Phuong H Nguyen

Philippe Derreumaux
email: philippe.derreumaux@ibpc.fr

Recent Computational Advances Regarding Amyloid-β and Tau Membrane Interactions in Alzheimer's Disease

Keywords: amyloid, aggregation, simulations, Alzheimer's disease, membrane

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1.Introduction

Amyloid-β Aβ proteins of 40 and 42 residues and tau isoforms of 352-421 residues which are linked to Alzheimer's disease (AD) have the propensity to aggregate into amyloid fibrils with a cross-β structure [START_REF] Nasica-Labouze | Amyloid β Protein and Alzheimer's Disease: When computer simulations complement experimental studies[END_REF][START_REF] Nguyen | Amyloid oligomers: A joint experimental/computational perspective on Alzheimer's disease, Parkinson's disease, type II diabetes, and amyotrophic lateral sclerosis[END_REF], and multiple polymorphs as observed by Scheres et al. and Tycko et al. [START_REF] Shi | Structure-based classification of tauopathies[END_REF][START_REF] Lee | Structures of brain-derived 42-residue amyloid-β fibril polymorphs with unusual molecular conformations and intermolecular interactions[END_REF]. Aggregation proceeds through primary and secondary (surface-catalysis and fragmentation) nucleation mechanisms, fibril growth and depolymerization in various experimental conditions [START_REF] Michaels | Dynamics of oligomer populations formed during the aggregation of Alzheimer's Aβ42 peptide[END_REF].

The Aβ42 sequence consists of hydrophilic, charged N-terminal residues 1-16, the central hydrophobic core (CHC, residues 17-21), a hydrophilic region (residues [START_REF] Viles | Imaging amyloid-β membrane interactions; ion-channel pores and lipidbilayer permeability in Alzheimer's disease[END_REF][START_REF] Ciudad | Aβ(1-42) tetramer and octamer structures reveal edge conductivity pores as a mechanism for membrane damage[END_REF][START_REF] Tian | 3D-visualization of amyloid-β oligomer interactions with lipid membranes by cryo-electron tomography[END_REF][START_REF] Flagmeier | Direct measurement of lipid membrane disruption connects kinetics and toxicity of Aβ42 aggregation[END_REF][START_REF] Saha | Ganglioside-enriched phospholipid vesicles induce cooperative Aβ oligomerization and membrane disruption[END_REF][START_REF] Rana | Cu and Zn interactions with Aβ peptides: consequence of coordination on aggregation and formation of neurotoxic soluble Aβ oligomers[END_REF][START_REF] Budvytyte | The interactions of amyloid β aggregates with phospholipid membranes and the implications for neurodegeneration[END_REF] and the hydrophobic residues 30-42. Numerous studies reported that low molecular weight (LMW) oligomers of Aβ generated during the lag phase of aggregation or released from the fibrils were key players in AD [START_REF] Nasica-Labouze | Amyloid β Protein and Alzheimer's Disease: When computer simulations complement experimental studies[END_REF][START_REF] Selkoe | The amyloid hypothesis of Alzheimer's disease at 25 years[END_REF][START_REF] Bigi | Amyloid fibrils act as a reservoir of soluble oligomers, the main culprits in protein deposition diseases[END_REF]. The aggregation kinetics of Aβ42 in aqueous solution is continuously studied to understand the impact of pH variation [START_REF] Tian | pH dependence of amyloid-β fibril assembly kinetics: unravelling the microscopic molecular processes[END_REF], N-terminal residues [START_REF] Thacker | Role of hydrophobicity at the N-terminal region of Aβ42 in secondary nucleation[END_REF] and mixing with C-terminal truncated species such as Aβ24 [START_REF] Nguyen | Insights into the mixture of Aβ24 and Aβ42 peptides from atomistic simulations[END_REF]. Computational structure characterization of Aβ42 and tau monomer/dimer in aqueous solution is pursued [START_REF] Popov | Insight into the structure of the "unstructured" tau protein[END_REF][START_REF] Stelzl | Global structure of the intrinsically disordered protein tau emerges from its local structure[END_REF][START_REF] Chakraborty | Differences in the free energies between the excited states of Aβ40 and Aβ42 monomers encode their aggregation propensities[END_REF][START_REF] Santuz | Small Oligomers of Aβ42 Protein in the bulk solution with AlphaFold2[END_REF][START_REF] Nguyen | Self-assembly of amyloid-beta (Aβ) peptides from solution to near in vivo conditions[END_REF].

Tau oligomers are toxic in vitro seeding the propagation of AD pathology [START_REF] Jucker | Self-propagation of pathogenic protein aggregates in neurodegenerative diseases[END_REF], and tau297-391 fragment formed fibrils under physiological conditions similar to those found in AD brain tissues [START_REF] Biasetti | Tau (297-391) forms filaments that structurally mimic the core of paired helical filaments in Alzheimer's disease brain[END_REF]. Single immunogold-labelling transmission electron microscope (TEM) and fluorescence spectroscopy revealed the presence of tyrosine-tyrosine crosslink at position 310 on AD brain-derived tau oligomers and fibrils [START_REF] Maina | Dityrosine cross-links are present in Alzheimer's disease-derived tau oligomers and paired helical filaments (PHF) which promote the stability of the PHF-core tau (297-391) in vitro[END_REF].

The etiology of AD is linked in part to the mediated effects of Aβ and tau on neuronal cell membranes. Atomic force spectroscopy (AFM) revealed that self-assembly of Aβ was enhanced and occurred at nanomolecular concentrations on two lipid bilayers formed by 1palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC, PC) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine (POPS, PS) [START_REF] Banerjee | Interaction of Aβ42 with membranes triggers the self-assembly into oligomers[END_REF]. The presence of cholesterol in the membrane enhanced primary nucleation of Aβ42 by several orders of magnitude compared to aqueous solution results, as assessed by Thioflavin T (ThT) fluorescence [START_REF] Habchi | Cholesterol catalyses Aβ42 aggregation through a heterogeneous nucleation pathway in the presence of lipid membranes[END_REF]. Experimental techniques used to study the amyloid-membrane interactions through the carpeting, detergent like (removal of lipids) and amyloid-pore hypothesis and to study experimental imaging Aβ membrane interactions were recently reviewed [START_REF] Petersen | Probing the interactions between amyloidogenic proteins and bio-membranes[END_REF][START_REF] Viles | Imaging amyloid-β membrane interactions; ion-channel pores and lipidbilayer permeability in Alzheimer's disease[END_REF].

Structures of Aβ-membrane assemblies are challenging experimentally as they are metastable and heterogeneous. Among the new experimental results, using mass spectrometry and nuclear magnetic resonance (NMR) spectroscopy in docecylphosphocholine (DPC) micelles, Carulla et al. at pH 9.0 provided the high-resolution structure of Aβ42 tetramer and octamer and revealed edge conductivity pores as a mechanism for membrane damage.

The tetramer conformation comprises a six stranded β-sheet core with the two external Aβ peptides forming β-hairpins (Figure 1). 23 Cryo-electron tomography determined 3D nano-scale images of the interactions of various Aβ assemblies and liposomes. Aβ oligomers and protofibrils were found to bind to the lipid vesicles, and insert and carpet the upper-leaflet of the bilayer, allowing Aβ oligomers to form a network of Aβ-linked liposomes. In contrast, the monomeric and fibrillar Aβ species have relatively little impact on the membrane [START_REF] Tian | 3D-visualization of amyloid-β oligomer interactions with lipid membranes by cryo-electron tomography[END_REF]. It was also evidenced that Aβ oligomers generated during secondary surface nucleation disrupt membrane integrity, and time-resolved fluorescence microscopy of individual synthetic vesicles demonstrated that the disruption of lipid bilayers correlates with the levels of secondary nucleation-generated Aβ42 oligomers [START_REF] Flagmeier | Direct measurement of lipid membrane disruption connects kinetics and toxicity of Aβ42 aggregation[END_REF]. Experiments also showed that ganglioside-enriched phospholipid vesicles induced cooperative Aβ oligomerization and membrane disruption [START_REF] Saha | Ganglioside-enriched phospholipid vesicles induce cooperative Aβ oligomerization and membrane disruption[END_REF]. Although influences of different metal ions or lipid vesicles on the aggregation of Aβ peptides have been extensively studied [START_REF] Nguyen | Amyloid oligomers: A joint experimental/computational perspective on Alzheimer's disease, Parkinson's disease, type II diabetes, and amyotrophic lateral sclerosis[END_REF][START_REF] Rana | Cu and Zn interactions with Aβ peptides: consequence of coordination on aggregation and formation of neurotoxic soluble Aβ oligomers[END_REF][START_REF] Budvytyte | The interactions of amyloid β aggregates with phospholipid membranes and the implications for neurodegeneration[END_REF], their combined effects are less understood. It was shown, however, that the co-effect of Cu 2+ and lipid vesicles led to the rapid formation abundant Aβ40 LMW oligomers containing β-sheet rich structures [START_REF] Zhu | The co-effect of copper and lipid vesicles on Aβ aggregation[END_REF].

Surface-enhanced infrared absorption spectroscopy and atomic force microscopy (AFM) were used to study the structural morphology of Aβ42 aggregating on distinct twodimensional self-assembled monolayers (SAMs). On hydrophobic interfaces, hydrophobic interactions with the C-terminus of Aβ42 result in the formation of small oligomers with a small content of β-sheet structure. On hydrophilic interfaces, hydrogen-bond interactions and electrostatic interactions promote the formation of large oligomers with β-sheet structure [START_REF] Zhu | Revealing the nanoarchitectonics of amyloid β-aggregation on two-dimensional biomimetic membranes by surfaceenhanced infrared absorption spectroscopy[END_REF]. Solid-state NMR (ss-NMR) spectroscopy was used to explore the site-specific interactions between Aβ40 peptides and synaptic plasma membranes extracts from rat brain tissues. It was found that, at the membrane-associated nucleation stage, the residues G25-V36 initialized the assembling of low order β-sheet structures and the residues F19-G25 were closely closely with lipids [START_REF] Kenyaga | Early stage β-amyloid-membrane interactions modulate lipid dynamics and influence structural interfaces and fibrillation[END_REF]. Using high speed AFM and nanoscale infrared spectroscopy (IR) on Aβ42 L34T and G37C variants with a POPC/sphingomyelin (SM)/cholesterol/ monosialotetrahexosyl-ganglioside (GM1) membrane, Molinari et al. showed that membrane disruption was associated to small oligomers with antiparallel β-sheet structure [START_REF] Feuillie | High speed AFM and nanoinfrared spectroscopy investigation of Aβ1-42 peptide variants and their interaction with POPC/SM/Chol/GM1 model membranes[END_REF]. It is worth noting that nonequilibrium flowing conditions promote aggregation of Aβ on 1,2dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayers [START_REF] Ida | Promoted aggregation of Aβ on lipid bilayers in an open flowing system[END_REF].

Various studies have reported the presence of both extracellular and intracellular Aβ assemblies. Using large unilamellar vesicles to model membranes at different locations, including the inner leaflet (IL) and outer leaflet (OL) of the plasma membrane, late endosomes, the endoplasmatic reticulum (ER), and the Golgi apparatus, Aβ42 aggregation was monitored by fibril mass concentration as a function of time. Aβ42 aggregation enhancement was observed in IL, OL and late endosomes. The membrane in the inner leaflet consists of 22% PC, 40% PE, 26% PS and 12% chol (cholesterol), the membrane in the outer leaflet has 30% PC, 5% PS, 35% SM and 30% chol, and the membrane in late endosomes consists of 40% PC, 15% PE, 7% SM, 23% chol and 11% BMP (bis(monoacyl-glycero)phosphate). Aβ42 aggregation inhibition was observed in Golgi membrane consisting of 43% PC, 17% PE (phosphatidylethanolamine), 9% PI (phosphatidylinositol), 17% SM and 14% chol, and in the ER membrane consisting of 52% PC, 26% PE, 9% PI and 13% chol [START_REF] Baumann | A kinetic map of the influence of biomimetic lipid model membranes on Aβ42 aggregation[END_REF].

In comparison to Aβ, the number of experimental studies on LMW tau oligomersmembranes is fairly small. It is known that tau oligomers interact with plasma membrane by multiple binding modes with the N-terminal projection domain (residues 1-243 containing a proline-rich region), and the R1-R4 repeats (residues 244-369) [START_REF] Nasica-Labouze | Amyloid β Protein and Alzheimer's Disease: When computer simulations complement experimental studies[END_REF][START_REF] Azouz | Interaction of tau construct K18 with model lipid membranes[END_REF]. Tau interacts with phospholipid tails facilitating translocation across the membrane and forms stable proteinlipid complexes involved in cell-to-cell transport [START_REF] Sallaberry | Tau and membranes: interactions that promote folding and condensation[END_REF]. Like Aβ oligomers, tau oligomers can remodel and disrupt membranes, extract lipids and form pores, and these effects are modulated by protein concentration and lipid compositions [START_REF] Lasagna-Reeves | The formation of tau pore-like structures is prevalent and cell specific: possible implications for the disease phenotypes[END_REF][START_REF] Ait-Bouziad | Discovery and characterization of stable and toxic Tau/phospholipid oligomeric complexes[END_REF][START_REF] Yao | Distinct lipid membrane-mediated pathways of Tau assembly revealed by single-molecule analysis[END_REF].

The aim of this review is to report on recent computational studies starting as the date of 2020 aimed at understanding the effects of Aβ40 and Aβ42 alloforms and long tau isoforms on and in cell membranes and vice versa, and the interactions between free lipids and Aβ peptides.

Adsorption and insertion of Amyloid-β.

Determining the structures of Aβ-membrane assemblies is a computational challenge. The interaction of Aβ monomer with membranes was investigated by a series of simulations. Using CHARMM36m force field and molecular dynamics (MD) simulation, Strodel et al. showed partial insertion of Aβ42/POPC complex into a 1,2-dioleoyl-sn-glycero-3phosphocholine (DOPC) lipid bilayer, and a deeper insertion of parts of Aβ42 compared to a single peptide [START_REF] Fatafta | Disorder-to-order transition of the amyloid-β peptide upon lipid binding[END_REF]. Alonso et al. investigated the interactions of Aβ42 monomer with lipid bilayers consisting of POPC and small amounts (1-5 mol%) of GM1. Using MD simulations with the GROMOS force field, isothermal calorimetry and Langmuir balance experiments, they showed that Aβ42 adsorbs, and does not insert into ganglioside-containing phospholipid membranes in the liquid-disordered (Ld) state. They also found that GM1, up to 3 mol%, increased Aβ42 binding to the bilayer [START_REF] Ahyayauch | β-Amyloid (1-42) peptide adsorbs but does not insert into ganglioside-containing phospholipid membranes in the liquid-disordered state: modelling and experimental studies[END_REF]. Using the same experimental techniques, and a membrane consisting of 47.5% POPC, 47.5% SM and 5% GM1, they found that Aβ42 monomer, but also oligomers and to a lesser extent fibril preparations inserted into membranes in liquidordered (Lo) state [START_REF] Ahyayauch | The interaction of Aβ42 peptide in monomer, oligomer or fibril forms with sphingomyelin/cholesterol/ganglioside bilayers[END_REF].

Hamiltonian replica exchange molecular dynamics simulations with the OPLS force field were performed to determine the impact of oxidized (ox) G25, G29 and G33 residues on the interactions of the monomeric Aβ42 peptide with a membrane consisting of 70% POPC, 25% cholesterol, and 5% of GM1. Owen et al. found that Aβ42 wild-type (WT) and Aβ42-oxG25 peptides have a lower tendency to bind to GM1 than Aβ42-oxG29 and Aβ42-oxG33, and the WT monomer has a higher propensity to insert into the membrane than the three oxidized alloforms [START_REF] Fatafta | Role of oxidized Gly25, Gly29, and Gly33 residues on the interactions of Aβ1-42 with lipid membranes[END_REF]. 2.5 μs MD simulation of Aβ42-Cu 2+ with a DMPC bilayer revealed that the presence of calcium ions mediated membrane perturbation, and inhibited the penetration of Aβ42 monomer into the membrane [START_REF] Boopathi | Calcium inhibits penetration of Alzheimer's Aβ1 -42monomers into the membrane[END_REF]. Interestingly, the decrease of bending rigidity of POPC membrane, as a result of the incorporation of Aβ40 and Aβ42 monomers, was observed using MD studies and experimental flicker-noise techniques [START_REF] Drabik | Effect of amyloid-β monomers on lipid membrane mechanical parameters-potential implications for mechanically driven neurodegeneration in Alzheimer's disease[END_REF]. Finally, Localito et al. studied the interaction of monomeric alpha-helical Aβ40 (WT, H13P, H14P, L17P and F20P) using three replicates with a single DEPC lipid. From their simulations, they hypothesized that the alphahelix is a fundamental requirement to fulfill the lipid-chaperon model [START_REF] Tempra | The role of alpha-helix on the structure-targeting drug design of amyloidogenic proteins[END_REF]. The dynamics of Aβ dimers at the surface or inserted into multiple membrane models were also explored. In the first study carried out by Chang et al., all-atom Brownian dynamics simulations were used to study the association of two distinct Aβ42 monomer conformations on SAM surfaces. The conformations include the fibril-like β-rich structure and a random coil structure with little alpha-helix content. Four SAM surfaces were used, including undecanethiol (hydrophobic, referred to as CH3-SAM), 11-mercapto-1-undecanol (hydrophilic, OH-SAM), 11-amino-1-undecanethiol (cationic, NH + -SAM), and 11-mercaptoundecanoic acid (anionic, COO --SAM) on a gold substrate. Monomers started to diffuse from a random position at a height of 40 nm above the SAM surfaces. A total of 1000 trajectories for each rigid-body protein conformation was performed to calculate the association and residence times on the four SAM surfaces. For three SAM surfaces, the exception being NH + -SAM, the averaged monomer-dimer association time was on the order of 9-10 μs for the β-rich conformation, and 5 μs for the random coil conformation, indicating a 5-35% decrease in association time due to the presence of a surface. The residence time was found to vary from 7.4 (OH-SAM) to 8.8 (CH3-SAM) μs. The monomer-dimer association time on NH + -SAM with heterogeneous charge distribution could not be assessed as the monomers were not able to associate because they are strongly bound to the SAM. Addition of Na + greatly enhanced the diffusion on the COO --SAM. This finding emphasizes the importance of considering the role of Na + in vitro [START_REF] Cholko | Amyloid-β (Aβ42) peptide aggregation rate and mechanism on surfaces with widely varied properties: insights from Brownian dynamics simulations[END_REF].

In a second μs MD simulation, Lyubchenko et al. examined the formation of Aβ42 dimer modelled by the ff99sb-ildn force field with a POPC bilayer. They revealed a β-sheet content of 10% and an alpha-helix content fluctuating between 10 and 35%, with the Nterminal residues and residues 29-31 having the highest propensity to interact. Of interest is that the on-surface aggregation process is dynamic and oligomers assembled on the surface can dissociate into the solution. This result suggests that on-surface aggregation is one mechanism by which Aβ42 oligomeric species in solution are produced [START_REF] Banerjee | Interaction of Aβ42 with membranes triggers the self-assembly into oligomers[END_REF].

In a third μs MD simulation, Strodel et al. compared Aβ42 dimerization, modelled by the CHARMM36m force field, in aqueous solution and at a lipid bilayer surface mimicking a neuronal membrane composed of 38% PC, 24% PE, 5% PS, 20% chol, 9% SM and 4% GM1.

They found that the neuronal membrane reduces the dynamics of membrane-bound A𝛽42 and inhibits 𝛽-sheet formation (β-sheet content of 28%) due to hydrogen bonds with the sugar groups of GM1. This result runs in contrast to the dimerization in the aqueous phase characterized by a random coil to 𝛽-sheet transition which leads to a 𝛽-sheet content of 36% similar to the content observed in A𝛽 fibrils. Insertion of the peptides into the hydrophobic region of the membrane was not observed, and the membrane was marginally affected [START_REF] Fatafta | Amyloid-β peptide dimers undergo a random coil to β-sheet transition in the aqueous phase but not at the neuronal membrane[END_REF].

In a fourth study, Fazli et al. performed three MD simulations of 200 ns each at three temperatures and the OPLS force field for proteins to explore the early interaction steps of two separated parallel Aβ40 peptides with helix-structure content spanning residues 15-37 partially inserted into a DPPC bilayer. Upon association, the helical region becomes disrupted to two smaller fragments with a kink and the dimeric Aβ species has two types of distribution in DPPC at 300, 310 and 330 K. In the first distribution, the two peptides remained embedded in top leaflet, while in the second distribution, at least one of the peptides penetrates into the bottom leaflet, leading to local disordering of DPPC membrane [START_REF] Kargar | Dimerization of Aβ40 inside dipalmitoylphosphatidylcholine bilayer and its effect on bilayer integrity: Atomistic simulation at three temperatures[END_REF].

Guo and Wang used atomistic MD simulations for a total of 48 μs to investigate the effects of cholesterol on Aβ42 dimerization in a lipid DOPC bilayer containing different molar ratios of cholesterol (0, 20, and 40 mol %). Cholesterol reduces the time required for the formation of stable dimers and exerts two effects on Aβ-membrane interactions. Firstly, cholesterol promotes the extraction of the C-terminal region from the membrane to aqueous solution. At the ratios of 0 and 20 mol %, Aβ peptides are attached at the membrane-water interface, but at a ratio of 40 mol %, they are repelled to water with high structural flexibility.

Secondly, cholesterol weakens Aβ-membrane interactions, thereby enhancing inter-peptide interactions [START_REF] Wang | Concentration-dependent effects of cholesterol on the dimerization of Amyloid-β peptides in lipid bilayers[END_REF].

Another coarse-grained (CG) 120 μs MD simulations, performed by Parisini et al., investigated the interactions between trimeric or hexameric Aβ40 fibrils with either a 100% DPPC bilayer, a 70% DPPC-30% chol bilayer or a 50% DPPC-50% chol bilayer. Spontaneous binding of the Aβ40 fibrils to the membranes was captured with the CHC (residues 17-21), the K16 residue and the C-terminal hydrophobic residues involved in the process. Moreover, they showed that, while the Aβ40 fibril does not bind to the 100% DPPC bilayer, its binding affinity to the membrane increases with the amount of cholesterol [START_REF] Agrawal | A coarse-grained molecular dynamics investigation on spontaneous binding of Aβ1-40 fibrils with cholesterol-mixed DPPC bilayers[END_REF].

Coarse-grained Martini MD simulations, by Cheng et al., revealed the binding of Aβ17-42 fibrillar dimers to pentamers to interfacial liquid-ordered (Lo) and liquid-disordered (Ld) regions in phase separated lipid rafts with diverse membrane-bound conformational states [START_REF] Cheng | Coarse-grained MD simulations reveal beta-amyloid fibrils of various sizes bind to interfacial liquid-ordered and liquid-disordered regions in phase separated lipid rafts with diverse membranebound conformational states[END_REF]. CG Martini simulations of several μs, generated by Cruz et al., showed the role of cholesterol on binding of Aβ11-42 and Aβ17-42 fibrils to lipid bilayers containing 30 and 50% cholesterol by promoting electrostatic interactions [START_REF] Dias | Role of cholesterol on Binding of amyloid Fibrils to lipid bilayers[END_REF]. By using atomistic MD simulations, amyloid-β dodecamer disrupts the neuronal membrane more strongly than the mature fibril [START_REF] Nguyen | Amyloid β dodecamer disrupts the neuronal membrane more strongly than the mature fibril: understanding the role of oligomers in neurotoxicity[END_REF] with the peptide and membrane parameterized by the CHARMM36m and CHARMM36 force fields, respectively.

Detergent effect of Amyloid-β.

Amyloid-β oligomers have a profound detergent-like effect on lipid membrane bilayers [START_REF] Nguyen | Amyloid oligomers: A joint experimental/computational perspective on Alzheimer's disease, Parkinson's disease, type II diabetes, and amyotrophic lateral sclerosis[END_REF].

Cholesterol, a component of membranes, is well-recognized as a risk factor in AD. Cholesterol is present in AD senile plaques with a molar ratio of 1:1 [START_REF] Panchal | Enrichment of cholesterol in microdissected Alzheimer's disease senile plaques as assessed by mass spectrometry[END_REF] and cholesterol levels in the brain correlate with the severity of dementia in AD patients [START_REF] Cutler | Involvement of oxidative stress-induced abnormalities in ceramide and cholesterol metabolism in brain aging and Alzheimer's disease[END_REF]. Nguyen and Derreumaux performed atomistic replica exchange molecular dynamics and replica exchange with solute tempering on the dimer/trimer of Aβ42 with cholesterol at a ratio 1:1 [START_REF] Nguyen | Effect of cholesterol molecules on Aβ1-42 wild-type and mutants trimers[END_REF][START_REF] Ngo | Cholesterol molecules alter the energy landscape of small Aβ1-42 Oligomers[END_REF]. They found that the binding spots of cholesterol involve essentially the CHC and residues L30-M35. A nonnegligible contribution of the residues D22-K28 and the N-terminus residues was however detected. Cholesterol was rarely inserted into the aggregates, but rather attached as dimers and trimers at the surface of Aβ42 trimers, proposing therefore that cholesterol acts as a glue to speed up the formation of larger aggregates. The formation of larger size Aβ42 aggregates due to the presence of free cholesterol was confirmed by AFM images of Aβ42/cholesterol on a lipid bilayer and it was shown that these aggregates can accumulate in the bulk solution [START_REF] Hashemi | Free cholesterol accelerates Aβ selfassembly on membranes at physiological concentration[END_REF].

The impact of free GM1, abundant in mammalian brains, on the two Aβ isoforms was investigated by a combined NMR-MD study performed by Brooks et al. This study revealed the formation of well-ordered, structurally compact GM1+Aβ complexes, altering therefore Aβ aggregation [START_REF] Chakravorty | Free gangliosides can alter amyloid-β aggregation[END_REF]. The presence of free fatty acids such as lauric acid was found computationally by Hansmann to stabilize ring-like and barrel-shaped Aβ42 oligomers [START_REF] Khatua | Effect of lauric acid on the stability of Aβ42 oligomers[END_REF].

Similar to the simulation results of Aβ42/cholesterol, simulations of Aβ42 monomer with 1,2dimyristoyl-sn-glycero-3-phosphocholine (DMPC) provided evidence that the unfolded Aβ42 peptide adhered to the lipid cluster rather than embedded into it [START_REF] Andrews | How do salt and lipids affect conformational dynamics of Aβ42 monomers in water?[END_REF]. MD simulations in the μs time scale revealed that three free POPC lipids triggered a disorder-order (alpha-helix, βstrand) transition in Aβ42 monomer [START_REF] Fatafta | Amyloid-β peptide dimers undergo a random coil to β-sheet transition in the aqueous phase but not at the neuronal membrane[END_REF].

4.Amyloid-β Pore formation.

Membrane-embedded Aβ species with membrane conductance, which do not display ThT fluorescence signal, can have a wide range of conformations and oligomer sizes [START_REF] Nguyen | Amyloid oligomers: A joint experimental/computational perspective on Alzheimer's disease, Parkinson's disease, type II diabetes, and amyotrophic lateral sclerosis[END_REF]. Some form well-defined pores [START_REF] Österlund | Native ion mobility-mass spectrometry reveals the formation of β-barrel shaped amyloid-β hexamers in a membrane-mimicking environment[END_REF][START_REF] Quist | Amyloid ion channels: a common structural link for protein-misfolding disease[END_REF][START_REF] Ngo | Impact of A2T and D23N mutations on tetrameric Aβ42 barrel within a dipalmitoylphosphatidylcholine lipid bilayer membrane by replica exchange molecular dynamics[END_REF], made for instance of six stranded β-sheet and β-sandwich structures (Figure 1), and other species are spherical without any evidence of discrete channel or pore formation. Atomistic MD simulations showed that many concentric β-barrels are consistent with image averaged electron micrographs [START_REF] Durell | The amyloid concentric β-barrel hypothesis: Models of amyloid beta 42 oligomers and annular protofibrils[END_REF][START_REF] Sepehri | Putative structures of membrane-embedded amyloid β oligomers[END_REF], and revealed the importance of Aβ oligomer β-sheet edge conformations in membrane permeabilization [START_REF] Matthes | Molecular dynamics simulations reveal the importance of amyloid-beta oligomer β-sheet edge conformations in membrane permeabilization[END_REF]. Interestingly, using MD simulations, quantum mechanics, and experimental techniques, La Rosa et al.

showed that Aβ40 can also form alpha-helix channels through the GxxG motif [START_REF] Rando | GxxxG motif stabilize ionchannel like pores through Cα-H•••O interaction in Aβ (1-40)[END_REF].

In a recent study, the dynamics of a S-shaped Aβ42 cross-β hexamer model inserted into a lipid bilayer membrane was explored by Nguyen and Derreumaux using two atomistic MD simulations, each of two microseconds [START_REF] Nguyen | An S-shaped Aβ42 cross-β hexamer embedded into a lipid bilayer reveals membrane disruption and permeability[END_REF]. The initial model was characterized by the CHC and residues 30-42 embedded into a DOPC bilayer membrane (Figure 2). Structural secondary, tertiary and quaternary rearrangements were observed leading to two distinct metastable species, hexamer and two trimers, accompanied by membrane disruption and water permeation. The work provides evidence of hexamer and trimers with the N-terminal residues located in the top and bottom leaflets of membrane and a minimal lifetime of several microseconds. Some conformations, but not the majority, have the CHC and C-terminal hydrophobic residues exposed to solvent. The MD simulations also show that residues 1-10 in both trimers of run 1 and in trimer 1 of run 2, and residues 1-16 in trimer 2 of run 2 are exposed to solvent (Figure 3). This result is consistent with many simulations of Aβ42 oligomers partially embedded in the membrane [START_REF] Nguyen | Amyloid oligomers: A joint experimental/computational perspective on Alzheimer's disease, Parkinson's disease, type II diabetes, and amyotrophic lateral sclerosis[END_REF]. We do not find evidence of β-hairpins in the Nterminus, as reported for Aβ42 dimers in DOPC bilayers [START_REF] Press-Sandler | Molecular insights into the primary nucleation of polymorphic amyloid β dimers in DOPC lipid bilayer membrane[END_REF]. Overall, the high solvent accessibility of the residues 1-16 may help understand the linking of liposomes through Aβ oligomers, as it has been assessed by cryo-electron tomography. [START_REF] Viles | Imaging amyloid-β membrane interactions; ion-channel pores and lipidbilayer permeability in Alzheimer's disease[END_REF]

Tau-membrane Interactions.

Zhou et al. reported computational results of tau K19 (R1, R3 and R4) monomer bound to a POPC/POPS membrane using the ff14SB force field for proteins [START_REF] Macainsh | Partial mimicry of the microtubule binding of tau by its membrane binding[END_REF]. Based on previous electron paramagnetic resonance (EPR) results which established the presence of one helix in each repeat [START_REF] Georgieva | Tau binds to lipid membrane surfaces via short amphipathic helices located in its microtubule-binding repeats[END_REF], their biased MD simulations of microsecond timescale showed that the three amphipathic helices stably bind to a POPC-POPS membrane and revealed an important difference in membrane binding stability between the repeats R1 and R3 and R4. In each amphipathic helix, however, a lysine conserved among the microtubule-binding regions, along with other charged and polar sidechains, interacts with lipid headgroups. Furthermore, a conserved valine along with two other nonpolar sidechains insert into the hydrophobic region of the membrane. These two conserved residues forming similar interactions with microtubules as observed from the cryo-EM microtubule-bound structure of tau202-395 [START_REF] Brotzakis | A structural ensemble of a tau-microtubule complex reveals regulatory tau phosphorylation and acetylation mechanisms[END_REF], Zhou et al. proposed that this partial mimicry facilitates the transfer of tau from membranes to microtubules [START_REF] Macainsh | Partial mimicry of the microtubule binding of tau by its membrane binding[END_REF].

Nguyen and Derreumaux performed MD simulations of tau R3-R4 domain monomer at the surface of a DOPC-DOPS lipid bilayer, the residues 306-378 forming an amyloid fibril core of a full-length tau in the brain of patients with AD [START_REF] Nguyen | Molecular dynamics simulations of the tau R3-R4 domain monomer in the bulk Solution and at the surface of a lipid bilayer model[END_REF]. The two simulations showed that the surface of the membrane does not induce β-sheet formation and leads to an ensemble of structures very different from those in the bulk solution. They also revealed the dynamical interactions of the membrane-bound state of the tau R3-R4 monomer, allowing insertion of the PHF6 motif (residues 306-311) and its flanking residues (312-318) and residues 376-378.

As tau dimers are observed in cells and in the cerebrospinal fluid of AD patients [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], Nguyen and Derreumaux performed MD simulations on tau R3-R4 domain dimer, and transient adsorption of the PHF6 motif on the membrane as the results of the high propensity of PHF6 to form parallel β-sheets, and insertion of the C-terminal R4 region into the membrane [START_REF] Nguyen | Molecular dynamics simulations of the tau amyloid fibril core dimer at the surface of a lipid bilayer model: I. In Alzheimer's disease[END_REF].

There are therefore differences between the monomer and the dimer results. To what extent, the dimer results can be extrapolated to full-length tau remains to be determined, as the R2 repeat interacts with negatively charged vesicles [START_REF] Ait-Bouziad | Discovery and characterization of stable and toxic Tau/phospholipid oligomeric complexes[END_REF].

Using 15 μs coarse-grained Martini MD simulations followed by all-atom (AMBER99sb and Slipid force fields) 200 ns MD simulations with the residues spanning the R2-R3 domain initially adopting the fibril cryo-EM conformation, the transient interactions of tau K18 (containing the four repeats) oligomers (dimer and tetramer) on three lipid rafts (control-raft, modified CO-raft containing GM1 clusters on one leaflet (GM-raft), and modified CO-raft containing PS clusters on one leaflet (PS-raft)) were investigated. Their rafts systems included in all cases DPPC, DLPC, and cholesterol. It was found that tau K18 preferred to bind to the boundary domains (Lod) created by the coexisting Lo and Ld domains in the lipid rafts.

Stronger binding of tau K18 oligomers to the GM1 and phosphatidylserine (PS) domains was reported, and K18-induced lipid chain order disruption and tau K18 β-sheet formation were also detected. The results suggest that GM1 and PS domains, located in the outer and inner leaflets of the neuronal membranes, respectively are specific membrane domain targets of tau oligomers, and the Lod domains are not. Clearly much longer all-atom MD simulations are required to identify more stable β-sheet structures on the raft surfaces [START_REF] Cheng | Exploring membrane binding targets of disordered human tau aggregates on lipid rafts using multiscale molecular dynamics simulations[END_REF].

Finally, the interactions of tau fibrils with membrane lipids were studied by a multiscale simulation. Based on CG Martini protocol followed by all-atom CHARMM36 force field 400 ns MD simulations, Bargava et al. studied the interactions of R3-R4 tau filament consisting of two protofibrils with 14 membrane systems consisting of POPC, 1-palmitoyl-2-oleoyl-sn-glycero-3phosphatidylethanolamine (POPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylglycerol (POPG) along with cholesterol at seven different compositions. Tau proteins interact differentially with the zwitterionic compared to the charged lipid membranes, with the negatively charged POPG lipid membranes increasing the binding propensity of the tau fibrils.

Addition of cholesterol modifies tau binding affinity to the membrane. The binding of tau fibril leads to the loss of β-sheet of the tau residues, destabilized β-sheet regions depending on the lipid composition and the percentage of cholesterol concentration, and changed the membrane properties, including thickness and order parameters of the tails [START_REF] Chowdhury | The effect of lipid composition on the dynamics of tau fibrils[END_REF].

Conclusions.

We have focused on recent simulations aimed at understanding the adsorption and insertion modes of the two main amyloid proteins associated with AD in various membrane models. Our experimental and computational knowledges on aggregation and structures of tau isoforms are moving at a much slower pace than those of Aβ.

Major challenges are identified in the field. For instance, new experimental methods of biomolecular processes in membrane spanning the microsecond time resolution and detecting populations of intermediates below the percent range would be very useful to validate the MD-generated models. The impact of fluid flow on lipid bilayers -amyloid protein interactions should also be investigated both experimentally and computationally, and it is known that cells have extracellular matrices that may have very different behaviors compared to vesicles, and planar lipid bilayers in the absence of membrane protein receptors.

Most simulations start from alpha-helical and fibrillar states and repeating the simulations with antiparallel orientations of the peptides and longer timescales would provide more information on the conformational ensemble and its impacts on membrane. Recent computations showed that free lipids (cholesterol, GM1) and fatty acids alter the energy landscape of Aβ42 species and cholesterol induces the formation of much larger Aβ42 aggregate sizes and this might generate species more difficult to clean from the brain interstitial system. More information on the very large gap between simulations and in vivo conditions can be found in Ref. [START_REF] Nguyen | Self-assembly of amyloid-beta (Aβ) peptides from solution to near in vivo conditions[END_REF].

Figure 1 .

 1 Figure 1. Experimentally-derived conformation of the Aβ42 tetramer in a membrane model with a six stranded β-sheet core and the two external Aβ peptides forming β-hairpins as proposed in Ref. 23.

Figure 2 .

 2 Figure 2. Initial conformation of the Aβ42 hexamer. View in the x direction parallel to the fibril axis. We show the ribbon structure of the hexamer, the phosphate atoms (tan) and the O21 and O22 atoms of the glycerol (black). Also shown are the Ca atom of V12 (yellow), Q15 (blue), V18 (orange), E22 (purple) and K28 (red)[START_REF] Nguyen | An S-shaped Aβ42 cross-β hexamer embedded into a lipid bilayer reveals membrane disruption and permeability[END_REF].

Figure 3 .

 3 Figure 3. MD-generated insertion depths of the residues belonging to trimer 1 and trimer 2 in two time-intervals, 0-100 ns and 1900-2000 ns. (A) and (B) refer to MD run 1 at 303 K, and (C) and (D) to MD run 2 at 310 K [70]. The three chains in aqueous solution at the upper leaflet of the membrane are referred to as trimer 1 and the other three chains at the lower leaflet of the membrane are referred to as trimer 2.

Acknowledgments:

We acknowledge support the "Initiative d'Excellence" program from the French State, Grant "DYNAMO", ANR-11-LABX-0011.

Funding: This research received no external funding.

Institutional Review Board Statement: Not relevant.

Informed Consent Statement: Not applicable.

Data Availability Statement: Not applicable as it is a review article.

AUTHOR INFORMATION

ORCID: Derreumaux: 0000-0001-9110-5585, Phuong H. Nguyen: 0000-0003-1284-967X, phuong.nguyen@ibpc.fr Author Contributions: Conceptualization, P.H Nguyen and P. Derreumaux; writing-original draft preparation, both authors; writing-review and editing, both authors. All authors have read and agreed to the published version of the manuscript."

Conflicts of Interest:

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.