Philippe Derreumaux

Viet Hoang Man

Junmei Wang

Phuong H Nguyen

Tau R3-R4 Domain Dimer of the Wild Type and Phosphorylated Ser356 Sequences. I. In Solution by Atomistic Simulations

In Alzheimer's disease, neurofibrillary lesions correlate with cognitive deficits and consist of inclusions of tau protein with cross-β structure. A stable dimeric form of soluble tau has been evidenced in the cells, but its high-resolution structure is missing in solution. We know, however, that cryo-electron microscopy (c-EM) of full-length tau in the brain of an individual with AD displays a core of eight β-sheets with a C-shaped architecture spanning the R3-R4 repeat domain, while the rest of the protein is very flexible. To address the conformational ensemble of the dimer, we performed atomistic replica exchange molecular dynamics simulations on the tau R3-R4 domain starting from the c-EM configuration. We find that the wild type tau R3-R4 dimer explores elongated, Ushaped, V-shaped and globular forms rather than the C-shape. Phosphorylation of Ser356, pSer356, is known to block the interaction between the tau protein and the amyloid-β42 peptide. Standard molecular dynamics simulations of this phosphorylated sequence for a total of 5 microseconds compared to its wild type counterpart show a modulation of the population of β-helices and accessible topologies, and a decrease of intermediates near the fibril like conformers.

INTRODUCTION

The intracellular formation of tau tangles and the extracellular formation of amyloid-β (Aβ) senile plaques are the two hallmarks in the brain of Alzheimer's disease (AD) patients. [START_REF] Selkoe | The Amyloid Hypothesis of Alzheimer's Disease at 25 Years[END_REF][START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simulations Complement Experimental Studies[END_REF] The misfolding and aggregation of these two intrinsically disordered proteins (IDPs) pass through cellular membranes, spread across different brain regions and talk to each other. [START_REF] Ittner | Amyloid-β and Tau--A Toxic Pas de Deux in Alzheimer's Disease[END_REF][START_REF] Mohamed | Spreading of Tau Pathology in Alzheimer's Disease by Cell-to-Cell Transmission[END_REF][START_REF] Sanders | Distinct Tau Prion Strains Propagate in Cells and Mice and Define Different Tauopathies[END_REF] In human brain, the Aβ peptides consist mainly of 40 and 42 amino acids but also of many truncated and Nterminally modified Aβ versions. [START_REF] Wirths | Emerging Roles of N-and C-terminally Truncated Aβ Species in Alzheimer's Disease[END_REF] Full-length tau (2N4R, 441 residues) consists of a charged N-terminal region, a proline-rich region PRR followed by four repeats (labelled R1 to R4) that under physiological conditions bind to the axonal microtubule, and a C-terminal region. Tau, predominantly found in axons, is present as six isoforms ranging from 352 amino acids to its full length. Tau has as many as 84 putative phosphorylation sites targeting serine, threonine and tyrosine amino acids mainly localized in the PPR and C-terminal regions. [START_REF] Goedert | Propagation of Tau Aggregates and Neurodegeneration[END_REF] Tau isolated from patients shows on average 20 modified phosphorylation sites, and the ratios of isoforms and the level of phosphorylation contribute to its normal and abnormal activity. [START_REF] Goedert | Propagation of Tau Aggregates and Neurodegeneration[END_REF][START_REF] Wang | in Physiology and Pathology[END_REF][START_REF] Fichou | The Elusive Tau Molecular Structures: Can We Translate the Recent Breakthroughs into New Targets for Intervention?[END_REF][START_REF] Hefti | Tau Phosphorylation and Aggregation in the Developing Human Brain[END_REF] Disease-linked modifications very often favour the occurrence of the tau domain repeat R1-R4 spanning residues 244-368, also called K18, [START_REF] Spillantini | Pathology and Neurodegeneration[END_REF] and this region recapitulates much of the aggregation property of tau441 in animal models. [START_REF] Stöhr | A 31-residue Peptide induces Aggregation of tau's Microtubule-Binding Region in Cells[END_REF] The K19 tau construct includes the three repeats R1, R3 and R4. There is experimental evidence that the two hexapeptides called PHF6* (residues 275-280 in R2) and PHF6 (residues 306-311 in R3) are essential for tau aggregation and amyloid formation. [START_REF] Mohamed | Spreading of Tau Pathology in Alzheimer's Disease by Cell-to-Cell Transmission[END_REF][START_REF] Von Bergen | Assembly of Tau Protein into Alzheimer Paired Helical Filaments Depends on a Local Sequence Motif ((306)VQIVYK(311)) Forming Beta Structure[END_REF] In addition, formation of fibrillar tau aggregates is enhanced in the presence of polyanions such as heparin and RNA molecules and can be seeded in the presence of preformed tau aggregates in vitro and in cells. [START_REF] Frost | Propagation of Tau Misfolding from the Outside to the Inside of a Cell[END_REF] Cryo-electron microscopy (c-EM) of the tau 2N4R protein from the brain of an individual with AD has revealed the amyloid fibril core of eight β-strands adopting a C-shaped architecture spanning residues 306-378 and thus including the R3-R4 domain, and no well-defined structure elsewhere. Two types of tau fibrils with in-register parallel β-sheets were revealed with different packing and orientation of the filaments. [START_REF] Fitzpatrick | Cryo-EM Structures of Tau Filaments from Alzheimer's Disease[END_REF] In contrast, in vitro heparin-fibrillized 2N4R tau displays a different picture. The rigid core spans R2-R3 and adopts a hairpin-like conformation, R1 and R4 repeats with β-strand character are semi-rigid, PRR displays large-amplitude anisotropic motions, and the two termini are flexible. [START_REF] Dregni | In vitro 0N4R Tau Fibrils Contain a Monomorphic β-sheet Core Enclosed by Dynamically Heterogeneous Fuzzy Coat Segments[END_REF] However, double electron-electron resonance spectroscopy showed that heparininduced tau filaments are markedly different from AD filaments. [START_REF] Fichou | Heparininduced Tau Filaments are Structurally Heterogeneous and Differ from Alzheimer's Disease Filaments[END_REF] Looking at the fibrils of tau fragments, the N-acetylated PHF6-amide peptide forms parallel βsheets by its own. [START_REF] Goux | The Formation of Straight and Twisted Filaments from Short Tau Peptides[END_REF] The fragment 306-336 spanning the R3 repeat forms cross-β structure with parallel β-sheets and three β-strands, and is able to induce aggregation of tau's microtubule-binding region in cells. [START_REF] Stöhr | A 31-residue Peptide induces Aggregation of tau's Microtubule-Binding Region in Cells[END_REF] Tau oligomers interactions with Aβ peptides have been explored by numerous experimental techniques. Soluble Aβ dimers isolated from AD brains induce tau hyperphospholyration. [START_REF] Jin | Soluble Amyloid beta-protein Dimers Isolated from Alzheimer Cortex directly Induce Tau Hyperphosphorylation and Neuritic Degeneration[END_REF] Guo et al. suggested that the intracellular binding of soluble Aβ40/42 peptides to soluble nonphosphorylated 2N4R tau protein promotes tau phosphorylation and Aβ nucleation using ELISA, Western blotting and surface plasmon resonance. [START_REF] Guo | Abeta and Tau Form Soluble Complexes that may Promote Self Aggregation of both into the Insoluble Forms Observed in Alzheimer's Disease[END_REF] Using multiple biophysical experiments, Wallin et al. showed that the full-length tau protein of 441 amino acids blocks in vitro amyloid formation of the Aβ40 peptide at the oligomeric stage and the Aβ40 monomer remains unstructured in the presence of tau. [START_REF] Wallin | The Neuronal Tau Protein Blocks in Vitro Fibrillation of the Amyloid-β (Aβ) Peptide at the Oligomeric Stage[END_REF] Interestingly, phosphorylation of Thr212, Ser214, Ser356 and Ser396 completely blocks Aβ42 binding. [START_REF] Guo | Abeta and Tau Form Soluble Complexes that may Promote Self Aggregation of both into the Insoluble Forms Observed in Alzheimer's Disease[END_REF] As NMR structures of tau monomer and oligomers are not available, computer simulations were used with various force fields and protein/solvent representations to characterize the dominant states of full-length and tau constructs. In contrast to many simulations on Aβ peptides, 2,22-29 a few simulations were carried out on tau. Small oligomers of PHF6 fragment, [START_REF] Levine | Regulation and Aggregation of Intrinsically Disordered Peptides[END_REF][START_REF] Matthes | Driving Forces and Structural Determinants of Steric Zipper Peptide Oligomer Formation Elucidated by Atomistic Simulations[END_REF] and the dimer of the fragment spanning residues 273-284 (containing PHF6* and called R2/wt), [START_REF] Eschmann | Signature of an Aggregation-prone Conformation of Tau[END_REF] were investigated by atomistic MD simulations. The self-assembly of individual and binary mixtures of the tau fragments R3/wt (spanning residues 306-317 and containing PHF6) and R2/wt was characterized by replica exchange molecular dynamics simulations (REMD). [START_REF] Ganguly | Tau Assembly: The Dominant Role of PHF6 (VQIVYK) in Microtubule Binding Region Repeat R3[END_REF] Computational formation of PHF6 fibril was also studied by much simpler protein representations. [START_REF] Smit | Primary Fibril Nucleation of Aggregation Prone Tau Fragments PHF6 and PHF6[END_REF][START_REF] Cheon | Influence of Temperature on Formation of Perfect Tau Fragment Fibrils using PRIME20/DMD Simulations[END_REF] Combining NMR spectroscopy and the conformational algorithm Flexiblemeccano, Akoury et al. remodelled the equilibrium ensemble of tau K18 monomer by an aggregation enhancer polyglutamic. [START_REF] Akoury | Remodeling of the Conformational Ensemble of the Repeat Domain of Tau by an Aggregation Enhancer[END_REF] Tau441 monomer conformation was investigated using Monte Carlo simulations, a coarse-grained (CG) model, repulsive Lennard-Jones interactions and single molecule fluorescence resonance energy transfer-derived mean inter-residue separations constraints. It was found that the mean radius of gyration (Rg) of tau increases from 5.1 to 6.0 ± 0.5 nm at 293 K upon addition of heparin. [START_REF] Nath | The Conformational Ensembles of α-synuclein and tau: Combining Single-molecule FRET and Simulations[END_REF] Baul et al. characterized the structural features of IDPs from 20 to 441 amino acids and were able using CG simulations to reproduce the experimental Rg, and the full scattering intensity profiles in excellent agreement with small-angle X-ray scattering experiments. [START_REF] Baul | Sequence Effects on Size, Shape, and Structural Heterogeneity in Intrinsically Disordered Proteins[END_REF] Recently, Popov et al. used atomistic discrete molecular dynamics (DMD) guided by structural proteomics data resulting from short-range cross-linkers (reagents) and mass spectrometry experiments to characterize the monomeric structure of tau441 in solution. [START_REF] Popov | Insight into the Structure of the "Unstructured[END_REF] The most populated clusters were found to deviate by less than 0.3 nm RMSD (root mean square deviation) from the DMD structures by unbiased atomistic MD simulations of 50 ns in 3 replicates. In solution, tau consists of an ensemble of compact globular conformations with transient a-helices and β-strands, with the C-terminal and N-terminal regions confined on both sides on the core. Interestingly, the R3-R4 domain contains seven out of eight beta-strands (exception being the β2 strand) of the fibril core reported by c-EM. This result runs in contrast to atomistic REMD simulations of tau K18 and K19 monomers, using 48 replicas each of 100 ns starting from 24 different structures obtained by multiple approaches including on-line servers, albeit high β-sheet content and large hydrophobic surface exposure of the motifs PHF6* and PHF6 were identified. [START_REF] Luo | Structural Insight into Tau Protein's Paradox of Intrinsically Disordered Behavior, Self-Acetylation Activity, and Aggregation[END_REF] Finally, Nussinov et al. showed that filaments of 3R and 4R tau proteins are distinct [START_REF] Siddiqua | Conformational Basis for Asymmetric Seeding Barrier in Filaments of Three-and Four-Repeat Tau[END_REF] and studied cross-seeding and conformational selection between 3R and 4R human tau proteins. [START_REF] Yu | Cross-seeding and Conformational Selection between Three-and Four-Repeat Human Tau Proteins[END_REF] They also investigated how single mutations changed the population of four-repeat tau fibrils, [START_REF] Meyer | Single Mutations in Tau Modulate the Populations of Fibril Conformers through Seed Selection[END_REF] and demonstrated that the C-shaped form is stable only for R3-R4, while R1-R2 adopts a linear shape using all-atom 100 ns MD simulations of octamers starting from the c-EM C-shaped structure. [START_REF] Li | The Distinct Structural Preferences of Tau Protein Repeat Domains[END_REF] As the formation of tau dimers appears to be the rate-limiting step for tau aggregation in vitro, [START_REF] Schweers | Oxidation of Cysteine 322 in the Repeat Domain of Microtubule-associated Protein Tau Controls the in vitro Assembly of Paired Helical Filaments[END_REF] a stable dimeric form of soluble tau has been evidenced in the cells, [START_REF] Wegmann | Formation, Release, and Internalization of Stable Tau Oligomers in Cells[END_REF] and a lot of the tau protein detected in cerebrospinal fluid from AD patients has a molecular weight similar to dimers and oligomers of truncated tau, [START_REF] Takeda | Seed-competent High-molecular-weight Tau Species Accumulates in the Cerebrospinal Fluid of Alzheimer's Disease Mouse Model and Human Patients[END_REF] knowledge of the equilibrium tau dimer ensemble is critical. Because folding tau2N4R dimer from randomly chosen states is impossible at an atomic level of description by computer simulations, [START_REF] Tuffery | Flexibility and Binding Affinity in Protein-Ligand, Protein-Protein and Multi-Component Protein Interactions: Limitations of Current Computational Approaches[END_REF] here we resort to the c-EM structure of the R3-R4 repeat for starting our REMD simulations in explicit solvent. This structure is reasonable as a starting point for the dimer, as the tau441 conformation in solution [START_REF] Popov | Insight into the Structure of the "Unstructured[END_REF] and the c-EM configuration [START_REF] Fitzpatrick | Cryo-EM Structures of Tau Filaments from Alzheimer's Disease[END_REF] display very high similarity of β-strands.

Then, using the most populated REMD centroids, the impact of phosphorylation at Ser356 known to block Aβ42 peptide, 20 is analysed by using 5 µs MD simulations at 305 K on both the wild type and its phosphorylated tau306-378 dimeric counterpart.

METHODS

We used the GROMACS version 2018 for MD and REMD simulations. [START_REF] Abraham | GROMACS: High Performance Molecular Simulations through Multi-Level Parallelism from Laptops to Supercomputers[END_REF] The all-atom force field AA-OPLS [START_REF] Jorgensen | The OPLS [optimized potentials for liquid simulations] Potential Functions for Proteins, Energy Minimizations for Crystals of Cyclic peptides and Crambin[END_REF] was used for both sequences because AA-OPLS parameters are available for the phosphorylated serine amino acid. [START_REF] Rapp | Hydrogen Bond Strengths in Phosphorylated and Sulfated Amino Acid Residues[END_REF] Tau306-378 is capped by acetyl and amide at N-and C-termini, and at pH 7 has deprotonated Glu and Asp, protonated Arg and Lys, and neutral His with a protonated Ne atom.

All the simulation parameters such as the time-step, the calculation of electrostatic interactions and van der Waals interactions with cut-off distances, as well as the algorithm to control the temperature are described in Ref. 52. The TIP3P water model was used in all cases. [START_REF] Jorgensen | Comparison of Simple Potential Functions for Simulating Liquid Water[END_REF] The c-EM structure of WT tau306-378 dimer, shown on Figure 1, was first centred in a very large octahedron box of dimension 10.3 nm, i.e., with a water shell of 1.5 nm. In total, the system consists of 27 139 water molecules, 10 chloride ions, and a total number of 83 719 atoms. The WT system was first minimized and equilibrated at 305 K by a 1 ns MD simulation with backbone and side-chain restraints, and explored by a first REMD simulation with 60 replicas each of 30 ns from 305 to 370 K. The REMD simulation was then pursued using 40 replicas from 305 to 370 K, each of 35 ns, in a smaller water box (octahedron box of dimension 8 nm), resulting in 38 776 atoms. As 305 and 370 K are that the two temperatures shared by the two REMD, the starting structure of a replica at a given temperature in the second REMD was selected from the last structure of the first REMD, which has the closest temperature to the given temperature. Reducing the water box size reduces the CPU time significantly, 8 ns of the second REMD simulations requiring 1 week by using 40 nodes, and 24 cores per node.

Each of the five dominant REMD-identified free energy minima was subject to 1µs MD simulation for WT (with 10 chloride ions), and 1µs MD for pSer356 (with 8 chloride ions) in a large octahedron box of dimension 10.4 nm, resulting on average in 84 808 atoms. Overall, REMD data were recorded every 100 ps, and MD data were recorded every 10 ps. A total of 495 000 MD snapshots per system, the first 50 ns being excluded, was used to determine the physical impact of phosphorylation.

The time-averaged secondary structure composition of all systems was predicted using Stride program. [START_REF] Frishman | Knowledge-based Protein Secondary Structure Assignment[END_REF] An intermolecular and intra-molecular sidechain contact between hydrophobic residues or a side chain salt-bridge contact between two charged residues was considered formed when the smallest distance is less than 0.46 nm. A hydrogen bond was defined when the distance between the donor and the acceptor is shorter than 0.35 nm, and the angle of donorhydrogen -acceptor is larger than 135 0 . Rg, Ca RMSD and surface accessible to solvent (SASA) were calculated with GROMACS tools. The trajectories were also analysed by computing free energy landscapes and distributions of specific intramolecular and intermolecular side chain -side chain contacts.

RESULTS AND DISCUSSION

The atomistic REMD simulation in explicit solvent used an average of 50 replicas for 65 ns. Though equilibrium is not reached, we can however assess conformational sampling by the average of exchange rates between consecutive replicas (24% for the first REMD, and 20% for the second REMD, data not shown), and a qualitative trend can be given on the REMD-derived conformational ensemble of the WT tau R3-R4 dimer at 305 K.

The Rg of the dimer and each monomer is 2.3 nm in the fibril. The Rg distributions of the dimer, chain 1 and chain 2 at 305 K show a first peak at 1.75, 1.62 nm and 1.72 nm (populations of 22, 28, 25%), a second peak at 2.5 nm of lower populations (10%) followed by a tail up to 2.9 nm (Figure 2). The secondary structure (SS) content of the dimer at 305 K, characterized by β-sheet: 36 ± 4, turn: 21 ± 3 and coil: 43 ± 4 %, varies substantially from the SS in the fibril: β-sheet: 57.5, turn: 8 and coil: 34.3 %. The β-sheet, coil and turn contents along the sequence of the two chains are shown in Figure 3. We identified 8 β-sheet regions as in the fibril structure. In the fibril, the β1 to β8 strands or sheets encompass residues 306-311, 313-322, 327-331, 336-341, 343-347, 349-354, 356-363 and 368-378, respectively. In the predicted structures, the β1, β3, β4 and β8 regions are maintained with a β-sheet averaged over the expected residues > 50%, and it is noted that the PHF6 region averages about 75% of β-sheet (Figure 3A). The β5 region keeps only the two residues 333-334 out of six residues for 70%, and the β2, β6 and β7 regions are only populated 40% (β6 and β7) and 30% (β2) of the simulation. The β-sheets β4 and β5, and the β-sheets β5 and β6 are separated by turn contents > 50% (Figure 3B), whereas the remaining β-sheets are separated by coils (Figure 3C).

Figure 4 shows the free energy landscape (FEL) at 305 K projected on the total number of side chain contacts and the Ca RMSD with respect to the fibril structure. Averaged over 0.5 ns MD simulation at 305 K, the dimer in its fibril state has 121 side-chain contacts. Two-dimensional Hartigan-Wong k-means algorithm [START_REF] Hartigan | Algorithm AS 136: A K-Means Clustering Algorithm[END_REF] was used to classify all REMD generated conformations into to five clusters, and their populations were calculated using the size of each cluster as described in Ref. 52. The five clusters of similar populations, the exception being the fifth cluster of 9%, have a number of side chain contacts varying from 112 (S5) to 148 (S3) and RMSD varying from 1.17 (S4) to 1.45 nm (S2). Increasing the number of clusters by k-means would be more accurate, as we identify few states of low populations deviating by 0.9 and 1.7 nm, but our second goal is to determine the impact of phosphorylation on the dominant states and, as shown below, these centroids are very dynamic.

The clusters S1, S3 and S4 have seven β-sheets, β8 at the C-terminus lacking, S2 displays eight β-sheets with shorter lengths compared to the fibril structure, e.g., β8 encompassing residues 371-376 vs. 368-378 in the fibril state, and S5 has the first five β-sheets. The positions of the β-sheets in each cluster are given in Supporting Information. All clusters have a β-sheet content of 42%, the exception being S5 with 27%. Their morphologies vary from the c-EM C-shape as seen by the differences in the intra-and inter-molecular contact maps between the configurations (Figure S1). The c-EM C-shape is characterized by one β-sheet spanning β1-β2-β8, a loop spanning residues 323-335 and 355-367 terminated by a β-helix spanning residues 336-354.

Figure 4 shows that the S1 state is the most extended, characterized by a dynamic β1-β2-β8 motif (β8 sheet RMSD of 0.24 nm with the PHF6 β1-sheet partially formed), a conserved β-helix motif (RMSD of 0.21 nm) and a much less curved loop region than in c-EM. S2 with a V shape has the β1-β2-β8 motif (β1-β2-β8 RMSD of 0.35) and a different loop conformation inducing a change in the orientation of the β-helix (pointing outward rather than inward). The S3 and S5 states are globular and compact with almost all of the features of the c-EM configuration altered: the β-helix motif is dynamic (RMSD of 0.30 nm in S3 and 0.34 nm in S5), the β1-β2 sheet is fluctuating (RMSD of 0.38 nm in S3, and 0.88 nm in S5) and the β8 sheet is either well-formed in S3 (RMSD of 0.29 nm) or destabilized in S5 (RMSD of 0.5 nm). S3 is also characterized by a six-stranded βsheet spanning the β-sheets β1, β8 and β6. Finally, S4 has a U-shaped configuration with a labile β1-β2-β8 sheet (RMSD of 0.54 nm) and a well-defined β-helix. Overall, the PHF6 motif is well maintained in S2, S3 and S4, and the β-helix motif is very well maintained in S4, S1 and S2 (RMSD from 0.15 to 0.21 nm).

Next, each of the five centroids was used as a starting conformation for 1µs MD simulation at 305 K on the WT and its pSer356 counterpart. Figure S2 shows the Ca RMSD deviation as a function of time for each run. The states S3 and S5 remain near their starting structures (RMSD of 0.5 nm), and the states S1, S2 and S4 reach 1.0 nm after 1µs, independently of the sequence. The secondary structure compositions averaged over the time interval 50-1000 ns of all runs are given in SI. The β-sheet content decreases from 35.5 to 26% (run S1) and to 30.7% (run S3), but averaged over all simulations, the β-sheet content decreases slightly from 30.9 to 27.6% and the coil content increases moderately from 42.5 to 46.6% upon phosphorylation.

Differences in the conformational ensembles explored by the five WT and pSer356 1 µs MD simulations can be pictured by the broad distributions of the intra-molecular distances between the Cβ atoms of V306-F378 (N-and Cterminus), L325-V363 (centre of the loop region) and V339-I354 (end-to-end distance of β-helix) averaged over the time interval 50-1000 ns of all runs (Figure S3). The two distributions, proximal to the site of phosphorylation 356, with distances between 0.4 and 2.5 nm, are more impacted than the V306-F378 distribution, with distances between 0.4 and 3.0 nm. There is however no significant impact of phosphorylation on the three distributions. The dynamics of both systems can also be characterized by the distributions of intermolecular Ca distances characterizing the interface of six β-sheets (Figure 5). PSer356 reduces the population of contacts by a factor of 2-3 (e.g., I354-I354, panel 5d), a factor of 1.5 (V306-V306, panel 5a), a factor of 5 (V339-V339, panel 5c), and augments the population of formed contacts between V363-V363 by a factor of 1.2 (panel 5e).

The 1 µs MD-generated snapshots of all runs are shown in Figure 6. Upon phosphorylation, there are substantial reorganizations in the final extended S1 state (RMSD of 1.3 nm between the two runs, with the pSer356 and WT S1 final states deviating by 1.8 and 1.1 nm from the c-EM conformation). The V-shaped S2 state remains formed in the final conformations (RMSD of 1.1 nm between the two runs, with the pSer356 and WT S2 final states deviating by 1.2 and 1.0 nm from the c-EM conformation). Upon pSer356, the U-shaped S4 state converts to a globular shape vs. a V-shape in WT, RMSD of 1.5 nm between the two runs, and final structures deviating by 1.2 nm from the c-EM configuration. Starting from the S3 and S5 globular states, pSer356 leads to smaller structural rearrangements in the final states (RMSD of 0.7 nm in run S3 and 0.4 nm in run S5, with the pSer356 and WT S3, S5 final states deviating by 1.3-1.5 nm from the c-EM conformation).

The intra-and inter-molecular side chain -side chain probability contact maps using the last 50 ns of the ten simulations are shown in Figures S4-S6. Considering probabilities greater than 0.8, the introduction of two negative charges at residue 356 reduces by 10% the total number of intra-and inter-peptide side chain contacts averaged over all simulations.

The pSer356-induced conformational change on the secondary structure along the sequence can be analysed into two groups: simulations S3/S5, and simulations S1/S2/S4 as the final MD S3 and S5 states remain globular and therefore pSer356 stabilize these topologies, while the S1, S2 and S4 intermediates between the fibrillar and globular forms are impacted by pSer356.

PSer356 converts a U shape to a globular state (S4 run), stabilizes the V-shape intermediate (S2 run) or further extends the elongated intermediate state (S1).

At the residue level in the S3/S5 simulations, phosphorylation does not impact much the turn per residue (Figure S7b). PSer356 decreases the β-sheet signal of residues 315-319 (β2 strand), residues 336-337 (β4 strand) and residues 353-354 (β6 strand) from 50 to 10-30%, and increases the β-sheet of residues 343-345 (β5 strand) from 20 to 55% (Figure S7a). This is accompanied by changes of the coil and turn contents in the same three regions (Figures S7b-S7c). We note that a few residues of the β1, β3 and β8 sheets are formed 100% of the time.

PSer356 has different effects on the secondary structure of the S1/S2/S4 simulations. Phosphorylation decreases the β-sheet signal of residues 336-340 (β4 strand) from 50% to 15%, and increases the β-sheet signal of the C-terminal of β7 strand and of the residues 371-327 of β8 strand from 50 to 90% (Figure S8a). In contrast to the S3/S5 results, only the β3-sheet is formed 100% of the time and the β2-sheet percentage is close to zero, inducing variations in the turn and coil characters of many residues (Figure S8b-c).

Taken together our results indicate that both the WT and pSer356 systems exist in many different intra-molecular conformations and display distinct heterogeneous interfaces between the two chains. The diverse populations of dimeric structures help understand the oligomer diversity observed by single molecule fluorescence studies during the heparin-induced aggregation of the repeat region of tau. [START_REF] Kjaergaard | Oligomer Diversity during the Aggregation of the Repeat Region of Tau[END_REF] The fact that pSer356 reduces the population of intermediates near the fibril like conformers is also consistent with recent in vitro experiments reporting that WT K18 develops seeding activity more rapidly than pSer356 K18 in the presence of heparin. [START_REF] Haj-Yahya | Site-Specific Hyperphosphorylation Inhibits, Rather than Promotes, Tau Fibrillization, Seeding Capacity and Its Microtubule Binding[END_REF] Another important aspect of our 5 µs MD simulations on each species is that the β-helix motif covering residues 336-354 displays a RMSD between 0.15 and 0.4 nm in 30% of the WT conformational ensemble, and this population decreases to 5% in the pSer356 ensemble. Figure S9 shows a representative MD structure from the S4 simulation superposed on the c-EM configuration (RMSD of 0.15 nm). The specific residue-residue interactions stabilizing this motif are described in Ref. 15. This result is important as the β-helix region has been identified in the prion-forming domain of HET-s and plays a crucial role for infection. [START_REF] Wasmer | Amyloid Fibrils of the HET-s(218-289) Prion Form a Beta Solenoid with a Triangular Hydrophobic Core[END_REF] This motif is mediated by specific interactions and several specific residues in this β-solenoid core can modulate prion efficacy and propagation. [START_REF] Daskalov | Contribution of Specific Residues of the β solenoid Fold to HET-s Prion Function, Amyloid Structure and Stability[END_REF] This indicates that the effect of pSer356 is deleterious for the dimer in terms of β-helix stability and scaffold for prion-like properties, while pSer356 has been suggested to be beneficial in opening the structure of the monomer. [START_REF] Popov | Insight into the Structure of the "Unstructured[END_REF] It is to be noted that our results on the phosphorylation of Ser356 cannot be generalized to other phosphorylation positions and a specific combination of phosphorylation sites making tau more or less prone to aggregation phosphorylation sites. [START_REF] Fichou | The Elusive Tau Molecular Structures: Can We Translate the Recent Breakthroughs into New Targets for Intervention?[END_REF] In this context, Mancera et al. found by MD simulations that the double pThr231/pSer235 phosphorylation pattern induced an increase of transient alpha-helix and polyproline II conformations in the monomer of tau225-250, [START_REF] Lyons | Molecular Dynamics Simulation of the Phosphorylation-induced Conformational Changes of a Tau Peptide Fragment[END_REF] while we do not observe almost any helices in both our WT and pSer356 systems. Similarly, Xu et al. found by using a multi-scale computational procedure that hyperphosphorylation in the N-and C-terminal regions of tau 441 filament models increases the solvent accessibility of the repeat R1-R4 domain. [START_REF] Xu | How Does Hyperphopsphorylation Promote Tau Aggregation and Modulate Filament Structure and Stability?[END_REF] Our simulations show that the SASA averaged over our models does not change much: 106.6 nm 2 for fibril state, 102 nm 2 for WT dimer and 104 nm 2 for pSer356 dimer.

CONCLUSIONS

Our atomistic REMD and MD simulations indicate that the configurations available to the dimer of WT tau R3-R4 domain spanning residues 306-378 encompass elongated, U-shaped, V-shaped and globular structures rather than the c-EM C-shaped conformation determined for amyloids fibrils of the full-length tau protein.

Comparison of the molecular ensembles shows that phosphorylation of Ser356 not only perturbs the population of the β-helix motif spanning residues 336-354, but also induces distinct heterogeneous interfaces between the two chains compared to its WT counterpart. pSer356 modulates the population of distinct architectures by increasing the number of globular shapes and is deleterious in stabilizing intermediates near the fibril like conformers. It will be interesting to determine whether (a) the recent force fields designed for folding structured and intrinsically disordered proteins, [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomistic Simulations. II. In Aqueous Solution[END_REF] and (b) the N-and C-terminal flanking regions may lead to different equilibrium structures.

The interest of having structural ensemble of tau dimers is that we can now look at the mechanistic interactions between Aβ42 and tau dimers at seminal steps of AD pathogenesis. This future study based on coarse-grained models, [START_REF] Sterpone | The OPEP Protein Model: From Single Molecules, Amyloid Formation, Crowding and Hydrodynamics to 31 DNA/RNA Systems[END_REF][START_REF] Derreumaux | Generating Ensemble Averages for Small Proteins from Extended Conformations by Monte Carlo Simulations[END_REF] which represents a significant step compared to previous MD simulations focusing on the interactions of very short [START_REF] Do | Interactions between Amyloid-β and Tau Fragments Promote Aberrant Aggregates: Implications for Amyloid Toxicity[END_REF] and of the truncated Aβ17-42 peptide and one specific tau fragments of both partners, [START_REF] Miller | Synergistic Interactions between Repeats in Tau Protein and Aβ Amyloids may be Responsible for Accelerated Aggregation via Polymorphic States[END_REF] may be useful for the rational design of inhibitors of tau and Aβ toxicities. [START_REF] Doig | Inhibition of Protein Aggregation and Amyloid Formation by Small Molecules[END_REF][START_REF] Doig | Why Is Research on Amyloid-β Failing to Give New Drugs for Alzheimer's Disease?[END_REF][START_REF] Zheng | Inhibition of the Self-Assembly of Aβ and of Tau by Polyphenols: Mechanistic Studies[END_REF] ASSOCIATED CONTENT

Supporting Information

Additional REMD simulation results: β-sheet locations in the five centroids, and intra-molecular and inter-molecular contact maps of the predicted centroids and the c-EM configuration. Additional MD simulation results of the wild-type and the phosphorylated Ser356 dimer: backbone RMSD from the REMD-predicted centroids, secondary structure compositions, distribution of three intra-molecular distances, contact maps of all final MD generated structures, secondary structure profiles along the sequence, and a representative MD structure. The material is available free of charge via the Internet at http://pubs.acs.org.

Figure 1 .

 1 Figure 1. Structure of the cryo-EM R3-R4 tau fibril spanning the amino acids 306-378 from Alzheimer's patient brain. We report important hydrophobic residues stabilizing the C-shape form (V306-F378, L325-V363 and V339-I354), the site of phosphorylation (S356), and the 8 b-sheets. Intra-molecular distances between Cb atoms of V306-F378, L325V363 and V339-I354 are 1.0, 0.66 and 0.57 nm, respectively. Inter-molecular distance between Ca atoms of V306-V306, L325-L325, V339-V339, I354-I354, V363-V363 and F378-F378 is 0.49 nm. The b-helix spans residues 336-354, that is the b4-b6 region.

Figure 2 .

 2 Figure 2. Distributions of the radius of gyration of each chain and the dimer of WT tau306-378 at 305 K using the time interval 5-65 ns from REMD simulation.

Figure 3 .

 3 Figure 3. Secondary structure along the sequence of the WT tau306-378 dimer at 305 K from REMD simulations. The helix content consisting of 3-10 helix is not shown as only a signal spanning the residues 315-323 is observed in chain B with a population of 3%. Chains A and B are in black and red.

Figure 4 .

 4 Figure 4. Free energy landscape of the WT tau306-378 dimer at 305 K projected on the number of inter side chain contacts and the Ca RMSD with respective to the native fibril structure. Representative structures of the five free energy basins, S1 to S5, are shown with their populations. A ball shows the N-terminus, chain A is in blue and chain B is in red. The colour scale is in kcal/mol.

Figure 5 .

 5 Figure 5. Distributions of intermolecular distances between the Ca atoms of two specific residues averaged over the five MD simulations of WT and pSer356. For each simulation we consider the time interval 50 ns to 1000 ns

Figure 6 :

 6 Figure 6: Initial REMD centroids (S1 to S5) and their final MD structures for the WT and pSer356 systems. The N-terminal amino acids are visualized by red and blue balls, and the Ca positions of the two Ser356 and pSer356 residues by green balls. The Ca RMSD deviation between the final WT and pSer356 structures is 1.3 nm (run S1), 1.1 nm (run S2), 0.8 nm (run S3), 1.5 nm (run S4) and 0.4 nm (run S5).

ACKNOWLEDGMENTS

We thank the support of CINES (grants A0050710633 and A0060710174), University of Paris, and the French State (Grant "DYNAMO", ANR-11-LABX-0011-01, and "CACSICE", ANR-11-EQPX-0008). PD thanks the support of CNRS and Université de Paris.

AUTHOR INFORMATION

Corresponding Author *E-mail: philippe.derreumaux@tdtu.edu.vn.

ORCID

Junmei Wang : 0000-0002-9607-8229 Viet Hoang Man : 0000-0002-8907-6479 Phuong H. Nguyen: 0000-0003-1284-967X Philippe Derreumaux: 0000-0001-9110-5585

Notes

The authors declare no competing financial interest.

TOC Graphics


Son Tung Ngo

Phuong H Nguyen

Philippe Derreumaux

Stability of Aβ11-40 Trimers with Parallel and An;parallel β-Sheet Organiza;ons in a Membrane-Mimicking Environment by Replica Exchange Molecular Dynamics Simula;on

The aggrega;on of the Amyloid (Aβ) pep;de of 39-43 amino acids into plaques is observed in the brain of Alzheimer's disease (AD) pa;ents, but the mechanisms underlying the neurotoxicity of Aβ oligomers are s;ll elusive. One suggested ini;al mechanism is related to the implica;ons of amyloid membrane interac;ons, but characteriza;on of these assemblies is challenging by experimental means. In this study, we have explored the stability of a trimer of Aβ11-40 in parallel and an;parallel βsheet structures for the wild-type sequence and its F20W mutant in a DPPC membrane using atomis;c replica exchange molecular dynamic simula;ons. We show that both the U-shape organiza;on and the assembly of β-hairpins are maintained in the membrane and are resistant to the muta;on F20W. In contrast the models are destabilized by the F19P muta;on. Overall, our results indicate that these two assemblies represent minimal seeds or nuclei for the forma;on of either amyloid fibrils, a variety of βbarrel pores or various aggregates for many Aβ sequences in a membrane-mimicking environment.

INTRODUCTION

Several millions of people are affected by Alzheimer's disease (AD). [START_REF] Querfurth | Alzheimer's Disease[END_REF] There is a general consensus that the low molecular weight oligomers of the amyloid-beta (Aβ) pep;de consis;ng of 39-43 amino acids ini;ate a series of events leading to neuronal death. [START_REF] Selkoe | The Amyloid Hypothesis of Alzheimer's Disease at 25 Years[END_REF][START_REF] Doig | Why Is Research on Amyloid-β Failing to Give New Drugs for Alzheimer's Disease?[END_REF] High-resolu;on knowledge of Aβ oligomers interac;ng with the membrane is experimentally challenging because these interac;ons and the oligomer popula;ons are heterogeneous, very dynamic and vary with membrane composi;on and Aβ amino acid sequence. [START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simula;ons Complement Experimental Studies[END_REF] Amyloid oligomer affinity of Aβ and other amyloid proteins with membrane and their interac;ons have been explored by a variety of experimental techniques such as transmission electron microscopy (TEM), atomic force microscopy (AFM), nuclear magne;c resonance (NMR), ion mobility -mass spectrometry, small angle neutron scagering, infrared and fluorescence spectroscopies and electric recording. [START_REF] Kayed | on of Lipid Bilayers is a Common Conforma;on-Dependent Ac;vity of Soluble Amyloid Oligomers in Protein Misfolding Diseases[END_REF][START_REF] Liu | on of Amyloid Beta Protein Misfolding and Fibrillogenesis by a Lipid Oxida;on Product[END_REF][START_REF] Arispe | velel Ca;on Channels Formed by Alzheimer Disease Amyloid beta-protein (Abeta P-(1-40)) in Bilayer Membranes[END_REF][START_REF] Gillman | vity and Architecture of Pyroglutamate-Modified Amyloid-β (AβpE3-42) Pores[END_REF][START_REF] Fusco | Structural Basis of Membrane Disrup;on and Cellular Toxicity by α-Synuclein Oligomers[END_REF] From these observa;ons, several Aβ-induced membrane effects have been captured and three generic models have been proposed: the carpe;ng model with accumula;on of amyloid oligomers on membrane surface leading to bilayer deforma;on, the detergent model where Aβ oligomers have an important detergent-like effects on lipid membrane bilayers and remove lipid molecules from the bilayer, and the amyloid pore hypothesis. [START_REF] Kayed | on of Lipid Bilayers is a Common Conforma;on-Dependent Ac;vity of Soluble Amyloid Oligomers in Protein Misfolding Diseases[END_REF][START_REF] Berthelot | What Does Make an Amyloid Toxic: Morphology, Structure or Interac;on with Membrane?[END_REF][START_REF] Bode | Amyloid-β Oligomers Have a Profound Detergent-like Effect on Lipid Membrane Bilayers, Imaged by Atomic Force and Electron Microscopy[END_REF] Among the long list of experimental results, Aβ monomers have much lower membrane affinity than the small oligomers, [START_REF] Sarkar | Thermodynamically Stable Amyloid-β Monomers Have Much Lower Membrane Affinity Than the Small Oligomers[END_REF] membrane-bound tetramer and trimer Aβ oligomers correlate with toxicity towards cultured neurons, [START_REF] Jana | Membrane-bound Tetramer and Trimer Aβ Oligomeric Species Correlate with Toxicity towards Cultured Neurons[END_REF] and a single-molecule study reported that trimers and tetramers may be the smallest Aβ40 oligomers in the anionic lipid bilayers and could be the origin of neurotoxicity. [START_REF] Ding | β-Amyloid (1-40) Pep;de Interac;ons with Supported Phospholipid Membranes: A Single-molecule Study[END_REF] Carulla et al. reported, based on sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE), electric recording, circular dichroism (CD) and NMR experiments, that Aβ42 tetramers assemble into β-barrels with an inner pore diameter of 0.7 nm in a membrane-mimicking environment, but it is not the case for Aβ40. [START_REF] Serra-Ba;Ste | Aβ42 Assembles into Specific β-Barrel Pore-Forming Oligomers in Membrane-Mimicking Environments[END_REF] Recently, ion mobility -mass spectrometry reveals the forma;on of β-barrel shaped Aβ42 hexamers in a membrane-mimicking environment based on comparing experimental and calculated collision cross-sec;ons, while Aβ40 mostly formed dimers and trimers. [START_REF] Österlund | ve Ion Mobility-Mass Spectrometry Reveals the Forma;on of β-Barrel Shaped Amyloid-β Hexamers in a Membrane-Mimicking Environment[END_REF] Channel-like annular oligomers formed by Aβ pep;des were also reported by AFM with inner cavity pores of 2.0-2.5 nm. [START_REF] Lashuel | Disease: Amyloid Pores from Pathogenic Muta;ons[END_REF] Very interes;ngly, the trodusquemine molecule enhances Aβ42 aggrega;on, but suppresses toxicity by inhibi;ng Aβ oligomers binding to cell membranes. [START_REF] Limbocker | Trodusquemine Enhances Aβ42 Aggrega;on but Suppresses Its Toxicity by Displacing Oligomers from Cell Membranes[END_REF] Due to the transient character of amyloid oligomers, amyloid membrane interac;ons either on the surface or inserted into membrane models have mo;vated the use of computer simula;ons based on different levels of protein, lipid and solvent representa;ons. [START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simula;ons Complement Experimental Studies[END_REF][START_REF] Sahoo | onal Insights into Lipid Assisted Pep;de Misfolding and Aggrega;on in Neurodegenera[END_REF][START_REF] Zhang | Molecular Simula;ons of Amyloid Structures, Toxicity, and Inhibi[END_REF][START_REF] Dong | Binding of Protofibrillar Aβ Trimers to Lipid Bilayer Surface Enhances Aβ Structural Stability and Causes Membrane Thinning[END_REF] A molecular dynamics (MD) simu-la;on showed that protofibrillar Aβ trimers might be the smallest seeding nucleus on the self-assembled monolayer surfaces. [START_REF] Wang | Alzheimer Abeta(1-42) Monomer Adsorbed on The Self-Assembled Monolayers[END_REF] Aβ dimeriza;on on a membrane surface was also inves;gated by all-atom MD simula;ons. [START_REF] Davis | A Molecular Dynamics Study of The Early Stages of Amyloid-beta(1-42) Oligomeriza;on: The Role of Lipid Membranes[END_REF] Based on atomis;c MD simula;ons of dimers and pentamers of Aβ17-42, Jang et al.

suggested that a trimer with a strand-turn-strand (U-shaped) fibrillar mo;f is the minimal oligomer size to insert into the membrane. [START_REF] Jang | Mechanisms for the Inser;on of Toxic, Fibril-like β-Amyloid Oligomers into the Membrane[END_REF] Brown and Bevan performed MD simula;ons of Aβ42 tetramer in the presence of a pure POPC or cholesterol-rich rak model membrane and observed the forma;on of rodlike structures. [START_REF] Brown | Molecular Dynamics Simula;ons of Amyloid β-Pep;de (1-42): Tetramer Forma;on and Membrane Interac[END_REF] Feng et al. carried out atomis;c MD simula;ons of Aβ42 dimers differing in the orienta;on of the two pep;des to study the structural stability and damaging effect on a DPPC membrane, they suggested one stable dimeric unit. [START_REF] Feng | Study of Structural Stability and Damaging Effect on Membrane for four Aβ42 Dimers[END_REF] Strodel and Wales used basin-hopping global op;miza;on tempering and an oligomer genera;on procedure to iden;fy the most stable structures for the Aβ42 pep;de monomer and oligomers (up to octamer) inserted into an implicit lipid bilayer. [START_REF] Strodel | Transmembrane Structures for Ahzeihmer's Abeta(1-42)-oligomers[END_REF] Of par;cular interest is that the most stable conforma;on of the monomer embedded in the implicit membrane displays the U-shaped mo;f observed in synthe;c Aβ40 amyloid fibrils in vitro, and they proposed Aβ42 pore models composed of tetramer to decamer subunits. Atomis;c MD and poten;al of mean force simula;ons reported that Aβ11-42 pep;de oligomers larger than dimers are more likely to lead to lipid deforma;on and water channels in a POPC membrane. [START_REF] Xiang | on of the Interac;on of Amyloid β Pep;de (11-42) Oligomers with a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) Membrane Using Molecular Dynamics Simula;on[END_REF] Recently, we designed atomic structures of β-barrel Aβ40 and Aβ42 tetramers in a membrane model. [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomis;c Simula;ons. I. In a Bilayer Mimicking a Neuronal Membrane[END_REF] These models consist of four β-hairpins spanning approximately residues 14-35; this hairpin has already been discussed with a non-negligible probability by dimer simula;ons of Aβ40 and Aβ42 pep;des, [START_REF] Tarus | Structures of the Alzheimer's Wild-Type Aβ1-40 Dimer from Atomis;c Simula;ons[END_REF][START_REF] Cao | Self-Assembly Pathways of β-Sheet-Rich Amyloid-β(1-40) Dimers: Markov State Model Analysis on Millisecond Hybrid-Resolu;on Simula;ons[END_REF][START_REF] Man | High-Resolu;on Structures of the Amyloid-β 1-42 Dimers from the Comparison of Four Atomis;c Force Fields[END_REF] and Aβ fragments [START_REF] Chebaro | Structures and Thermodynamics of Alzheimer's Amyloid-beta Abeta(16-35) Monomer and Dimer by Replica Exchange Molecular Dynamics Simula;ons: Implica;on for Full-length Abeta Fibrilla;on[END_REF][START_REF] Chebaro | Structures of Aβ17-42 Trimers in Isola;on and with Five Small-Molecule Drugs Using a Hierarchical Computa[END_REF] in aqueous solu;on. Using extensive replica exchange molecular dynamics (REMD) simula;ons, the tetrameric β-barrel made of two dis;nct β-hairpins is dras;cally destabilized for Aβ40 with respect to Aβ42 in a bilayer mimicking a neuronal membrane. [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomis;c Simula;ons. I. In a Bilayer Mimicking a Neuronal Membrane[END_REF] As β-barrels consis;ng of one layer of strands have been evidenced by X-ray micro-crystallography for an 11-residue pep;de [START_REF] Laganowsky | Atomic View of a Toxic Amyloid Small Oligomer[END_REF] and by simula;ons for various short-amyloid pep;des using mul;ple representa;ons and sampling techniques in aqueous solu;on, [START_REF] Melquiond | Structures of Soluble Amyloid Oligomers from Computer Simula;ons[END_REF][START_REF] Bellesia | Effect of Beta-sheet Propensity on Pep;de Aggrega[END_REF][START_REF] De Simone | Low Molecular Weight Oligomers of Amyloid Pep;des Display Beta-barrel Conforma-;ons: A Replica Exchange Molecular Dynamics Study in Explicit Solvent[END_REF][START_REF] Sterpone | The OPEP Protein Model: From Single Molecules, Amyloid Forma;on, Crowding and Hydrodynamics to DNA/RNA Systems[END_REF][START_REF] Sun | β-barrel Oligomers as Common Intermediates of Pep;des Self-Assembling into Cross-β Aggregates[END_REF] we found using enhanced sampling and the CHARM-M36m-TIP3P force field designed for intrinsically disordered proteins [START_REF] Huang | CHARM-M36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins[END_REF] that Aβ42 barrel tetramer, but not its Aβ40 counterpart, is likely to exist in aqueous solu;on. [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomis;c Simula;ons. II. In Aqueous Solu;on[END_REF] In the present study, based on previous experimental and theore;cal results on other systems, namely the co-existence of mul;ple intramolecular structures, we have tested by enhanced sampling simula;ons whether Aβ trimers with U-shape (fibril-like) conforma;ons or resul;ng from hairpin assembly are likely states for the wild-type sequence embedded in a membrane. We emphasize that folding and self-assembly of a trimer of Aβ from randomly chosen conforma;ons in a membrane are not againable at an atomis;c level, free of any collec;ve variables. [START_REF] Sahoo | onal Insights into Lipid Assisted Pep;de Misfolding and Aggrega;on in Neurodegenera[END_REF][START_REF] Tuffery | Flexibility and Binding Affinity in Protein-Ligand, Protein-Protein and Mul;-Component Protein Interac;ons: Limita;ons of Current Computa;onal Approaches[END_REF] To further reduce the computer ;me, the N-terminus (residues 1-10) is excluded as this region is evidenced to be disordered in a membrane-mimicking environment, [START_REF] Serra-Ba;Ste | Aβ42 Assembles into Specific β-Barrel Pore-Forming Oligomers in Membrane-Mimicking Environments[END_REF] and the N-truncated Aβ9-42 pep;de forms toxic ion channel in the lipid bilayers. [START_REF] Jang | Disordered Amyloidogenic Pep;des May Insert into the Membrane and Assemble into Common Cyclic Structural Mo;fs[END_REF] MD and REMD simula;ons are ideal tools to examine the impact of specific muta;ons on the conforma;onal ensemble of Aβ pep;des. We demonstrated by atomis;c REMD simula;ons that A2V and A2T muta;ons dras;cally change the conforma;onal ensemble of Aβ monomer and dimer in aqueous solu;on. [START_REF] Nguyen | Impact of the A2V Muta;on on the Heterozygous and Homozygous Aβ1-40 Dimer Structures from Atomis;c Simula;ons[END_REF][START_REF] Nguyen | Familial Alzheimer A2V Muta;on Reduces the Intrinsic Disorder and Completely Changes the Free Energy Landscape of the Aβ1-28 Monomer[END_REF][START_REF] Nguyen | on Mechanism of Alzheimer Aβ40 Pep;des: The High Content of Intrapep;de-Stabilized Conforma;ons in A2V and A2T Heterozygous Dimers Retards Amyloid Fibril Forma;on[END_REF] Nussinov and coworkers have determined by MD simula;ons the impact of single muta;ons and N-terminally modified truncated Aβ variants on the stability of double-sheets pores in membranes. [START_REF] Gillman | vity and Architecture of Pyroglutamate-Modified Amyloid-β (AβpE3-42) Pores[END_REF][START_REF] Jang | Disordered Amyloidogenic Pep;des May Insert into the Membrane and Assemble into Common Cyclic Structural Mo;fs[END_REF] In this work, we have examined the effect of the muta;ons F20W and F19P. This choice is mo;ved by the fact that these muta;ons are located in the central hydrophobic core (CHC) spanning residues 17-21, recognized as driving Aβ β-sheet and amyloid fibril forma;on. [START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simula;ons Complement Experimental Studies[END_REF] The subs;tuted tryptophan at amyloid-Aβ residue 20 experiences different environments aker fibril forma;on compared to the WT sequence in vitro, but both WT and F20W pep;des display similar aggrega;on kinetics. [START_REF] Mcdonough | Subs;tuted Tryptophans at Amyloid-β(1-40) Residues 19 and 20 Experience Different Environments aker Fibril Forma;on[END_REF] In contrast, the F19P muta;on forms small Aβ aggregates and prevents the forma;on of the nucleus and therefore blocks fibril forma;on in vitro. [START_REF] Bernstein | Amyloid beta-Protein: Monomer Structure and Early Aggrega;on States of Abeta42 and its Pro19 Alloform[END_REF][START_REF] Daly | Conforma;onal Changes in Amyloid-beta (12-28) Alloforms Studied Using Ac;on-FRET[END_REF] By using MD simula;ons, Nussinov et al. found that F19P destabilizes the pore ability of Aβ17-42 and Aβ42 pep;des, pores consis;ng of annular Ushaped β-sheets, and this muta;on prevents ions permea;ng across the bilayer. [START_REF] Jang | Disordered Amyloidogenic Pep;des May Insert into the Membrane and Assemble into Common Cyclic Structural Mo;fs[END_REF] Here, through the applica;on of REMD simula;ons to Aβ11-40 WT and its F20W mutant starting from our two β-sheet organiza;ons, and MD simula;ons with WT and F19P sequences, we can validate our models and determine their robustness.

MATERIALS AND METHODS

Ini;al structures of the parallel and an;parallel β-sheets

The parallel (P) Aβ11-40 trimer with U-shaped conforma;ons was extracted from the Aβ11-40 amyloid fibril structure. [START_REF] Ber;Ni | A New Structural Model of Aβ40 Fibrils[END_REF] The an;parallel (AP) trimer with β-hairpin conforma;ons was extracted from our Aβ beta-barrel [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomis;c Simula;ons. I. In a Bilayer Mimicking a Neuronal Membrane[END_REF] by dele;ng the hairpin 4; that is our barrel consists of the assembly of two types of hairpins (hairpin 1 and hairpins 2/3 having different intramolecular structures). All pep;des were subs;tuted at posi;on 20 by a tryptophan or at posi;on 19 by a proline using PyMOL tool. [START_REF] Schrödinger | The PyMOL molecular graphics system[END_REF] The (x, y, z) dimensions of the lipid bilayers are: 6.418 x 6.444 x 4.00 nm for the parallel Aβ β-sheet model and 6.766 x 6.792 x 4.00 nm for the an;parallel Aβ model. All systems were solvated by a 3-par-;cle water model. The parallel F20W trimer is centered in a rectangular box of nm and consists of 125 DPPC molecules, 3923 water molecules, 3 Na + ions for a total number of 16,987 atoms vs. 16,975 atoms for its parallel WT counterpart. The an;-parallel F20W and WT systems are centered into a rectangular box of nm. The AP F20W system comprises 124 DPPC molecules, 3736 water molecules, and 3 Na + atoms for a total of 18,296 atoms, vs. 18,284 for the AP WT system. The ini;al AP and P trimer structures are shown in Fig-

ure 1.
REMD and MD simula;ons REMD simula;ons were carried out using GROMACS version 5.1.3, 53 the united-atom force field GRO-MOS 53a6 [START_REF] Oostenbrink | A Biomolecular Force Field Based on the Free Enthalpy of Hydra;on and Solva;on: The GROMOS Force-Field Parameter Sets 53A5 and 53A6[END_REF] for the pep;des, the Berger force field [START_REF] Berger | Molecular Dynamics Simula;ons of a Fluid Bilayer of Dipalmitoylphospha;dylcholine at Full Hydra;on, Constant Pressure and Constant Temperature[END_REF] for the DPPC lipid bilayer and the SPC water model. [START_REF] Berendsen | Intermolecular Forces[END_REF] The pep;des at pH 7 have NH3 + and CO2 -termini, deprotonated Glu and Asp, protonated Arg and Lys, and neutral His with a protonated Nepsilon atom. Following earlier computa;onal studies, simula-;ons were performed with periodic boundary condi;ons, a ;me step of 2 fs using LINCS, the velocity Verlet integrator, the Nose-Hoover thermostat, electrosta;c interac;ons were calculated using the par-;cle mesh Ewald (PME) method and a cut-off of 0.9 nm, and Van der Waals interac;ons used a cut-off of 0.9 nm. [START_REF] Ngo | In Silico Studies of Solvated F19W Amyloid β (11-40) Trimer[END_REF][START_REF] Ngo | Replica Exchange Molecular Dynamics Study of the Amyloid Beta (11-40) Trimer Penetra;ng a Membrane[END_REF] Star;ng from the ini;al conforma;on, each system was minimized using steepest descent method using weak backbone constraints followed by 500 ps of NVT simula;ons with a weak harmonic force on the protein atom posi;ons and the system was further relaxed by 1 ns free of any restraints at 324 K. Each relaxed system was then subject to REMD. Parallel F20W Aβ11-40 trimer was inves;gated using 32 replicas ranging from 321 to 423 K, each replica for 350 ns, as for the parallel WT Aβ11-40 trimer. [START_REF] Ngo | Replica Exchange Molecular Dynamics Study of the Amyloid Beta (11-40) Trimer Penetra;ng a Membrane[END_REF] The an;parallel WT and F20W Aβ11-40 trimers used 28 replicas between 321 and 408 K, each replica for 350 ns. Temperature values for the replicas are given in Supplementary Informa-;on (SI). Exchanges between replicas were agempted every 1ps.

The two β-sheet organiza;ons were also subject to MD simula;ons of 250 ns at 324 K with the WT and F19P sequences star;ng from the most stable predicted REMD conforma;ons of the WT sequence.

In these simula;ons, we used the CHARMM36m force field for the proteins and lipids, and the modified TIP3P force field for water. [START_REF] Huang | CHARM-M36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins[END_REF]

Analysis

An intermolecular and intramolecular side-chain contact is defined when the smallest distance between two side-chain residues of any chains is shorter than 0.45 nm. The hydrogen bond is considered formed when the distance between the donor and the acceptor is shorter than 0.35 nm, and the angle of donor -hydrogen -acceptor is larger than 135 0 . A side chain salt-bridge is defined when the distance between two charged groups is smaller than 0.46 nm. The radius of gyra;on (Rg) is computed 6.418 × 6.444 × 7.597 6.766 × 6.792 × 7.097

with GROMACS tools. The secondary structure composi;ons are calculated using DSSP package. [START_REF] Touw | A Series of PDB-Related Databanks for Everyday Needs[END_REF] The collision cross sec;on (CCS) of each system is calculated using the trajectory method of the IMPACT program. [START_REF] Marklund | Collision Cross Sec;ons for Structural Proteomics[END_REF] The free energy landscape is constructed using GROMACS tool "sham" projected on the backbone root-mean-square devia;on (RMSD) using the full sequences and the number of intermolecular side-chain contacts (SC). The lipid order parameters were calculated using the formula:

where C is carbon, D is deuterium, and θ is the MD/REMD-averaged angle between the molecular axis given by Ci-1 -Ci+1 vector and the bilayer normal.

RESULTS AND DISCUSSION

REMD simula;on convergence and data analysis of the parallel WT trimer at 324 K have already been described in Ref. 58; 324 K is selected because membrane DPPC lipid bilayers have a phase transi;on at 315 K. For the three new REMD simula;ons, the average of exchange rates between neighboring replicas is on the order of 21% (Figure S1) and there is a sa;sfactory propaga;on of the 1st (black) and last (28 th or 32th in red) replicas over the temperature range (Figure S2). The convergence of each new simula;on at 324 K is demonstrated by the nice overlap of the distribu;ons of the four RMSD, Rg, CCS and β-sheet metrics using the intervals 200-280 ns and 200-350 ns (Figures S3-S5).

There are clear differences in the distribu;ons between the four systems at 324 K. Upon F20W muta-;on, the mean Rg value increases from 1.42 ± 0.02 to 1.49 ± 0.02 nm in the parallel organiza;on, but remains constant in the an;parallel organiza;on (1.47 ± 0.02 nm for WT, 1.44 ± 0.04 nm for F20W).

This conforma;onal change in the parallel architecture is further illustrated by the mean CCS values ranging from 13.42 ± 0.31 nm 2 in WT vs. 14.19 ± 0.31 nm 2 in F20W. In contrast, the averaged CCS values remain centered at 14.35 ± 0.40 nm 2 for WT and F20W in the an;parallel architecture.

In the parallel structure, the β-sheet content changes upon F20W muta;on increasing from 40 ± 7% in WT to 47 ± 4%, accompanied by a reduced coil content of 51 ± 4% in F20W vs. 57 ± 7% in WT. The βsheet content is higher in an;parallel structure, independently of the sequence, that is 50 ± 6% for WT and 52 ± 5% for F20W, with a coil content amoun;ng to 48 ± 7% in WT and 45 ± 6% in F20W. The propensity to form specific secondary structures along each amino acid averaged over the three chains is shown in Figure 2 for the four systems. The results reveal that in the parallel organiza;on the F20W muta;on increases mainly the β-strand percentage of the CHC region and residue 30, while the coil and turn contents remain rela;vely unmodified. In the an;parallel organiza;on, the secondary structure profiles of the WT and F20W pep;des superpose rela;vely well, except the turn content of

S CD = 1 2 3cos 2 θ -1
residues 25-26 (increase from 15% in WT to 30% in F20W) and the coil content of residues 24-28 (decrease of 10% from WT to F20W). Note that in all systems, the alpha-helix content is 0% and the turn content is 2-3%.

To inves;gate how the F20W muta;on impacts the conforma;onal ensemble, we looked at sidechain and H-bond contact maps, and found that the maps change ligle upon muta;on star;ng either from the parallel or the an;parallel configura;ons (data not shown). Table 1 lists the mean number and standard devia;on of the total number of intramolecular and intermolecular for the side chain and Hbond contacts in the four systems. The values of the four metrics do not change from WT to F20W in the an;parallel structure. It is found however that the mean value of intramolecular H-bonds is reduced by 50% from WT to F20W in the parallel structure. Varia;on is also observed for the percentage of the intramolecular salt-bridge D23-K28 formed varying from 30% (WT) to 2% (F20W) in the parallel configura;on and from 6% (WT) to 16% (F20W) in the an;parallel configura;on, but not for the intermolecular salt-bridges K16-D23 and K16-D22 (Table 2).

A clustering analysis was performed using a backbone RMSD cutoff of 0.3 nm using the full sequences. The number of clusters is reduced from 25 to 8 upon F20W muta;on star;ng from the parallel β-sheet configura;on, and from 13 to 8 upon F20W muta;on star;ng from the an;parallel sheet configura;on, indica;ng that the F20W muta;on confers less conforma;onal freedom of the Aβ pep-;des in the membrane. Figures 3 and4 show the free energy landscape of the four systems projected on the backbone RMSD and the number of intermolecular side-chain contacts, along with the representa;ve structure of each significant free energy minimum. The structural characteris;cs of these minima are described in Table 3.

For the trimers in parallel structure (Figure 3), we find seven dominant states for the WT sequence designated as WP1-WP7 with popula;ons varying between 19% (WP4) and 6% (WP1). All seven minima totaling 66% of the full conforma;onal space preserve the U-shaped conforma;ons with a rather constant CCS value (13.2 -13.8 nm 2 ) and a β-sheet content varying between 56 (WP2) and 34 (WP1) %. The minima differ, however, in their posi;ons within the membrane and the residues located in the extracellular part: residues 11-13 and 25-28 (WP2, WP4, WP5 and WP7 for a popula;on of 42%) or the same previous residues with the N-terminal hydrophobic residues 39 and 40 (WP1, WP3 and WP6 for a popula;on of 22%). Upon F20W muta;on, there are five dominant states represen;ng 79% of the full conforma;onal space, with MP3 (44%), MP1 (16%) and MP4 (13%), represen;ng a popula;on of 73%, that have high β-sheet content (46-54%), and CCS values varying between 13.4 (MP3) and 15.1 (MP1) nm [START_REF] Selkoe | The Amyloid Hypothesis of Alzheimer's Disease at 25 Years[END_REF] . Overall, compared to the WT sequence, the F20W muta;on increases the β-sheet content, the CCS value of some minima and the number of conforma;ons with the residue 40 in the extracellular part (63%), but does not impact the fluidity of the membrane (see Figure S6).

It is interes;ng that the Aβ11-40 trimer with fibrillar conforma;on remains stable in the membrane.

This finding further supports previous MD simula;ons, having much less sampling capabili;es than our REMD, proposing that the Aβ17-42 trimer with a strand-turn-strand (U-shaped) fibrillar mo;f is the minimal oligomer size to insert into a DOPC membrane. [START_REF] Jang | Mechanisms for the Inser;on of Toxic, Fibril-like β-Amyloid Oligomers into the Membrane[END_REF] Taken with the MD simula;on results of Aβ17-42 dimer, [START_REF] Jang | Mechanisms for the Inser;on of Toxic, Fibril-like β-Amyloid Oligomers into the Membrane[END_REF] our REMD simula;on results in a DPPC membrane strongly suggest that the trimer in parallel structure might be a nucleus for larger cross-β aggregates within the membrane. Our finding that the F20W muta;on slightly modifies the free energy landscape of the WT sequence, although inducing change in local flexibility and reducing heterogeneity of the conforma;on ensemble, is reminiscent of Aβ40 F20W aggrega;on kine;cs in aqueous solu;on that reported a difference in the inner core and homogeneity of the fibril. [START_REF] Mcdonough | Subs;tuted Tryptophans at Amyloid-β(1-40) Residues 19 and 20 Experience Different Environments aker Fibril Forma;on[END_REF] Of interest also is that the impact of F20W muta;on is much less severe than the A21G muta;on, known to lead to early-onset AD, [START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simula;ons Complement Experimental Studies[END_REF] which was found on the same system to destabilize much more the U-shaped conforma;on. [START_REF] Ngo | The Effects of A21G Muta;on on Transmembrane Amyloid Beta(11-40 Trimer : An In Silico Study[END_REF] Next we characterized the trimers in an;parallel structure (Figure 4). For the WT sequence, we find five dominant states designated as WA1-WA5 with three states of equal popula;on (23%). Upon F20W muta;on, there are two states MA1-MA2 of equal popula;on (47%). Although the seven states differ in terms of CCS, Rg, CCS, RMSD, number of intermolecular side-chain contacts, loca;on of β-strands, they all display at a coarse-grained level the same generic topology, that is a four-stranded β-sheet made of Upon F20 W muta;on, the third hairpin is misaligned and more disordered with a significant increase of the loop region. The hairpin 3 consists of β-strands spanning residues 16-22 and 31-37 and a loop spanning residues 23-29 in MA1, residues 14-21 and 30-39 (strands) and 22-27 (loop) in WA2, residues 18-20 and 32-35 (strands) and 22-30 (loop) in MA3 and residues 14-22, 31-39 (strands) and 23-30 (loop) in WA4. As a consequence of these conforma;onal differences, the number of extracellular residues varies muta;on, with the N-terminus (residues 11-14) and loop region (residues 23-27) for the WT sequence, and the more of less same N-terminus and loop region residues along with the two Cterminus residues for the F20W sequence. As for the trimer in parallel structure, the trimer in an;parallel structure for the WT and F20W sequence does not impact the lipid order parameters of the membrane (Figure S6).

It is interes;ng that at least two well-packed and formed β-hairpins stabilized by a more disordered hairpin remain formed inserted into the membrane for the WT and F20W sequences. These two hairpins have however dis;nct intramolecular conforma;ons, spanning for example residues 16-38 and 13-35, and differ therefore from the hairpin spanning residues 17-36 proposed by Strodel and Wales, [START_REF] Strodel | Transmembrane Structures for Ahzeihmer's Abeta(1-42)-oligomers[END_REF] and Graslund et al. [START_REF] Österlund | ve Ion Mobility-Mass Spectrometry Reveals the Forma;on of β-Barrel Shaped Amyloid-β Hexamers in a Membrane-Mimicking Environment[END_REF] This finding makes it clear that this trimer represent a stable seed for crea;ng a large variety of pores made of a single wall (single layer) of β-hairpins (4-mers, 6-mers and 12-mers) within the membrane.

It is important to determine to what extent our results depend on other muta;ons and the force field. To this end, we performed MD simula;ons of the WT and F19P trimers with the charmm36m/ TIP3P-modified force field star;ng from the most populated REMD structures from the two WT systems: WP4 (for the parallel structure) and WA4 (for the an;parallel structure). Our total MD trajectory of 1 microsecond at 324K for the four systems makes it clear that both WT trimers deviates ligle from their ini;al structures with a plateau at a RMSD of 0.30 nm from 100 to 250 ns, see (A) and (C) in Figure 5. In contrast, the F19P muta;on induces much larger RMSD devia;on at 250 ns: about 0.55-0.6 nm for F19P in parallel and an;parallel structures, see (B) and (D) in Figure 5. Figure 6 shows the representa-;ve structures of the 4 systems based on cluster analysis of the trajectories between 230 and 250 ns.

The results on the WT sequence are similar between the GROMOS53a6/Berger/SPC and the CHARM-M36m/TIP3P-modified force fields, small RMSD differences and differences of 7% of β-sheet content.

The result of our F19P simula;on star;ng from a U-shaped conforma;on helps understand why the impact of F19P subs;tu;on induces a collapse of the Aβ17-42 and Aβ42 pores. [START_REF] Jang | Disordered Amyloidogenic Pep;des May Insert into the Membrane and Assemble into Common Cyclic Structural Mo;fs[END_REF] The result of our F19P simula;on star;ng from three β-hairpins shows a clear trend, although the simula;ons have certainly not reached equilibrium, that is the F19P subs;tu;on clearly changes the packing and orienta;on of the hairpin assembly.

CONCLUSION

In summary, based on extensive REMD simula;ons on the WT and F20 Aβ11-40 trimer with GRO-MOS53a6/Berger/SPC force field, and MD simula;ons on the WT trimer with CHARMM36m/ TIP3Pmodified force field, we have demonstrated that the trimer of Aβ11-40 can coexist in a U-shape fibrillar organiza;on and an assembly of three dis;nct β-hairpins in a DPPC membrane. These results indicate that these two trimer assemblies are seeds (or nuclei) for the forma;on of larger aggregates with fibrillar conforma;ons, and the forma;on of larger fully closed β-barrels. Based on previous experimental [START_REF] Serra-Ba;Ste | Aβ42 Assembles into Specific β-Barrel Pore-Forming Oligomers in Membrane-Mimicking Environments[END_REF][START_REF] Österlund | ve Ion Mobility-Mass Spectrometry Reveals the Forma;on of β-Barrel Shaped Amyloid-β Hexamers in a Membrane-Mimicking Environment[END_REF][START_REF] Bode | Ion Channel Forma;on by Amyloid-β42 Oligomers but Not Amyloid-β40 in Cellular Membranes[END_REF] and theore;cal observa;ons, [START_REF] Nguyen | Tetrameric Aβ40 and Aβ42 β-Barrel Structures by Extensive Atomis;c Simula;ons. I. In a Bilayer Mimicking a Neuronal Membrane[END_REF] that is Aβ42 has a much higher propensity for amyloid pore than Aβ40, we can clearly assume that our two trimeric β-sheet assemblies will be more stable for Aβ11-42 than Aβ11-40. In contrast, our simula;ons show that the two models are destabilized by the F19P muta;on. he authors use the U-shape fibril structure as starting model for the trimer. Given the fact that there are more recent AB42 fibril structures resolved, such as the S-shape fibril by the Ishii or Linse groups, I am wondering if these conformations could also lead to a similar behavior (ref to be given).

β-barrels made of amyloid pep;des can form under various condi;ons, in aqueous solu;on, [START_REF] Laganowsky | Atomic View of a Toxic Amyloid Small Oligomer[END_REF] in a membrane, [START_REF] Serra-Ba;Ste | Aβ42 Assembles into Specific β-Barrel Pore-Forming Oligomers in Membrane-Mimicking Environments[END_REF][START_REF] Österlund | ve Ion Mobility-Mass Spectrometry Reveals the Forma;on of β-Barrel Shaped Amyloid-β Hexamers in a Membrane-Mimicking Environment[END_REF] and on the surface of carbon nanotubes. [START_REF] Fu | Induced Beta-Barrel Forma;on of the Alzheimer's Abeta25-35 Oligomers on Carbon Nanotube Surfaces: Implica;on for Amyloid Fibril Inhibi;on[END_REF] It is remarkable that the β-hairpin propensity of amyloid pep;des has been evidenced by solu;on-phase NMR of Aβ, alpha-synuclein, IAPP-affibody complexes, and triangular forms of β-hairpins and their packing to form hexamers and dodecamers have been observed by X-ray crystallography of macrocyclic β-hairpins in aqueous solu;on. [START_REF] Kreutzer | ng the Structures of Amyloid Oligomers with Macrocyclic beta-Hairpin pep;des : Insights into Alzheimer's Disease and Other Amyloid Diseases[END_REF] Whether these triangular assemblies can form in membranes remain to be determined. Also it is of interest to determine the effect of membrane composi;on such as cholesterol, monosialotetrahexosylganglioside (GM1), POPS lipid, and omega3 and omega6 fagy acids, [START_REF] Nasica-Labouze | Amyloid beta Protein and Alzheimer's Disease: When Computer Simula;ons Complement Experimental Studies[END_REF][START_REF] Dominguez | Impact of Membrane Lipid Composi;on on the Structure and Stability of the Transmembrane Domain of Amyloid Precursor Protein[END_REF][START_REF] Owen | Physiologically-Relevant Levels of Sphingomyelin, but not GM1, Induces a β-Sheet-Rich Structure in the Amyloid-β(1-42) Monomer[END_REF][START_REF] Lu | Amyloid-β(29-42) Dimeric Conforma;ons in Membranes Rich in Omega-3 and Omega-6 Polyunsaturated Fagy Acids[END_REF] on the stability of the two βsheet assemblies with parallel and an;parallel structures.

Finally, because that the amyloid landscape is highly heterogeneous and sensi;ve to experimental condi;ons, [START_REF] Jang | Disordered Amyloidogenic Pep;des May Insert into the Membrane and Assemble into Common Cyclic Structural Mo;fs[END_REF] we cannot neglect that, beyond β-sheet amyloid pores, pores made of helical Aβ pep;des may also exist. [START_REF] Arispe | velel Ca;on Channels Formed by Alzheimer Disease Amyloid beta-protein (Abeta P-(1-40)) in Bilayer Membranes[END_REF][START_REF] Österlund | ve Ion Mobility-Mass Spectrometry Reveals the Forma;on of β-Barrel Shaped Amyloid-β Hexamers in a Membrane-Mimicking Environment[END_REF][START_REF] Ngo | Probable Transmembrane Amyloid α-Helix Bundles Capable of Conduc;ng Ca 2+ Ions[END_REF][START_REF] Pannuzzo | cal Model and Mul;scale Simula;ons of Aβ Pep;de Aggrega;on in Lipid Membranes: Towards a Unifying Descrip;on of Conforma;onal Transi;ons, Oligomeriza;on and Membrane Damage[END_REF] ASSOCIATED CONTENT Suppor;ng Informa;on Temperatures in REMD simula;ons. Addi;onal figures S1-S6 report analysis on the three new REMD simula;ons: the exchange rates between consecu;ve replicas, the propaga;on of two replicas over the temperature index, the distribu;on of four metrics at two ;me intervals, and the ;me-averaged of the lipid order parameters. The material is available free of charge via the Internet at hgp://pubs.acs.org. TOC GRAPHICS

  two well-defined β-hairpins stabilized and recovered in part by the third hairpin. While in WT sequence, the N-and C-terminus of the third β-hairpin are well aligned with the four strands β-sheet; this hairpin kinks at residues 17, 18 and 33, and becomes perpendicular to the four-stranded β-sheet. Although the MA1 and MA2 structures are globally very similar, the β-strands in the four strands β-sheet span residues 16-23 and 29-36 (hairpin 1 in grey) and residues 14-22 and 27-34 (hairpin 1 in red) in MA1, and residues 16-22 and 31-38 (hairpin 1 in grey) and residues 13-22 and 26-35 (hairpin 2 in red) in MA1. Also, the loop of the third hairpin consists of residues 25-28 in MA1 and residues 24-29 in MA2; and there are side chain interac;ons between the CHC of the third hairpin and residues 31 and 32 of the second hairpin (in grey) in MA1 or residues 20, 31 and 35 of the second hairpin in MA2.

Figure 1 .

 1 Figure 1. Initial conformations. (A) Parallel F20W trimer with the side-chain atoms of W20 (shown in red); the residues 11-13 and 26-28 are in the extracellular part. (B) Antiparallel F20W trimer with the side-chain atoms of W20 shown in red; the extracellular residues consist of residues 24-25 of chain A, residues 11-14 of chain B, and residues 11-13 of chain; hairpin 1 in chain A is grey, hairpin 2 in chain B is orange and hairpin 3 in chain C is in yellow. C). The green ball denoted the N-terminus of each Aβ11-40 peptide. Tan spheres represent the phosphorus atoms of DPPC membrane. For simplicity, the solvent is not shown.

Figure 2 .

 2 Figure 2. The secondary structure composition along the amino acid sequence for the F20W and WT peptides in parallel (P, left panels) and anti-parallel (AP, right panels) organizations. The metrics of the WT peptide in P structure are taken from Ref. 58.

Figure 3 .

 3 Figure 3. The free energy landscape of the transmembrane Aβ trimers in parallel structure projected on the backbone RMSD and the number of intermolecular SC contacts. (A) WT trimer, in which, the seven main minima WP1-WP7 are located by black arrows at (RMSD; Number of SC) values of (0.83, 36.0), (0.71, 42.1), (0.63, 44.2), (0.59, 43.0), (0.45, 41.8), (0.50, 48.2), and (0.59, 37.5), respectively. (B) F20W trimer with the five main minima MP1-MP5 located at (0.60; 40.2), (0.54; 44.0), (0.45; 45.1), (0.60; 39.0) and (0.48; 37.9).

Figure 4 .

 4 Figure 4. The free energy landscape of the transmembrane Aβ trimers in anti-parallel structure projected on the backbone RMSD and the number of intermolecular SC contacts. (A) The WT system, in which, the main five minima WA1-WA5 are located at (RMSD; Number of SC) values of (0.54; 27.4), (0.54; 36.1), (0.62; 23.2), (0.64; 31.9), and (0.70; 34.0). (B) The F20W system where the main minima MA1 and MA2 are located at (0.53; 31.2) and (0.63; 30.1), respectively.

Figure 5 .

 5 Figure 5. Time evolution of the RMSD of the four systems using CHARM36m/TIP3P-modified force field. (A) refers to WT parallel, (B) to F19P parallel, (C) to WT antiparallel and (D) to F19P antiparallel MD simulations.

Figure 6 .

 6 Figure 6. Representative structures of the MD-generated systems using CHARM36m/TIP3Pmodified force field. (A) shows the structure for the WT parallel, (B) for the F19P parallel, (C)

Table 1 .

 1 The average and standard deviation number of intermolecular and intramolecular HB and SC contacts for the P/AP F20W and WT systems. The results are the number of intermolecular contacts between any two chains and the number of intra-molecular contacts per chain. The values for WT (P) are obtained from Ref.58.

Table 2 .

 2 The percentage of intra-/intermolecular D23-K28, K16-D23, and K16-E22 salt bridges (SB) formed in the P/AP WT and F20W and WT trimers. The values for WT (P) are obtained from Ref.58.

	System	Intra-HB	Intra-SC	Inter-HB	Inter-SC
	F20W (P)	6.03 ± 2.25	130.41 ± 8.18	11.23 ± 1.11	42.59 ± 3.31
	WT (P)	11.27 ± 2.39	141.36 ± 6.27	10.53 ± 1.65	42.69 ± 4.06
	F20W (AP)	15.64 ± 1.66	190.35 ± 4.56	4.06 ± 0.59	30.80 ± 2.28
	WT (AP)	14.34 ± 1.98	181.51 ± 7.05	3.89 ± 0.81	30.98 ± 4.40
		F20W (P)	WT (P)	F20W (AP)	WT (AP)
	Intra-SB D23-K28	2 ± 5	30 ± 10	16 ± 9	6 ± 6
	Inter-SB K16-D23	0 ± 0	0 ± 0	0 ± 0	2 ± 2
	Inter-SB K16-E22	0 ± 0	0 ± 0	27 ± 6	22 ± 5

Table 3 .

 3 Structural description of the main free energy minima of the WT and F20W P/AP systems. The F20W states in the parallel structure are denoted by MP1, MP2, MP3, MP4, and MP5, the F20W states in the anti-parallel structure by MA1 and MA2, while the corresponding WT states are WP1, WP2, WP3, WP4, WP5, WP6 in the parallel structure and WP7 and WA1, WA2, WA3, WA4, and WA5 in the antiparallel structure.

	Shape	Rg	CCS	β-	Coil-	Turn-	Population	Extracellular residues
		(nm)	(nm 2 )	con-	con-	con-	(%)
				tent	tact	tent
				(%)	(%)	(%)
	MP1	1.50	14.73	46	52	2	16	12-13 and 27-28
	MP2	1.47	13.85	42	58	0	5	11-13, 25-27, and 39-40
	MP3	1.47	13.41	54	46	0	44	11-12, 26-28, and 40
	MP4	1.51	15.06	46	52	2	13	11-13, 24-27, and 40
	MP5	1.46	13.57	44	53	2	4	11-13, 25-27, and 40
	MA1	1.43	13.90	60	37	3	47	11-13 and 25-27 of chain B, 23-26 of chain
								A, 11-14 of chain C
	MA2	1.48	14.72	56	39	5	47	11-14 and 25-27 of chain B, 23-26 of chain
								A, 12-14 of chain C
	WP1	1.41	13.84	34	66	0	6	11-13, 25-27, and 39-40
	WP2	1.42	13.22	56	44	0	13	11-13 and 25-29
	WP3	1.45	13.72	40	57	3	10	11-13, 25-27, and 39-40
	WP4	1.43	13.11	46	52	2	19	11-13, and 25-28
	WP5	1.43	13.13	47	51	2	7	11-13 and 25-28
	WP6	1.42	13.03	54	44	2	6	11-13, 25-28, and 40
	WP7	1.46	13.69	46	51	3	10	11-13 and 25-28
	WA1	1.43	14.25	50	48	2	3	11-13 and 25-29 of chain B, 23-25 of chain
								A, 42 of chain B, 11-14 of chain C
	WA2	1.45	14.52	57	41	2	22	12-14 and 25-27 of chain B, 23-26 of chain
								A, 11-14 of chain C,
	WA3	1.48	14.90	41	59	0	14	11-14, 25-27 and 39-40 of chain B, 22-24
								of chain A, 11-14 of chain C
	WA4	1.47	14.24	57	41	2	24	11-14 and 25-27 of chain B, 11-12 and 23-
								25 of chain A, 11-14 of chain C
	WA5	1.50	14.85	52	41	7	23	12-14, 25-28 and 40 of chain B, 23-25 of
								chain A, 11-15 of chain C, 11-13 of chain
								A

ACKNOWLEDGMENTS

We thank the support of the Vietnam Na;onal Founda;on for Science & Technology Development (NAFOSTED) under the grant number 104.99-2019.57, University of Paris, and the French State (Grant "DYNAMO", ANR-11-LABX-0011-01, and "CACSICE", ANR-11-EQPX-0008)

AUTHOR INFORMATION

Corresponding Author *E-mail: philippe.derreumaux@tdtu.edu.vn.

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