulations
To extend conformational sampling, dimer structures obtained from the MD simulations on Anton were subjected to the accelerated MD (aMD) simulation method. The simulation procedure was adopted from the description by Pierce et al. 75 and the website (URL: http://ambermd.org/tutorials/advanced/ tutorial22/) using Amber 14 soware package. 76 Briey, dimer conformations from the last frame of the MD simulation on Anton and from the two lowest energy minima were solvated, neutralized, and kept at 150 mM NaCl, and energy minimized, before being submitted for 500 ns aMD simulations. Simulations utilized the same force eld and water model as previous simulations.

Monte Carlo pulling simulations
The Monte Carlo pulling method was performed to simulate AFM force spectroscopy experiments using our previously described procedure 58 and a modied PROFASI package. 77 Briey, the two Ca of the N-terminal Cys residues of each monomer were dened as the pulling groups. A virtual spring was attached onto each pulling group and used to stretch them during the pulling process. The energy dynamics of the spring were calculated using the A2A spring function (PROFASI package) with the total energy during the course of pulling described by, where E(x) describes the energy without an external force, k and t are the spring constant of the virtual spring, and L 0 is the initial distance between the two Ca atoms. L(x) represents the real-time distance between the Ca atoms while x denotes the protein conformation being probed. When v ¼ 0.083 fm per MC step, it mimics the pulling speed of 500 nm s À1 ; which was used for all MCP simulations.

Analysis methodology
Cluster analysis was performed using the GROMOS method of clustering and root-mean square deviation (RMSD) as input for the protein backbone, as previously described. 50 To remove rotational and translational motion of the backbone, atoms were centered in the box and t using the progressive method of trjconv.
We monitored secondary structure dynamics according to the method developed by Thirumalai's group. 78 Briey, if the dihedral angles from two consecutive residues satisfy the denition of an a-helix (À80 # f # À48 and À59 # j # À27 ) or b-strand (À150 # f # À90 and 90 # j # 150 ), the structures are considered to be a or b conformations, respectively. The changes of secondary structure over time are monitored by, The principal component analysis of backbone dihedrals (dPC) 79 was used to generate the energy landscape and identify the representative structures of the minima. The Fortran program 79 written by Dr Yuguang Mu was used to perform this analysis.
Intra-peptide contact probability maps were generated based on Ca atom contacts within the monomers using the GROMACS mdmat analysis tool.

Ab40 monomer structure
We performed all-atom MD simulations of Ab40 monomers to identify the most representative monomer structure. We adopted the approach from our recent simulations of the Ab42 dimer. 69 Briey, the Ab40 monomer structure was simulated for 500 ns, the most representative structure was then identied using cluster analysis. The results of the cluster analysis are shown in Fig. S1. † Twelve clusters were identied, with the 1 st cluster comprising 47.5% of the entire population. The representative structure of this cluster contains a large a-helical segment in the central region of the peptide and is otherwise unstructured. Two copies of this structure were used to characterize the dimer conformation.

Characterization of Ab40 dimer formation
Two dimer systems were generated by placing copies of the monomer structure in orthogonal (90 ) or parallel orientations, with respect to the long peptide axis, at 4 nm CoM distance, Fig. 1 right column. Both dimer conformations were then simulated for 4 ms on the Anton supercomputer.
To determine if the dimer simulations had converged, we monitored the time-dependent change in secondary structure of the peptides, Fig. 1 le column. The graphs show that for the orthogonal conguration, a-helical content uctuates with a decreasing tendency up to the 1 ms mark, aer which the helical portion increases over the next 1 ms span, Fig. 1a. Meanwhile, the b-content remains stable at approximately 5%, with minor uctuations, until approximately 3.5 ms; aer which a conversion from a-helical to b-structure is observed, with bcontent reaching a maximum of $12% at the end of the simulation. For the parallel conguration on the other hand, both ahelical to b-structure content uctuate throughout the simulation, with averages of approximately 15% and 5%, respectively, Fig. 1b. This suggests that, for both congurations, a local equilibrium state has not been reached.
The free energy landscape of the dimer was generated using dihedral principal component analysis, Fig. S2. † For both dimer congurations, several distinct energy minima were found. Furthermore, both congurations show a rough and discontinuous energy landscape. This, in combination with the timeresolved change in secondary structure, suggests that the dimers are trapped in local energy minima, leading to insufficient sampling of the conformational space. To overcome this problem and to enhance the sampling of the conformational space, we extended the dimer simulation using accelerated MD simulations (see specics in Methods) allowing us to potentially reach sampling enhancement by several orders of magnitude. 75

Accelerated MD simulations of dimers
The energy landscapes from the aMD simulations of the dimer are presented in Fig. S3. † Several well-dened and separated energy minima were identied for the orthogonal system, Fig. S3a, † while the parallel system only has few energy minima that are clustered in the same region of the energy landscape, Fig. S3b. † It is clear from the energy landscape that a larger portion of the conformation space was sampled during aMD simulation. The results were then pooled and the concatenated data set (3 ms total) underwent dPC analysis again, Fig. 2 top. The snapshots in the gure depict representative structures from the two lowest energy minima. It is evident, that the dimer does not adopt long b-structures but has a mixture of short helices and b-structures.
The secondary structure of the dimers was characterized using DSSP. 80 Each monomer was investigated separately with the results being displayed as residue specic probabilities, Fig. 2 bottom. Monomer 1 shows greater than 40% propensity for helix formation in residues 3-7, 11-13, and 25-29. b-Structures are overall less likely compared to helices, however regions 10-30 and 35-38 have on average greater than 20% chance of bstructures. Monomer 2 on the other hand is more diverse, the helix probability is localized around residues 11-20, while collectively b-structures are more probable in the N-and Cterminal segments in residues 3-10 and 21-38, respectively.
To analyze the conformational diversity of the dimers we performed cluster analysis using the pooled aMD data. Similar to the analysis performed for monomers, clustering was performed using RMSD of backbone atoms between all pairs of structures with a cut-off at 4.5Å. Representative structures for the rst 20 clusters are depicted in cartoon representation and relative populations on Fig. 3. Structurally the clusters, with few exceptions, exhibit similar trends of low a-helical and b-structural content and high degree of unstructured regions. This is also evident from DSSP of the representative structures, Table  S1. † Further characterization reveal that the dimers are very similar geometrically, having gyration radii and volume within a few % of each other, Table S1. † However, the structures show larger variability in the solvent accessible surface area (SASA), ranging from $50 to 60 nm 2 . The main difference within the clusters arise from the different congurations of monomers.
To identify segments important for the interaction of Ab40 monomers, we performed analysis of the pair-wise residue interactions. Intra-peptide contact probability maps were generated based on Ca atom contacts within the monomers, Fig. S4. † For monomer 1, interactions in three segments stand out, residues 5-12, residues 16-23, and residues 30-40, Fig. S4a. † The interactions within these three segments reveal that the monomer during the simulations, with high probability, is found in a compact turn-like conformation with C-terminal interacting with the central segment of the peptide. Monomer 2 on the other hand is more dynamic with few residues interacting within the Nterminal region and the 16-23 segment, Fig. S4b. † The interaction patterns of the two monomers reveal that, apart from neighbor residue interactions, the main difference is found in the way the two monomers interact with the 16-23 region; for monomer 1 the interaction happens with residues 33-38, while for monomer 2 it is residue 28-32, Fig. 4a.
The inter-peptide interactions of the dimer were obtained using the pair-wise interactions of Ca atom between the monomers, Fig. 4b. The contact map reveals that the interactions between the two monomers occur in the central region of the peptide as well as between the N-and C-terminals and the two C-termini. Comparison of the contact data and the dimer structures, revealed by cluster analysis on Fig. 3, shows that the 20 most populated clusters are a mixture of different conformations that all contain N-C terminal interactions, with a few congurations also containing C-C terminal interactions.  Monomer 1 primarily interacts through its central and Cterminal segments, while monomer 2 interacts through the Nand C-terminal regions.

Validation of dimer conformations
To validate the simulation results, as well as identify the experimentally relevant conformations, we used the Monte Carlo pulling approach to simulate AFM pulling experiments and to compare the simulated results with experimental data. 11 The rupture force and interaction patterns for the top candidates are presented in Fig. 5. The interaction patterns of the simulated dissociation processes were normalized with respect to the experimentally obtained contour lengths. Experimentally observed values for the dissociation force was 56.6 AE 20.5 pN (STD), approximated using a Gaussian distribution, with a twopeak distribution of the interaction pattern favoring interaction in the N-terminal and central regions. 11 The dimer obtained following analysis of the MD simulations on Anton (Fig. S2 †), named "MD" on Fig. 5, shows a distinct three-peak interaction pattern, with majority of interactions located in the N-terminal and central regions of the proteins, while the dissociation force is 36.5 AE 18.4 pN. Dimer conformations from the two most populated clusters (cluster 1 and cluster 2) from Fig. 3 (following the aMD simulations) produce rupture forces of 61.7 AE 27.5 pN and 35.6 AE 17.7 pN, respectively. Similar to the MD dimer, the two aMD conformations produce the distinct three-peak interaction pattern. However, cluster 1 shows a very large C-terminal peak. However, the dissociation of dimer cluster 1 is statistically similar to the experimentally observed results, using a non-parametric twosample Kolmogorov-Smirnov with 0.05 signicance.
To characterize the interaction pattern and the dissociation force of a dimer (within brils) with high b-structure content, we created two dimer conformations from NMR structures of Ab40 brils with different morphologies (PDB IDs: 2LMN (wildtype) and 2MVX (Osaka mutant)). The dissociation patterns for the two bril dimers are signicantly different compared to experimental results and the results obtained for the MD and aMD dimers, Fig. S5. † Although, the bril dimers contain the three-peak interaction pattern, the patterns are signicantly different; for the 2LMN dimer the majority of interactions happen within the central part of the dimers, while for 2MVX dimer the interactions are dominated by the N-and Cterminals.  Each dataset shows a scatter plot of normalized distance vs. force, a histogram of force (blue), and a histogram of normalized distance (red); normalization was performed based on the experimentally observed contour lengths. Peak values, obtained using Gaussian distribution function, are presented above each peak of the histogram. Cluster 01 and 02 are conformations from Fig. 3, while "MD" is the most populated cluster following MD simulation. Statistical analysis was performed using twosample Kolmogorov-Smirnov test with 0.05 significance level; only cluster 01 was statistically similar to the experimental data set, with p > 0.066.

Discussion
Although the behavior of Ab peptides have been subject to numerous studies, our present study presents a number of new features about the Ab40 dimers. The equilibrated monomer structure, used as the initial conformation to characterize the dimerization process, is in line with recent data obtained using NMR and simulations of the Ab proteins, which showed that the monomer has unstructured segments and can assume helical secondary structure. 10,81 Another interesting feature of the monomer structure is the presence of a turn on each side of the central helix, the turn conformation is believed to be the rst folding event in the structural transition of Ab proteins and important for the aggregation process. 5,82,83 Our computational analysis of the aggregation of Ab40 into dimers reveal a broad range of peptide structures and very dynamic feature of the dimers. In particular, we did not identify signicant b-conformation in the monomers within the dimer, Fig. 3. The interaction of two monomers lead to conformational transitions within the monomers, accompanied by change in local structure of the peptides, leading to the formation of a stable dimer. Investigation of the dimer structures showed that the Ab40 dimers exhibit a heterogeneous ensemble of conformations that contain a diverse number of structures. Dimers are stabilized by interactions in the N-terminal region (residues 5-12), in the central hydrophobic region (residues [16][17][18][19][20][21][22][23], and in the Cterminal region (residues 30-40); with inter-peptide interactions focused around the N-and C-terminals. The 20 most populated clusters are a mixture of different conformations that all contain N-C terminal interactions, with a few congurations also containing C-C terminal interactions. Similar observations regarding the interaction pattern of Ab40 dimers have been presented by Tarus et al. 84 The authors showed that regions, identied in our simulations, were also interacting and important for the stability of the dimer. However, unlike the dimer conformations identied here, their dimers contained signicant b-structure content. More recent ndings from the same group 85 show that the dimers structures are more diverse and do not contain a large extent of bstructure, and that the dimer is stabilized by nonspecic interactions. The low b-structure content is in agreement with our ndings, and also can explain the role of structural plasticity in the interactions of Ab oligomers with binding partners and ultimately their toxicity. The structural exibility of the dimer may also play a role in the aggregation progression, where the free energy cost of transitioning from less ordered states is much less compared to dimeric states with high level of ordered b-structures.
We validated the dimer conformations using MCP approach to simulate the force-induced dissociation of the dimers and compared the obtained force and interaction patterns with experimental results. The simulations were performed at conditions identical to the experimental ones 11 and allowed us to identify the dimer conformation of cluster 01 as the most probable dimer probed during experiments. Probing of dimer conformations with high degree of b-structure content, adopted from bril structures, showed that such dimers produce dissociation forces signicantly different compared to experiment as well as our simulated dimers. Furthermore, the interaction pattern of high bcontent dimers was strongly shied compared to experiments.
Comparing the Ab40 dimer with the Ab42 dimer, analyzed in our recent publication, 69 shows that the Ab42 dimer is stabilized by interactions in the central region (residues 16-23) between the two monomers as well as C-C terminal interactions through residues 30-36 and 36-42. Interactions also occur between the N-termini of the two monomers. Suggesting that the two extra C-terminal amino acids of Ab42 affects the spatial orientation within the dimer as well as the inter-peptide interaction pattern of the monomers. These nding are in line with recent nding about the monomeric Ab peptides, 81 which show that while the two alloforms show similar structural elements, their conformations are different and that in turn has a large effect on the inter-molecular interactions of the peptides.

Conclusions
All-atom MD simulations allowed us to structurally characterize Ab40 dimers. Structures were organized in clusters, with $54% represented in the 20 most populated clusters. Dimers are stabilized by interactions in the central hydrophobic region (residues 17-21) as well as N-C terminal interactions (residues 1-10 and 30-40), through hydrophobic interactions and H-bonds. Ab40 dimer did not show parallel in-register b-sheet structures, as one may expect based on the known structures of Ab brils. Comparison of Ab40 to Ab42 dimers revealed differences in their conformations. Ab40 dimers are stabilized primarily by interactions within the central hydrophobic regions and the N-terminal regions, whereas Ab42 dimers are stabilized by interactions in the central and Cterminal regions. Ab40 dimers are more dynamic compared to Ab42 dimers. Comparison, based on MCP simulations, between Ab40 and Ab42 showed that overall, the dimers of both alloforms exhibit similar interaction strengths. However, the interaction maps, and more importantly the patterns, clearly show differences.

Conflicts of interest
Authors declare no competing interests.